## Math Department Courses

# Course Descriptions

## Mat 121. Calculus I

An introduction to the theory of differential and integral calculus for functions of one variable. Includes the concepts of limit, continuity, derivatives, and indefinite integrals and definite integrals, culminating in the Fundamental Theorem of Calculus. Applications to related rates and optimization problems.

## Mat 122. Calculus II

Differentiation and integration of logarithmic functions, exponential functions, and inverse trigonometric functions. Study of polar coordinates, conic sections, and various integration techniques. Applications to computations of volumes, surface areas, and centers of mass.

## Math 243. Discrete Mathematics I

A survey of the math topics which are foundational to computer science: functions, relations, sets, basic logic, proof techniques, combinatorics, graphs and trees, discrete probability. No prerequisite. Satisfies the Abstraction and Formal Reasoning LADR.

## Mat 160. Special Topics

## Mat 212. Mathematics for Elementary Teachers

Emphasizes problem solving, fundamental mathematical concepts and applying mathematical principles to non-routine problems. Introduction to numeration systems, theory of arithmetic, combinatorics, probability, statistics, familiar number sets and their properties (naturals, integers, rationals, irrationals, reals) and functions.

## Mat 217. Applied Statistics

Use of graphs and numerical summaries to describe data from individual variables and to investigate relationships among variables. Design of statistical experiments. Survey of fundamental concepts of probability, including sampling distributions. Use of sample data to estimate, and to test hypotheses about, unknown parameters.

## Mat 220. Logic, Sets and Relations

An introduction to the foundations of mathematics, with emphasis on developing basic reasoning skills needed for constructing proofs.

## Mat 221. Calculus III

Differentiation and integration of vector-values functions. Study of functions of several variables, including partial derivatives and multiple integrals. Detailed study of infinite sequences and series.

## Mat 224. Linear Algebra

Systems of linear equations and their solutions. Study of the algebraic properties and applications of vectors, matrices and linear transformations.

## Mat 231. Differential Equations

Survey of basic techniques for describing dynamical systems by means of equations involving derivatives of functions, and of methods for finding functions which satisfy these equations.

## Mat 260. Special Topics

## Mat 307. Directed Study

## Mat 311. History of Mathematics

Survey of important discoveries in mathematics and the

historical contexts in which they were made. Topics will include major mathematical developments

beginning with the Ancient Greeks and tracing the development through Hindu, Arabic and

European mathematics up to the modern developments of the 20th century.

## Mat 320. Introduction to Number Theory

Explores properties of the integers such as divisibility

and congruence, linear diophantine equations, prime numbers, the Fundamental Theorem of

Arithmetic, Fermat's little theorem, Euler's Theorem, Euler's phi function, computing powers and

roots in modular arithmetic, and public key cryptography.

## Mat 321. Introduction to Real Analysis

Development of the algebraic and topological properties of the real number system and the theoretical foundations of differential and integral calculus. Strongly recommended for students considering post-graduate study in mathematics.

## Mat 323. Introduction to Complex Analysis

Study of complex numbers and functions of a

complex variable. Topics include algebra and geometry of the complex plane, derivatives, integrals,

power series, Laurent series, and residue theory.

## Mat 324. Algebraic Systems

Study of concepts abstracted from algebraic properties of the classical number systems, including groups, rings, fields, order relations, and equivalence relations.

## Mat 327. Probability and Statistics

Calculus-based survey, including axioms of probability, discrete and continuous variables, standard probability functions (binomial, normal, Poisson, etc), mathematical expectation, generating functions, and a brief introduction to the estimation and hypothesis testing.

## Mat 339. Foundations of Geometry

Survey of ancient, classical and modern views regarding the nature of space, the description of spatial structures and the organization of facts about space into deductive theories.

## Mat 343. Discrete Mathematics

Includes selected topics from graph theory and combinatorics: connectivity, colorings, cliques, planarity, directed graphs, cuts and flows, principle of inclusion and exclusion.

## Mat 357. Internship

Off-campus supervised experience in mathematics.

## Mat 359. Introduction to Topology

Study of concepts, growing out of and underlying geometry and calculus, which have become important in physics, chemistry, logic, and computer science. Careful development of abstract notions such as topological spaces, continuity, topological equivalence, connectedness, and dimension, and related philosophical and historical matters in mathematics and liberal arts generally.

## Mat 360. Special Topics

Topics may be drawn from analysis with complex variables, introduction to functional analysis, category theory, mathematical logic and model theory, recursive function theory, topology, universal algebra, or other areas.

## Mat 370. Directed Study

Individual study of topics such as those listed under 360.

## Mat 437. Topics in Probability and Statistics

Content varies.

## Mat 461. Advanced Seminar

Student-led inquiry/research in an area of mathematics such as real or complex analysis, topology, algebra, etc. Content varies. May be repeated for credit.