Science

MATHEMATICS AND COMPUTER SCIENCE

Professors Hemler, Lins; Associate Professors Jayne, Pendergrass; Assistant Professors Jaiyeola, Loeb, Strayer Chair: Rebecca L. Jayne Students may choose one of two majors in the discipline of mathematics: Mathematics or Applied Mathematics. A major in Mathematics requires at least 11 courses. A major in Applied Mathematics requires at least 10 courses.

All students majoring in either Mathematics or Applied Mathematics must complete Mathematics 141, 142, 231, 242, 254. In addition, a major in Applied Mathematics requires Mathematics 222, 421, Computer Science 261/271 as well as two electives in Mathematics at the 200-level or higher. At least one of these electives must be at the 400-level. Computer Science 262/272 may be substituted for the other Mathematics elective. A major in Mathematics requires Mathematics 431, 441, two electives at the 200-level or higher, and two additional electives at the 300-level or above. One elective may be Computer Science 261/271.

A major in Computer Science requires at least 11 courses and two corequisite laboratory courses: Computer Science 261/271, 262/272, 361, 362, 461, and 480; Mathematics 141 and 254; and three additional courses, at least two of which must be Computer Science courses at the 200-level or above. A student may use either Computer Science 161 or Physics 106 for the third course. The department recommends that students who intend to teach mathematics complete a major in Mathematics. The department recommends that students who intend to pursue a career in engineering complete a major in either Mathematics or Applied Mathematics; it is recommended that these students take Mathematics 243 and 342 and Computer Science 261/271 and 262/272.

The requirements for a minor in Mathematics are 19 credit hours from the following Mathematics courses: 141, 142, 231, 242, and one additional 3 or 4 credit hour course in Mathematics at the 300-level or above. The requirements for a minor in Computer Science are 17 credit hours from the following Computer Science courses: 261/271, 262/272, 361, and two electives in Computer Science, at least one of which is at the 300-level or above.

COMPUTER SCIENCE

COMPUTER SCIENCE 161. (3) INTRODUCTION TO COMPUTING. An overview of computing, with consideration given to its impact upon today’s society. Topics may include history, applications, computer organization, programming languages, algorithms, and computability. A student cannot receive credit for Computer Science 161 if he has passed any other college course in Computer Science. Prerequisite: none. Offered: each semester. COMPUTER SCIENCE 261. (3) COMPUTER SCIENCE I. Discussion of algorithms, programs, and computers. Extensive work in the preparation, running, debugging, and documenting of programs. Problem-solving is emphasized. Prerequisite: none. Corequisite: Computer Science 271. Offered: each semester.

COMPUTER SCIENCE 262. (3) COMPUTER SCIENCE II. A continuation of Computer Science 261 but with emphasis on language structures and applications of those structures not normally covered in a first course. Programming efficiency, documentation standards, and programming style are emphasized. Prerequisite: Computer Science 261. Corequisite: Computer Science 272. Offered: spring semester. COMPUTER SCIENCE 271. (1) COMPUTER SCIENCE LABORATORY I. This laboratory course is designed to enhance the student’s understanding of the concepts covered in the co-requisite lecture course through experimentation and observation. Topics include software engineering, algorithmic problem solving, programming control structures, class definition and instantiation fundamentals, file input/output, and elementary data processing. Prerequisite: none. Corequisite: Computer Science 261. Offered: each semester.

COMPUTER SCIENCE 272. (1) COMPUTER SCIENCE LABORATORY II. This laboratory course is designed to enhance the student’s understanding of the concepts covered in the co-requisite lecture course through experimentation and observation. Topics include advanced software engineering, algorithmic problem solving, pointers, dynamic memory allocation, templates, and inheritance as implemented in the C++ programming language. Prerequisite: Computer Science 271. Corequisite: Computer Science 262. Offered: spring semester. COMPUTER SCIENCE 308. (3) PROGRAMMING LANGUAGES. A study of the design and implementation of programming languages. Concepts such as non-procedural languages, scope rules, data types and data sharing, control structures, block structure, recursion, storage management, formal specification of syntax and semantics, parsing, and interpreters. Prerequisite: Computer Science 262. Offered: fall semester of even-numbered years. COMPUTER SCIENCE 321. (3) CRYPTOGRAPHY. An introduction to both classical and modern methods of cryptography with emphasis on how classical number theory has been applied to problems of modern cryptography in recent years. Topics to include digital signatures, algorithms and protocols for public and private key cryptography, and systems for secure communications such as e-mail. Ethical and political issues having to do with secure communications are also discussed. Prerequisites: Computer Science 262 and Mathematics 254. Offered: spring semester of even-numbered years. COMPUTER SCIENCE 331. (3) COMPUTER GRAPHICS. This course covers the principles of two-dimensional and threedimensional computer graphics, including the mathematical theory underlying those principles. Topics include the graphics pipeline, drawing basic shapes in two and three dimensions, linear transformations, meshes, clipping, shading, lighting, textures, and various graphics algorithms. Prerequisites: Computer Science 262 and Mathematics 141. Offered: fall semester of oddnumbered years. COMPUTER SCIENCE 351. (3) ARTIFICIAL INTELLIGENCE. A broad introduction to the field of Artificial Intelligence. Topics may be chosen from the Turing Test, expert systems, game playing, machine learning, neural networks, automated theorem proving, natural language understanding, and robotics. Programming languages for Artificial Intelligence, such as Lisp and Prolog, are also studied. Prerequisites: Computer Science 262 and Mathematics 254.

COMPUTER SCIENCE 361. (3) COMPUTER ORGANIZATION. A machine-level view of computing. Topics may include computer arithmetic and data representation, assembly language programming and the assembly process, machine instruction sets, microprogramming and digital logic. Prerequisite: Computer Science 262. Offered: fall semester.

COMPUTER SCIENCE 362. (3) DATA STRUCTURES AND ALGORITHMS. A continuation of the study of data structures begun in Computer Science 262, with emphasis on the analysis of algorithms associated with such structures. Topics to include data structures such as stacks, queues, trees, and graphs, algorithm design strategies and complexity analysis. Prerequisites: Mathematics 254 and Computer Science 361. Offered: spring semester. COMPUTER SCIENCE 410. (3) OPERATING SYSTEMS. An historical study of operating systems with an emphasis on how some classical problems of concurrency, such as mutual exclusion and deadlock, have been solved. Additional topics to be chosen from memory management, virtual storage organization, paging, segmentation, process management and scheduling, and interrupt handling. Prerequisite: Computer Science 361. Offered: spring semester of oddnumbered years. COMPUTER SCIENCE 461. (3) THEORY OF COMPUTING. An introduction to theoretical computer science. Abstract models of computers are used to help investigate the limitations of computing. Topics may include computability, complexity, automata, formal languages and grammars, and the Chomsky hierarchy. Prerequisite: Computer Science 362. Offered: fall semester.

COMPUTER SCIENCE 480. (3) ADVANCED TOPICS IN COMPUTER SCIENCE. Topics may be chosen from among compiler design, symbolic computation, computational complexity, program verification and correctness, and database theory. Prerequisite: Computer Science 461, or consent of instructor. Offered: spring semester.

MATHEMATICS

MATHEMATICS 105. (1) PREPARATION FOR CALCULUS. A course designed to maximize students’ potential to succeed in calculus by reinforcing basic mathematical skills. Specific topics include functions and their graphs, algebra, and trigonometry. Students may not selfenroll in Mathematics 105; rather they are placed in the course based on the results of a departmental assessment of calculus readiness. Offered: Each semester.

MATHEMATICS 111. (3) MATHEMATICS AND SOCIETY. An exploration of the mathematical techniques used to solve problems in society. Specific topics are chosen from among the following: voting and power; division and apportionment; graph theory and scheduling; cryptography, game theory, symmetry, and form; and probability. Students who have completed any course in mathematics above Mathematics 111 cannot receive credit for Mathematics 111. Prerequisite: none. Offered: each semester. MATHEMATICS 121. (4) STATISTICS. Introduction to probability and statistics. Exploratory data analysis. Discrete and continuous random variables, estimation, hypothesis testing. Prerequisite: none. Offered: each semester. MATHEMATICS 130. (4) FINITE MATHEMATICAL MODELS. A course emphasizing the use of finite mathematics in modeling real-world phenomena. Specific topics are chosen from among the following: matrix algebra, graph theory, cryptography, Leontief inputoutput models, linear programming, probability, counting methods, game theory, and Markov chains. Prerequisite: none. MATHEMATICS 140. (4) CALCULUS FOR ECONOMICS. A study of differential and integral calculus and its applications. Topics include differentiation of elementary functions in one and several dimensions, integration of polynomials, and constrained and unconstrained optimization in one and several variables. Prerequisite: Economics 101 and satisfactory performance on a departmental assessment. Students who have any credit at Hampden-Sydney for the study of calculus may not take this course. Offered: each semester.

MATHEMATICS 141. (4) CALCULUS I. Elementary functions, limits, derivatives, optimization, the definite integral, and the Fundamental Theorem of Calculus. Prerequisite: satisfactory performance on a departmental assessment. Offered: each semester.

MATHEMATICS 142. (4) CALCULUS II. Functions defined by integrals, inverses, applications and techniques of integration, infinite series. Prerequisite: Mathematics 141 or the equivalent. Offered: each semester. MATHEMATICS 212. (3) INTRODUCTION TO THE HISTORY OF MATHEMATICS. A survey, from Babylonian mathematics through Greek mathematics, including some topics from modern mathematics, and illuminating G. Cantor’s dictum that the essence of mathematics is its freedom to change. An extensive student project is required. Prerequisite: Mathematics 142, or consent of the instructor.

MATHEMATICS 222. (3) STATISTICAL METHODS. A project-based study of sampling distributions, estimation, and hypothesis testing. Major topics are classical and nonparametric analysis of variance, and regression analysis. Students use a variety of statistical software to produce both individual and group projects. Prerequisite: Mathematics 121, or consent of the instructor. Offered: spring semester. MATHEMATICS 231. (4) LINEAR ALGEBRA. Matrix arithmetic, vectors, abstract vector spaces, linear transformations, inner products, and eigenvalues, with some emphasis on applications and computing. Prerequisite: Mathematics 142. Offered: spring semester.

MATHEMATICS 242. (4) CALCULUS III. Plane curves, polar coordinates, vector analysis of curves, infinite series, approximation, partial derivatives, line integrals, and double integrals. Prerequisite: Mathematics 142. Offered: fall semester.

MATHEMATICS 243. (3) DIFFERENTIAL EQUATIONS. Analytic and numerical solutions of ordinary differential equations. Existence and uniqueness of solutions. Solutions of linear systems. Prerequisite: Mathematics 231 and 242, or consent of the instructor. Offered: fall semester.

MATHEMATICS 254. (3) PROOF AND ABSTRACTION. An introduction to logic, set theory, and the discrete structures most often used in mathematics and computer science. Students will learn foundational proof techniques. Additional topics may include number theory, graph theory, and combinatorics. Prospective mathematics, applied mathematics, and computer science majors should take Math 254 during the spring of sophomore year. Prerequisite: Mathematics 142 or both Mathematics 141 and Computer Science 261. Offered: fall semester.

MATHEMATICS 323. (3) ENGINEERING MATHEMATICS. An introduction to mathematical tools, techniques and software widely used in engineering, applied mathematics, and the sciences. Topics include partial differential equations, transform methods, orthogonal functions, Fourier series, and complex variables. A survey of widely used software packages for mathematical modeling and simulation is also included in the course. Other topics may be included at the discretion of the instructor. Prerequisite: Mathematics 243 or Physics 326; or Mathematics 231 with permission of instructor. Offered: spring semester of odd-numbered years. MATHEMATICS 331. (4) OPTIMIZATION. A mathematical introduction to optimization. Linear programming, integer programming, transportation and assignment problems, game theory, nonlinear programming, and decision analysis. Prerequisite: Mathematics 231. Offered: on sufficient demand.

MATHEMATICS 334. (3) ELEMENTARY NUMBER THEORY. An introduction to the theory of numbers. Prerequisite: Mathematics 231. Offered: on sufficient demand. MATHEMATICS 342. (3) NUMERICAL ANALYSIS. Solutions to problems of analysis by numerical methods and the study of error in numerical processes. Prerequisites: Mathematics 231 and 242. Offered: spring semester of even-numbered years. MATHEMATICS 343. (3) VECTOR ANALYSIS. Line and surface integrals, classical theorems of vector analysis. Prerequisites: Mathematics 231 and 242. Offered: on sufficient demand.

MATHEMATICS 345. (3) APPLIED MATHEMATICS. Mathematical models and topics in advanced mathematics with application to the natural and social sciences. Prerequisites: Mathematics 231 and 242, or consent of the instructor. Offered: fall semester of evennumbered years. MATHEMATICS 421. (3) PROBABILITY AND STATISTICS I. Discrete and continuous probability distributions, moment-generating functions, and limit theorems. Prerequisite: Mathematics 242. Corequisite: Mathematics 254. Offered: fall semester of oddnumbered years. MATHEMATICS 422. (3) PROBABILITY AND STATISTICS II. The theory underlying estimation and hypothesis testing, and its application in one- and two-sample problems. Prerequisite: Mathematics 421. Offered: spring semester of even-numbered years. MATHEMATICS 431. (3) ALGEBRAIC STRUCTURES. Groups, rings, fields, and linear algebra. Prerequisites: Mathematics 231 and 254. Offered: spring semester of odd-numbered years. MATHEMATICS 432. (3) ADVANCED ALGEBRA. Select topics in algebra, which may include field extensions, Galois Theory, or algebraic coding. Prerequisite: Mathematics 431. Offered: on sufficient demand.

MATHEMATICS 441. (3) INTERMEDIATE ANALYSIS. Further investigation of the calculus of one real variable. Continuity, uniform convergence, differentiation, and integration. Prerequisites: Mathematics 231, 242, and 254. Offered: spring semester of evennumbered years.

MATHEMATICS 444. (3) COMPLEX ANALYSIS. An introduction to the theory of complex functions. Prerequisite: Mathematics 242. Offered: on sufficient demand.

MATHEMATICS 448. (3) TOPOLOGY. Elementary topological concepts. Prerequisite: Mathematics 441. Offered: on sufficient demand.

MATHEMATICS 451. (3) GEOMETRY. An axiomatic approach to Euclidean geometry and an introduction to non-Euclidean geometries. Prerequisite: Mathematics 231. MATHEMATICS 461-462. (3-3) DEPARTMENTAL DISTINCTION IN MATHEMATICS. A scholarly project conducted in close consultation with a supervising professor. Prerequisites: permission of the instructor for 461; 461 and permission of the instructor for 462. Offered: on demand.