**MAT500. Combinatorics and Graph Theory . 3 Credits.**

Combinatorial and graphical techniques for complexity analysis, generating functions, recurrence relations, Polya's Theory of Counting, graph theory, NP-complete problems.

#### Restrictions:

- Must have the following level: Graduate

**MAT510. Geometry for Elementary and Middle School Teachers . 3 Credits.**

This course provides a geometric experience which clarifies, extends, and unifies geometric topics in Euclidean, analytic, transformational, and projective geometries. This course is open only to students doing graduate course work in elementary or middle school education in the School of Education.

#### Restrictions:

- Must have the following level: Graduate
- Must have the following field(s) of study (major, minor or concentration):
- Adolescence Ed: Mathematics (107A)
- Mathematics (206)
- Adolescence Ed: Mathematics (037A)

**MAT511. Theory of Groups . 3 Credits.**

First course in algebraic structures. Basic set theory and number theory. Axioms of groups. Homomorphisms, isomorphisms, and quotient groups. For MS in Education degree students only. Not open to undergraduates. Students must complete 21 credits beyond Calculus 2 with a C- or better before taking this course.

#### Prerequisites:

- MAT 252 with a minimum grade of D-

#### Restrictions:

- Must have the following level: Graduate
- Must have the following field(s) of study (major, minor or concentration): Mathematics (206)

**MAT512. Real and Complex Number Systems . 3 Credits.**

Survey and development of number systems from the natural numbers to the complex numbers. Basic theory and properties. Applications to high school mathematics. For MS in Education degree students only. Not open to undergraduates. Students must complete 21 credits beyond Calculus 2 with a C- or better before taking this course.

#### Restrictions:

- Must have the following level: Graduate
- Must have the following field(s) of study (major, minor or concentration): Mathematics (206)

**MAT513. The Joys of Geometry . 3 Credits.**

Topics in modern geometry such as finite geometries, transformations, non-Euclidean and projective geometries, Mascheroni constructions. Axiomatic approach is often used. Proofs constitute an important part of the course. For MS in Education degree students only. Not open to undergraduates.

#### Restrictions:

- Must have the following level: Graduate
- Must have the following field(s) of study (major, minor or concentration):
- Adolescence Ed: Mathematics (037A)
- Adolescence Ed:Mathematics (037B)
- Math
- Science
- Technology: 1-6 (013M)

**MAT514. Linear Algebra with Applications to Geometry . 3 Credits.**

Matrices, linear transformations, and quadratic forms. Solutions of linear systems. Applications to analytic geometry of 2, 3, or n dimensions. For MS in Education degree students only. Not open to undergraduates. Students must complete 21 credits beyond Calculus 2 with a C- or better before taking this course.

#### Restrictions:

- Must have the following level: Graduate
- Must have the following field(s) of study (major, minor or concentration): Mathematics (206)

**MAT517. History of Mathematics . 3 Credits.**

Topics in mathematics from a historical perspective. The course may be a survey of the history of mathematics or it may concentrate on a few specific topics. In either case, students are required to solve problems and to prove theorems. Recommended for MS in Education degree students. Students must complete 21 credits beyond Calculus 2 with a C- or better before taking this course.

#### Restrictions:

- Must have the following level: Graduate
- Must have the following field(s) of study (major, minor or concentration): Mathematics (206)

**MAT518. Theory of Rings and Fields . 3 Credits.**

Rings, Fields and their extensions. Introduction to Galois Theory. Solutions of equations by radicals. For MS in Education degree students only. Not open to undergraduates.

#### Prerequisites:

- MAT 511 with a minimum grade of C-

#### Restrictions:

- Must have the following level: Graduate

**MAT519. Sequences, Series, and Their Applications . 3 Credits.**

Sequences of real and complex numbers. Convergence criteria, series, uniform convergence, definition of functions by series and Taylor's theorem. For MS in Education degree students only. Not open to undergraduates. Students must complete 21 credits beyond Calculus 2 with a C- or better before taking this course.

#### Restrictions:

- Must have the following level: Graduate
- Must have the following field(s) of study (major, minor or concentration): Mathematics (206)

**MAT520. Statistics for Elementary/Middle School Teachers . 3 Credits.**

Liberal arts course in basic statistical ideas and their application to public policy and education. Emphasis on statistical reasoning and numerical arguments. Focus on drawing conclusions from data taken from diverse settings and contexts.

#### Restrictions:

- Must have the following level: Graduate
- Must have the following field(s) of study (major, minor or concentration):
- Adolescence Ed: Mathematics (107A)
- Mathematics (206)
- Adolescence Ed: Mathematics (037A)

**MAT531. Point Set Topology I . 3 Credits.**

Part of a two-semester sequence covering the fundamental theorems of geometric topology in abstract topological and metric spaces.

#### Restrictions:

- Must have the following level: Graduate

**MAT532. Point Set Topology II . 3 Credits.**

Part of a two-semester sequence covering the fundamental theorems of geometric topology in abstract topological and metric spaces.

#### Restrictions:

- Must have the following level: Graduate

**MAT541. Complex Analysis I . 3 Credits.**

Provides a foundation for advanced work in analysis. Differentiation, Cauchy-Riemann Equations, elementary functions, conformal mapping, expansions, and analytic continuation.

#### Restrictions:

- Must have the following level: Graduate

**MAT543. Real Analysis I . 3 Credits.**

Part of a two-semester sequence covering the following topics: The real number system, topology of Rn, measure theory, and the Lebesque integral. Convergence theorems, differentiation, and Lebesque decompositions. Fubini's theorem, Radon-Nikodym theorem, and other advanced topics.

#### Restrictions:

- Must have the following level: Graduate

**MAT544. Real Analysis II . 3 Credits.**

Part of a two-semester sequence covering the following topics: The real number system, topology of Rn, measure theory, and the Lebesque integral. Convergence theorems, differentiation, and Lebesque decompositions. Fubini's theorem, Radon-Nikodym theorem, and other advanced topics.

#### Prerequisites:

- MAT 543 with a minimum grade of C-

#### Restrictions:

- Must have the following level: Graduate

**MAT561. Abstract Algebra I . 3 Credits.**

Part of a two-semester sequence covering the following topics: Groups, rings, integral domains, fields, modules, and vector spaces.

#### Restrictions:

- Must have the following level: Graduate

**MAT562. Abstract Algebra II . 3 Credits.**

Part of a two-semester sequence covering the following topics: Groups, rings, integral domains, fields, modules, and vector spaces.

#### Prerequisites:

- MAT 561 with a minimum grade of C-

#### Restrictions:

- Must have the following level: Graduate

**MAT563. Topics in Algebra I . 3 Credits.**

Topics chosen by the instructor, may include structure theory of Abelian groups, commutative rings and finite fields, lattice theory, universal algebra. Students must complete 21 credits beyond Calculus 2 with a C- or better before taking this course.

#### Restrictions:

- Must have the following level: Graduate

**MAT590. Thesis in Mathematics . 1-12 Credits.**

Writing and preparation of an expository or original thesis under the guidance of graduate faculty. Required form available in the Records and Registration Office.

#### Restrictions:

- Must have the following level: Graduate

**MAT593. Math Selected Topic. 3-12 Credits.**

Selected topics courses are regularly scheduled courses that focus on a particular topic of interest. Descriptions are printed in the Schedule of Classes each semester. Selected topics courses may be used as elective credit and may be repeated for credit, provided that the topic of the course changes.

#### Restrictions:

- Must have the following level: Graduate

**MAT594. Fieldwork in Math . 0 Credits.**

#### Restrictions:

- Must have the following level: Graduate

**MAT595. Indep Study Math. 1-3 Credits.**

#### Restrictions:

- Must have the following level: Graduate

**MAT599. Comprehensive Exam Workshop. 0 Credits.**

Non-credit workshop for students who wish to devote the semester immediately following the completion of their coursework to prepare for the comprehensive exam.

#### Restrictions:

- Must have the following level: Graduate
- Must have the following field(s) of study (major, minor or concentration): Mathematics (206)

**MAT795. Indep Study Math. 1-6 Credits.**

#### Restrictions:

- Must have the following level: Graduate

**MAT799. Continued Registration. 1 Credit.**

#### Restrictions:

- Must have the following level: Graduate