# Courses & Requirements

## Requirements for the Mathematics Major

The minimum number of credits required to fulfill a mathematics major is 38.

All mathematics majors are required to take an exit exam: the Mathematics Major Field Test from the Educational Testing Service.

### Required Courses

### MAT-118: Calculus I (4.00)

Introduction to the basic concepts of differential and integral calculus, emphasizing conceptual understanding and applications. Topics are covered from a graphical, algebraic and numerical perspective. Mathematical writing is emphasized.

### MAT-119: Calculus II (4.00)

Continuation of 118. Topics include the integral and its applications, techniques of integration, improper integrals and an introduction to series and differential equations.

Course requisites: 118 with a minimum grade of C-

### MAT-204: The Art of Mathematical Thinking (4.00)

An introduction to the study of the role of proof in mathematics, mathematical writing and grammar and abstraction and critical thinking, using topics from areas such as set theory, logic, discrete mathematics and number theory.

Course requisites: 119 with a grade of C- or better.

### MAT-206: Linear Algebra (4.00)

Real and abstract vector spaces, linear transformations, matrices and determinants, with applications to systems of linear equations, geometry and other selected topics.

Course requisites: 119 with a grade of C- or better

### MAT-220: Multivariable Calculus (4.00)

MULTIVARIABLE CALCULUS--The geometry of curves and surfaces and the calculus of functions of two or more variables, including partial differentiation, multiple integrals, and vector analysis.

Course requisites: 119 with a minimum grade of C-

### MAT-321: Abstract Algebra (4.00)

Important algebraic structures, including groups, rings, integral domains, and fields.

Course requisites: 204 and 206 with a grade of C- or better

### MAT-480: Mathematics Seminar (2.00)

Integrates topics in a variety of areas of undergraduate mathematics and emphasizes problem-solving, writing and speaking skills. Open to seniors with majors in mathematics, mathematics-economics or mathematics-physics and to minors in mathematics or others with permission.

### Elective Courses

At least three additional 300-level courses from at least two of the following groups:

#### Group 1

### MAT-331: Real Analysis (4.00)

The topology of the real number system and the axiom of completeness. Rigorous development of some central ideas in analysis including limits, continuity of functions, and convergence of sequences and series. Offered alternate years.

Course requisites: 204 with a grade of C- or better

### MAT-352: Complex Variables (4.00)

The algebra of complex numbers, analytic functions, elementary functions, linear fractional transformations, mappings, integrals, power series, Laurent series, and residue calculus. Offered alternate years.

Course requisites: 220 with a grade of C- or better

#### Group 2

### MAT-314: Modern Geometries (4.00)

A study of axiomatic systems in geometry, including affine, projective, Euclidean and nonEuclidean geometries, and the historical background of their development. Offered on an occasional basis.

Course requisites: 204 and 220 with a grade of C- or better

### MAT-316: Topology (4.00)

Topological spaces, continuity, compactness, and connectedness, with special emphasis on metric spaces. Offered alternate years.

Course requisites: 204 and 220 with a grade of C- or better

### MAT-317: Number Theory (4.00)

Divisibility, prime numbers, Diophantine equations, congruence of numbers, methods of solving congruencies, quadratic reciprocity, and applications to cryptology. Offered alternate years.

Course requisites: 204 with a grade of C- or better

#### Group 3

### MAT-309: Differential Equations (4.00)

First- and second-order differential equations, higher order, linear ordinary differential equations, existence and uniqueness theorems and applications.

Course requisites: 206 or 220 with a grade of C- or better

### MAT-311: Chaotic Dynamical Systems (4.00)

Chaos theory and dynamical systems. Topics include fractals, bifurcations, measurement of chaos, and behavior of orbits. Possible applications to physics, biology, astronomy, and the social sciences. Offered alternate years.

Course requisites: 206 or 220 with a grade of C- or better

### MAT-325: Mathematical Models and Applications (4.00)

Development of techniques of model building. Applications to illustrate the techniques drawn principally from the natural and social sciences. Offered alternate years.

Course requisites: 206 or 220 with a grade of C- or better

### MAT-326: Math in the City (4.00)

Students will act as professional mathematical consultants for a local business, research center, or government organization. The organization will provide a problem of local, national, and/or global interest, and students will learn and apply appropriate mathematical modeling techniques. Offered on an occasional basis.

Course requisites: MAT-206 or MAT-220

### MAT-328: Probability (4.00)

Introduction to the mathematical field of probability, including discrete and continuous random variables, distributions, expectations, moments, and joint distributions.

Course requisites: MAT-206 or 220 with a grade of C- or better

## Requirements for the Mathematics Minor

The mathematics minor is designed for those students who wish to study mathematics significantly beyond the introductory level and focus on an area of special interest without accomplishing a major. A student planning a minor in mathematics is required to consult with the depatment to ensure the coherence and relevance of the program of study planned.

### Required Courses

### MAT-118: Calculus I (4.00)

Introduction to the basic concepts of differential and integral calculus, emphasizing conceptual understanding and applications. Topics are covered from a graphical, algebraic and numerical perspective. Mathematical writing is emphasized.

### MAT-119: Calculus II (4.00)

Continuation of 118. Topics include the integral and its applications, techniques of integration, improper integrals and an introduction to series and differential equations.

Course requisites: 118 with a minimum grade of C-

### Elective Courses (choose one)

### MAT-204: The Art of Mathematical Thinking (4.00)

An introduction to the study of the role of proof in mathematics, mathematical writing and grammar and abstraction and critical thinking, using topics from areas such as set theory, logic, discrete mathematics and number theory.

Course requisites: 119 with a grade of C- or better.

### MAT-206: Linear Algebra (4.00)

Real and abstract vector spaces, linear transformations, matrices and determinants, with applications to systems of linear equations, geometry and other selected topics.

Course requisites: 119 with a grade of C- or better

### MAT-220: Multivariable Calculus (4.00)

MULTIVARIABLE CALCULUS--The geometry of curves and surfaces and the calculus of functions of two or more variables, including partial differentiation, multiple integrals, and vector analysis.

Course requisites: 119 with a minimum grade of C-

### Additional Courses

At least three additional courses at the 200 or 300 level, one of which must be at the 300 level.