# 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. Prerequisite: Based on placement results, some students may require a mathematics review course.

### 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. Prerequisite: MATH-111 Calculus I or equivalent.

### 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. Prerequisite: MATH-111 Calculus I.

### MATH-203 Math and Music

An exploration of 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. Prerequisites: MATH-112 Calculus II and MATH-201 Linear Algebra.

### 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. Prerequisite: MATH-111 Calculus I.

### MATH-231 Foundations of Analysis

A rigorous study of the theoretical basis of (single-variable) differntial and integral calculus: limits, continuity, differentiation, and integration. Prerequisite: MATH-112 Calculus II.

### MATH-235 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. Can computer models simulate key characteristics of life, such as behavior, motivation, reproduction, adaptation, perception and even intelligence? Proponents of strong artificial life believe that computers will eventually serve not only to model life processes but will actually think and be alive. These contentions are compared and contrasted with an emphasis on the current status and future implications of strong artificial life. This course is meant to be accessible to both majors and nonmajors. Same as CSCI:434. Prerequisites: Junior or senior standing and completion of the Analytic Thought and Scientific Explanations Central Curriculum requirements. Does not count for mathematics or computer science major credit.

### MATH-321 Abstract Algebra

A more detailed study of algebraic structures. Introduces fundamental concepts of groups, rings and fields. Prerequisites: MATH-201 Linear Algebra and MATH-221 Discrete Structures.

### 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. Prerequisites: MATH-201 Linear Algebra and MATH-221 Discrete Structures.

### 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. Same as CSCI-351. Prerequisites: MATH-111 Calculus I; MATH-112 Calculus II is suggested.

### 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. Same as CSCI-352. Prerequisites: MATH-112 Calculus II, MATH-201 Linear Algebra, and MATH-351 Numerical Computing.

### MATH-353 Differential Equations

Introduces theory, basic solution methods, qualitative analysis, and applications of ordinary differential equations. Prerequisites: sophomore standing, MATH-112 Calculus II, and MATH-201 Linear Algebra or intructor's permission.

### 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. Same as CSCI-355. Prerequisites: MATH-112 Calculus II, MATH-201 Linear Algebra, MATH-108 Introduction to Statistics, and MATH-221 Discrete Structures or permission of instructor.

### 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. Same as CSCI-370. Prerequisite: MATH-221 Discrete Structures.

### 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. Prerequisites: MATH-112 Calculus II and MATH-221 Discrete Structures.

### MATH-415 Complex Analysis

Calculus using complex numbers. Includes power series, analytic functions, poles, residues, contour integrals and applications. Prerequisites: MATH-211 Multivariate Calculus and MATH-221 Discrete Structures.

### 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. Prerequisites: MATH-211 Multivariate Calculus and MATH-108 Introduction to Statistics.

### 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. Same as CSCI-482. Prerequisites: MATH-221 Discrete Structures and CSCI-281 Data Structures.

### MATH-500 Senior Colloquium

Experience in individual research and presentation of topics in mathematics. The one-semester-hour version culminates in a presentation to an audience of faculty and students. The two-semester-hour version also includes a paper. Prerequisite: Senior major or department permission.

### 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. Prerequisite: instructor's permission.

### MATH-502 Independent Study

Individual work for capable students under faculty supervision. Scheduled courses are approved for independent study only under extraordinary circumstances. Whether the course counts as a 400-level course for majors will be decided on an individual basis. Prerequisite: Department approval and instructor's consent.

### MATH-503 Independent Research

A research project leading to a substantive paper on a selected topic in mathematics. By arrangement with a department instructor. Prerequisite: junior or senior standing and department permission.

### MATH-599 Mathematics Internship

Full-time mathematics-related employment at an industrial firm or a public service organization. Prerequisite: senior standing, appropriate mathematics background courses, and permission of departmental internship coordinator.