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The department of mathematical sciences offers the following degrees: BA in Mathematics (including a pre-actuarial/financial mathematics track), BA/MA in Mathematics (students can receive up to 12 credit hours of graduate courses towards the BA degree, and the remaining graduate courses up to 30 credit hours towards the MA), MA in Mathematics (30 credit hours), and PhD in Mathematics.
Graduate courses in mathematics are open to undergraduate students who successfully completed multivariable calculus and linear algebra.
A mathematics placement examination is required of all students planning to take Math. Students must take this test before registering for MATH 1412.
1010 Excursions in Mathematics 3 credits
This course is intended for non-science majors and Education majors. Several topics will be taught in depth from the following list: Sets of numbers, geometry, elements of probability and statistics, consumer mathematics, linear programming.
1160 Precalculus 4 credits
Number systems, functions, equations, and inequalities; algebra of polynomials, exponentials, and logarithms; analytic geometry of lines and circles; vectors, trigonometry, and complex numbers. (lecture: 3 hours; recitation: 2 hours). Prerequisites: two years of high school mathematics and placement by examination.
1410 Fundamentals of Calculus 4 credits
This course is designed for students majoring in biology, pre-health sciences, or any other major except mathematics, computer science, physics, engineering, chemistry, and physical sciences. Topics include functions, limits, derivatives, and integrals, and problem solving methods, including optimization and related rates problems. Emphasis is placed on developing and interpreting models from a variety of disciplines, on analyzing data, and on graphing and numerical computations. (lecture: 3 hours; recitation: 1 hour). Prerequisite: Pre-Calculus—high school Algebra and Trigonometry.
1412, 1413 Calculus I, II 4 credits
First semester: limits, derivatives, and integrals; continuous and differentiable functions, mean value theorem, chain rule, implicit differentiation. Applications: curve sketching, maxima and minima, related rates, motion, area. Trigonometric, inverse trigonometric, logarithmic and exponential functions. Second semester: methods of integration, area, moments, volume. Indeterminate forms, improper integrals, sequences and series. Parametric equations, arc length and polar coordinates. (lecture: 3 hours; recitation: 2 hours).Prerequisites: three years of high school mathematics and placement by examination or MATH 1160.
1504 Discrete Structures 4 credits
Boolean algebra and predicate calculus; proof methods; sets, functions, and relations; combinatorics; graph theory and algorithms; mathematical induction and recursion; probability and average case analysis of algorithms. (lecture: 3 hours; recitation: 2 hours) Prerequisite: three years of high school mathematics.
1510 Multivariable Calculus 4 credits
Limits and continuity in Euclidean spaces; partial derivatives, gradient, and chain rule; maxima and minima with constraints; multiple integrals, cylindrical and spherical coordinates; vector calculus; theorems of Green, Gauss, and Stokes. Prerequisite: MATH 1413.
1520, 1521 Advanced Calculus I, II 3 credits
Real numbers; theorems on limits; continuous, differentiable, and integrable functions; sequences and series of functions; metric space methods, fixed points, existence theorems for differential equations; implicit function theorem. Prerequisites: MATH 1413 and permission of the instructor.
1523 Introduction to Analysis 3 credits
Familiarizes students with analytic tools and ideas that are of practical significance for a variety of applications along with an awareness of the foundations, interrelations, and limitations of those methods. Prerequisites: MATH 1510, 2105.
1540 Functions of a Complex Variable 3 credits
Analytic functions, Cauchy Riemann equations, Cauchy integral formula, residue theory, conformal mappings. Prerequisite: MATH 1520 or permission of the instructor.
2105 Linear Algebra 3 credits
Systems of linear equations, Gaussian elimination, matrices, matrix algebra; vector spaces, linear transformations, similarity; inner product spaces; determinants; eigenvalues and eigenvectors, diagonalization; quadratic forms; canonical forms; spectral theory; applications. Prerequisite: MAT 1412.
2168 Elementary Number Theory 3 credits
Properties of integers, Euclidean algorithm, unique factorization, arithmetic functions, perfect numbers, linear and quadratic congruences, public-key encryption.
2215 Modern Algebra 3 credits
Basic concepts of an algebraic system, a sub-system, a factor-system, an isomorphism and a homomorphism. Examples and initial results from the theory of groups, rings, and fields. The second semester will be devoted to advanced topics, including recent developments. Prerequisite: MATH 2105 or permission of the instructor.
2461 Probability Theory 3 credits
Discrete and continuous sample spaces; combinatorial analysis; density and distribution functions of random variables; expectation and variance; independence and conditional probability; law of large numbers; central limit theorem; generating functions; random walk and ruin problems. Prerequisite: MATH 1413.
2462 Mathematical Statistics 3 credits
Application of probability theory to the classical parametric models: moment-generating functions, chisquare and t distributions, central limit theorem, sampling distributions, maximum likelihood and interval estimation, confidence intervals, hypothesis testing; nonparametric models; the Bayesian controversy. Examples from natural science and social and behavioral research. Prerequisite: MATH 2461.
2601 Differential Equations 3 credits
Classification of differential equations; existence and uniqueness of solutions; initial-value problems, boundary-value problems; power series methods, integral transforms; numerical algorithms and error estimation; topological methods. Prerequisite: MAT 1413.
2651 Numerical Analysis 3 credits
Finite difference calculus; numerical solution of differential equations and linear systems of equations; iterative methods; computation of eigenvalues and eigenvectors. Advanced elective. Prerequisite: MATH 1413
2901 Mathematics of Finance 3 credits
Discrete models for options, pricing derivatives,continuous stock price models, Brownian motion, the Black-Scholes formula, the Black-Scholes differential equation, hedging options, dynamic programming, bond price models, yield curves, forwards and futures, Keynes interest rate parity formula. Prerequisite: familiarity with differential equations.
3301, 3302, 3303, 3304 Topics in Modern Mathematics 3 credits.
Selected subjects in analysis, algebra, geometry, actuarial, and applied mathematics. Students may register for up to four semesters with permission of the Department Chair. Prerequisites: junior status and permission of the instructor.