https://math.byu.edu/wiki/api.php?action=feedcontributions&feedformat=atom&user=Ls5 2026-07-15T23:38:08Z User contributions MediaWiki 1.26.3 https://math.byu.edu/wiki/index.php?title=Math_97&diff=3806 2024-10-18T23:59:07Z

<p>Ls5: /* Offered */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Intermediate Algebra<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (0:2:1)<br /> <br /> === Offered ===<br /> This course is not offered on BYU campus, but may be available at the BYU Salt Lake Center and through [http://is.byu.edu/site/courses/description.cfm?title=MATH-097-200 Independent Study].<br /> <br /> === Prerequisite ===<br /> High school algebra.<br /> <br /> === Description ===<br /> Elementary logic, real number system, equations and inequalities (linear, polynomial, rational, and radical expressions), graphing, function notation, inverse function, exponential functions, systems of equations, variations.<br /> <br /> == Desired Learning Outcomes ==<br /> When you have successfully completed this course, you should be able to do the following:<br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> # Use the Basics of Algebra<br /> # Use Algebra for Problem Solving<br /> # Use and Understand Graphs, Functions, and Linear Equations<br /> # Use and Understand Systems of Linear Equations<br /> # Use Linear Equations for Problem Solving<br /> # Use and Understand Inequalities<br /> # Use Inequalities for Problem Solving<br /> # Use and Understand Polynomials and Polynomial Functions<br /> # Use and Understand Rational Expressions, Rational Equations, and Rational Functions<br /> # Use and Understand Exponents and Rad<br /> # Use and Understand Quadratic Functions and Quadratic Equations<br /> <br /> === Prerequisites ===<br /> Successful completion of high school algebra.<br /> <br /> === Minimal learning outcomes ===<br /> <br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> [[Category:Courses|097]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_380:_Mathematical_Foundations_of_Data_Science&diff=3805 2024-10-02T15:15:00Z

<p>Ls5: /* Courses for which this course is prerequisite */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Mathematical Foundations of Data Science<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> Contact Department<br /> <br /> === Prerequisite ===<br /> [[Math 112]]<br /> <br /> === Description ===<br /> Mathematical aspects of data science, including high-dimensional geometry and linear algebra, optimization, and probabilistic modeling.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Minimal learning outcomes ===<br /> # Geometry and linear algebra in high-dimensional space<br /> #* Working in high-dimensional space<br /> #* Intro to dimension reduction (including for visualization and computational necessity)<br /> #* Johnson-Lindenstrauss<br /> #* SVD<br /> #** For dimension reduction<br /> #** For data compression<br /> #** PCA<br /> #** Use to solve the normal equation of OLS, even with collinearity<br /> #* More about eigenvalues and eigenvectors and their uses<br /> #* Non-linear dimension reduction (e.g., Isomap/LLE) #* Quotient Groups<br /> # Optimization<br /> #* Motivation: Overview of Machine Learning—it’s all just optimization and sampling<br /> #* Gradients and Hessians and what they tell us about the loss landscape<br /> #* Symbolic and automatic differentiation (sympy and autograd)<br /> #* Gradient descent<br /> #* Newton and Quasi-Newton<br /> #* Regularization<br /> # Probabilistic Modeling<br /> #* Basic distributions, both discrete and continuous<br /> #* MLE is an optimization problem that usually cannot be solved analytically<br /> #* Use modeling and optimization skills to solve an interesting problem:<br /> #** Clustering<br /> #** Prediction<br /> #** Anomaly detection<br /> <br /> === Textbooks ===<br /> <br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> [[Category:Courses|380]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_380:_Mathematical_Foundations_of_Data_Science&diff=3804 2024-10-02T15:10:33Z

<p>Ls5: /* Minimal learning outcomes */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Mathematical Foundations of Data Science<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> Contact Department<br /> <br /> === Prerequisite ===<br /> [[Math 112]]<br /> <br /> === Description ===<br /> Mathematical aspects of data science, including high-dimensional geometry and linear algebra, optimization, and probabilistic modeling.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Minimal learning outcomes ===<br /> # Geometry and linear algebra in high-dimensional space<br /> #* Working in high-dimensional space<br /> #* Intro to dimension reduction (including for visualization and computational necessity)<br /> #* Johnson-Lindenstrauss<br /> #* SVD<br /> #** For dimension reduction<br /> #** For data compression<br /> #** PCA<br /> #** Use to solve the normal equation of OLS, even with collinearity<br /> #* More about eigenvalues and eigenvectors and their uses<br /> #* Non-linear dimension reduction (e.g., Isomap/LLE) #* Quotient Groups<br /> # Optimization<br /> #* Motivation: Overview of Machine Learning—it’s all just optimization and sampling<br /> #* Gradients and Hessians and what they tell us about the loss landscape<br /> #* Symbolic and automatic differentiation (sympy and autograd)<br /> #* Gradient descent<br /> #* Newton and Quasi-Newton<br /> #* Regularization<br /> # Probabilistic Modeling<br /> #* Basic distributions, both discrete and continuous<br /> #* MLE is an optimization problem that usually cannot be solved analytically<br /> #* Use modeling and optimization skills to solve an interesting problem:<br /> #** Clustering<br /> #** Prediction<br /> #** Anomaly detection<br /> <br /> === Textbooks ===<br /> <br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_380:_Mathematical_Foundations_of_Data_Science&diff=3803 2024-10-02T15:09:54Z

<p>Ls5: /* Minimal learning outcomes */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Mathematical Foundations of Data Science<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> Contact Department<br /> <br /> === Prerequisite ===<br /> [[Math 112]]<br /> <br /> === Description ===<br /> Mathematical aspects of data science, including high-dimensional geometry and linear algebra, optimization, and probabilistic modeling.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Minimal learning outcomes ===<br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> # Geometry and linear algebra in high-dimensional space<br /> #* Working in high-dimensional space<br /> #* Intro to dimension reduction (including for visualization and computational necessity)<br /> #* Johnson-Lindenstrauss<br /> #* SVD<br /> #** For dimension reduction<br /> #** For data compression<br /> #** PCA<br /> #** Use to solve the normal equation of OLS, even with collinearity<br /> #* More about eigenvalues and eigenvectors and their uses<br /> #* Non-linear dimension reduction (e.g., Isomap/LLE) #* Quotient Groups<br /> # Optimization<br /> #* Motivation: Overview of Machine Learning—it’s all just optimization and sampling<br /> #* Gradients and Hessians and what they tell us about the loss landscape<br /> #* Symbolic and automatic differentiation (sympy and autograd)<br /> #* Gradient descent<br /> #* Newton and Quasi-Newton<br /> #* Regularization<br /> # Probabilistic Modeling<br /> #* Basic distributions, both discrete and continuous<br /> #* MLE is an optimization problem that usually cannot be solved analytically<br /> #* Use modeling and optimization skills to solve an interesting problem:<br /> #** Clustering<br /> #** Prediction<br /> #** Anomaly detection<br /> <br /> &lt;/div&gt;<br /> <br /> === Textbooks ===<br /> <br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_380:_Mathematical_Foundations_of_Data_Science&diff=3802 2024-10-02T15:08:31Z

<p>Ls5: /* Minimal learning outcomes */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Mathematical Foundations of Data Science<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> Contact Department<br /> <br /> === Prerequisite ===<br /> [[Math 112]]<br /> <br /> === Description ===<br /> Mathematical aspects of data science, including high-dimensional geometry and linear algebra, optimization, and probabilistic modeling.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Minimal learning outcomes ===<br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> # Geometry and linear algebra in high-dimensional space<br /> #* Working in high-dimensional space<br /> #* Intro to dimension reduction (including for visualization and computational necessity)<br /> #* Johnson-Lindenstrauss<br /> #* SVD<br /> #** For dimension reduction<br /> #** For data compression<br /> #** PCA<br /> #** Use to solve the normal equation of OLS, even with collinearity<br /> #* More about eigenvalues and eigenvectors and their uses<br /> #* Non-linear dimension reduction (e.g., Isomap/LLE) #* Quotient Groups<br /> # Optimization<br /> #* Motivation: Overview of Machine Learning—it’s all just optimization and sampling<br /> #* Gradients and Hessians and what they tell us about the loss landscape<br /> #* Symbolic and automatic differentiation (sympy and autograd)<br /> #* Gradient descent<br /> #* Newton and Quasi-Newton<br /> #* Regularization<br /> # Probabilistic Modeling<br /> #* Basic distributions, both discrete and continuous<br /> #* MLE is an optimization problem that usually cannot be solved analytically<br /> #* Use modeling and optimization skills to solve an interesting problem:<br /> ##* Clustering<br /> ##* Prediction<br /> ##* Anomaly detection<br /> <br /> &lt;/div&gt;<br /> <br /> === Textbooks ===<br /> <br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_380:_Mathematical_Foundations_of_Data_Science&diff=3801 2024-10-02T15:04:46Z

<p>Ls5: /* Minimal learning outcomes */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Mathematical Foundations of Data Science<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> Contact Department<br /> <br /> === Prerequisite ===<br /> [[Math 112]]<br /> <br /> === Description ===<br /> Mathematical aspects of data science, including high-dimensional geometry and linear algebra, optimization, and probabilistic modeling.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Minimal learning outcomes ===<br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> # Geometry and linear algebra in high-dimensional space<br /> ** Working in high-dimensional space<br /> ** Intro to dimension reduction (including for visualization and computational necessity)<br /> #* Johnson-Lindenstrauss<br /> #* SVD<br /> ##* For dimension reduction<br /> ##* For data compression<br /> ##* PCA<br /> ##* Use to solve the normal equation of OLS, even with collinearity<br /> #* More about eigenvalues and eigenvectors and their uses<br /> #* Non-linear dimension reduction (e.g., Isomap/LLE) #* Quotient Groups<br /> # Optimization<br /> #* Motivation: Overview of Machine Learning—it’s all just optimization and sampling<br /> #* Gradients and Hessians and what they tell us about the loss landscape<br /> #* Symbolic and automatic differentiation (sympy and autograd)<br /> #* Gradient descent<br /> #* Newton and Quasi-Newton<br /> #* Regularization<br /> # Probabilistic Modeling<br /> #* Basic distributions, both discrete and continuous<br /> #* MLE is an optimization problem that usually cannot be solved analytically<br /> #* Use modeling and optimization skills to solve an interesting problem:<br /> ##* Clustering<br /> ##* Prediction<br /> ##* Anomaly detection<br /> <br /> &lt;/div&gt;<br /> <br /> === Textbooks ===<br /> <br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_380:_Mathematical_Foundations_of_Data_Science&diff=3800 2024-10-02T15:03:59Z

<p>Ls5: /* Minimal learning outcomes */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Mathematical Foundations of Data Science<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> Contact Department<br /> <br /> === Prerequisite ===<br /> [[Math 112]]<br /> <br /> === Description ===<br /> Mathematical aspects of data science, including high-dimensional geometry and linear algebra, optimization, and probabilistic modeling.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Minimal learning outcomes ===<br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> # Geometry and linear algebra in high-dimensional space<br /> ## Working in high-dimensional space<br /> #* Intro to dimension reduction (including for visualization and computational necessity)<br /> #* Johnson-Lindenstrauss<br /> #* SVD<br /> ##* For dimension reduction<br /> ##* For data compression<br /> ##* PCA<br /> ##* Use to solve the normal equation of OLS, even with collinearity<br /> #* More about eigenvalues and eigenvectors and their uses<br /> #* Non-linear dimension reduction (e.g., Isomap/LLE) #* Quotient Groups<br /> # Optimization<br /> #* Motivation: Overview of Machine Learning—it’s all just optimization and sampling<br /> #* Gradients and Hessians and what they tell us about the loss landscape<br /> #* Symbolic and automatic differentiation (sympy and autograd)<br /> #* Gradient descent<br /> #* Newton and Quasi-Newton<br /> #* Regularization<br /> # Probabilistic Modeling<br /> #* Basic distributions, both discrete and continuous<br /> #* MLE is an optimization problem that usually cannot be solved analytically<br /> #* Use modeling and optimization skills to solve an interesting problem:<br /> ##* Clustering<br /> ##* Prediction<br /> ##* Anomaly detection<br /> <br /> &lt;/div&gt;<br /> <br /> === Textbooks ===<br /> <br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_380:_Mathematical_Foundations_of_Data_Science&diff=3799 2024-10-02T15:01:48Z

<p>Ls5: /* Minimal learning outcomes */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Mathematical Foundations of Data Science<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> Contact Department<br /> <br /> === Prerequisite ===<br /> [[Math 112]]<br /> <br /> === Description ===<br /> Mathematical aspects of data science, including high-dimensional geometry and linear algebra, optimization, and probabilistic modeling.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Minimal learning outcomes ===<br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> # Geometry and linear algebra in high-dimensional space<br /> #* Working in high-dimensional space<br /> #* Intro to dimension reduction (including for visualization and computational necessity)<br /> #* Johnson-Lindenstrauss<br /> #* SVD<br /> ##* For dimension reduction<br /> ##* For data compression<br /> ##* PCA<br /> ##* Use to solve the normal equation of OLS, even with collinearity<br /> #* More about eigenvalues and eigenvectors and their uses<br /> #* Non-linear dimension reduction (e.g., Isomap/LLE) #* Quotient Groups<br /> # Optimization<br /> #* Motivation: Overview of Machine Learning—it’s all just optimization and sampling<br /> #* Gradients and Hessians and what they tell us about the loss landscape<br /> #* Symbolic and automatic differentiation (sympy and autograd)<br /> #* Gradient descent<br /> #* Newton and Quasi-Newton<br /> #* Regularization<br /> # Probabilistic Modeling<br /> #* Basic distributions, both discrete and continuous<br /> #* MLE is an optimization problem that usually cannot be solved analytically<br /> #* Use modeling and optimization skills to solve an interesting problem:<br /> ##* Clustering<br /> ##* Prediction<br /> ##* Anomaly detection<br /> <br /> &lt;/div&gt;<br /> <br /> === Textbooks ===<br /> <br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_371:_Abstract_Algebra_1.&diff=3798 2024-09-17T19:50:01Z

<p>Ls5: /* Courses for which this course is prerequisite */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Abstract Algebra 1.<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> F, W, Sp<br /> <br /> === Prerequisite ===<br /> [[Math 290]], [[Math 213]].<br /> <br /> === Description ===<br /> Groups, group homomorphisms, rings, ideals, and polynomials.<br /> <br /> == Desired Learning Outcomes ==<br /> This course is aimed at undergraduate mathematics and mathematics education majors. It is a first course in abstract algebra. In addition to being an important branch of mathematics in its own right, abstract algebra is now an essential tool in number theory, geometry, topology, and, to a lesser extent, analysis. Thus it is a core requirement for all mathematics majors. Outside of mathematics, algebra also has applications in cryptography, coding theory, quantum chemistry, and physics.<br /> <br /> === Prerequisites ===<br /> The chief prerequisite for this course is [[Math 290]]. In [[Math 290]], students should learn basic logic, basic set theory, the division algorithm, Euclidean algorithm, and unique factorization theorem for integers, equivalence relations, functions, and mathematical induction. As these topics are of high importance in Math 371, it might be prudent for the instructor to review them at the beginning of the semester.<br /> <br /> === Minimal learning outcomes ===<br /> Students should achieve mastery of the topics listed below. This means that they should know all relevant definitions, correct statements of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts. The students should be able to demonstrate their mastery by solving non-trivial problems related to these concepts, and by proving simple (but non-trivial) theorems about the below concepts, related to, but not identical to, statements proven by the text or instructor.<br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> # Group Theory<br /> #* Basic Definitions<br /> #* Examples of groups<br /> #* Subgroups<br /> #* Lagrange’s Theorem<br /> #* Homomorphisms<br /> #* Normal Subgroups<br /> #* Quotient Groups<br /> #* Isomorphism Theorems<br /> #* Cauchy’s Theorem<br /> #* Direct Products<br /> #* The Symmetric Group<br /> #* Even and odd Permutations<br /> #* Cycle Decompositions<br /> # Ring Theory<br /> #* Basic Definitions<br /> #* Examples of rings (both commutative and noncommutative)<br /> #* Ideals<br /> #* Ring homomorphisms<br /> #* Quotient rings<br /> #* Prime and maximal ideals<br /> #* Polynomial rings<br /> #* Factorization in polynomial rings<br /> #* Field of fractions of a domain<br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/div&gt;<br /> <br /> === Textbooks ===<br /> <br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> * Hungerford: Abstract Algebra: An Introduction<br /> * Herstein: Abstract Algebra<br /> <br /> === Additional topics ===<br /> Beyond the minimal learning outcomes, instructors are free to cover additional topics. These may include (but are certainly not limited to): Sylow’s theorems, the fundamental theorem of finite abelian groups, the simplicity of ''A&lt;sub&gt;n&lt;/sub&gt;'', Burnside’s Theorem, Polya counting, isometries of '''R'''&lt;sup&gt;3&lt;/sup&gt; and regular solids, straight-edge and compass constructions, the 2- and 4-squares theorems, the RSA algorithm, wallpaper groups, coding theory, or latin squares. Instructors are free to use new approaches to the teaching of the material, as long as the minimal learning outcomes are achieved.<br /> === Courses for which this course is prerequisite ===<br /> This course is required for [[Math 372]], [[Math 450]], [[Math 473]], [[Math 487]], [[Math 561]], [[Math 586]]. As a result it is essential that all required learning objectives be covered.<br /> <br /> [[Category:Courses|371]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_371:_Abstract_Algebra_1.&diff=3797 2024-09-17T19:49:47Z

<p>Ls5: /* Courses for which this course is prerequisite */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Abstract Algebra 1.<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> F, W, Sp<br /> <br /> === Prerequisite ===<br /> [[Math 290]], [[Math 213]].<br /> <br /> === Description ===<br /> Groups, group homomorphisms, rings, ideals, and polynomials.<br /> <br /> == Desired Learning Outcomes ==<br /> This course is aimed at undergraduate mathematics and mathematics education majors. It is a first course in abstract algebra. In addition to being an important branch of mathematics in its own right, abstract algebra is now an essential tool in number theory, geometry, topology, and, to a lesser extent, analysis. Thus it is a core requirement for all mathematics majors. Outside of mathematics, algebra also has applications in cryptography, coding theory, quantum chemistry, and physics.<br /> <br /> === Prerequisites ===<br /> The chief prerequisite for this course is [[Math 290]]. In [[Math 290]], students should learn basic logic, basic set theory, the division algorithm, Euclidean algorithm, and unique factorization theorem for integers, equivalence relations, functions, and mathematical induction. As these topics are of high importance in Math 371, it might be prudent for the instructor to review them at the beginning of the semester.<br /> <br /> === Minimal learning outcomes ===<br /> Students should achieve mastery of the topics listed below. This means that they should know all relevant definitions, correct statements of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts. The students should be able to demonstrate their mastery by solving non-trivial problems related to these concepts, and by proving simple (but non-trivial) theorems about the below concepts, related to, but not identical to, statements proven by the text or instructor.<br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> # Group Theory<br /> #* Basic Definitions<br /> #* Examples of groups<br /> #* Subgroups<br /> #* Lagrange’s Theorem<br /> #* Homomorphisms<br /> #* Normal Subgroups<br /> #* Quotient Groups<br /> #* Isomorphism Theorems<br /> #* Cauchy’s Theorem<br /> #* Direct Products<br /> #* The Symmetric Group<br /> #* Even and odd Permutations<br /> #* Cycle Decompositions<br /> # Ring Theory<br /> #* Basic Definitions<br /> #* Examples of rings (both commutative and noncommutative)<br /> #* Ideals<br /> #* Ring homomorphisms<br /> #* Quotient rings<br /> #* Prime and maximal ideals<br /> #* Polynomial rings<br /> #* Factorization in polynomial rings<br /> #* Field of fractions of a domain<br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/div&gt;<br /> <br /> === Textbooks ===<br /> <br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> * Hungerford: Abstract Algebra: An Introduction<br /> * Herstein: Abstract Algebra<br /> <br /> === Additional topics ===<br /> Beyond the minimal learning outcomes, instructors are free to cover additional topics. These may include (but are certainly not limited to): Sylow’s theorems, the fundamental theorem of finite abelian groups, the simplicity of ''A&lt;sub&gt;n&lt;/sub&gt;'', Burnside’s Theorem, Polya counting, isometries of '''R'''&lt;sup&gt;3&lt;/sup&gt; and regular solids, straight-edge and compass constructions, the 2- and 4-squares theorems, the RSA algorithm, wallpaper groups, coding theory, or latin squares. Instructors are free to use new approaches to the teaching of the material, as long as the minimal learning outcomes are achieved.<br /> === Courses for which this course is prerequisite ===<br /> This course is required for [[Math 372]], [[Math 450]], [[Math 473]] [[Math 487]], [[Math 561]], [[Math 586]]. As a result it is essential that all required learning objectives be covered.<br /> <br /> [[Category:Courses|371]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_313:_Elementary_Linear_Algebra&diff=3796 2024-03-14T18:24:34Z

<p>Ls5: Blanked the page</p> <hr /> <div></div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_303:_Math_for_Engineering_2&diff=3795 2024-03-14T18:14:59Z

<p>Ls5: </p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Mathematics for Engineering 2.<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (4:4:0)<br /> <br /> === Offered ===<br /> F, W<br /> <br /> === Prerequisite ===<br /> [[Math 302]] or [[Math 213]] and [[Math 314]].<br /> <br /> === Description ===<br /> ODEs, Laplace transforms, Fourier series, PDEs.<br /> <br /> == Desired Learning Outcomes ==<br /> This course is designed to give students from the College of Engineering the mathematics background necessary to succeed in their chosen field.<br /> <br /> === Prerequisites ===<br /> Students are expected to have completed [[Math 302]] or [[Math 314]].<br /> <br /> === Minimal learning outcomes ===<br /> Students should achieve mastery of the topics below.<br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> # Some Basic Mathematical Models; Direction Fields<br /> #* Model physical processes using differential equations.<br /> #* Sketch the direction field (or slope field) of a differential equation using a computer graphing program.<br /> #* Describe the behavior of the solutions of a differential equation by analyzing its slope field. Identify any equilibrium solutions.<br /> # Solutions of Some Differential Equations; Classification of Differential Equations<br /> #* Solve basic initial value problems; obtain explicit solutions if possible.<br /> #* Characterize the solutions of a differential equation with respect to initial values.<br /> #* Use the solution of an initial value problem to answer questions about a physical system.<br /> #* Determine the order of an ordinary differential equation. Classify an ordinary differential equation as linear or nonlinear.<br /> #* Verify solutions to ordinary differential equations.<br /> #* Determine the order of a partial differential equation. Classify a partial differential equation as linear or nonlinear.<br /> #* Verify solutions to partial differential equations.<br /> # Linear First Order Equations with Variable Coefficients<br /> #* Identify and solve first order linear equations.<br /> #* Analyze the behavior of solutions.<br /> #* Solve initial value problems for first order linear equations.<br /> # Separable First Order Equations<br /> #* Identify and solve separable equations; obtain explicit solutions if possible.<br /> #* Solve initial value problems for separable equations, and analyze their solutions.<br /> #* Apply the transformation $y=xv(x)$ to obtain a separable equation, if possible.<br /> # Modeling with First Order Equations<br /> #* Construct models of tank problems using differential equations. Analyze the models to answer questions about the physical system modeled.<br /> #* Construct growth and decay problems using differential equations. Analyze the models to answer questions about the physical system modeled.<br /> #* Construct models of problems involving force and motion using differential equations. Analyze the models to answer questions about the physical system modeled.<br /> #Differences Between Linear and Nonlinear Equations<br /> #* Recall and apply the existence and uniqueness theorem for first order linear differential equations.<br /> #* Recall and apply the existence and uniqueness theorem for first order differential equations (both linear and nonlinear).<br /> #* Summarize the nice properties of linear equations. Contrast with nonlinear equations.<br /> # Autonomous Equations and Population Dynamics<br /> #* Determine and classify the equilibrium solutions of an autonomous equation as asymptotically stable, semistable or unstable by analyzing a graph of $\dfrac{dy}{dt}$ versus $y$. Sketch the phase line.<br /> #* Analyze solutions of the logistic equation and other autonomous equations.<br /> # Exact Equations and Integrating Factors<br /> #* Identify whether or not a differential equation is exact.<br /> #* Solve exact differential equations with or without initial conditions, and obtain explicit solutions if possible.<br /> #* Use integrating factors to convert a differential equation to an exact equation and then solve.<br /> #* Determine an integrating factor of the form $\mu(x)$ or $\mu(y)$ which will convert a non-exact differential equation to an exact equation, if possible.<br /> # Introduction to Second Order Equations<br /> #* Determine the characteristic equation of a second order linear differential equation with constant coefficients.<br /> #* Solve second order linear differential equations with constant coefficients that have a characteristic equation with real and distinct roots.<br /> #* Describe the behavior of solutions.<br /> #* Convert a second order differential equation to a first order differential equation in the following cases: i) y&quot;=f(t,y'), ii) y&quot;=f(y,y').<br /> # Fundamental Solutions of Linear Homogeneous Equations; the Wronskian<br /> #* Recall and apply the existence and uniqueness theorem for second order linear differential equations.<br /> #* Recall and verify the principal of superposition for solutions of second order linear differential equations.<br /> #* Evaluate the Wronskian of two functions.<br /> #* Determine whether or not a pair of solutions of a second order linear differential equations constitute a fundamental set of solutions.<br /> #* Recall and apply Abel's theorem.<br /> # Complex Roots of the Characteristic Equation<br /> #* Use Euler's formula to rewrite complex expressions in different forms.<br /> #* Solve second order linear differential equations with constant coefficients that have a characteristic equation with complex roots.<br /> #* Solve initial value problems and analyze the solutions.<br /> # Repeated Roots; Reduction of Order<br /> #* Solve second order linear differential equations with constant coefficients that have a characteristic equation with repeated roots.<br /> #* Solve initial value problems and analyze the solutions.<br /> #* Apply the method of reduction of order to find a second solution to a given differential equation.<br /> # Nonhomogeneous Equations; Method of Undetermined Coefficients<br /> #* For a nonhomogeneous second order linear differential equation, determine a suitable form of a particular solution that can be used in the method of undetermined coefficients.<br /> #* Apply the method of undetermined coefficients to solve nonhomogeneous second order linear differential equations.<br /> #* Solve initial value problems and analyze the solutions.<br /> # Variation of Parameters; Reduction of Order<br /> #* Apply the method of variation of parameters to solve nonhomogeneous second order linear differential equations with or without initial conditions.<br /> #* Apply the method of reduction of order to solve nonhomogeneous second order linear differential equations with or without initial conditions.<br /> # Mechanical Vibrations<br /> #* Model undamped mechanical vibrations with second order linear differential equations, and then solve. Analyze the solution. In particular, evaluate the frequency, period, amplitude, phase shift, and the position at a given time.<br /> #* Model damped mechanical vibrations with second order linear differential equations, and then solve. Analyze the solution. In particular, evaluate the quasi frequency, quasi period, and the behavior at infinity.<br /> #* Define critically damped and overdamped. Identify when these conditions exist in a system.<br /> # Forced Vibrations<br /> #* Model forced, undamped mechanical vibrations with second order linear differential equations, and then solve. Analyze the solution.<br /> #* Describe the phenomena of beats and resonance. Determine the frequency at which resonance occurs.<br /> #* Model forced, damped mechanical vibrations with second order linear differential equations, and then solve. Determine and analyze the solutions, including the steady state and transient parts.<br /> # General Theory of nth Order Linear Equations<br /> #* Recall and apply the existence and uniqueness theorem for higher order linear differential equations.<br /> #* Recall the definition of linear independence for a finite set of functions. Determine whether a set of functions is linearly independent or linearly dependent.<br /> #* Use the Wronskian to determine if a set of solutions form a fundamental set of solutions.<br /> #* Recall the relationship between Wronskian and linear independence for a set of functions, and for a set of solutions.<br /> #* Apply the method of reduction of order to solve higher order linear differential equations.<br /> # Homogeneous Equations with Constant Coefficients<br /> #* Apply Euler's formula to write a complex number in exponential form. Find the distinct complex roots of a number.<br /> #* Determine the characteristic equation of higher order linear differential equations.<br /> #* Solve higher order linear differential equations.<br /> #* Solve initial value problems.<br /> # The Method of Undetermined Coefficients<br /> #* For a nonhomogeneous higher order linear differential equation, determine a suitable form of a generalized particular solution that can be applied in the method of undetermined coefficients.<br /> #* Use the method of undetermined coefficients to solve nonhomogeneous higher order linear differential equations.<br /> #* Solve initial value problems.<br /> # The Method of Variation of Parameters<br /> #* Use the method of variation of parameters to solve nonhomogeneous higher order linear differential equations.<br /> #* Solve initial value problems.<br /> # Review of Power Series<br /> #* Determine the radius of convergence of a power series.<br /> #* Find the power series expansion of a function.<br /> #* Manipulate expressions involving summation notation. Change the index of summation.<br /> # Series Solutions near an Ordinary Point, Part I<br /> #* Find the general solution of a differential equation using power series.<br /> #* Solve initial value problems. Analyze the solution.<br /> # Series Solutions near an Ordinary Point, Part II<br /> #* Given an initial value problem, use the differential equation to inductively determine the terms in the power series of the solution, expanded about the initial value.<br /> #* Determine a lower bound for the radius of convergence of a series solution.<br /> # Euler Equations<br /> #* Find the general solution to an Euler equation in the cases of real distinct roots, equal roots, and complex roots.<br /> #* Solve initial value problems for Euler equations and analyze their solutions.<br /> # Definition of Laplace Transform<br /> #* Sketch a piecewise defined function. Determine if it is continuous, piecewise continuous or neither.<br /> #* Evaluate Laplace transforms from the definition.<br /> #* Determine whether an infinite integral converges or diverges.<br /> # Solution of Initial Value Problems<br /> #* Evaluate inverse Laplace transforms.<br /> #* Use Laplace transforms to solve initial value problems.<br /> #* Evaluate Laplace transforms using the derivative identity given in Problem 28 (p. 322) of the textbook.<br /> # Step Functions<br /> #* Sketch the graph of a function that is defined in terms of step functions.<br /> #* Convert piecewise defined functions to functions defined in terms of step functions and vice versa.<br /> #* Find the Laplace transform of a piecewise defined function.<br /> #* Apply the shifting theorems (Theorems 6.3.1 and 6.3.2) to evaluate Laplace transforms and inverse Laplace transforms.<br /> # Differential Equations with Discontinuous Forcing Functions<br /> #* Use Laplace transforms to solve differential equations with discontinuous forcing functions.<br /> #* Analyze the solutions of differential equations with discontinuous forcing functions.<br /> # Impulse Functions<br /> #* Define an idealized unit impulse function.<br /> #* Use Laplace transforms to solve differential equations that involve impulse functions.<br /> #* Analyze the solutions of differential equations that involve impulse functions.<br /> # The Convolution Integral<br /> #* Evaluate the convolution of two functions from the definition.<br /> #* Prove and disprove properties of the convolution operator.<br /> #* Evaluate the Laplace transform of a convolution of functions.<br /> #* Use the convolution theorem to evaluate inverse Laplace transforms.<br /> #* Solve initial value problems using convolution.<br /> # Introduction to Systems of First Order Equations<br /> #* Transform a higher order linear differential equation into a system of first order linear equations.<br /> #* Transform a system of first order linear equations to a single higher order linear equation.<br /> #* Model physical systems that involve more than one unknown function with a system of differential equations.<br /> #* Recall and apply methods of linear algebra.<br /> # Basic Theory of Systems of First Order Linear Equations<br /> #* Recall and verify the superposition principle for first order linear systems.<br /> #* Relate the Wronskian to linear independence and a fundamental set of solutions.<br /> # Homogeneous Linear Systems with Constant Coefficients<br /> #* Sketch a direction field and a phase portrait for a homogeneous linear system with constant coefficients.<br /> #* Find the general solution of a homogeneous linear system with constant coefficients in the case of real, distinct eigenvalues.<br /> #* Determine if the origin is a saddle point or a node for a homogeneous linear system. Classify a node as asymptotically stable or unstable.<br /> #* Find general solutions, solve initial value problems, and analyze their solutions.<br /> # Complex Eigenvalues<br /> #* Sketch a direction field and a phase portrait for a homogeneous linear system with constant coefficients.<br /> #* Find the general solution of a homogeneous linear system with constant coefficients in the case of complex eigenvalues.<br /> #* Classify the origin as a saddle point, a node, a spiral point or a center.<br /> #* Solve and analyze physical problems modeled by systems of differential equations.<br /> # Fundamental Matrices<br /> #* Determine a fundamental matrix for a system of equations.<br /> #* Solve initial value problems using a fundamental matrix.<br /> #* Prove identities using fundamental matrices.<br /> # Repeated Eigenvalues<br /> #* Sketch a direction field and a phase portrait for a homogeneous linear system with constant coefficients.<br /> #* Find the general solution of a homogeneous linear system with constant coefficients in the case of repeated eigenvalues.<br /> #* Identify improper nodes. Classify them as asymptotically stable or unstable.<br /> #* Solve initial value problems.<br /> # Nonhomogeneous Linear Systems<br /> #* Use diagonalization to solve nonhomogeneous linear systems.<br /> #* Use the method of undetermined coefficients to solve nonhomogeneous linear systems.<br /> #* Use the method of variation of parameters to solve nonhomogeneous linear systems.<br /> #* Solve initial value problems.<br /> # Two-Point Boundary Value Problems<br /> #* Solve boundary value problems involving linear differential equations.<br /> #* Find the eigenvalues and the corresponding eigenfunctions of a boundary value problem.<br /> # Fourier Series<br /> #* Identify functions that are periodic. Determine their periods.<br /> #* Find the Fourier series for a function defined on a closed interval.<br /> #* Determine the $m$th partial sum of the Fourier series of a function. Compare to the function.<br /> # The Fourier Convergence Theorem<br /> #* Find the Fourier series for a periodic function.<br /> #* Recall and apply the convergence theorem for Fourier series.<br /> # Even and Odd Functions<br /> #* Determine whether a given function is even, odd or neither.<br /> #* Sketch the even and odd extensions of a function defined on the interval [0,L].<br /> #* Find the Fourier sine and cosine series for the function defined on [0,L].<br /> #* Establish identities involving infinite sums from Fourier series.<br /> # Separation of Variables; Heat Conduction in a Rod<br /> #* Apply the method of separation of variables to solve partial differential equations, if possible.<br /> #* Find the solutions of heat conduction problems in a rod using separation of variables.<br /> # Other Heat Conduction Problems<br /> #* Solve steady state heat conduction problems in a rod with various boundary conditions.<br /> #* Analyze the solutions.<br /> # The Wave Equation; Vibrations of an Elastic String<br /> #* Solve the wave equation that models the vibration of a string with fixed ends.<br /> #* Describe the motion of a vibrating string.<br /> # Laplace's Equation<br /> #* Solve Laplace's equation over a rectangular region for various boundary conditions.<br /> #* Solve Laplace's equation over a circular region for various boundary conditions.<br /> <br /> &lt;/div&gt;<br /> <br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> [[Category:Courses|303]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_372:_Abstract_Algebra_2.&diff=3794 2024-03-14T18:13:24Z

<p>Ls5: </p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Abstract Algebra 2.<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> W<br /> <br /> === Prerequisite ===<br /> [[Math 371]].<br /> <br /> === Description ===<br /> Fields, Galois theory, solvability of polynomials by radicals.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Prerequisites ===<br /> <br /> Students need to have mastered [[Math 371]] (group theory and ring theory) prior to enrolling in Math 372.<br /> <br /> This is a second course in abstract algebra focusing on field theory. The course is aimed at undergraduate mathematics majors, and it is strongly recommended for students intending to complete a graduate degree in mathematics. In addition to being an important branch of mathematics in its own right, abstract algebra is now an essential tool in number theory, geometry, topology, and, to a lesser extent, analysis. Outside of mathematics, algebra also has applications in cryptography, coding theory, quantum chemistry, and physics.<br /> <br /> === Minimal learning outcomes ===<br /> Students should achieve mastery of the topics listed below. This means that they should know all relevant definitions, correct statements of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts. The students should be able to demonstrate their mastery by solving non-trivial problems related to these concepts, and by proving simple (but non-trivial) theorems about the below concepts, related to, but not identical to, statements proven by the text or instructor.<br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> # Ring Theory<br /> #* Ideals and ring homomorphisms<br /> #* Quotient rings<br /> #* Prime and maximal ideals<br /> #* Polynomial rings over fields<br /> #* Factorization in polynomial rings<br /> #* Irreducible polynomials<br /> #* Polynomial division algorithm<br /> # Field Theory<br /> #* Extensions of fields<br /> #* Field extensions via quotients in polynomial rings<br /> #* Automorphisms of fields<br /> #* Finite fields<br /> #* Fields of characteristic 0 and prime characteristic<br /> #* Splitting fields<br /> #* Galois extensions and Galois groups<br /> #* The Galois correspondence<br /> #* Fundamental Theorem of Galois Theory<br /> #* Fundamental Theorem of Algebra<br /> #* Roots of unity<br /> #* Solvability by radicals<br /> #* Ruler and compass constructions<br /> #* Insolvability of the quintic<br /> <br /> &lt;/div&gt;<br /> <br /> === Textbooks ===<br /> <br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *Joseph Rotman, ''Galois Theory (Second Edition)'', Springer, 1998.<br /> <br /> *David Dummit and Richard Foote, ''Abstract Algebra (Third Edition)'', Wiley, 2003. (The chapters on fields and Galois theory, and some of the material on rings.)<br /> <br /> *Ian Stewart, ''Galois Theory (Third Edition)'', Chapman Hall, 2004.<br /> <br /> *David Cox, ''Galois Theory (Second Edition)'', Wiley, 2012.<br /> <br /> === Additional topics ===<br /> <br /> The instructor may cover additional topics beyond the minimal requirements. Possible topics include (but are not limited to): introduction to algebraic numbers, applications of field extensions to cryptography, applications of field extensions to diophantine analysis, relations of field theory to algebraic geometry, construction of algebraically closed fields using Zorn's lemma, introduction to computer calculations in abstract algebra.<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> [[Category:Courses|372]]<br /> [[Math 586]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_380:_Mathematical_Foundations_of_Data_Science&diff=3793 2024-03-14T17:48:37Z

<p>Ls5: Created page with &quot;== Catalog Information == === Title === Mathematical Foundations of Data Science === (Credit Hours:Lecture Hours:Lab Hours) === (3:3:0) === Offered === Contact Department...&quot;</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Mathematical Foundations of Data Science<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> Contact Department<br /> <br /> === Prerequisite ===<br /> [[Math 112]]<br /> <br /> === Description ===<br /> Mathematical aspects of data science, including high-dimensional geometry and linear algebra, optimization, and probabilistic modeling.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Minimal learning outcomes ===<br /> <br /> === Textbooks ===<br /> <br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_450:_Combinatorics&diff=3792 2024-03-14T17:38:35Z

<p>Ls5: Blanked the page</p> <hr /> <div></div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_413_Advanced_Linear_Algebra&diff=3791 2024-03-14T17:38:12Z

<p>Ls5: </p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Advanced Linear Algebra<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> F and possibly W<br /> <br /> === Prerequisite ===<br /> [[Math 213]] is required. [[Math 290]]. [[Math 371]] recommended, but not required.<br /> <br /> === Description ===<br /> Theory and advanced topics of linear algebra.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> &lt;strong&gt;Prove:&lt;/strong&gt; Students will be able to prove central linear-algebraic results, as well as other results with similar derivations.<br /> <br /> &lt;strong&gt;Distinguish:&lt;/strong&gt; Students will be able to distinguish between true and plausibly-sounding false propositions in the language of linear algebra.<br /> <br /> &lt;strong&gt;Construct:&lt;/strong&gt; Students will be able to construct examples and counterexamples illustrating relations between different linear-algebraic concepts.<br /> <br /> &lt;strong&gt;Categorize:&lt;/strong&gt; Students will be able to categorize linear-algebraic structures according to their properties.<br /> <br /> &lt;strong&gt;Calculate:&lt;/strong&gt; Students will be able to calculate precisely and efficiently, choosing appropriate methods.<br /> <br /> === Prerequisites ===<br /> [[Math 371]] recommended, but not required.<br /> <br /> === Minimal learning outcomes ===<br /> # Linear equations (row operations, matrix multiplication, and invertibility)<br /> # Vector spaces<br /> # Linear transformations (algebra of linear transformations, isomorphisms, linear functionals, duality)<br /> # Polynomials and determinants (algebra of polynomials, polynomial ideals, determinant functions, permutations and uniqueness of determinants)<br /> # Jordan canonical form and elementary canonical forms (invariant subspaces, simultaneous diagonalization and triangulation, direct-sum decompositions, rational forms, Jordan form)<br /> # Inner product spaces (inner product spaces, linear functionals and adjoints, unitary operators, normal operators)<br /> <br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> <br /> [[Category:Courses|413]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_411:_Numerical_Methods&diff=3790 2024-03-14T17:37:17Z

<p>Ls5: </p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Numerical Methods.<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> W (odd years)<br /> <br /> === Prerequisite ===<br /> [[Math 334]]<br /> <br /> === Description ===<br /> Iterative solvers for linear systems, eigenvalue, eigenvector approximations, numerical solutions to nonlinear systems, numerical techniques for initial and boundary value problems, elementary solvers for PDEs. [This official course description appears to differ with current standard practice, in that iterative solvers of linear systems are taught in [[Math 410]].]<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Prerequisites ===<br /> <br /> The formal prerequisites reflect the fact that incoming students should have basic knowledge of ordinary differential equations and have had a first course in numerical methods. Indirectly, the prerequisites ensure that students have had multivariable calculus.<br /> <br /> === Minimal learning outcomes ===<br /> Students should be able to describe, derive, and implement the numerical methods listed below. They should be able to explain the advantages and disadvantages of each method. They should understand error analysis and be able to make practical decisions based on the outcomes of that analysis.<br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> <br /> # Numerical solution of initial-value problems<br /> #* Taylor methods<br /> #** Euler's method<br /> #* Runge-Kutta methods<br /> #** Runge-Kutta-Fehlberg method<br /> #* Multi-step methods<br /> #* Implicit methods<br /> #* Extrapolation methods<br /> #* Stability<br /> #* Stiff differential equations<br /> # Numerical solution of boundary-value problems<br /> #* Shooting methods<br /> #* Finite-difference methods<br /> #* Rayleigh-Ritz method<br /> # Numerical solution of nonlinear systems of equations<br /> #* Newton's method<br /> #* Quasi-Newton methods<br /> #* Steepest-descent methods<br /> # Approximation theory<br /> #* Least-squares approximation<br /> #* Orthogonal polynomials<br /> #** Chebyshev polynomials<br /> #* Rational function approximation<br /> #* Trigonometric polynomial approximation<br /> #* Fast Fourier transforms<br /> # Numerical computation of eigenvalues and eigenvectors<br /> #* Power Method<br /> # Partial differential equations<br /> #* Finite-difference methods<br /> #** For elliptic equations<br /> #** For parabolic equations<br /> #** For hyperbolic equations<br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/div&gt;<br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> * Richard L. Burden and J. Douglas Faires, ''Numerical Analysis (9th Edition)'', Brooks Cole, 2010.<br /> <br /> === Additional topics ===<br /> <br /> If time permits, students could be given an introduction to finite element methods.<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> [[Category:Courses|411]]<br /> <br /> None.</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_410:_Intro_to_Numerical_Methods&diff=3789 2024-03-14T17:36:54Z

<p>Ls5: </p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Introduction to Numerical Methods.<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> F (even years)<br /> <br /> === Prerequisite ===<br /> [[Math 314]]. CS 111<br /> <br /> === Description ===<br /> Root finding, interpolation, curve fitting, numerical differentiation and integration, multiple integrals, direct solvers for linear systems, least squares, rational approximations, Fourier and other orthogonal methods. [This official course description appears to differ with current standard practice, in that iterative solvers of linear systems are taught in this course, while &quot;Fourier and other orthogonal methods&quot; are postponed until [[Math 411]].]<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Prerequisites ===<br /> <br /> Students are required to have had multivariable calculus.<br /> <br /> === Minimal learning outcomes ===<br /> <br /> Students should be able to describe, derive, and implement the numerical methods listed below. They should be able to explain the advantages and disadvantages of each method. They should understand error analysis and be able to make practical decisions based on the outcomes of that analysis.<br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> # Numerical solution of equations of one variable<br /> #* Bisection method<br /> #* Secant method<br /> #* Fixed-point iteration<br /> #** Newton's method<br /> #** Error analysis<br /> #* Polynomial equations<br /> # Interpolation<br /> #* Lagrange interpolation<br /> #* Divided-difference methods<br /> #* Hermite interpolation<br /> #* Cubic spline interpolation<br /> # Numerical differentiation<br /> #* Derivation of formulas<br /> #** Backward-difference<br /> #** Forward-difference<br /> #** Centered-difference<br /> #** Error analysis<br /> #* Richardson's extrapolation<br /> # Numerical integration<br /> #* Newton-Cotes formulas<br /> #* Composite integration<br /> #* Adaptive quadrature<br /> #* Gaussian quadrature<br /> #* Multiple integrals<br /> #* Error analysis<br /> # Numerical solution of linear systems<br /> #* Direct methods<br /> #** Gaussian elimination<br /> #*** Pivoting strategies<br /> #** Factorization methods<br /> #* Iterative methods<br /> #** Jacobi iteration<br /> #** Gauss-Seidel iteration<br /> #** Relaxation methods<br /> <br /> <br /> <br /> <br /> &lt;/div&gt;<br /> <br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> * Richard L. Burde and J. Douglas Faires, ''Numerical Analysis (9th Edition)'', Brooks Cole, 2010.<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> Math 410 is the introductory numerical analysis course and is a prerequisite for the other 3 numerical analysis courses: Math [[Math 411|411]], [[Math 510|510]], and [[Math 511|511]]. It is also a prerequisite for [[Math 480]].<br /> <br /> <br /> [[Category:Courses|410]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_352:_Introduction_to_Complex_Analysis&diff=3788 2024-03-14T17:35:44Z

<p>Ls5: </p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Introduction to Complex Analysis.<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> F, W, Su<br /> <br /> === Prerequisite ===<br /> [[Math 290]], [[Math 314]] and either [[Math 341]] or concurrent enrollment.<br /> <br /> === Description ===<br /> Complex algebra, analytic functions, integration in the complex plane, infinite series, theory of residues, conformal mapping.<br /> <br /> == Desired Learning Outcomes ==<br /> This course is aimed at undergraduates majoring in mathematical and physical sciences and engineering. In addition to being an important branch of mathematics in its own right, complex analysis is an important tool for differential equations (ordinary and partial), algebraic geometry and number theory. Thus it is a core requirement for all mathematics majors. It contributes to all the expected learning outcomes of the Mathematics BS (see [http://learningoutcomes.byu.edu]).<br /> <br /> === Prerequisites ===<br /> Students are expected to have completed and mastered [[Math 290]], and to have taken or to have concurrent enrollment in [[Math 341]] (Theory of Analysis) to provide the necessary understanding of the modes of thought of mathematical analysis.<br /> <br /> === Minimal learning outcomes ===<br /> Students should achieve mastery of the topics listed below. This means that they should know all relevant definitions, the full statements of the major theorems, and examples of the various concepts. Further, students should be able to solve non-trivial problems related to these concepts, and prove simple theorems in analogy to proofs given by the instructor.<br /> <br /> # Complex numbers, moduli, exponential form, arguments of products and quotients, roots of complex numbers, regions in the complex plane.<br /> # Limits, including those involving the point at infinity. Open, closed and connected sets. Continuity, derivatives.<br /> # Analytic functions, Cauchy-Riemann equations, harmonic functions, finding the harmonic conjugate.<br /> # Elementary functions in the complex plane: exponential and log functions, complex exponents, trigonometric and hyperbolic functions and their inverses.<br /> # Contour integrals, upper bounds for moduli, primitives, Cauchy-Goursat theorem, Cauchy integral formulae, Liouville theorem, maximum modulus theorem.<br /> # Taylor series, Laurent series, integration and differentiation of power series, uniqueness of series representation, multiplication and division of power series.<br /> # Isolated singularities, behavior near a singularity. Residue theorem, its application to improper integrals, Jordan's lemma. Argument principle, Rouche's theorem.<br /> #Conformal mappings. Moebius transformations.<br /> <br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> These are at the instructor's discretion as time allows. Possibilities include applications of complex analysis in physics.<br /> <br /> === Courses for which this course is prerequisite ===<br /> This course is required for [[Math 532]] and [[Math 587|587]]. It is needed by anyone proceeding to graduate studies in mathematics. As a result it is essential that ALL required learning objectives be covered.<br /> <br /> [[Category:Courses|352]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_345:_Mathematical_Analysis_1_Lab&diff=3787 2024-03-14T17:34:48Z

<p>Ls5: </p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Mathematical Analysis 1 Lab<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (1:0:2)<br /> <br /> === Offered ===<br /> F<br /> <br /> === Prerequisite ===<br /> concurrent with [[Math 344]]. CS 111<br /> <br /> === Description ===<br /> Programming algorithms to implement the key mathematical methods taught in [[Math 344]]. Applications presented. Developing models and applying results of computations to the application domain.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Prerequisites ===<br /> <br /> === Minimal learning outcomes ===<br /> Students will program algorithms to implement the key mathematical methods taught in [[Math 344]]. Applications will be presented, and students will develop models and apply the results of the computations to the application domain.<br /> <br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> [[Category:Courses|345]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_342:_Theory_of_Analysis_2&diff=3786 2024-03-14T17:34:02Z

<p>Ls5: </p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Theory of Analysis 2.<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> F, W<br /> <br /> === Prerequisite ===<br /> [[Math 213]], [[Math 314]], [[Math 341]].<br /> <br /> === Description ===<br /> Rigorous treatment of calculus of several real variables; metric spaces, geometry and topology of Euclidean space, differentiation(,?) implicity(?) function theorem, integration on sets and manifolds.<br /> <br /> == Desired Learning Outcomes ==<br /> Math 342 is the multivariable sequel to [[Math 341]]. It provides a rigorous treatment of multivariable calculus. Unlike the case with [[Math 341]], Math 342 students are not required to have had an introductory course in the subject matter, so Math 342 needs to treat both computation and theory in some depth.<br /> <br /> === Prerequisites ===<br /> [[Math 341]] provides the single-variable results on which many of the multivariable results of Math 342 are based. [[Math 213]] provides the tools for describing the spaces in which differentiation and integration is performed.<br /> <br /> === Minimal learning outcomes ===<br /> Outlined below are topics that all successful Math 342 students should understand well. As evidence of that understanding, students should be able to demonstrate mastery of all relevant vocabulary, familiarity with common examples and counterexamples, knowledge of the content of the major theorems, understanding of the ideas in their proofs, and ability to make direct application of those results to related problems, including calculations.<br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> <br /> # Metric Spaces<br /> #* Open and closed sets<br /> #* Limit points and sequential limits<br /> #* Compactness (sequences and open covers)<br /> #* Connectedness<br /> #* Subspaces<br /> #* Boundedness<br /> #* Completeness<br /> #* Functional limits<br /> #* Continuity (including uniform and Lipschitz)<br /> #* The Contraction Mapping Theorem<br /> # Geometry and topology of '''R'''&lt;sup&gt;n&lt;/sup&gt;<br /> #* Dot product and Euclidean norm<br /> #* Components and convergence<br /> #* The Bolzano-Weierstrass Theorem<br /> #* The Heine-Borel Theorem<br /> #* Coordinate functions and continuity<br /> #* Algebraic continuity rules&lt;br&gt;&lt;br&gt;&lt;br&gt;<br /> # Differentiation of ''f'': ''D'' ⊆ '''R'''&lt;sup&gt;m&lt;/sup&gt; → '''R'''&lt;sup&gt;n&lt;/sup&gt;<br /> #* Directional, partial, and total derivatives<br /> #* Algebraic differentiation rules<br /> #* The Chain Rule<br /> #* The Mean Value Theorem<br /> #* Higher-order derivatives<br /> #* Taylor's Theorem<br /> #* The Second Derivative Test<br /> #* Lagrange multipliers<br /> #* Newton's method<br /> #* The Inverse Function Theorem<br /> #* The Implicit Function Theorem<br /> # Integration on ''n''-dimensional subsets of '''R'''&lt;sup&gt;n&lt;/sup&gt;<br /> #* Integrability of continuous functions<br /> #* Iterated integrals and Fubini's Theorem<br /> #* The Jacobian and change of variables<br /> #* Polar and spherical coordinates<br /> # Integration on manifolds<br /> #* Line and surface integrals<br /> #* Stokes' Theorem and special cases<br /> <br /> &lt;/div&gt;<br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> The theory of exterior algebra and differential forms is not a required topic, but instructors might find it useful to cover it. Instructors have the option of covering either the Riemann or (probably an abbreviated version of) the Lebesgue theory of integration.<br /> <br /> === Courses for which this course is prerequisite ===<br /> Math 342 is required for [[Math 547]] and [[Math 565]] and is recommended for some other courses.<br /> <br /> [[Category:Courses|342]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_342:_Theory_of_Analysis_2&diff=3785 2024-03-14T17:33:34Z

<p>Ls5: </p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Theory of Analysis 2.<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> F, W<br /> <br /> === Prerequisite ===<br /> [[Math 213]], [[Math 314]], [[Math 341|341]].<br /> <br /> === Description ===<br /> Rigorous treatment of calculus of several real variables; metric spaces, geometry and topology of Euclidean space, differentiation(,?) implicity(?) function theorem, integration on sets and manifolds.<br /> <br /> == Desired Learning Outcomes ==<br /> Math 342 is the multivariable sequel to [[Math 341]]. It provides a rigorous treatment of multivariable calculus. Unlike the case with [[Math 341]], Math 342 students are not required to have had an introductory course in the subject matter, so Math 342 needs to treat both computation and theory in some depth.<br /> <br /> === Prerequisites ===<br /> [[Math 341]] provides the single-variable results on which many of the multivariable results of Math 342 are based. [[Math 213]] provides the tools for describing the spaces in which differentiation and integration is performed.<br /> <br /> === Minimal learning outcomes ===<br /> Outlined below are topics that all successful Math 342 students should understand well. As evidence of that understanding, students should be able to demonstrate mastery of all relevant vocabulary, familiarity with common examples and counterexamples, knowledge of the content of the major theorems, understanding of the ideas in their proofs, and ability to make direct application of those results to related problems, including calculations.<br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> <br /> # Metric Spaces<br /> #* Open and closed sets<br /> #* Limit points and sequential limits<br /> #* Compactness (sequences and open covers)<br /> #* Connectedness<br /> #* Subspaces<br /> #* Boundedness<br /> #* Completeness<br /> #* Functional limits<br /> #* Continuity (including uniform and Lipschitz)<br /> #* The Contraction Mapping Theorem<br /> # Geometry and topology of '''R'''&lt;sup&gt;n&lt;/sup&gt;<br /> #* Dot product and Euclidean norm<br /> #* Components and convergence<br /> #* The Bolzano-Weierstrass Theorem<br /> #* The Heine-Borel Theorem<br /> #* Coordinate functions and continuity<br /> #* Algebraic continuity rules&lt;br&gt;&lt;br&gt;&lt;br&gt;<br /> # Differentiation of ''f'': ''D'' ⊆ '''R'''&lt;sup&gt;m&lt;/sup&gt; → '''R'''&lt;sup&gt;n&lt;/sup&gt;<br /> #* Directional, partial, and total derivatives<br /> #* Algebraic differentiation rules<br /> #* The Chain Rule<br /> #* The Mean Value Theorem<br /> #* Higher-order derivatives<br /> #* Taylor's Theorem<br /> #* The Second Derivative Test<br /> #* Lagrange multipliers<br /> #* Newton's method<br /> #* The Inverse Function Theorem<br /> #* The Implicit Function Theorem<br /> # Integration on ''n''-dimensional subsets of '''R'''&lt;sup&gt;n&lt;/sup&gt;<br /> #* Integrability of continuous functions<br /> #* Iterated integrals and Fubini's Theorem<br /> #* The Jacobian and change of variables<br /> #* Polar and spherical coordinates<br /> # Integration on manifolds<br /> #* Line and surface integrals<br /> #* Stokes' Theorem and special cases<br /> <br /> &lt;/div&gt;<br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> The theory of exterior algebra and differential forms is not a required topic, but instructors might find it useful to cover it. Instructors have the option of covering either the Riemann or (probably an abbreviated version of) the Lebesgue theory of integration.<br /> <br /> === Courses for which this course is prerequisite ===<br /> Math 342 is required for [[Math 547]] and [[Math 565]] and is recommended for some other courses.<br /> <br /> [[Category:Courses|342]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_334:_Ordinary_Differential_Equations&diff=3784 2024-03-14T17:32:42Z

<p>Ls5: </p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Ordinary Differential Equations.<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> F, W, Sp, Su<br /> <br /> === Prerequisite ===<br /> [[Math 113]] and [[Math 213]].<br /> <br /> === Description ===<br /> Methods and theory of ordinary differential equations.<br /> <br /> == Desired Learning Outcomes ==<br /> This course is aimed at students majoring in mathematical and physical sciences and mathematical education. The main purpose of the course is to introduce students to the theory and methods of ordinary differential equations. The course content contributes to all the expected learning outcomes of the Mathematics BS (see [http://learningoutcomes.byu.edu]).<br /> <br /> === Prerequisites ===<br /> Students are expected to have completed [[Math 113]], and [[Math 213]] (or [[Math 313]]) or be concurrently enrolled in [[Math 213]].<br /> <br /> === Minimal learning outcomes ===<br /> Students should achieve mastery of the topics below. This means that they should know all relevant definitions, full statements of the major theorems, and examples of the various concepts. Further, students should be able to solve non-trivial problems related to these concepts, and prove simple theorems in analogy to proofs given by the instructor.<br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> # First order equations<br /> #* Linear, separable, and exact equations<br /> #* Existence and uniqueness of solutions<br /> #* Linear versus nonlinear equations<br /> #* Autonomous equations<br /> #* Models and Applications<br /> # Higher order equations<br /> #* Theory of linear equations<br /> #* Linear independence and the Wronskian<br /> #* Homogeneous linear equations with constant coefficients<br /> #* Nonhomogeneous linear equations, method of undetermined coefficients and variation of parameters<br /> #* Mechanical and electrical vibrations<br /> #* Power series solutions<br /> #* The Laplace transform – definitions and applications <br /> # Systems of equations<br /> #* General theory<br /> #* Eigenvalue-eigenvector method for systems with constant coefficients<br /> #* Homogeneous linear systems with constant coefficients<br /> #* Fundamental matrices<br /> #* Nonhomogeneous linear systems, method of undetermined coefficients and variation of parameters<br /> #* Stability, instability, asymptotic stability, and phase plane analysis<br /> #* Models and applications<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/div&gt;<br /> <br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> These are at the instructor's discretion as time allows; applications to physical problems are particularly helpful.<br /> <br /> === Courses for which this course is prerequisite ===<br /> This course is required for [[Math 447]], [[Math 480]], [[Math 521]], [[Math 534]], [[Math 547]], and [[Math 634]].<br /> <br /> [[Category:Courses|334]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_321:_Algorithm_Design_and_Optimization_1_Lab&diff=3783 2024-03-14T17:31:50Z

<p>Ls5: </p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Algorithm Design and Optimization 1 Lab<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (1:0:2)<br /> <br /> === Offered ===<br /> F<br /> <br /> === Prerequisite ===<br /> concurrent with [[Math 320]], [[Math 345]], and CS 111<br /> <br /> === Description ===<br /> Programming algorithms and using functions to implement the optimization algorithms taught in [[Math 320]]. Applications presented. Developing models and applying results of computations to the application domain.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Prerequisites ===<br /> <br /> === Minimal learning outcomes ===<br /> Students will be able to model many applications effectively using the concepts covered in [[Math 320]]. They will be able to use software to do the computations that are central to these concepts, and will be able to interpret and apply the results of those computations in the contexts in which the models originated.<br /> <br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> [[Category:Courses|321]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_321:_Algorithm_Design_and_Optimization_1_Lab&diff=3782 2024-03-14T17:31:16Z

<p>Ls5: </p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Algorithm Design and Optimization 1 Lab<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (1:0:2)<br /> <br /> === Offered ===<br /> F<br /> <br /> === Prerequisite ===<br /> concurrent with [[Math 320]], [[Math 345]], and [[CS 111]]<br /> <br /> === Description ===<br /> Programming algorithms and using functions to implement the optimization algorithms taught in [[Math 320]]. Applications presented. Developing models and applying results of computations to the application domain.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Prerequisites ===<br /> <br /> === Minimal learning outcomes ===<br /> Students will be able to model many applications effectively using the concepts covered in [[Math 320]]. They will be able to use software to do the computations that are central to these concepts, and will be able to interpret and apply the results of those computations in the contexts in which the models originated.<br /> <br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> [[Category:Courses|321]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_222:_Seminar_in_Math_2&diff=3781 2024-03-14T17:28:16Z

<p>Ls5: Blanked the page</p> <hr /> <div></div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_191:_Seminar_in_Math_1&diff=3780 2024-03-14T17:26:36Z

<p>Ls5: </p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Seminar in Mathematics 1.<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (.5:1:0)<br /> <br /> === Offered ===<br /> F<br /> <br /> === Prerequisite ===<br /> <br /> <br /> === Description ===<br /> Introduction to majoring in mathematics at BYU with an emphasis of departmental and university opportunities, careers options, and current topics in mathematics.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Prerequisites ===<br /> <br /> === Minimal learning outcomes ===<br /> <br /> Students should be familiar with the following items: <br /> <br /> 1. scholarships, undergraduate research, departmental activities, and summer programs available to BYU mathematics majors; <br /> <br /> 2. career options available to mathematics majors;<br /> <br /> 3. several current research topics in mathematics; and<br /> <br /> 4. aspects of the culture of the mathematics community.<br /> <br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> [[Category:Courses|191]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_119&diff=3779 2024-03-14T17:25:58Z

<p>Ls5: Blanked the page</p> <hr /> <div></div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_112:_Calculus_1&diff=3778 2024-03-14T17:16:46Z

<p>Ls5: </p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Calculus 1. <br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (4:5:0)<br /> <br /> === Offered ===<br /> F, W, Sp, Su<br /> <br /> === Prerequisite ===<br /> <br /> <br /> === Description ===<br /> Differential and integral calculus: limits; continuity; the derivative and applications; extrema; the definite integral; fundamental theorem of calculus; L'Hopital's rule.<br /> <br /> === Note ===<br /> Honors also.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> This course is designed for students majoring in the mathematical and physical sciences, engineering, or mathematics education and for students minoring in mathematics or mathematics education. Calculus is the foundation for most of the mathematics studied at the university level. The mastery of calculus requires well-developed skills, clear conceptual understanding, and the ability to model phenomena in a variety of settings. Calculus 1 develops the concepts of limit, derivative, and integral, and is fundamental for many fields of mathematics. This course contributes to all the expected learning outcomes of the Mathematics BS (see [http://learningoutcomes.byu.edu]).<br /> <br /> === Prerequisites ===<br /> Students are expected to have completed a high school course in college algebra and trigonometry sometimes called pre-calculus or to take [[Math 110]] and [[Math 111|111]].<br /> <br /> === Minimal learning outcomes ===<br /> Students should achieve mastery of the topics below. This means that they should know all relevant definitions, full statements of the major theorems, and examples of the various concepts. Further, students should be able to solve non-trivial problems related to these concepts, and prove simple theorems in analogy to proofs given by the instructor. Previous final exams (see [https://math.byu.edu/undergraduate/prev_exams.php]) give specific examples of the level of understanding that is expected.<br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> # Limits and derivatives<br /> #* The limit of a function<br /> #* Laws for calculating limits<br /> #* The definition of a limit<br /> #* Continuity<br /> #* The derivative as the slope of a tangent line<br /> #* The derivative as a rate of change<br /> # Differentiation rules<br /> #* Standard rules for derivatives including power, sum, product, and quotient rules<br /> #* The chain rule<br /> #* Derivatives of trigonometric functions<br /> #* Derivatives of exponential and logarithmic functions&lt;br&gt;<br /> # Applications of differentiation<br /> #* Exponential growth and decay<br /> #* Related rates problems<br /> #* Linear approximations<br /> #* Maximum and minimum values<br /> #* The Mean Value Theorem<br /> #* L’Hospital’s Rule<br /> #* Curve sketching<br /> # Integrals<br /> #* Indefinite integrals<br /> #* Basic formulas for antiderivatives that come from derivative rules<br /> #* The substitution rule for integration<br /> #* Definite integrals<br /> #* Area under a curve<br /> #* Fundamental Theorem of Calculus<br /> &lt;/div&gt;<br /> <br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> These are at the instructor's discretion as time allows. Some suggested topics are hyperbolic functions, Newton’s method, and velocity and acceleration problems.<br /> <br /> === Courses for which this course is prerequisite ===<br /> This course is required for [[Math 113]], [[Math 290]] (or concurrent enrollment), [[Math 313]], and [[Math 362]].<br /> <br /> [[Category:Courses|112]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_215&diff=3777 2023-09-12T19:20:12Z

<p>Ls5: Redirected page to Math 215: Computational Linear Algebra</p> <hr /> <div>#REDIRECT [[Math 215: Computational Linear Algebra]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_213&diff=3776 2023-09-12T18:54:36Z

<p>Ls5: Redirected page to Math 213: Elementary Linear Algebra</p> <hr /> <div>#REDIRECT [[Math 213: Elementary Linear Algebra]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_213&diff=3775 2023-09-12T18:53:05Z

<p>Ls5: Redirected page to Math 213: Elementary Linear Algebra.</p> <hr /> <div>#REDIRECT [[Math 213: Elementary Linear Algebra.]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_213&diff=3774 2023-09-12T18:25:06Z

<p>Ls5: </p> <hr /> <div>Math 213:</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_213&diff=3773 2023-09-12T18:12:18Z

<p>Ls5: Created page with &quot;Math 213&quot;</p> <hr /> <div>Math 213</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_371:_Abstract_Algebra_1.&diff=3772 2023-09-11T21:51:48Z

<p>Ls5: /* Prerequisite */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Abstract Algebra 1.<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> F, W, Sp<br /> <br /> === Prerequisite ===<br /> [[Math 290]], [[Math 213]].<br /> <br /> === Description ===<br /> Groups, group homomorphisms, rings, ideals, and polynomials.<br /> <br /> == Desired Learning Outcomes ==<br /> This course is aimed at undergraduate mathematics and mathematics education majors. It is a first course in abstract algebra. In addition to being an important branch of mathematics in its own right, abstract algebra is now an essential tool in number theory, geometry, topology, and, to a lesser extent, analysis. Thus it is a core requirement for all mathematics majors. Outside of mathematics, algebra also has applications in cryptography, coding theory, quantum chemistry, and physics.<br /> <br /> === Prerequisites ===<br /> The chief prerequisite for this course is [[Math 290]]. In [[Math 290]], students should learn basic logic, basic set theory, the division algorithm, Euclidean algorithm, and unique factorization theorem for integers, equivalence relations, functions, and mathematical induction. As these topics are of high importance in Math 371, it might be prudent for the instructor to review them at the beginning of the semester.<br /> <br /> === Minimal learning outcomes ===<br /> Students should achieve mastery of the topics listed below. This means that they should know all relevant definitions, correct statements of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts. The students should be able to demonstrate their mastery by solving non-trivial problems related to these concepts, and by proving simple (but non-trivial) theorems about the below concepts, related to, but not identical to, statements proven by the text or instructor.<br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> # Group Theory<br /> #* Basic Definitions<br /> #* Examples of groups<br /> #* Subgroups<br /> #* Lagrange’s Theorem<br /> #* Homomorphisms<br /> #* Normal Subgroups<br /> #* Quotient Groups<br /> #* Isomorphism Theorems<br /> #* Cauchy’s Theorem<br /> #* Direct Products<br /> #* The Symmetric Group<br /> #* Even and odd Permutations<br /> #* Cycle Decompositions<br /> # Ring Theory<br /> #* Basic Definitions<br /> #* Examples of rings (both commutative and noncommutative)<br /> #* Ideals<br /> #* Ring homomorphisms<br /> #* Quotient rings<br /> #* Prime and maximal ideals<br /> #* Polynomial rings<br /> #* Factorization in polynomial rings<br /> #* Field of fractions of a domain<br /> <br /> <br /> <br /> <br /> <br /> <br /> &lt;/div&gt;<br /> <br /> === Textbooks ===<br /> <br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> * Hungerford: Abstract Algebra: An Introduction<br /> * Herstein: Abstract Algebra<br /> <br /> === Additional topics ===<br /> Beyond the minimal learning outcomes, instructors are free to cover additional topics. These may include (but are certainly not limited to): Sylow’s theorems, the fundamental theorem of finite abelian groups, the simplicity of ''A&lt;sub&gt;n&lt;/sub&gt;'', Burnside’s Theorem, Polya counting, isometries of '''R'''&lt;sup&gt;3&lt;/sup&gt; and regular solids, straight-edge and compass constructions, the 2- and 4-squares theorems, the RSA algorithm, wallpaper groups, coding theory, or latin squares. Instructors are free to use new approaches to the teaching of the material, as long as the minimal learning outcomes are achieved.<br /> === Courses for which this course is prerequisite ===<br /> This course is required for [[Math 372]], [[Math 450]], [[Math 487]], [[Math 561]], [[Math 586]]. As a result it is essential that all required learning objectives be covered.<br /> <br /> [[Category:Courses|371]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_413_Advanced_Linear_Algebra&diff=3771 2023-09-11T21:35:46Z

<p>Ls5: /* Prerequisite */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Advanced Linear Algebra<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> F and possibly W<br /> <br /> === Prerequisite ===<br /> [[Math 213]] is required. [[Math 371]] recommended, but not required.<br /> <br /> === Description ===<br /> Theory and advanced topics of linear algebra.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> &lt;strong&gt;Prove:&lt;/strong&gt; Students will be able to prove central linear-algebraic results, as well as other results with similar derivations.<br /> <br /> &lt;strong&gt;Distinguish:&lt;/strong&gt; Students will be able to distinguish between true and plausibly-sounding false propositions in the language of linear algebra.<br /> <br /> &lt;strong&gt;Construct:&lt;/strong&gt; Students will be able to construct examples and counterexamples illustrating relations between different linear-algebraic concepts.<br /> <br /> &lt;strong&gt;Categorize:&lt;/strong&gt; Students will be able to categorize linear-algebraic structures according to their properties.<br /> <br /> &lt;strong&gt;Calculate:&lt;/strong&gt; Students will be able to calculate precisely and efficiently, choosing appropriate methods.<br /> <br /> === Prerequisites ===<br /> [[Math 371]] recommended, but not required.<br /> <br /> === Minimal learning outcomes ===<br /> # Linear equations (row operations, matrix multiplication, and invertibility)<br /> # Vector spaces<br /> # Linear transformations (algebra of linear transformations, isomorphisms, linear functionals, duality)<br /> # Polynomials and determinants (algebra of polynomials, polynomial ideals, determinant functions, permutations and uniqueness of determinants)<br /> # Jordan canonical form and elementary canonical forms (invariant subspaces, simultaneous diagonalization and triangulation, direct-sum decompositions, rational forms, Jordan form)<br /> # Inner product spaces (inner product spaces, linear functionals and adjoints, unitary operators, normal operators)<br /> <br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> <br /> [[Category:Courses|413]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_413_Advanced_Linear_Algebra&diff=3770 2023-09-11T21:31:47Z

<p>Ls5: /* Prerequisite */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Advanced Linear Algebra<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> F and possibly W<br /> <br /> === Prerequisite ===<br /> [[Math 213: Elementary Linear Algebra]] is required. [[Math 371]] recommended, but not required.<br /> <br /> === Description ===<br /> Theory and advanced topics of linear algebra.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> &lt;strong&gt;Prove:&lt;/strong&gt; Students will be able to prove central linear-algebraic results, as well as other results with similar derivations.<br /> <br /> &lt;strong&gt;Distinguish:&lt;/strong&gt; Students will be able to distinguish between true and plausibly-sounding false propositions in the language of linear algebra.<br /> <br /> &lt;strong&gt;Construct:&lt;/strong&gt; Students will be able to construct examples and counterexamples illustrating relations between different linear-algebraic concepts.<br /> <br /> &lt;strong&gt;Categorize:&lt;/strong&gt; Students will be able to categorize linear-algebraic structures according to their properties.<br /> <br /> &lt;strong&gt;Calculate:&lt;/strong&gt; Students will be able to calculate precisely and efficiently, choosing appropriate methods.<br /> <br /> === Prerequisites ===<br /> [[Math 371]] recommended, but not required.<br /> <br /> === Minimal learning outcomes ===<br /> # Linear equations (row operations, matrix multiplication, and invertibility)<br /> # Vector spaces<br /> # Linear transformations (algebra of linear transformations, isomorphisms, linear functionals, duality)<br /> # Polynomials and determinants (algebra of polynomials, polynomial ideals, determinant functions, permutations and uniqueness of determinants)<br /> # Jordan canonical form and elementary canonical forms (invariant subspaces, simultaneous diagonalization and triangulation, direct-sum decompositions, rational forms, Jordan form)<br /> # Inner product spaces (inner product spaces, linear functionals and adjoints, unitary operators, normal operators)<br /> <br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> <br /> [[Category:Courses|413]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_413_Advanced_Linear_Algebra&diff=3769 2023-09-11T21:31:31Z

<p>Ls5: /* Prerequisite */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Advanced Linear Algebra<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> F and possibly W<br /> <br /> === Prerequisite ===<br /> [[MMath 213: Elementary Linear Algebra]] is required. [[Math 371]] recommended, but not required.<br /> <br /> === Description ===<br /> Theory and advanced topics of linear algebra.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> &lt;strong&gt;Prove:&lt;/strong&gt; Students will be able to prove central linear-algebraic results, as well as other results with similar derivations.<br /> <br /> &lt;strong&gt;Distinguish:&lt;/strong&gt; Students will be able to distinguish between true and plausibly-sounding false propositions in the language of linear algebra.<br /> <br /> &lt;strong&gt;Construct:&lt;/strong&gt; Students will be able to construct examples and counterexamples illustrating relations between different linear-algebraic concepts.<br /> <br /> &lt;strong&gt;Categorize:&lt;/strong&gt; Students will be able to categorize linear-algebraic structures according to their properties.<br /> <br /> &lt;strong&gt;Calculate:&lt;/strong&gt; Students will be able to calculate precisely and efficiently, choosing appropriate methods.<br /> <br /> === Prerequisites ===<br /> [[Math 371]] recommended, but not required.<br /> <br /> === Minimal learning outcomes ===<br /> # Linear equations (row operations, matrix multiplication, and invertibility)<br /> # Vector spaces<br /> # Linear transformations (algebra of linear transformations, isomorphisms, linear functionals, duality)<br /> # Polynomials and determinants (algebra of polynomials, polynomial ideals, determinant functions, permutations and uniqueness of determinants)<br /> # Jordan canonical form and elementary canonical forms (invariant subspaces, simultaneous diagonalization and triangulation, direct-sum decompositions, rational forms, Jordan form)<br /> # Inner product spaces (inner product spaces, linear functionals and adjoints, unitary operators, normal operators)<br /> <br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> <br /> [[Category:Courses|413]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_413_Advanced_Linear_Algebra&diff=3768 2023-09-11T21:29:30Z

<p>Ls5: /* Prerequisite */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Advanced Linear Algebra<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> F and possibly W<br /> <br /> === Prerequisite ===<br /> [[Math 213]] is required. [[Math 371]] recommended, but not required.<br /> <br /> === Description ===<br /> Theory and advanced topics of linear algebra.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> &lt;strong&gt;Prove:&lt;/strong&gt; Students will be able to prove central linear-algebraic results, as well as other results with similar derivations.<br /> <br /> &lt;strong&gt;Distinguish:&lt;/strong&gt; Students will be able to distinguish between true and plausibly-sounding false propositions in the language of linear algebra.<br /> <br /> &lt;strong&gt;Construct:&lt;/strong&gt; Students will be able to construct examples and counterexamples illustrating relations between different linear-algebraic concepts.<br /> <br /> &lt;strong&gt;Categorize:&lt;/strong&gt; Students will be able to categorize linear-algebraic structures according to their properties.<br /> <br /> &lt;strong&gt;Calculate:&lt;/strong&gt; Students will be able to calculate precisely and efficiently, choosing appropriate methods.<br /> <br /> === Prerequisites ===<br /> [[Math 371]] recommended, but not required.<br /> <br /> === Minimal learning outcomes ===<br /> # Linear equations (row operations, matrix multiplication, and invertibility)<br /> # Vector spaces<br /> # Linear transformations (algebra of linear transformations, isomorphisms, linear functionals, duality)<br /> # Polynomials and determinants (algebra of polynomials, polynomial ideals, determinant functions, permutations and uniqueness of determinants)<br /> # Jordan canonical form and elementary canonical forms (invariant subspaces, simultaneous diagonalization and triangulation, direct-sum decompositions, rational forms, Jordan form)<br /> # Inner product spaces (inner product spaces, linear functionals and adjoints, unitary operators, normal operators)<br /> <br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> <br /> [[Category:Courses|413]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_413_Advanced_Linear_Algebra&diff=3767 2023-09-11T21:29:08Z

<p>Ls5: /* Prerequisite */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Advanced Linear Algebra<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> F and possibly W<br /> <br /> === Prerequisite ===<br /> [[Math 290]] is required. [[Math 371]] recommended, but not required.<br /> <br /> === Description ===<br /> Theory and advanced topics of linear algebra.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> &lt;strong&gt;Prove:&lt;/strong&gt; Students will be able to prove central linear-algebraic results, as well as other results with similar derivations.<br /> <br /> &lt;strong&gt;Distinguish:&lt;/strong&gt; Students will be able to distinguish between true and plausibly-sounding false propositions in the language of linear algebra.<br /> <br /> &lt;strong&gt;Construct:&lt;/strong&gt; Students will be able to construct examples and counterexamples illustrating relations between different linear-algebraic concepts.<br /> <br /> &lt;strong&gt;Categorize:&lt;/strong&gt; Students will be able to categorize linear-algebraic structures according to their properties.<br /> <br /> &lt;strong&gt;Calculate:&lt;/strong&gt; Students will be able to calculate precisely and efficiently, choosing appropriate methods.<br /> <br /> === Prerequisites ===<br /> [[Math 371]] recommended, but not required.<br /> <br /> === Minimal learning outcomes ===<br /> # Linear equations (row operations, matrix multiplication, and invertibility)<br /> # Vector spaces<br /> # Linear transformations (algebra of linear transformations, isomorphisms, linear functionals, duality)<br /> # Polynomials and determinants (algebra of polynomials, polynomial ideals, determinant functions, permutations and uniqueness of determinants)<br /> # Jordan canonical form and elementary canonical forms (invariant subspaces, simultaneous diagonalization and triangulation, direct-sum decompositions, rational forms, Jordan form)<br /> # Inner product spaces (inner product spaces, linear functionals and adjoints, unitary operators, normal operators)<br /> <br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> <br /> [[Category:Courses|413]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_413_Advanced_Linear_Algebra&diff=3766 2023-09-11T21:28:51Z

<p>Ls5: /* Prerequisite */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Advanced Linear Algebra<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> F and possibly W<br /> <br /> === Prerequisite ===<br /> [[Math 215]] is required. [[Math 371]] recommended, but not required.<br /> <br /> === Description ===<br /> Theory and advanced topics of linear algebra.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> &lt;strong&gt;Prove:&lt;/strong&gt; Students will be able to prove central linear-algebraic results, as well as other results with similar derivations.<br /> <br /> &lt;strong&gt;Distinguish:&lt;/strong&gt; Students will be able to distinguish between true and plausibly-sounding false propositions in the language of linear algebra.<br /> <br /> &lt;strong&gt;Construct:&lt;/strong&gt; Students will be able to construct examples and counterexamples illustrating relations between different linear-algebraic concepts.<br /> <br /> &lt;strong&gt;Categorize:&lt;/strong&gt; Students will be able to categorize linear-algebraic structures according to their properties.<br /> <br /> &lt;strong&gt;Calculate:&lt;/strong&gt; Students will be able to calculate precisely and efficiently, choosing appropriate methods.<br /> <br /> === Prerequisites ===<br /> [[Math 371]] recommended, but not required.<br /> <br /> === Minimal learning outcomes ===<br /> # Linear equations (row operations, matrix multiplication, and invertibility)<br /> # Vector spaces<br /> # Linear transformations (algebra of linear transformations, isomorphisms, linear functionals, duality)<br /> # Polynomials and determinants (algebra of polynomials, polynomial ideals, determinant functions, permutations and uniqueness of determinants)<br /> # Jordan canonical form and elementary canonical forms (invariant subspaces, simultaneous diagonalization and triangulation, direct-sum decompositions, rational forms, Jordan form)<br /> # Inner product spaces (inner product spaces, linear functionals and adjoints, unitary operators, normal operators)<br /> <br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> <br /> [[Category:Courses|413]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_413_Advanced_Linear_Algebra&diff=3765 2023-09-11T21:26:28Z

<p>Ls5: /* Prerequisite */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Advanced Linear Algebra<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> F and possibly W<br /> <br /> === Prerequisite ===<br /> [[Math 213]] is required. [[Math 371]] recommended, but not required.<br /> <br /> === Description ===<br /> Theory and advanced topics of linear algebra.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> &lt;strong&gt;Prove:&lt;/strong&gt; Students will be able to prove central linear-algebraic results, as well as other results with similar derivations.<br /> <br /> &lt;strong&gt;Distinguish:&lt;/strong&gt; Students will be able to distinguish between true and plausibly-sounding false propositions in the language of linear algebra.<br /> <br /> &lt;strong&gt;Construct:&lt;/strong&gt; Students will be able to construct examples and counterexamples illustrating relations between different linear-algebraic concepts.<br /> <br /> &lt;strong&gt;Categorize:&lt;/strong&gt; Students will be able to categorize linear-algebraic structures according to their properties.<br /> <br /> &lt;strong&gt;Calculate:&lt;/strong&gt; Students will be able to calculate precisely and efficiently, choosing appropriate methods.<br /> <br /> === Prerequisites ===<br /> [[Math 371]] recommended, but not required.<br /> <br /> === Minimal learning outcomes ===<br /> # Linear equations (row operations, matrix multiplication, and invertibility)<br /> # Vector spaces<br /> # Linear transformations (algebra of linear transformations, isomorphisms, linear functionals, duality)<br /> # Polynomials and determinants (algebra of polynomials, polynomial ideals, determinant functions, permutations and uniqueness of determinants)<br /> # Jordan canonical form and elementary canonical forms (invariant subspaces, simultaneous diagonalization and triangulation, direct-sum decompositions, rational forms, Jordan form)<br /> # Inner product spaces (inner product spaces, linear functionals and adjoints, unitary operators, normal operators)<br /> <br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> <br /> [[Category:Courses|413]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_413_Advanced_Linear_Algebra&diff=3764 2023-09-11T21:26:05Z

<p>Ls5: /* Prerequisite */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Advanced Linear Algebra<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> F and possibly W<br /> <br /> === Prerequisite ===<br /> [[Math 112]] is required. [[Math 371]] recommended, but not required.<br /> <br /> === Description ===<br /> Theory and advanced topics of linear algebra.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> &lt;strong&gt;Prove:&lt;/strong&gt; Students will be able to prove central linear-algebraic results, as well as other results with similar derivations.<br /> <br /> &lt;strong&gt;Distinguish:&lt;/strong&gt; Students will be able to distinguish between true and plausibly-sounding false propositions in the language of linear algebra.<br /> <br /> &lt;strong&gt;Construct:&lt;/strong&gt; Students will be able to construct examples and counterexamples illustrating relations between different linear-algebraic concepts.<br /> <br /> &lt;strong&gt;Categorize:&lt;/strong&gt; Students will be able to categorize linear-algebraic structures according to their properties.<br /> <br /> &lt;strong&gt;Calculate:&lt;/strong&gt; Students will be able to calculate precisely and efficiently, choosing appropriate methods.<br /> <br /> === Prerequisites ===<br /> [[Math 371]] recommended, but not required.<br /> <br /> === Minimal learning outcomes ===<br /> # Linear equations (row operations, matrix multiplication, and invertibility)<br /> # Vector spaces<br /> # Linear transformations (algebra of linear transformations, isomorphisms, linear functionals, duality)<br /> # Polynomials and determinants (algebra of polynomials, polynomial ideals, determinant functions, permutations and uniqueness of determinants)<br /> # Jordan canonical form and elementary canonical forms (invariant subspaces, simultaneous diagonalization and triangulation, direct-sum decompositions, rational forms, Jordan form)<br /> # Inner product spaces (inner product spaces, linear functionals and adjoints, unitary operators, normal operators)<br /> <br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> <br /> [[Category:Courses|413]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_413_Advanced_Linear_Algebra&diff=3763 2023-09-11T20:53:48Z

<p>Ls5: /* Prerequisite */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Advanced Linear Algebra<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> F and possibly W<br /> <br /> === Prerequisite ===<br /> [[Math 213]] is required. [[Math 371]] recommended, but not required.<br /> <br /> === Description ===<br /> Theory and advanced topics of linear algebra.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> &lt;strong&gt;Prove:&lt;/strong&gt; Students will be able to prove central linear-algebraic results, as well as other results with similar derivations.<br /> <br /> &lt;strong&gt;Distinguish:&lt;/strong&gt; Students will be able to distinguish between true and plausibly-sounding false propositions in the language of linear algebra.<br /> <br /> &lt;strong&gt;Construct:&lt;/strong&gt; Students will be able to construct examples and counterexamples illustrating relations between different linear-algebraic concepts.<br /> <br /> &lt;strong&gt;Categorize:&lt;/strong&gt; Students will be able to categorize linear-algebraic structures according to their properties.<br /> <br /> &lt;strong&gt;Calculate:&lt;/strong&gt; Students will be able to calculate precisely and efficiently, choosing appropriate methods.<br /> <br /> === Prerequisites ===<br /> [[Math 371]] recommended, but not required.<br /> <br /> === Minimal learning outcomes ===<br /> # Linear equations (row operations, matrix multiplication, and invertibility)<br /> # Vector spaces<br /> # Linear transformations (algebra of linear transformations, isomorphisms, linear functionals, duality)<br /> # Polynomials and determinants (algebra of polynomials, polynomial ideals, determinant functions, permutations and uniqueness of determinants)<br /> # Jordan canonical form and elementary canonical forms (invariant subspaces, simultaneous diagonalization and triangulation, direct-sum decompositions, rational forms, Jordan form)<br /> # Inner product spaces (inner product spaces, linear functionals and adjoints, unitary operators, normal operators)<br /> <br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> <br /> [[Category:Courses|413]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_413_Advanced_Linear_Algebra&diff=3762 2023-09-11T20:53:07Z

<p>Ls5: /* Prerequisite */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Advanced Linear Algebra<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> F and possibly W<br /> <br /> === Prerequisite ===<br /> [[Math 213]] is a mandatory requirement. [[Math 371]] recommended, but not required.<br /> <br /> === Description ===<br /> Theory and advanced topics of linear algebra.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> &lt;strong&gt;Prove:&lt;/strong&gt; Students will be able to prove central linear-algebraic results, as well as other results with similar derivations.<br /> <br /> &lt;strong&gt;Distinguish:&lt;/strong&gt; Students will be able to distinguish between true and plausibly-sounding false propositions in the language of linear algebra.<br /> <br /> &lt;strong&gt;Construct:&lt;/strong&gt; Students will be able to construct examples and counterexamples illustrating relations between different linear-algebraic concepts.<br /> <br /> &lt;strong&gt;Categorize:&lt;/strong&gt; Students will be able to categorize linear-algebraic structures according to their properties.<br /> <br /> &lt;strong&gt;Calculate:&lt;/strong&gt; Students will be able to calculate precisely and efficiently, choosing appropriate methods.<br /> <br /> === Prerequisites ===<br /> [[Math 371]] recommended, but not required.<br /> <br /> === Minimal learning outcomes ===<br /> # Linear equations (row operations, matrix multiplication, and invertibility)<br /> # Vector spaces<br /> # Linear transformations (algebra of linear transformations, isomorphisms, linear functionals, duality)<br /> # Polynomials and determinants (algebra of polynomials, polynomial ideals, determinant functions, permutations and uniqueness of determinants)<br /> # Jordan canonical form and elementary canonical forms (invariant subspaces, simultaneous diagonalization and triangulation, direct-sum decompositions, rational forms, Jordan form)<br /> # Inner product spaces (inner product spaces, linear functionals and adjoints, unitary operators, normal operators)<br /> <br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> <br /> [[Category:Courses|413]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_636:_Advanced_Probability_1&diff=3761 2023-04-10T13:30:53Z

<p>Ls5: /* Catalog Information */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Advanced Probability 1.<br /> <br /> === Credit Hours ===<br /> 3<br /> <br /> === Offered ===<br /> Fall even years<br /> <br /> === Prerequisite ===<br /> [[Math 314]] and [[Math 341]]; and [[Math 431]] or Stat 370; or equivalents.<br /> <br /> === Description ===<br /> Foundations of the modern theory of probability with applications. Probability spaces, random variables, independence, conditioning, expectation, generating functions, and Markov chains.<br /> <br /> == Desired Learning Outcomes ==<br /> This should be an ''advanced'' course in probability and, therefore, clearly distinguishable from an introductory course like [[Math 431]]. Furthermore, it is supposed to be a course in the ''modern'' theory of probability, which suggests that it should be based on Kolmogorov's measure-theoretic approach or something equivalent.<br /> <br /> === Prerequisites ===<br /> The official prerequisite is multivariable calculus. Other prior courses that will contribute to student success include:<br /> * an introductory course in probability;<br /> * a course in rigorous mathematical reasoning;<br /> * an introductory course in analysis.<br /> <br /> === Minimal learning outcomes ===<br /> Outlined below are topics that all successful Math 543 students should understand well. As evidence of that understanding, students should be able to demonstrate mastery of all relevant vocabulary, familiarity with common examples and counterexamples, knowledge of the content of the major theorems, understanding of the ideas in their proofs, and ability to make direct application of those results to related problems.<br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> # Probability spaces<br /> #* Sigma-algebras and Borel sets<br /> #* Kolmogorov axioms<br /> #* Carathéodory's Extension Theorem<br /> #* Lebesgue-Stieltjes measure<br /> # Random variables<br /> #* Measurable maps<br /> #* Distributions and distribution functions<br /> # Independence<br /> #* Of events and classes of events<br /> #* Of random variables<br /> #* Borel-Cantelli Lemmas<br /> # Expectation<br /> #* Of arbitrary nonnegative random variables<br /> #* Of integrable real-valued random variables<br /> #* Of compositions<br /> #* Monotone Convergence Theorem<br /> #* Uniform integrability and dominated convergence<br /> # Conditioning<br /> #* Probability conditioned on a non-null set<br /> #* Expectation conditioned on a sigma-algebra<br /> #* Expectation conditioned on a random variable<br /> # Probability measures on product spaces<br /> # Strong Law of Large Numbers<br /> # Central Limit Theorem<br /> # Convergence of random variables<br /> #* Almost sure<br /> #* In probability<br /> #* L^p<br /> #* weak<br /> # Discrete-time Martingales&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;<br /> &lt;/div&gt;<br /> === Textbooks ===<br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> * Achim Klenke, ''Probability Theory: A Comprehensive Course'', Springer, 2008.<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> [[Math 637]]<br /> <br /> [[Category:Courses|636]]</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_621:_Matrix_Theory_1&diff=3760 2023-04-10T13:29:52Z

<p>Ls5: /* Catalog Information */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Matrix Theory 1.<br /> <br /> === Credit Hours ===<br /> 3<br /> <br /> === Offered ===<br /> Fall odd years<br /> <br /> === Prerequisite ===<br /> [[Math 570]].<br /> <br /> === Description ===<br /> Symmetric matrices, spectral graph theory, interlacing, the Laplacian matrix of a graph.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Prerequisites ===<br /> <br /> === Minimal learning outcomes ===<br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> <br /> &lt;/div&gt;<br /> <br /> 1. Students will learn simple relations between properties of an undirected graph and the eigenvalues of its adjacency matrix (called the spectrum of the graph).<br /> <br /> 2. Students will know the spectra of several simple classes of graphs: complete graphs, paths, cycles, stars, etc.<br /> <br /> 3. Students will be able to apply the theory of nonnegative matrices to spectral graph theory.<br /> <br /> 4. Students will know the characterization of a bipartite graph in terms of its graph spectrum. <br /> <br /> 5. Students will learn how graph parameters such as the clique number and chromatic number can be estimated by means of the spectrum of the graph.<br /> <br /> 6. Students will know the basic properties of the Laplacian matrix of a graph.<br /> <br /> 7. Students will understand the proof of the matrix tree theorem, know two forms of the theorem, and how to apply it.<br /> <br /> 8. Students will learn some of the deeper relationships between the Laplacian matrix and structural properties of a graph.<br /> <br /> === Textbooks ===<br /> <br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> Richard A Brualdi and Herbert J Ryser, Combinatorial Matrix Theory<br /> <br /> Dragos Cvetkovic, Peter Rowlinson, and Slobodan Simic, An Introduction to the Theory of Graph Spectra<br /> <br /> Chris Godsil and Gordon Royle, Algebraic Graph Theory<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> [[Category:Courses|621]]<br /> <br /> Math 622</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_621:_Matrix_Theory_1&diff=3759 2023-04-10T13:29:40Z

<p>Ls5: /* Credit Hours */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Matrix Theory 1.<br /> <br /> === Credit Hours ===<br /> 3<br /> <br /> <br /> === Offered ===<br /> Fall odd years<br /> <br /> === Prerequisite ===<br /> [[Math 570]].<br /> <br /> === Description ===<br /> Symmetric matrices, spectral graph theory, interlacing, the Laplacian matrix of a graph.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Prerequisites ===<br /> <br /> === Minimal learning outcomes ===<br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> <br /> &lt;/div&gt;<br /> <br /> 1. Students will learn simple relations between properties of an undirected graph and the eigenvalues of its adjacency matrix (called the spectrum of the graph).<br /> <br /> 2. Students will know the spectra of several simple classes of graphs: complete graphs, paths, cycles, stars, etc.<br /> <br /> 3. Students will be able to apply the theory of nonnegative matrices to spectral graph theory.<br /> <br /> 4. Students will know the characterization of a bipartite graph in terms of its graph spectrum. <br /> <br /> 5. Students will learn how graph parameters such as the clique number and chromatic number can be estimated by means of the spectrum of the graph.<br /> <br /> 6. Students will know the basic properties of the Laplacian matrix of a graph.<br /> <br /> 7. Students will understand the proof of the matrix tree theorem, know two forms of the theorem, and how to apply it.<br /> <br /> 8. Students will learn some of the deeper relationships between the Laplacian matrix and structural properties of a graph.<br /> <br /> === Textbooks ===<br /> <br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> Richard A Brualdi and Herbert J Ryser, Combinatorial Matrix Theory<br /> <br /> Dragos Cvetkovic, Peter Rowlinson, and Slobodan Simic, An Introduction to the Theory of Graph Spectra<br /> <br /> Chris Godsil and Gordon Royle, Algebraic Graph Theory<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> [[Category:Courses|621]]<br /> <br /> Math 622</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_621:_Matrix_Theory_1&diff=3758 2023-04-10T13:28:51Z

<p>Ls5: /* Catalog Information */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Matrix Theory 1.<br /> <br /> === Credit Hours ===<br /> 3<br /> <br /> <br /> === Credit Hours ===<br /> Fall odd years<br /> <br /> === Prerequisite ===<br /> [[Math 570]].<br /> <br /> === Description ===<br /> Symmetric matrices, spectral graph theory, interlacing, the Laplacian matrix of a graph.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Prerequisites ===<br /> <br /> === Minimal learning outcomes ===<br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> <br /> &lt;/div&gt;<br /> <br /> 1. Students will learn simple relations between properties of an undirected graph and the eigenvalues of its adjacency matrix (called the spectrum of the graph).<br /> <br /> 2. Students will know the spectra of several simple classes of graphs: complete graphs, paths, cycles, stars, etc.<br /> <br /> 3. Students will be able to apply the theory of nonnegative matrices to spectral graph theory.<br /> <br /> 4. Students will know the characterization of a bipartite graph in terms of its graph spectrum. <br /> <br /> 5. Students will learn how graph parameters such as the clique number and chromatic number can be estimated by means of the spectrum of the graph.<br /> <br /> 6. Students will know the basic properties of the Laplacian matrix of a graph.<br /> <br /> 7. Students will understand the proof of the matrix tree theorem, know two forms of the theorem, and how to apply it.<br /> <br /> 8. Students will learn some of the deeper relationships between the Laplacian matrix and structural properties of a graph.<br /> <br /> === Textbooks ===<br /> <br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> Richard A Brualdi and Herbert J Ryser, Combinatorial Matrix Theory<br /> <br /> Dragos Cvetkovic, Peter Rowlinson, and Slobodan Simic, An Introduction to the Theory of Graph Spectra<br /> <br /> Chris Godsil and Gordon Royle, Algebraic Graph Theory<br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> [[Category:Courses|621]]<br /> <br /> Math 622</div>

Ls5 https://math.byu.edu/wiki/index.php?title=Math_570:_Matrix_Analysis&diff=3757 2023-04-10T13:27:39Z

<p>Ls5: /* Catalog Information */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Matrix Analysis.<br /> <br /> === Credit Hours ===<br /> 3<br /> <br /> === Offered ===<br /> Winter (odd years) spring (even years)<br /> <br /> === Prerequisite ===<br /> [[Math 302]] or [[Math 313|313]]; or equivalents along with the undergraduate calculus sequence.<br /> <br /> === Description ===<br /> Special classes of matrices, canonical forms, matrix and vector norms, localization of eigenvalues, matrix functions, applications.<br /> <br /> == Desired Learning Outcomes ==<br /> Math 570 is a one semester course on matrix analysis. <br /> === Prerequisites ===<br /> <br /> Math 313 or 302 or equivalent and Math 112, 113, 314.<br /> <br /> === Minimal learning outcomes ===<br /> <br /> Outlined below are the minimal learning outcomes which all students in Math 570 should understand. As evidence of that understanding, students should be able to demonstrate mastery of relevant vocabulary, familiarity with common examples and counterexamples, knowledge of the major theorems, understanding of the ideas in their proofs, and ability to make direct application of those results to related problems. <br /> <br /> &lt;div style=&quot;-moz-column-count:2; column-count:2;&quot;&gt;<br /> <br /> &lt;/div&gt;<br /> <br /> Matrix arithmetic and Linear transformations,<br /> The theory of determinants including all proofs of their properties,<br /> Rank of a matrix and elementary matrices,<br /> Spectral theory,<br /> Shur's theorem,<br /> Principal invariants of trace and determinant,<br /> Quadratic forms and second derivative test,<br /> Gerschgorin's theorem,<br /> Abstract vector spaces and general fields,<br /> Axioms,<br /> Subspaces and bases,<br /> Applications to general fields,<br /> Linear transformations,<br /> Matrix of a linear transformation,<br /> Rotations,<br /> Eigenvalues and eigenvectors of linear transformations,<br /> Jordan Cannonical form and applications,<br /> Cayley Hamilton theorem,<br /> Markov chains and migration processes,<br /> Regular Markov matrices,<br /> Absorbing states and gambler's ruin, <br /> Inner product spaces,<br /> Gramm Schmidt process,<br /> Tensor product of vectors,<br /> Least squares,<br /> Fredholm alternative,<br /> Determinants and volume,<br /> Self adjoint operators,<br /> Simultaneous diagonalization,<br /> Spectral theory of self adjoint operators,<br /> Positive and negative linear transformations, <br /> Fractional powers,<br /> Polar decompositions and applications,<br /> Singular value decomposition,<br /> The Frobenius norm and approximation in this norm,<br /> Least squares and the Moore Penrose inverse,<br /> Norms for finite dimensional vector spaces,<br /> The p norms,<br /> The condition number,<br /> The spectral radius,<br /> Sequences and series of linear operators, Functions of linear transformations,<br /> Iterative methods for solutions of linear systems,<br /> <br /> === Textbooks ===<br /> <br /> Possible textbooks for this course include (but are not limited to):<br /> <br /> *<br /> Horn and Johnson, Friedberg, Insel and Spence, or equivalent.<br /> <br /> === Additional topics ===<br /> <br /> Numerical methods for finding eigenvalues,<br /> Power methods,<br /> The QR algorithm,<br /> Rational canonical form,<br /> <br /> === Courses for which this course is prerequisite ===<br /> <br /> None<br /> <br /> [[Category:Courses|570]]</div>

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