# Mathematics (MATH)

**090 Fundamentals of Mathematics** (3) Review of pre-algebra mathematics with an introduction to basic algebra. Topics include: real numbers, with an emphasis on fractions and decimals; percent notation; exponents; algebraic expressions; solving equations and inequalities; polynomials; and an introduction to graphing linear equations. Does not apply toward general education requirements or graduation requirements. Students taking this course must earn a grade of at least C- before enrolling in MATH 095. F10, S11, F11, S12

**095 Fundamentals of Algebra** (3) Review of elementary algebra topics typically studied in high school. Topics include: the real number system; linear equations and inequalities and their graphs; systems of linear equations and inequalities; polynomials; factoring polynomials; quadratic equations. Does not apply toward general education requirements or graduation requirements. Prerequisite: Acceptable score on the Mathematics Placement Test or completion of MATH 090 with a grade of at least C-. F10, S11, F11, S12

**102 Intermediate Algebra** (2) Review of intermediate algebra topics typically studied in high school. Topics include: rational expressions and equations; rational exponents; radical expressions and equations; complex numbers; functions; quadratic equations and functions; graphing techniques, conic sections; exponential and logarithmic functions and equations. Prerequisite: Acceptable score on the Mathematics Placement Test or completion of MATH 095 with a grade of at least C-. F10, S11, F11, S12

**112 Introduction to Contemporary Mathematics** (3) A liberal arts mathematics course presenting mathematics as a tool used by a wide range of professionals in modern society. Real-life examples are used to promote understanding of mathematics and its relationship to other areas of study. Mathematical problem solving is shown to influence everything from the success of savvy entrepreneurs to the fairness of voting practices. Examples such as the Traveling Salesman Problem and Arrow's Impossibility Theorem are taken from management science, statistics, social science and computer science. Satisfies the Mathematics requirement for general education. Students enrolling in MATH 112 should have an acceptable score on the Mathematics Placement Test or have completed an appropriate remedial course. MATH 095 is recommended. F10, S11, F11, S12

**115 Precalculus** (5) Covers the algebra and trigonometry required for calculus and analytic geometry. Topics include review of intermediate algebra; composite and inverse functions; polynomial and rational functions, exponential and logarithmic functions, trigonometric functions, identities, and equations; the binomial theorem; fundamentals of analytic geometry; and the conic sections. Satisfies the mathematics requirement for general education. Prerequisite: acceptable score on the Mathematics Placement Test or completion of MATH 102 with a grade of at least C-. F10, S11, F11, S12

**130 Elementary Statistics** (4) Introductory course for students of all disciplines. Includes descriptive statistics, the binomial and normal distributions, confidence intervals, linear regression; correlation; the t distribution; the Chi-square distribution; nonparametric tests of statistical inference; and understanding statistics in many different fields. Problems are taken from various fields dependent on statistical decision making. Satisfies the mathematics requirement for general education. Prerequisite: acceptable score on the Mathematics Placement Test or completion of MATH 095 with a grade of at least C-. F10, S11, F11, S12

**150 Finite Mathematics for Business** (3) Introduction to mathematics concepts and problem-solving techniques especially applicable in business, economics, biology, and the social sciences. Topics include: linear equations, linear functions, and graphs; systems of linear equations and matrices; linear inequalities, linear programming, and the simplex method sets and counting techniques; and fundamentals of probability. Satisfies the mathematics requirement for general education. Prerequisite: acceptable score on the Mathematics Placement Test or completion of MATH 095 with a grade of at least C-. F10, F11

**151 Calculus for Business, Life, and Social Sciences (**3) A short course in calculus including concepts and problem-solving techniques for students in business, economics, biology and the social sciences. Topics include algebraic, exponential and logarithmic functions; derivatives, and optimization problems; partial derivatives and Lagrange multipliers (as time permits). Satisfies the mathematics requirement for general education. Prerequisite: acceptable score on the Mathematics Placement Test or completion of MATH 102 with a grade of at least C-. F10, S11, F11, S12

**240 Calculus and Analytic Geometry I** (4) A first course in the fundamentals of calculus. Topics include: real numbers; functions; limits; continuity; derivatives, integrals; and applications. Prerequisite: acceptable score on the Mathematics Placement Test or completion of MATH 115 with a grade of at least C-or equivalent. F10, S11, F11, S12

**241 Calculus and Analytical Geometry II** (4) Continuation of MATH 240. Topics include: conic sections; transcendental functions; techniques of integration; indeterminate forms; improper integrals; and infinite series. Prerequisite: A grade of C- or better in MATH 240. F10, S11, F11, S12

**242 Calculus and Analytic Geometry III** (4) Continuation of MATH 241. Topics include: three-dimensional analytic geometry; vectors; partial derivatives; multiple integrals; line integrals; and surface integrals. Prerequisite: A grade of C- or better in MATH 241. S11, S12

**310/510 Introduction to Abstract Mathematics** (3) Fundamentals of formal mathematics emphasizing mathematical writing and types of formal proof. Includes significant coverage of topics in logic, set theory and number theory. Prerequisite: MATH 115. F10, S11, F11, S12

**315 Linear Algebra** (3) Introduction to the algebra and geometry of two- and three-dimensional space and extension to n-dimensional space. Topics include: line and coordinate vectors; systems of linear equations and their solution by reduction methods; matrix algebra; determinants; fundamentals of abstract vector spaces; linear independence, dimension theorems; linear transformations; eigenvalues and eigenvectors; diagonal matrices; quadratic forms; inner products ; and the Gram-Schmidt orthogonalization. Prerequisite: MATH 310. S11, S12

**320/520 Discrete Structures** (4) Continuation of MATH 310. Investigation of concepts of noncalculus mathematics used in computer science, operations research and other areas of applied mathematics. Topics include: relations and functions, recurrence relations, combinatorics, graph theory, and related algorithms. Cross-listed as CSCI 320/520. Prerequisite: MATH 310. F10, F11

**344/544 Differential Equations** (4) Introduction to the theory of ordinary differential equations including some coverage of series solutions, as time permits. Also covers various classical applications, such as spring mass systems. Prerequisite: MATH 241. S11

**362/562 Topics in Geometry** (3) Modern treatment of topics from Euclidean geometry with an introduction to other geometries. Appropriate for students in Elementary or Secondary Education or Secondary school mathematics teachers. Prerequisite: MATH 310. S11, S12

**370/570 Probability** (3) A first course in probability theory intended for students in mathematics, pre-engineering, and the sciences. Prerequisites: MATH 241 and MATH 310. F11

**371 Statistics** (4) Calculus-based statistics emphasizing applications intended for students in applied mathematics, economics and the sciences. Topics include: estimation and prediction; hypothesis testing; linear and multiple regression; F and t tests; analysis of variance; and non-parametric statistics. Prerequisite: MATH 241 and MATH 310. MATH 242 and MATH 370 are recommended. F10

**372 Actuarial Mathematics** (4) Introductory course in actuarial science. Topics may include risk models, life tables, life insurance and annuities, and pension funding. Prerequisite: MATH 370 or MATH 371. Offered as needed.

**380/580 Introduction to Mathematical Modeling** (4) Applied mathematics course emphasizing probabilistic models. Topics include: discrete-and continuous-time Markov chains; Monte Carlo estimates; queuing theory; reliability theory; Brownian motion; and financial mathematics. Prerequisites: MATH 241 and one of MATH 370, MATH 371. MATH 242 is recommended. Offered as needed.

**381 Special Projects** (1-4) Various individual and small-group projects carried out under the supervision of one or more instructors. Requires weekly progress reports plus a final report and/or a final exam. May be repeated, but no more than a total of four credits may be earned from both MATH 381 and CSCI 381. Pass-Fail only. Prerequisites: Preliminary project plan and an independent study contract. Offered as needed.

**385 Introduction to Operations Research** (3) Topics include Mathematical programming, (Linear programming problems, Transportation problems, Dynamic programming, Game Theory), Queuing Theory, Inventory Theory, Reliability Theory, and Simulation techniques. Prerequisites: MATH 301 and MATH 370.

**390 Mathematical Sciences Internship** (1-4) Work in an approved position to gain experience in solving real problems using computer science, mathematics, and statistics. Interns may receive salaried appointments with cooperating companies. Credits do not apply to any major or minor in Mathematics and Computer Sciences. Evaluation: Pass-Fail only. Offered as needed.

**391 Putnam Mathematical Competition** (1) Preparation for the national Putnam Mathematics Contest. Includes review of previous examination problems and lectures on selected topics. May be repeated for a total of three credits. Pass-Fail only. Consent of the instructor required. F10, F11

**399 Mathematical Sciences Seminar** (1) Students carry out individual investigations in current literature and present their findings to the entire department. Taken during senior year. Pass-Fail only. Prerequisite: Independent study contract.

**401/601 Formal Models for Computer Security** (4) Survey of formal mathematical models for computer security with in-depth examination of important features and characteristics. Includes an investigation of mathematical properties of these models as well as related cryptographic and system implementations. The models include classical lattice-based models as well as modern policy-based models such as the Bell-LaPadula model, no interference models, hybrid models, integrity models, and miscellaneous formal verification techniques. Prerequisite: MATH 310, CSCI 270. Offered as needed.

**421/621 Theory of Computation** (4) Thorough introduction to automata, formal languages and compatibility. Topics include: models of computation; regular and context-free languages; finite and pushdown automata; Turing machines; unsolvable decision problems; and fundamentals of computational complexity. Cross-listed as CSCI 421/621. Prerequisites: CSCI 320. F11

**425/625 Algorithm Design and Analysis** (4) Study of the design and analysis of algorithms that are based on elementary data structures such as queues, stacks and trees. Some graph and network algorithms (shortest paths, connectivity, coloring, flows, matchings), geometric algorithms (convex hulls, range search, nearest neighbors), NP-complexity, approximation algorithms (vertex cover, traveling salesman, scheduling), and introduction to randomized algorithms. Introduction to algorithm design techniques, including greedy algorithms, divide-and-conquer, and dynamic programming. Lower and upper bounds of program complexity are analyzed. Introduction to algorithms used in the area of information security. Cross-listed as CSCI 425/625. Prerequisites: CSCI 320. CSCI 202 recommended. F10

**437/637 Cryptography** (4) Study of the theory of cryptography together with applied programming projects. Topics include: discrete probability spaces; Shannon's theory of information and perfect secrecy; classical cryptosystems and cryptanalysis; authentication and key exchange; public key cryptosystems; elementary number theory, primality checking, the RSA cryptosystem; and Advanced Encryption Standard (AES). Cross-listed as CSCI 437. Prerequisite: CSCI 201, MATH 310. S11

**440/640 Real Analysis** (4) Fundamental concepts of limit, continuity, differentiability, and integrability of functions of one variable; convergence and uniform convergence of infinite series, and improper integrals. Prerequisites: MATH 242, MATH 301. F11

**455 Abstract Algebra** (4) Introduction to algebraic systems including groups, rings, integral domains and fields, homomorphisms and isomorphisms. Prerequisite: MATH 301. F10

**471/671 Introduction to Complex Variables** (4) Introduction to the study of analytic functions including series, residues, conformal mapping and applications. Prerequisite: MATH 242. S12

**475/675 Numerical Analysis** (4) Study of theory and applications of computational techniques for mathematical solutions emphasizing rapid approximation and error analysis. Topics include: solution to equations in one variable; polynomial approximations to functions; error analysis; numerical solutions to ordinary differential equations; boundary value problems. Cross-listed as CSCI 475/675. Prerequisite: MATH 242. Offered as needed.

**481/681 Special Topics** (1-4) In-depth study of specialized current topics in mathematical sciences. May be repeated when topics are different. Offered as needed.

**550 Elementary Number Theory** (3) Study of the system of integers including the division algorithm, greatest common divisor, fundamental theorem of arithmetic, congruences, diophantine equations, and arithmetic functions. Prerequisite: MATH 240 or consent of instructor. Offered as needed.