Math 290: Fundamentals of Mathematics. - Revision history

Dmd54: Added the current textbook.

2019-07-26T17:51:37Z

Added the current textbook.

Dmd54 at 17:48, 26 July 2019

2019-07-26T17:48:30Z

Ls5: /* Offered */

2016-02-05T20:43:09Z

‎Offered

AAEmpty: /* Courses for which this course is prerequisite */

2011-04-20T20:05:03Z

‎Courses for which this course is prerequisite

AAEmpty: moved Math 290 to Math 290: Fundamentals of Mathematics.

2011-01-19T22:37:22Z

moved Math 290 to Math 290: Fundamentals of Mathematics.

Cpg: /* Minimal learning outcomes */

2010-12-28T21:09:28Z

‎Minimal learning outcomes

Cpg at 14:50, 19 July 2010

2010-07-19T14:50:46Z

Cpg: New page: == Catalog Information == === Title === Fundamentals of Mathematics. === (Credit Hours:Lecture Hours:Lab Hours) === (3:3:0) === Offered === F, W === Prerequisite === Math 112 or co...

2009-06-04T19:10:08Z

New page: == Catalog Information == === Title === Fundamentals of Mathematics. === (Credit Hours:Lecture Hours:Lab Hours) === (3:3:0) === Offered === F, W === Prerequisite === Math 112 or co...

New page

== Catalog Information ==

=== Title ===
Fundamentals of Mathematics.

=== (Credit Hours:Lecture Hours:Lab Hours) ===
(3:3:0)

=== Offered ===
F, W

=== Prerequisite ===
[[Math 112]] or concurrent enrollment with instructor's consent.

=== Description ===
Achieving maturity in mathematical communication. Introduction to mathematical proof; methods of proof; analysis of proof; induction; logical reasoning.

== Desired Learning Outcomes ==
This course is aimed at undergraduate mathematics and mathematics education majors. It is a first course in mathematical thinking. It is intended as an introduction to mathematical proof, and students who finish the course should achieve maturity in mathematical communication.

=== Prerequisites ===
This course has no prerequisites.

=== Minimal learning outcomes ===
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.

<div style="-moz-column-count:2; column-count:2;">
# Set Theory
#* Set builder notation
#* Venn diagrams
#* De Morgan’s Laws
# Logic
#* Truth Tables
#* Quantifiers
#* Negations of statements with quantifiers
#* Implications
#* Biconditionals
# Proof Techniques
#* Direct proof
#* Proof by contrapositive
#* Proof by contradiction
# Relations
#* Reflexive, irreflexive, symmetric, transitive relations
#* Equivalence relations
#* Equivalence classes
# Functions
#* One-to-one and onto
#* Function composition
#* Inverse functions
#* Bijective functions
#* Permutations
# Mathematical Induction
#* Well ordering principle
#* Mathematical induction
#* Strong induction
#* The method of descent
# Cardinal Numbers
#* Numerical equivalence
#* Countable and uncountable sets
#* Schröder-Bernstein theorem
# Number Theory
#* Division algorithm
#* Euclid’s Algorithm
#* Infinitude of primes
#* Unique factorization

</div>
In addition, on completion of the course, students should understand the basic mathematical language concerning logic, sets, the standard number systems, deductive and inductive reasoning, and the structure of proof. They should be able to translate a mathematical statement into logical form and discuss its negation and its implications. They should be able to translate a simple argument into logical form and detect logical validity and flaws. They should be able to read, write, listen and speak using standard mathematical terminology and reasoning.

=== Additional topics ===
Beyond the minimal learning outcomes, instructors are free to cover additional topics. These may include (but are certainly not limited to): concepts of set theory, number theory, geometry, analysis, group theory, and ring theory. Instructors are free to use new approaches to the teaching of the material, as long as the core topics are adequately covered.
=== Courses for which this course is prerequisite ===
This course is required for almost all upper division course in the Mathematics department. There is a strong expectation that student who have taken this course will have a certain minimal preparation in mathematical thinking. As a result it is essential that all required learning outcomes be thoroughly covered.

[[Category:Courses|290]]

@@ Line 71: / Line 71: @@
 Possible textbooks for this course include (but are not limited to):
-* Darrin Doud and Pace P. Nielsen, <em><A HREF="https:math.byu.edu/~doud/Transition">A Transition to Advanced Mathematics</a></em>,
+* Darrin Doud and Pace P. Nielsen, <em>A Transition to Advanced Mathematics</em>, available at https://math.byu.edu/~doud/Transition/
 * Gary Chartrand, Albert D. Polimeni, and Ping Zhang, ''Mathematical Proofs:  A Transition to Advanced Mathematics (2nd Edition)'', Addison Wesley, 2007.

@@ Line 70: / Line 70: @@
 === Textbooks ===
 Possible textbooks for this course include (but are not limited to):
 * Gary Chartrand, Albert D. Polimeni, and Ping Zhang, ''Mathematical Proofs:  A Transition to Advanced Mathematics (2nd Edition)'', Addison Wesley, 2007.

@@ Line 8: / Line 8: @@
 === Offered ===
-F, W
+F, W, Sp
 === Prerequisite ===

@@ Line 77: / Line 77: @@
 Beyond the minimal learning outcomes, instructors are free to cover additional topics. These may include (but are certainly not limited to): concepts of set theory, number theory, geometry, analysis, group theory, and ring theory. Instructors are free to use new approaches to the teaching of the material, as long as the core topics are adequately covered.
 === Courses for which this course is prerequisite ===
-This course is required for almost all upper division course in the Mathematics department. There is a strong expectation that student who have taken this course will have a certain minimal preparation in mathematical thinking. As a result it is essential that all required learning outcomes be thoroughly covered.
+This course is required for almost all upper division course in the Mathematics department. There is a strong expectation that students who have taken this course will have a certain minimal preparation in mathematical thinking. As a result it is essential that all required learning outcomes be thoroughly covered.
 [[Category:Courses|290]]

← Older revision	Revision as of 22:37, 19 January 2011
(No difference)

@@ Line 23: / Line 23: @@
 === Minimal learning outcomes ===
-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.
+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.
 <div style="-moz-column-count:2; column-count:2;">

@@ Line 67: / Line 67: @@
 </div>
 In addition, on completion of the course, students should understand the basic mathematical language concerning logic, sets, the standard number systems, deductive and inductive reasoning, and the structure of proof. They should be able to translate a mathematical statement into logical form and discuss its negation and its implications. They should be able to translate a simple argument into logical form and detect logical validity and flaws. They should be able to read, write, listen and speak using standard mathematical terminology and reasoning.
 === Additional topics ===