Courses

MATH-099 College Mathematics Prep

Topics may include sets, radicals, polynomials, factoring, inequalities, linear and quadratic equations, functions, exponents, and simple descriptive statistics. Intended for students not ready for college credit math; placement in this course is determined by the Department of Mathematics.

MATH-101 Precalculus Mathematics

Topics include algebra, functions, graphing, exponents, logarithms, exponential functions, trigonometry and solving word problems.

MATH-105 Introductory Topics

This is a two-credit course meant to help education majors satisfy the Pennsylvania state requirement for six credits of college mathematics. Each course will cover a topic of the instructor's choice at an introductory level. Topics so far have included Symmetry, Counting, and Math and Music. This course does not count toward a math major or minor, and particular topics may overlap enough with other math courses to bar a student from taking both. Education majors will be given priority.

MATH-108 Introduction to Statistics

A basic introduction to data analysis, descriptive statistics, probability, Bayes' Theorem, distributions of random variables, and topics in statistical inference. (Students may earn credit for only one of the introductory statistics courses offered by the departments of Management, Psychology or Mathematics.)

MATH-111 Calculus I

Differentiation and integration of polynomials, exponentials, logarithms, and trigonometric functions; rules of differentiation; applications.

MATH-112 Calculus II

Techniques of integration, area, volume, and arc length. Also includes improper integrals, L'Hopital's rule, and power series.

MATH-200 Applied Math Credit

MATH-201 Linear Algebra

An elementary introduction to linear algebra. Topics include vectors, matrices, determinants, systems of linear equations, linear transformations, eigenvalues and eigenvectors. Also covers applications to computer graphics.

MATH-203 Math and Music

This course will explore the interplay of mathematics and music. Topics such as the Fourier theory of sound, consonance and dissonance, scales, temperament, digital signal processing, sound synthesis, twelve tone music theory and algorithmic composition will be covered in the course. Some knowledge of music theory and computer programming would be helpful but not required.

MATH-211 Multivariate Calculus

Calculus of several variables, partial derivatives, critical points, multiple integrals, gradient, curl, divergence, Green's Theorem and Stokes' Theorem.

MATH-221 Discrete Structures

An elementary approach to fundamental algebraic concepts. Emphasizes logic, proof techniques, relations, functions, graphs, Boolean algebra and computer logic. Also stresses modular arithmetic, algebraic structures, counting principles, coding theory and finite state machines.

MATH-231 Foundations of Analysis

A rigorous study of the theoretical basis of (single-variable) differntial and integral calculus: limits, continuity, differentiation, and integration.

MATH-321 Abstract Algebra

A more detailed study of algebraic structures. Introduces fundamental concepts of groups, rings and fields.

MATH-331 Geometry

A concentrated study of elementary geometry. Includes Euclidean and non-Euclidean geometries and selected topics such as symmetry, Penrose tilings, fractals, knots, mapmaking, and the shape of the universe.

MATH-351 Numerical Computing

An introduction to the computational techniques for solving mathematical problems. Topics include roots of non-linear equations, interpolation, numerical differentiation and integration, and numerical solutions of differential equations.

MATH-352 Numerical Analysis

. A theoretical study of the standard numerical techniques for solving mathematical problems. Topics include roots of non-linear equations, polynomial interpolation, solving systems of equations, numerical integration and numerical solutions of differential equations.

MATH-353 Differential Equations

Introduces theory, basic solution methods, qualitative analysis, and applications of ordinary differential equations.

MATH-355 Operations Research

Mathematical models and optimization techniques useful in decision making. Includes linear programming, game theory, integer programming, queuing theory, inventory theory, networks and reliability. Further topics, such as non-linear programming and Markov chains, as time permits.

MATH-370 Cryptology & Number Theory

Cryptology is the study of hiding the meaning of messages. Cryptology is an interesting venue for the study of its mathematical underpinnings {number theory, matrix algebra, probability and statistics} and as an opportunity to implement techniques by means of computer programs. We will consider monoalphabetic and polyalphabetic encryptions, public key cryptography, security, and anonymity.

MATH-411 Real Analysis

A deeper look at the fundamentals of calculus. Real numbers, point set theory, limits and the theory of continuity, differentiation and integration.

MATH-415 Complex Analysis

Calculus using complex numbers. Includes power series, analytic functions, poles, residues, contour integrals and applications.

MATH-434 Artificial Life

Science and mathematics describe natural phenomena so well that lines between real world events and the corresponding theoretical world events have become blurred. Proponents of strong artificial intelligence and artificial life believe that computers will eventually serve not only to model thinking and life processes but will actually think and be alive. These contentions will be compared and contrasted with an emphasis on the current status and future implications of strong artificial life.

MATH-441 Mathematical Statistics

A more detailed study of statistics. Topics include probability, multivariate distributions, Bayes' Theorem, statistical inference, estimation, decision theory, hypothesis testing, linear models and experimental design.

MATH-482 Theory of Computation

An introduction to the classical and contemporary theory of computation. Topics include the theory of automata and formal languages, computability by Turing machines and recursive functions, computational complexity and quantum computers.

MATH-500 Senior Colloquium

Experience in individual research and presentation of topics in mathematics. The one-hour version culminates in a presentation to an audience of faculty and students. The two-hour version also includes a paper.

MATH-501 Topics in Mathematics

Subject depends on students' and instructor's interests. Possibilities include: number theory, set theoretic foundations of mathematics, topology, graph theory, differential geometry and applied mathematics. Whether the course counts as a 400-level course for majors will be announced along with the course description.

MATH-502 Independent Study

Individual work for capable students under faculty supervision.

MATH-503 Independent Research

A research project leading to a substantive paper on a selected topic in mathematics. By arrangement with a department instructor.

MATH-599 Mathematics Internship

Full-time mathematics-related employment at an industrial firm or a public service organization.