## Mathematics and Computer Science Department

### Mathematics

**Learning Goals:**

- The student attains a firm foundation of fundamental mathematical concepts, methods and language sufficient to support further academic work or a career in areas requiring mathematical understanding.
- The student attains knowledge and skills to undertake independent learning beyond formal study.
- The student applies mathematical skills and knowledge to solve problems and analyze new situations in mathematics and related areas.
- The student communicates mathematical ideas, both orally and in writing, with clarity and precision.

### Computer Science

**Learning Goals:**

- The student attains knowledge of major computer science and mathematical concepts that will support the student's goals for further study or a career in computer science or related disciplines.
- The student develops the sufficient programming skills to support the student's goals.
- The student develops the ability to write professional documents in a style that is relevant to the student's goals.
- The student develops the ability to articulate computer science concepts.

**Double Major/Minor in Computer Science and Mathematics.** Because the computer science major already requires several mathematics courses, many computer science majors pick up a mathematics major or minor relatively easily. However, it is department policy that cross-listed elective courses (such as MATH-351/CSCI-351 Numerical Computing and MATH-352/CSCI/352 Numerical Analysis) count in only one major or minor at a time.

### Majors Offered

### Minors Offered

### MATH-099 College Mathematics Preparation

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. Grade is S/U. 0 SH.

### 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. 4 SH.

### MATH-105 Introductory Topics

This is a two-semester-hour 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. Prerequisites: Usually none. 2 SH.

### 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.) 4 SH. CC: Analytical Thought.

### MATH-109 Statistics for Social Sciences

This course covers basic descriptive and inferential statistical techniques used in analyzing social science research data. The student becomes familiar with ways to organize and analyze data, communicate research results, translate statistical jargon into meaningful English, and understand basic theories underlying statistics, e.g., elementary probability theory. 4 SH. CC: Analytical Thought.

### MATH-111 Calculus I

Differentiation and integration of polynomials, exponentials, logarithms and trigonometric functions rules of differentiation and applications. 4 SH. CC: Analytical Thought.

### 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. 4 SH. CC: Analytical Thought.

### MATH-180 Statistical Methods

This course provides a broad overview of introductory statistical methods and data analysis. Topics include descriptive statistics, probability, probability distributions, statistical inferences on population means and population variances, multiple comparisons, categorical data, data analysis using linear regression and multiple regression, design of experiments, and analysis of variance. 4 SH. CC: Analytical Thought.

### 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. 4 SH. CC: Analytical Thought.

### 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. Prerequisites: Sophomore standing and MATH-112 Calculus II. Some knowledge of music theory and computer programming would be helpful but is not required. 4 SH. CC: Interdisciplinary.

### 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. 4 SH.

### 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. 4 SH. CC: Analytical Thought.

### MATH-231 Foundations of Analysis

A rigorous study of the theoretical basis of single-variable differential and integral calculus: limits, continuity, differentiation and integration. Prerequisite: MATH-112 Calculus II and MATH-221 Discrete Structures. 2 SH.

### 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-235. Prerequisites: Sophomore standing and, to facilitate an elevated level of class discourse, completion of at least two of the following Central Curriculum requirements: Analytic Thought, Scientific Explanations or Ethics. 4 SH. CC: Ethics Intensive, Interdisciplinary.

### 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. 4 SH. CC: Writing Intensive.

### 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. 4 SH.

### MATH-351 Numerical Computing

An introduction to the computational techniques for solving mathematical problems. Topics include roots of nonlinear equations, interpolation, numerical differentiation and integration, and numerical solutions of differential equations. Same as CSCI-351. Prerequisite: MATH-111 Calculus I; MATH-112 Calculus II is suggested. 2 SH.

### MATH-352 Numerical Analysis

A theoretical study of the standard numerical techniques for solving mathematical problems. Topics include roots of nonlinear 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. 2 SH.

### 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 instructor's permission. 4 SH.

### 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 nonlinear programming and Markov chains, as time permits. Same as CSCI-355. Prerequisites: MATH-112 Calculus II, MATH-201 Linear Algebra, MATH-221 Discrete Structures, and either MATH-108 Introduction to Statistics or MATH-180 Statistical Methods or instructor's permission. 4 SH.

### MATH-370 Cryptology and 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 consider monoalphabetic and polyalphabetic encryptions, public key cryptography, security, and anonymity. Same as CSCI-370. Prerequisite: MATH-221 Discrete Structures. 4 SH.

### 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-231 Foundations of Analysis. 4 SH. CC: Writing Intensive.

### 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-231 Foundations of Analysis. 4 SH.

### 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 either MATH-108 Introduction to Statistics or MATH-180 Statistical Methods. 4 SH.

### 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 possibly quantum computers. Same as CSCI-482. Prerequisites: MATH-221 Discrete Structures and CSCI-281 Data Structures. 2 SH.

### 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. 1 or 4 SH. The 4 SH version satisfies the capstone requirement. CC: Oral Intensive for the 4-SH.

### 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. 2 or 4 SH.

### 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. 2 or 4 SH.

### MATH-503 Independent Research

A research project leading to a substantive paper on a selected topic in mathematics. By arrangement with a department instructor. Prerequisites: Junior or senior standing and department permission. 2 or 4 SH.

### MATH-599 Mathematics Internship

Full-time mathematics-related employment at an industrial firm or a public service organization. Prerequisites: Senior standing, appropriate mathematics background courses and department internship coordinator's permission. S/U grade. 2, 4 or 8 SH.

Department: Mathematical Sciences

Professor of Mathematical Sciences

Department: Mathematical Sciences

Professor of Mathematical Sciences

Department: Mathematical Sciences

Associate Professor of Mathematics & Computer Science

Department: Mathematical Sciences

Associate Professor of Mathematics & Computer Science

Department: Mathematical Sciences

Assistant Professor Computer Science

Department: Mathematical Sciences

Assistant Prof of Mathematics & Coord of Analytical Thought

Department: Mathematical Sciences

Assistant Professor of Mathematics

Department: Mathematical Sciences

Adjunct Faculty in Mathematics & Computer Science

**Departmental Honors.** The departmental honors program encourages and recognizes outstanding academic performance. To graduate with departmental honors, a mathematics major or computer science major must do the following:

- Have a minimum GPA of 3.50 in the department and 3.00 overall,
- Request admission to the program at the end of the junior year,
- Consult with a faculty adviser to design an honors-quality project and begin research as a first-semester senior taking MATH-503 Independent Research or CSCI-503 Independent Research,
- Complete the project during the second semester in MATH-500 Senior Colloquium or CSCI-500 Senior Colloquium,
- Successfully pass an oral exam covering a selection of math courses.

**Kappa Mu Epsilon.** Students who meet national standards for membership are eligible to join this national undergraduate mathematics honorary society.

### Mathematics

**Capstone. **The Capstone requirement may be satisfied by the four-semester-hour version of MATH-500 Senior Colloquium. Students need not fulfill the Capstone requirement in their major, but they usually do.

### Computer Science

**Capstone. **The capstone requirement may be satisfied with CSCI-472 Software Engineering Practicum, CSCI-483 Compiler Theory or CSCI-500 Senior Colloquium. Students need not fulfill the capstone requirement in their major, but they usually do. A capstone course taken as a junior does fulfill the requirement, but not as a sophomore.