MathWiki - User contributions [en]

Math 673: Algebra 3

2015-03-16T20:15:12Z

Sph:

== Catalog Information ==

=== Title ===
Algebra 3.

=== Credit Hours ===
3

=== Prerequisite ===
[[Math 572]] or equivalent.

=== Description ===

== Desired Learning Outcomes ==

=== Prerequisites ===
[[Math 572]] or equivalent.

=== Minimal learning outcomes ===
Students should achieve an advanced mastery of the topics listed below.

<div style="-moz-column-count:2; column-count:2;">
#Finite group theory: Sylow theory, Simple groups, solvable groups
#Representations of finite groups:
#Representations of associative algebras
#Semisimple rings
#Grobner bases

</div>
=== Textbooks ===

Possible textbooks for this course include (but are not limited to):

=== Additional topics ===

=== Courses for which this course is prerequisite ===

[[Category:Courses|673]]
This course is a prerequisite for [[Math 674]].

Math 673: Algebra 3

2015-03-16T20:14:38Z

Sph:

== Catalog Information ==

=== Title ===
Algebra 3.

=== Credit Hours ===
3

=== Prerequisite ===
[[Math 572]] or equivalent.

=== Description ===

== Desired Learning Outcomes ==

=== Prerequisites ===
[[Math 572]] or equivalent.

=== Minimal learning outcomes ===
Students should achieve an advanced mastery of the topics listed below.

<div style="-moz-column-count:2; column-count:2;">
#Finite group theory: Sylow theory, Simple groups, solvable groups
#Representations of finite groups:
#Representations of associative algebras
#Semisimple rings

</div>
=== Textbooks ===

Possible textbooks for this course include (but are not limited to):

=== Additional topics ===

=== Courses for which this course is prerequisite ===

[[Category:Courses|673]]
This course is a prerequisite for [[Math 674]].

Math 673: Algebra 3

2015-03-16T20:04:55Z

Sph:

== Catalog Information ==

=== Title ===
Algebra 3.

=== Credit Hours ===
3

=== Prerequisite ===
[[Math 572]] or equivalent.

=== Description ===

== Desired Learning Outcomes ==

=== Prerequisites ===
[[Math 572]] or equivalent.

=== Minimal learning outcomes ===
Students should achieve an advanced mastery of the topics listed below.

<div style="-moz-column-count:2; column-count:2;">
#Representations of finite groups
#Representations of associative algebras
#Semisimple rings
#Lie Groups
#Lie Algebras

</div>
=== Textbooks ===

Possible textbooks for this course include (but are not limited to):

=== Additional topics ===

=== Courses for which this course is prerequisite ===

[[Category:Courses|673]]
This course is a prerequisite for [[Math 674]].

Math 673: Algebra 3

2015-03-16T20:04:36Z

Sph:

== Catalog Information ==

=== Title ===
Algebra 3.

=== Credit Hours ===
3

=== Prerequisite ===
[[Math 572]] or equivalent.

=== Description ===

== Desired Learning Outcomes ==

=== Prerequisites ===
[[Math 572]] or equivalent.

=== Minimal learning outcomes ===
Students should achieve an advanced mastery of the topics listed below.

<div style="-moz-column-count:2; column-count:2;">
#Representations of finite groups
#Representations of associative algebras
#Semisimple rings
#Lie Groups
#Lie Algebra

</div>
=== Textbooks ===

Possible textbooks for this course include (but are not limited to):

=== Additional topics ===

=== Courses for which this course is prerequisite ===

[[Category:Courses|673]]
This course is a prerequisite for [[Math 674]].

Math 691R - Graduate Math Colloquium

2015-01-14T17:10:43Z

Sph: /* Minimal learning outcomes */

== Catalog Information ==

=== Title ===
Graduate Math Colloquium

=== (Credit Hours:Lecture Hours:Lab Hours) ===
(1:1:0)

=== Offered ===
F W Sp Su

=== Prerequisite ===

=== Description ===
Attend a diverse set of talks at the graduate level. Students will broaden their knowledge of recent and current research in mathematics.

Speakers will be faculty, visitors and students reporting on thesis work.

== Desired Learning Outcomes ==

=== Prerequisites ===

[[Math 371]] or equivalent

=== Minimal learning outcomes ===

Increased appreciation and understanding of the variety, beauty and utility of mathematics.

=== Textbooks ===
Possible textbooks for this course include (but are not limited to):

*

=== Additional topics ===

=== Courses for which this course is prerequisite ===

[[Category:Courses|691R]]

Math 644: Harmonic Analysis

2014-12-03T20:22:07Z

Sph:

== Catalog Information ==

=== Title ===
Harmonic Analysis.

=== Credit Hours ===
3

=== Prerequisite ===
[[Math 532]], [[Math 541|541]].

=== Description ===
Harmonic analysis on the torus and in Euclidean space; pointwise and norm convergence of Fourier series and functional-analytic aspects of Fourier transforms emphasized.

== Desired Learning Outcomes ==

=== Prerequisites ===

[[Math 532]], [[Math 541|541]].
=== Minimal learning outcomes ===

Periodic functions and Fourier series;

Convergence of Fourier series;

Spaces of functions on R^n

The space of compactly supported functions, functions of compact support and the algebraic structure of those spaces, i.e., convolution.

The Fourier transform of rapidly decreasing functions and L^2 functions, inversion formula and Plancherel theorems.

Introduction to distribution theory and the continuous linear functionals on function spaces. How to differentiate distributions. The Fourier transform of distributions.

Application of the Fourier transform to differential equations. In particular we will discuss the heat equation and the wave equation.

Hermite functions and polynomials.

Other integral transforms. In particular, we will discuss the continuous wavelet transform, derive a Plancherel formula and an inversion formula.

Other relevant topics may also be covered.
=== Textbooks ===

Possible textbooks for this course include (but are not limited to):

*

=== Additional topics ===

=== Courses for which this course is prerequisite ===

[[Category:Courses|644]]

Math 644: Harmonic Analysis

2014-12-03T20:21:36Z

Sph:

== Catalog Information ==

=== Title ===
Harmonic Analysis.

=== Credit Hours ===
3

=== Prerequisite ===
[[Math 532]], [[Math 541|541]].

=== Description ===
Harmonic analysis on the torus and in Euclidean space; pointwise and norm convergence of Fourier series and functional-analytic aspects of Fourier transforms emphasized.

== Desired Learning Outcomes ==

=== Prerequisites ===

=== Minimal learning outcomes ===

Periodic functions and Fourier series;

Convergence of Fourier series;

Spaces of functions on R^n

The space of compactly supported functions, functions of compact support and the algebraic structure of those spaces, i.e., convolution.

The Fourier transform of rapidly decreasing functions and L^2 functions, inversion formula and Plancherel theorems.

Introduction to distribution theory and the continuous linear functionals on function spaces. How to differentiate distributions. The Fourier transform of distributions.

Application of the Fourier transform to differential equations. In particular we will discuss the heat equation and the wave equation.

Hermite functions and polynomials.

Other integral transforms. In particular, we will discuss the continuous wavelet transform, derive a Plancherel formula and an inversion formula.

Other relevant topics may also be covered.
=== Textbooks ===

Possible textbooks for this course include (but are not limited to):

*

=== Additional topics ===

=== Courses for which this course is prerequisite ===

[[Category:Courses|644]]

Math 644: Harmonic Analysis

2014-12-03T20:20:26Z

Sph:

== Catalog Information ==

=== Title ===
Harmonic Analysis.

=== Credit Hours ===
3

=== Prerequisite ===
[[Math 532]], [[Math 541|541]].

=== Description ===
Harmonic analysis on the torus and in Euclidean space; pointwise and norm convergence of Fourier series and functional-analytic aspects of Fourier transforms emphasized.

== Desired Learning Outcomes ==

=== Prerequisites ===

=== Minimal learning outcomes ===

Periodic functions and Fourier series;

Convergence of Fourier series;

Spaces of functions on R^n

The space of compactly supported functions, functions of compact support and the algebraic structure of those spaces, i.e., convolution.

The Fourier transform of rapidly decreasing functions and L^2 functions, inversion formula and Plancherel theorems.

Introduction to distribution theory and the continuous linear functionals on function spaces. How to differentiate distributions. The Fourier transform of distributions.

Application of the Fourier transform to differential equations. In particular we will discuss the heat equation and the wave equation.

Hermite functions and polynomials.

Other integral transforms. In particular, we will discuss the continuous wavelet transform, derive a Plancherel formula and an inversion formula
=== Textbooks ===

Possible textbooks for this course include (but are not limited to):

*

=== Additional topics ===

=== Courses for which this course is prerequisite ===

[[Category:Courses|644]]

Math 644: Harmonic Analysis

2014-12-03T20:19:50Z

Sph:

== Catalog Information ==

=== Title ===
Harmonic Analysis.

=== Credit Hours ===
3

=== Prerequisite ===
[[Math 532]], [[Math 541|541]].

=== Description ===
Harmonic analysis on the torus and in Euclidean space; pointwise and norm convergence of Fourier series and functional-analytic aspects of Fourier transforms emphasized.

== Desired Learning Outcomes ==

=== Prerequisites ===

=== Minimal learning outcomes ===

Periodic functions and Fourier series;

Convergence of Fourier series;

Spaces of functions on R^n

In particular, we will discuss the space of compactly supported functions, functions of compact support and the algebraic structure of those spaces, i.e., convolution.

The Fourier transform of rapidly decreasing functions and L^2 functions, inversion formula and Plancherel theorems.

Introduction to distribution theory and the continuous linear functionals on function spaces. How to differentiate distributions. The Fourier transform of distributions.

Application of the Fourier transform to differential equations. In particular we will discuss the heat equation and the wave equation.

Hermite functions and polynomials.

At the end, we will also discuss some other integral transforms. In particular, we will discuss the continuous wavelet transform, derive a Plancherel formula and an inversion formula
=== Textbooks ===

Possible textbooks for this course include (but are not limited to):

*

=== Additional topics ===

=== Courses for which this course is prerequisite ===

[[Category:Courses|644]]

Math 674: Lie Groups and Algebras

2014-10-29T21:23:29Z

Sph: /* Description */

== Catalog Information ==

=== Title ===
Lie Groups and Algebras

=== Credit Hours ===
3

=== Offered ===
Upon request.

=== Prerequisite ===
673, equivalent, or teacher approval.

=== Description ===
Basic concepts of Lie Groups and algebras including root systems, algebraic groups, and representation theory.
Other topics may be presented.

== Desired Learning Outcomes ==

=== Prerequisites ===
[[Math 673]] or equivalent.

=== Minimal learning outcomes ===
Basic concepts of Lie Groups and algebras including root systems, algebraic groups, and representation theory.
Possible applications to physics or to other areas of mathematics.

=== Textbooks ===

Possible textbooks for this course include (but are not limited to):

Humphreys, James E. Introduction to Lie algebras and representation theory. Second printing, revised. Graduate Texts in Mathematics, 9. Springer-Verlag, New York-Berlin, 1978.

Bump, Daniel Lie groups. Second edition. Graduate Texts in Mathematics, 225. Springer, New York, 2013. xiv+551

=== Additional topics ===
Any advanced topic in Algebra including Galois theory, Grobner bases, Representation theory, Invariant theory, etc.

=== Courses for which this course is prerequisite ===

[[Category:Courses|674]]
None.

Math 674: Lie Groups and Algebras

2014-10-29T21:22:56Z

Sph: /* Minimal learning outcomes */

== Catalog Information ==

=== Title ===
Lie Groups and Algebras

=== Credit Hours ===
3

=== Offered ===
Upon request.

=== Prerequisite ===
673, equivalent, or teacher approval.

=== Description ===
Basic concepts of Lie Groups and algebras including root systems, algebraic groups, and representation theory.

== Desired Learning Outcomes ==

=== Prerequisites ===
[[Math 673]] or equivalent.

=== Minimal learning outcomes ===
Basic concepts of Lie Groups and algebras including root systems, algebraic groups, and representation theory.
Possible applications to physics or to other areas of mathematics.

=== Textbooks ===

Possible textbooks for this course include (but are not limited to):

Humphreys, James E. Introduction to Lie algebras and representation theory. Second printing, revised. Graduate Texts in Mathematics, 9. Springer-Verlag, New York-Berlin, 1978.

Bump, Daniel Lie groups. Second edition. Graduate Texts in Mathematics, 225. Springer, New York, 2013. xiv+551

=== Additional topics ===
Any advanced topic in Algebra including Galois theory, Grobner bases, Representation theory, Invariant theory, etc.

=== Courses for which this course is prerequisite ===

[[Category:Courses|674]]
None.

Math 674: Lie Groups and Algebras

2014-10-29T21:21:45Z

Sph: /* Additional topics */

== Catalog Information ==

=== Title ===
Lie Groups and Algebras

=== Credit Hours ===
3

=== Offered ===
Upon request.

=== Prerequisite ===
673, equivalent, or teacher approval.

=== Description ===
Basic concepts of Lie Groups and algebras including root systems, algebraic groups, and representation theory.

== Desired Learning Outcomes ==

=== Prerequisites ===
[[Math 673]] or equivalent.

=== Minimal learning outcomes ===
Basic concepts of Lie Groups and algebras including root systems, algebraic groups, and representation theory.

=== Textbooks ===

Possible textbooks for this course include (but are not limited to):

Humphreys, James E. Introduction to Lie algebras and representation theory. Second printing, revised. Graduate Texts in Mathematics, 9. Springer-Verlag, New York-Berlin, 1978.

Bump, Daniel Lie groups. Second edition. Graduate Texts in Mathematics, 225. Springer, New York, 2013. xiv+551

=== Additional topics ===
Any advanced topic in Algebra including Galois theory, Grobner bases, Representation theory, Invariant theory, etc.

=== Courses for which this course is prerequisite ===

[[Category:Courses|674]]
None.

Math 674: Lie Groups and Algebras

2014-10-29T21:19:59Z

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

== Catalog Information ==

=== Title ===
Lie Groups and Algebras

=== Credit Hours ===
3

=== Offered ===
Upon request.

=== Prerequisite ===
673, equivalent, or teacher approval.

=== Description ===
Basic concepts of Lie Groups and algebras including root systems, algebraic groups, and representation theory.

== Desired Learning Outcomes ==

=== Prerequisites ===
[[Math 673]] or equivalent.

=== Minimal learning outcomes ===
Basic concepts of Lie Groups and algebras including root systems, algebraic groups, and representation theory.

=== Textbooks ===

Possible textbooks for this course include (but are not limited to):

Humphreys, James E. Introduction to Lie algebras and representation theory. Second printing, revised. Graduate Texts in Mathematics, 9. Springer-Verlag, New York-Berlin, 1978.

Bump, Daniel Lie groups. Second edition. Graduate Texts in Mathematics, 225. Springer, New York, 2013. xiv+551

=== Additional topics ===
Any advanced topic in Algebra including Galois theory, Grobenr bases, representation theory, invariant theory, etc.

=== Courses for which this course is prerequisite ===

[[Category:Courses|674]]
None.

Math 674: Lie Groups and Algebras

2014-10-29T21:19:25Z

Sph: /* Prerequisite */

== Catalog Information ==

=== Title ===
Lie Groups and Algebras

=== Credit Hours ===
3

=== Offered ===
Upon request.

=== Prerequisite ===
673, equivalent, or teacher approval.

=== Description ===
Basic concepts of Lie Groups and algebras including root systems, algebraic groups, and representation theory.

== Desired Learning Outcomes ==

=== Prerequisites ===
[[Math 673]] or equivalent.

=== Minimal learning outcomes ===
Basic concepts of Lie Groups and algebras including root systems, algebraic groups, and representation theory.

=== Textbooks ===

Possible textbooks for this course include (but are not limited to):

Humphreys, James E. Introduction to Lie algebras and representation theory. Second printing, revised. Graduate Texts in Mathematics, 9. Springer-Verlag, New York-Berlin, 1978.

Bump, Daniel Lie groups. Second edition. Graduate Texts in Mathematics, 225. Springer, New York, 2013. xiv+551

=== Additional topics ===
Any advanced topic in Algebra including Galois theory, Grobenr bases, representation theory, invariant theory, etc.

=== Courses for which this course is prerequisite ===

[[Category:Courses|674]]

Math 674: Lie Groups and Algebras

2014-10-29T21:18:51Z

Sph: /* Description */

== Catalog Information ==

=== Title ===
Lie Groups and Algebras

=== Credit Hours ===
3

=== Offered ===
Upon request.

=== Prerequisite ===

=== Description ===
Basic concepts of Lie Groups and algebras including root systems, algebraic groups, and representation theory.

== Desired Learning Outcomes ==

=== Prerequisites ===
[[Math 673]] or equivalent.

=== Minimal learning outcomes ===
Basic concepts of Lie Groups and algebras including root systems, algebraic groups, and representation theory.

=== Textbooks ===

Possible textbooks for this course include (but are not limited to):

Humphreys, James E. Introduction to Lie algebras and representation theory. Second printing, revised. Graduate Texts in Mathematics, 9. Springer-Verlag, New York-Berlin, 1978.

Bump, Daniel Lie groups. Second edition. Graduate Texts in Mathematics, 225. Springer, New York, 2013. xiv+551

=== Additional topics ===
Any advanced topic in Algebra including Galois theory, Grobenr bases, representation theory, invariant theory, etc.

=== Courses for which this course is prerequisite ===

[[Category:Courses|674]]

Math 674: Lie Groups and Algebras

2014-10-29T21:18:21Z

Sph: /* Additional topics */

== Catalog Information ==

=== Title ===
Lie Groups and Algebras

=== Credit Hours ===
3

=== Offered ===
Upon request.

=== Prerequisite ===

=== Description ===

== Desired Learning Outcomes ==

=== Prerequisites ===
[[Math 673]] or equivalent.

=== Minimal learning outcomes ===
Basic concepts of Lie Groups and algebras including root systems, algebraic groups, and representation theory.

=== Textbooks ===

Possible textbooks for this course include (but are not limited to):

Humphreys, James E. Introduction to Lie algebras and representation theory. Second printing, revised. Graduate Texts in Mathematics, 9. Springer-Verlag, New York-Berlin, 1978.

Bump, Daniel Lie groups. Second edition. Graduate Texts in Mathematics, 225. Springer, New York, 2013. xiv+551

=== Additional topics ===
Any advanced topic in Algebra including Galois theory, Grobenr bases, representation theory, invariant theory, etc.

=== Courses for which this course is prerequisite ===

[[Category:Courses|674]]

Math 674: Lie Groups and Algebras

2014-10-29T21:17:01Z

Sph: /* Offered */

== Catalog Information ==

=== Title ===
Lie Groups and Algebras

=== Credit Hours ===
3

=== Offered ===
Upon request.

=== Prerequisite ===

=== Description ===

== Desired Learning Outcomes ==

=== Prerequisites ===
[[Math 673]] or equivalent.

=== Minimal learning outcomes ===
Basic concepts of Lie Groups and algebras including root systems, algebraic groups, and representation theory.

=== Textbooks ===

Possible textbooks for this course include (but are not limited to):

Humphreys, James E. Introduction to Lie algebras and representation theory. Second printing, revised. Graduate Texts in Mathematics, 9. Springer-Verlag, New York-Berlin, 1978.

Bump, Daniel Lie groups. Second edition. Graduate Texts in Mathematics, 225. Springer, New York, 2013. xiv+551

=== Additional topics ===

=== Courses for which this course is prerequisite ===

[[Category:Courses|674]]

Math 674: Lie Groups and Algebras

2014-10-29T21:16:44Z

Sph: /* Textbooks */

== Catalog Information ==

=== Title ===
Lie Groups and Algebras

=== Credit Hours ===
3

=== Offered ===

=== Prerequisite ===

=== Description ===

== Desired Learning Outcomes ==

=== Prerequisites ===
[[Math 673]] or equivalent.

=== Minimal learning outcomes ===
Basic concepts of Lie Groups and algebras including root systems, algebraic groups, and representation theory.

=== Textbooks ===

Possible textbooks for this course include (but are not limited to):

Humphreys, James E. Introduction to Lie algebras and representation theory. Second printing, revised. Graduate Texts in Mathematics, 9. Springer-Verlag, New York-Berlin, 1978.

Bump, Daniel Lie groups. Second edition. Graduate Texts in Mathematics, 225. Springer, New York, 2013. xiv+551

=== Additional topics ===

=== Courses for which this course is prerequisite ===

[[Category:Courses|674]]

Math 674: Lie Groups and Algebras

2014-10-29T21:14:19Z

Sph: /* Minimal learning outcomes */

Math 675R: Special Topics in Algebra.

2010-05-21T19:52:57Z

Sph:

== Catalog Information ==

=== Title ===
Special Topics in Algebra.

=== Credit Hours ===
3

=== Prerequisite ===
[[Math 672]].

=== Description ===

Advanced topics in algebra drawn from pure and applied mathematics. Possible topics include: representation theory, Lie groups and Lie algebras, geometric group theory, Galois theory, algebraic number theory, computational algebra, Category theory, Grobner bases, algebraic geometry, algebraic combinatorics, cryptanalysis, finite group theory, modular forms, commutative algebra, homological algebra, group cohomology, character theory of finite groups, mathematical physics, ring theory.

== Desired Learning Outcomes ==

=== Prerequisites ===
Students are expected to have completed the graduate algebra sequence [[Math 671]] and [[Math 672]].

=== Minimal learning outcomes ===

These will depend on the topic chosen.

<div style="-moz-column-count:2; column-count:2;">

</div>

=== Additional topics ===

Past topics chosen include:

# Representations of algebras and finite groups, using the book by Curtis and Reiner.
# Modular forms using a book by Kilford "Modular forms: a classical and computational introduction."
# Lie algebras, using a book by J Humphreys.
# Lie groups, using the book "Lie groups, Lie algberas and representations", by Brian C. Hall.

=== Courses for which this course is prerequisite ===

[[Category:Courses|675]]

Math 675R: Special Topics in Algebra.

2010-05-21T16:15:49Z

Sph:

== Catalog Information ==

=== Title ===
Special Topics in Algebra.

=== Credit Hours ===
3

=== Prerequisite ===
[[Math 672]].

=== Description ===

Advanced topics in algebra drawn from pure and applied mathematics. Possible topics include: representation theory, Lie groups and Lie algebras, geometric group theory, Galois theory, algebraic number theory, computational algebra, Category theory, Grobner bases, algebraic geometry, algebraic combinatorics, cryptanalysis, finite group theory, modular forms, commutative algebra, homological algebra, group cohomology, character theory of finite groups, mathematical physics, ring theory.

== Desired Learning Outcomes ==

=== Prerequisites ===
Students are expected to have completed the graduate algebra sequence [[Math 671]] and [[Math 672]].

=== Minimal learning outcomes ===

These will depend on the topic chosen.

<div style="-moz-column-count:2; column-count:2;">

</div>

=== Additional topics ===

Past topics chosen include:

# Representations of algebras and finite groups, using the book by Curtis and Reiner.
# Modular forms using a book by Kilford "Modular forms: a classical and computational introduction."
# Lie algebras, using a book by J Humphreys.

=== Courses for which this course is prerequisite ===

[[Category:Courses|675]]

Math 675R: Special Topics in Algebra.

2010-05-21T16:15:05Z

Sph:

== Catalog Information ==

=== Title ===
Special Topics in Algebra.

=== Credit Hours ===
3

=== Prerequisite ===
[[Math 672]].

=== Description ===

Advanced topics in algebra drawn from pure and applied mathematics. Possible topics include: representation theory, Lie groups and Lie algebras, geometric group theory, Galois theory, algebraic number theory, computational algebra, Category theory, Grobner bases, algebraic geometry, algebraic combinatorics, cryptanalysis, finite group theory, modular forms, commutative algebra, homological algebra, group cohomology, character theory of finite groups, mathematical physics, ring theory.

== Desired Learning Outcomes ==

=== Prerequisites ===
Students are expected to have completed the graduate algebra sequence [[Math 671]] and [[Math 672]].

=== Minimal learning outcomes ===

These will depend on the topic chosen.

<div style="-moz-column-count:2; column-count:2;">

</div>

=== Additional topics ===

Past topics chosen include:

# Representations of algebras and finite groups, using the book by Curtis and Reiner.

# Modular forms using a book by Kilford "Modular forms: a classical and computational introduction."

# Lie algebras, using a book by J Humphreys.

=== Courses for which this course is prerequisite ===

[[Category:Courses|675]]

Math 675R: Special Topics in Algebra.

2010-05-21T16:14:06Z

Sph:

== Catalog Information ==

=== Title ===
Special Topics in Algebra.

=== Credit Hours ===
3

=== Prerequisite ===
[[Math 672]].

=== Description ===

Advanced topics in algebra drawn from pure and applied mathematics. Possible topics include: representation theory, Lie groups and Lie algebras, geometric group theory, Galois theory, algebraic number theory, computational algebra, Category theory, Grobner bases, algebraic geometry, algebraic combinatorics, finite group theory, modular forms, commutative algebra, homological algebra, group cohomology, character theory of finite groups, mathematical physics, ring theory.

== Desired Learning Outcomes ==

=== Prerequisites ===
Students are expected to have completed the graduate algebra sequence [[Math 671]] and [[Math 672]].

=== Minimal learning outcomes ===

These will depend on the topic chosen.

<div style="-moz-column-count:2; column-count:2;">

</div>

=== Additional topics ===

Past topics chosen include:

# Representations of algebras and finite groups, using the book by Curtis and Reiner.

# Modular forms using a book by Kilford "Modular forms: a classical and computational introduction."

# Lie algebras, using a book by J Humphreys.

=== Courses for which this course is prerequisite ===

[[Category:Courses|675]]

Math 675R: Special Topics in Algebra.

2010-05-21T16:04:32Z

Sph:

== Catalog Information ==

=== Title ===
Special Topics in Algebra.

=== Credit Hours ===
3

=== Prerequisite ===
[[Math 672]].

=== Description ===

Advanced topics in algebra drawn from pure and applied mathematics. Possible topics include: representation theory, Lie groups and Lie algebras, geometric group theory, Galois theory, algebraic number theory, computational algebra, Category theory, Grobner bases, algebraic geometry, algebraic combinatorics, finite group theory, modular forms, commutative algebra, homological algebra, group cohomology, character theory of finite groups, mathematical physics, ring theory.

== Desired Learning Outcomes ==

=== Prerequisites ===
Students are expected to have completed the graduate algebra sequence [[Math 671]] and [[Math 672]].

=== Minimal learning outcomes ===

These will depend on the topic chosen.

<div style="-moz-column-count:2; column-count:2;">

</div>

=== Additional topics ===

Past topics chosen include: (1) Representations of algebras and finite groups, using the book by Curtis and Reiner. (2) Modular forms using a book by Kilford "Modular forms: a classical and computational introduction." (3) Lie algebras, using a book by J Humphreys.

=== Courses for which this course is prerequisite ===

[[Category:Courses|675]]

Math 675R: Special Topics in Algebra.

2010-05-21T16:03:24Z

Sph:

== Catalog Information ==

=== Title ===
Special Topics in Algebra.

=== Credit Hours ===
3

=== Prerequisite ===
[[Math 672]].

=== Description ===

Advanced topics in algebra drawn from pure and applied mathematics. Possible topics include: representation theory, Lie groups and Lie algebras, geometric group theory, Galois theory, algebraic number theory, computational algebra, Category theory, Grobner bases, algebraic geometry, algebraic combinatorics, finite group theory, modular forms, commutative algebra, homological algebra, group cohomology, character theory of finite groups, mathematical physics, ring theory.

== Desired Learning Outcomes ==

=== Prerequisites ===
Students are expected to have completed the graduate algebra sequence [[Math 671]] and [[Math 672]].

=== Minimal learning outcomes ===

These will depend on the topic chosen.

<div style="-moz-column-count:2; column-count:2;">

</div>

=== Additional topics ===

Past topics chosen include: representations of algebras and finite groups, using the book by Curtis and Reiner. Modular forms using a book by Kilford "Modular forms: a classical and computational introduction."

=== Courses for which this course is prerequisite ===

[[Category:Courses|675]]

Math 675R: Special Topics in Algebra.

2010-05-21T16:00:25Z

Sph:

== Catalog Information ==

=== Title ===
Special Topics in Algebra.

=== Credit Hours ===
3

=== Prerequisite ===
[[Math 672]].

=== Description ===

Advanced topics in algebra drawn from pure and applied mathematics. Possible topics include: representation theory, Lie groups and Lie algebras, geometric group theory, Galois theory, algebraic number theory, computational algebra, Category theory, Grobner bases, algebraic geometry, algebraic combinatorics, finite group theory, commutative algebra, homological algebra, group cohomology, character theory of finite groups, mathematical physics, ring theory.

== Desired Learning Outcomes ==

=== Prerequisites ===
Students are expected to have completed the graduate algebra sequence [[Math 671]] and [[Math 672]].

=== Minimal learning outcomes ===

These will depend on the topic chosen.

<div style="-moz-column-count:2; column-count:2;">

</div>

=== Additional topics ===

Past topics chosen include: representations of algebras and finite groups, using the book by Curtis and Reiner.

=== Courses for which this course is prerequisite ===

[[Category:Courses|675]]

Math 675R: Special Topics in Algebra.

2010-05-21T15:58:37Z

Sph:

== Catalog Information ==

=== Title ===
Special Topics in Algebra.

=== Credit Hours ===
3

=== Prerequisite ===
[[Math 672]].

=== Description ===

Advanced topics in algebra drawn from pure and applied mathematics. Possible topics include: representation theory, Lie groups and Lie algebras, geometric group theory, Galois theory, algebraic number theory, computational algebra, Category theory, Grobner bases, algebraic geometry, algebraic combinatorics, finite group theory, commutative algebra, homological algebra, group cohomology, character theory of finite groups, mathematical physics, ring theory.

== Desired Learning Outcomes ==

=== Prerequisites ===
Students are expected to have completed the graduate algebra sequence [[Math 671]] and [[Math 672]].

=== Minimal learning outcomes ===

These will depend on the topic chosen.

<div style="-moz-column-count:2; column-count:2;">

</div>

=== Additional topics ===

=== Courses for which this course is prerequisite ===

[[Category:Courses|675]]

Math 675R: Special Topics in Algebra.

2010-05-21T15:55:45Z

Sph:

== Catalog Information ==

=== Title ===
Special Topics in Algebra.

=== Credit Hours ===
3

=== Prerequisite ===
[[Math 672]].

=== Description ===

Advanced topics in algebra drawn from pure and applied mathematics. Possible topics include: representation theory, Lie groups and Lie algebras, geometric group theory, Galois theory, algebraic number theory, computational algebra, Category theory, Grobner bases, algebraic geometry, algebraic combinatorics, finite group theory, commutative algebra, homological algebra, character theory of finite groups, mathematical physics, ring theory.

== Desired Learning Outcomes ==

=== Prerequisites ===
Students are expected to have completed the graduate algebra sequence [[Math 671]] and [[Math 672]].

=== Minimal learning outcomes ===

These will depend on the topic chosen.

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=== Additional topics ===

=== Courses for which this course is prerequisite ===

[[Category:Courses|675]]

Math 675R: Special Topics in Algebra.

2010-05-21T15:53:42Z

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Math 675R: Special Topics in Algebra.

2010-05-21T15:50:04Z

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Math 675R: Special Topics in Algebra.

2010-05-21T15:48:50Z

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Math 675R: Special Topics in Algebra.

2010-05-21T15:45:37Z

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