## MATHEMATICS

## DEPARTMENT

This introductory course in abstract algebra focuses mainly on number theory, with an introduction to groups and fields. Number-theoretic concepts include divisibility, primes and their distribution, congruence arithmetic, linear Diophantine equations and systems, number-theoretic functions, Euler's Theorem, primitive roots, and selected special topics. Prerequisites: Math 256 or MATH 301 with a grade of C or higher.

This course continues the study of abstract algebra and is focused mainly on groups, with some exploration of rings and fields as time allows. Group-theoretic topics include subgroups, normal subgroups and quotient groups, and some counting principles. A wide variety of examples will be explored. Prerequisites: MATH 441 with a grade of C or above.

An introduction to differential and integral calculus. Derivatives are developed for: algebraic, logarithmic, exponential, trigonometric, and inverse trigonometric functions. The Riemann integral and the first form of the Fundamental Theorem of Calculus are introduced. Definite integrals and anti-derivatives are developed for basic algebraic, exponential, logarithmic, and trigonometric functions. Applications of key concepts are integrated throughout the course. This course satisfies the general education mathematics requirement. Prerequisites: MATH 114A and MATH 114B with Cs or higher, or Math placement level 4.

CALCULUS II
MATH 241
MATH
(4.00 credits)

This course is a continuation of differential and integral calculus. Topics include integration techniques, improper integrals, applications, differential equations, Taylor polynomials, and infinite series. This course emphasizes the mastery of key concepts and their applications. Prerequisites: MATH 231 with a grade of C or above.

CALCULUS III
MATH 251
MATH
(4.00 credits)

An introduction to multivariable calculus; topics include vectors, curves, partial derivatives, gradients, multiple and iterated integrals, and Green's and Stokes' theorems. Prerequisites: MATH 241 with a grade of C or above OR Math 232 with a grade of C or above.

This course investigates geometry from an advanced perspective. Building on students' knowledge of Euclidean geometry from high school coursework, topics include axiomatic systems, neutral, Euclidean, and non-Euclidean geometries; introduction of geometries such as projective, finite, vector, and transformational; historical development of geometry; and use of technology to model and explore geometric relationships. Prerequisites: Math 256 or MATH 301 with a grade of C or higher.

This course continues the study of analysis shifting from the real numbers to complex numbers. Topics include functions of a complex variable, Cauchy's theorem, residue theory, power series, and other topics as time allows. Prerequisites: Math 233 or Math 251 with a grade of C or higher - AND - Math 256 or Math 301 with a grade of C or higher. Math 431 recommended.

Theory of ordinary differential equations with an emphasis on problems of the physical world which are modeled well by differential equations. Topics include first order equations, second order and higher linear equations, series solutions, and a brief introduction to numerical methods and partial differential equations as time permits. Prerequisites: MATH 241 with a grade of C or above; MATH 251 highly recommended.

DISCRETE MATHEMATICS
MATH 256
MATH
(3.00 credits)

This course introduces students interested in math or computer science to a level of abstraction and argumentation appropriate to those fields as well as providing some of the foundational mathematics and more importantly, ways of thinking needed for success in either field. In addition, the course provides students the opportunity to see connections between the two fields such as those between symbolic logic and digital logic circuits or between recurrence and induction. Topics include: logic, methods of proof, sequences, induction, recursion, set theory, functions, relations, counting, probability, graphs, trees, analysis of algorithm efficiency.
Prerequisites: MATH 231 with a grade of C or higher OR completion of MATH 101, MATH 114A, or MATH 121 and CS 178, CS 179, or CS 180 with grades of C or higher.

INDEPENDENT STUDY - MATHEMATICS
MATH 379
MATH
(1.00 credits)

Independent study of selected topics in mathematics developed by the student with the approval and direction of the instructor. Prerequisites: consent of instructor.

INDEPENDENT STUDY - MATHEMATICS
MATH 279
MATH
(1.00 credits)

Independent study of selected topics in mathematics developed by the student with the approval and direction of the instructor. Prerequisites: consent of instructor.

INDEPENDENT STUDY - MATHEMATICS
MATH 479
MATH
(1.00 credits)

Independent reading and research of selected topics in mathematics developed by the student with the approval and direction of the instructor. Prerequisites: consent of instructor.

Besides being a body of knowledge, Mathematics is a way of thinking, a different lens for viewing the world. This course uses games, puzzles, and classic problems to introduce problem solving techniques and some of the big ideas that have fascinated mathematicians over the centuries. With its focus on exploration, discovery, and collaboration, we'll prioritize mathematics as a process rather than a product. Prerequisites: Math placement level two or higher, or math placement level one and concurrent enrollment in MATH 099A .

An introduction to linear algebra including vector spaces, matrices, linear transformations, eigenvalues and eigenvectors; emphasis on gaining theoretical insights through computation, developing facility with elementary proof, and applying the concepts and computational methods to solve real world problems. Prerequisites: MATH 231 or Math 256 with a grade of B or better

Selected topics in mathematics, mathematics education, and applications. With individualized mentoring, students will investigate significant mathematics independently and present findings in oral and written form at a variety of levels and to varying audiences. Integrated throughout the course students will 1) consider how topics are situated in the history and development of mathematics as a liberal art, and in the world; 2) reflect, as future mathematics educators and practitioners, upon: Who am I and who can I become? What are the needs and opportunities of the world? What is my role in building a more just and compassionate world? Prerequisites: COR 2, junior/senior standing, and a declared major in Mathematics; or consent of the instructor.

Algebra preparation necessary for success in calculus. Topics include: algebraic properties of linear, quadratic, polynomial, rational, exponential and logarithmic functions and their graphs. Combined with MATH 114B: Precalculus B: Trigonometry, the two courses comprise a complete overview of algebra and trigonometry required for calculus. This course satisfies the general education mathematics requirement. Prerequisites: Math placement level three or higher, or math placement level two and concurrent enrollment in MATH 099C .

Trigonometry preparation necessary for success in calculus. Topics include: trigonometric functions and their inverses, including identities, graphs, and applications. Combined with MATH 114A the two courses comprise a complete overview of algebra and trigonometry required for calculus. Prerequisites: Math placement level four or higher, or MATH 114A with a grade of C or higher, or concurrent enrollment in MATH 114A and consent of instructor.

A calculus-based introduction to probability. Topics include combinatorics, discrete and continuous probability distributions and joint probability, binomial, Poisson, exponential, and normal distributions, expected value, variance, and moment generating functions. This course will provide a solid introduction to probability and prepare interested students for the first actuarial exam. Prerequisites: MATH 241 with a grade of C or above.

The course introduces analysis as a tool for a deeper understanding of calculus. With the least upper bound axiom of the real numbers as its starting point, the course develops the foundations necessary to work with limits and prove results from calculus. Topics include sequences, series, power series, derivatives, and integrals. Time permitting, the course will explore how the same tools are used in more advanced settings. Prerequisites: MATH 251 with a grade of C or higher - AND - Math 256 or MATH 301 with a grade of C or higher.

Course includes descriptive and inferential statistics with the emphasis on drawing meaningful conclusions from data. Topics include measures of central tendency and dispersion, the normal distribution, z-tests, t-tests, linear regression, analysis of variance, Chi-Square tests, and other topics as time permits. This course satisfies the general education mathematics requirement. Prerequisites: Math placement level two or higher, or math placement level one and concurrent enrollment in MATH 099B.

SUCCESS IN MATHEMATICAL THINKING
MATH 099D
MATH
(2.00 credits)

This course is intended for students who may need additional instruction on the material covered in Mathematical Thinking for Elementary Teachers . Topics covered will include strengthening quantitative literacy and improving math study skills. Must be taken concurrently with MATH 127. Cross-listed: None. Offered: F/S. Prerequisite: ACT Math score of 16 or above; or ALEKS test score of 31 or above.

SUCCESS IN PRE-CALCULUS
MATH 099C
MATH
(2.00 credits)

This course is intended for students who may need additional instruction on the material covered in Pre-Calculus. Topics covered will include strengthening quantitative literacy and improving math study skills. Must be taken concurrently with MATH 114A. Prerequisites: Math placement level two or higher, and concurrent enrollment in MATH 114A .

SUCCESS IN PROBLEM SOLVING
MATH 099A
MATH
(2.00 credits)

This course is intended for students who may need additional instruction on the material covered in Introduction to Problem Solving. Topics covered will include strengthening quantitative literacy and improving math study skills. Must be taken concurrently with MATH 101 .

SUCCESS IN STATS
MATH 099B
MATH
(2.00 credits)

This course is intended for students who may need additional instruction on the material covered in Statistics. Topics covered will include strengthening quantitative literacy and improving math study skills. Must be taken concurrently with MATH 121 . Prerequisites: Math placement level one or higher, and concurrent enrollment in MATH 121 .

TOPICS IN MATHEMATICS
MATH 372
MATH
(3.00 - 4.00 credits)

Study of selected topics in mathematics. Prerequisites: Consent of instructor

TOPICS IN MATHEMATICS
MATH 472
MATH
(3.00 credits)

Study of selected topics in mathematics. Prerequisites: Consent of instructor

This course focuses on properties of spaces invariant under homeomorphisms. Topics include continuity, homeomorphisms, connectedness, compactness, manifolds, the classification of closed, compact surfaces, the Euler characteristic, the fundamental group, and knot theory. Prerequisites: Math 256 or MATH 301 with a grade of C or higher; MATH 461 recommended.