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# Courses at the 500-level

Fundamental concepts in the theory of calculus are presented. Topics include limits, continuity and uniform continuity, differentiation, the Riemann integral, sequences and series, and convergence criteria.*3 credit hours*

**Prerequisites:**

- MATH 300
- MATH 314

Techniques and concepts of the algebra and calculus of functions of one complex variable are studied, including trigonometric, exponential, and logarithmic functions.*3 credit hours*

**Prerequisites:**

- prior or concurrent enrollment in MATH 314

The foundations of set theory and logic are studied in the context of their application in the construction of number systems, from the natural numbers through the reals.*3 credit hours*

**Prerequisites:**

- MATH 300
- MATH 314
- MATH 432
- or consent of department chair
*or consent of the department chair*

Advanced topics in geometry are studied, such as foundations and axiom systems, finite and non-Euclidean geometries. Possible additional topics are projective geometry, convexity, and topology. Proofs are stressed.*3 credit hours*

**Prerequisites:**

- MATH 300

Study is made of sets and sequences, various topological spaces, including metric, compactness, connectedness, curves, and mappings.*3 credit hours*

**Prerequisites:**

- MATH 314
- MATH 300

Selected topics in the development of groups, rings, modules, and fields are covered, including homomorphisms, permutation groups, basic Galois Theory, ring extension problems, and ideals.*3 credit hours*

**Prerequisites:**

- MATH 300
- MATH 315
- MATH 432

Varying topics in mathematical proof are examined, from number systems and functions to abstract spaces.*3 credit hours*

**Prerequisites:**

- Consent of department chair

Varying topics in applied mathematics are examined, from numerical and analytical investigations to modeling.*3 credit hours*

**Prerequisites:**

- consent of department chair
*or consent of the department chair*

Varying topics in pure mathematics are examined, from number theory and advanced geometries to abstract algebra.*3 credit hours*

**Prerequisites:**

- consent of department chair.

A continuation of Mathematics 512, topics include sequences of functions, functions of several variables, and an introduction to Lebesgue measure.*3 credit hours*

**Prerequisites:**

- MATH 300
- MATH 512

A continuation of Mathematics 515, this course develops the theory underlying functions of complex variables and includes Taylor and Laurent series, Rouche’s Theorem, and analytic continuation.*3 credit hours*

**Prerequisites:**

- MATH 300
- MATH 512
- MATH 515

A particular branch of algebra is examined in depth. Possible topics include group theory, ring theory, field theory, semigroup theory, homological algebra, and automata theory. This course may be repeated for credit with a change in content.*3 credit hours*

**Prerequisites:**

- MATH 300
- MATH 532
*or consent of the department chair*

Students analyze the structure of number and operations in grades K-6 mathematics. Students learn to make connections beyond the elementary level. Topics include place, value, operations, and number systems. Hybrid course.*3 credit hours*

**Prerequisites:**

- Elementary-level teacher certification and at least two years of teaching experience

Students analyze the structure of functions and algebra in grades K-6 mathematics. Students learn to make connections beyond the elementary level. Topics include variables, patterns, and equations. Hybrid course.*3 credit hours*

**Prerequisites:**

- Elementary-level teacher certification and at least two years of teaching experience

Students analyze the structure of geometry and measurement in grades K-6 mathematics. Students learn to make connections beyond the elementary level. Topics include equivalence, shape, and reasoning. Hybrid course.*3 credit hours*

**Prerequisites:**

- Elementary-level teacher certification and at least two years of teaching experience

Students examine the structure of data analysis and statistics in grades K-6 mathematics. Students learn to make connections beyond the elementary level. Topics include question formation, data analysis, and inference. Hybrid course.*3 credit hours*

**Prerequisites:**

- Elementary-level teacher certification and at least two years of teaching experience

Students examine the structure of problem analysis in grades K-6 mathematics. Students learn to make connections beyond the elementary level. Topics include problem selection, problem strategies, and problem posing. Hybrid course.*3 credit hours*

**Prerequisites:**

- Elementary-level teacher certification and at least two years of teaching experience