Professor Douglas Reinelt, Department Chair
Professors: John Chen, Ian Gladwell, Richard Haberman, Peter Moore, George Reddien, Lawrence Shampine, Richard Williams; Associate Professors: Thomas Carr, Robert Davis, Mogens Melander, Montie Monzingo, Johannes Tausch; Assistant Professors: Vladimir Ajaev, Bruce Ayati, Yeo-Jin Chung, Bruce Fabijonas, Takashi Nishikawa; Lecturers: Linda Neal, Judy Newell, Carol Seets.
Requirements for the Bachelor of Science Degree With a Major in Mathematics. The B.S. degree in mathematics reflects contemporary trends in mathematics by incorporating computer science, mathematical and computational modeling, natural science, and statistics courses. This degree is particularly appropriate for students who wish to proceed toward careers in industry concentrating on analytical problem solving, or toward graduate schools in any mathematical science area. Computer science, economics, electrical engineering, mechanical engineering, management science, physics, and chemistry provide attractive opportunities as areas for a double major with mathematics. With a minimum of 21 approved advanced hours in the major, the following courses are required:
With a minimum of 21 approved advanced hours in the major, the following courses are required:
Fundamental Mathematics: MATH 1337, 1338, 2339, 2343 -- 12
Natural Science: Choose two from PHYS 1303, 1304; CHEM 1303, 1304; BIOL 1401, 1402; GEOL 1301 -- 6
Computer Science: CSE 1340 or 1341 -- 3
Statistics: STAT 4340/CSE 4340/EMIS 4340 (Student may substitute STAT 5340/CSE 5370/5370) -- 3
Advanced Mathematics Elective: MATH 3000+ course -- 3
Specialization in one of the following five areas: 15
In each specialization, five courses must be taken with a minimum of two courses at the 4000+ level, including at least one MATH 4000+ course.
I. Applied and/or Numerical Mathematics
MATH 3315/CSE 3365 (mandatory)
Four from MATH 3334, 3337, 3353, 5315, 5316, 5331, 5332, 5334, 5353, EMIS 3360
II. Computer Science and Computer Engineering
MATH 3315/CSE 3365 (mandatory), CSE 4381 (mandatory)
Three from MATH 3353, 5315, 5316, 5332
MATH 3315/CSE 3365 (mandatory), MATH 3337 (mandatory)
One from Group I: MATH 5315, 5331, 5332, 5334
Two from Group II: EE 3322, 3330, 3372, 5330, 5332, 5360, 5362, 5372Mechanical Engineering
Two from Group II: ME 4360, 5302, 5320, 5322, 5336/MATH 6336, 5361, 5386
IV. Operations Research
MATH 3315/CSE 3365 (mandatory) EMIS 3360 (mandatory)
Two from Group I: MATH 3353, 5315, 5316, 5332, 5353
One from Group II: EMIS 5361, 5362, 5369, STAT 5344/EMIS 5364
V. Pure Mathematics
Five from MATH 3308, 3337, 3353, 4338, 4351, 4355, 5331, 5332, 5353, 5381
Requirements for the Bachelor of Arts Degree With a Major in Mathematics. The B.A. degree in Mathematics is designed for students who need a traditional mathematics degree leading to careers in teaching, industry, business, and government. It is particularly attractive when combined with liberal arts, social science, or business administration as a double major. The requirements are the same as for the Bachelor of Science degree except that there is no natural science requirement. In exceptional circumstances, the Department of Mathematics may choose to waive one course (three term-credit hours) in mathematics.
MATH 6000-level courses may also be taken for either major by students who have fulfilled the prerequisites and have departmental permission.
NOTE: All mathematics majors, either B.S. or B.A., must receive a grade of at least C- in all courses taken in fulfillment of the requirements for the mathematics major.
Requirements for the Mathematics Minor. MATH 1337, 1338, 2339, and nine hours selected from mathematics courses at the advanced (3000+) level. MATH 2343 (Elementary Differential Equations) may replace an advanced-level mathematics course. All courses in the minor must be passed with a grade of C or higher.
For All Undergraduates: After a student matriculates to SMU, transfer credit for neither MATH 1309 nor MATH 1337 will be approved.
1303. Precalculus for Business. Inequalities, absolute value, graphs, functions, basic analytic geometry, polynomials, logarithms, exponentials, linear equations, and mathematics of finance. Prerequisite: High school algebra. No credit given if taken after any calculus course. Credit not given for both 1303 and 1304. Intended for students planning to take MATH 1309.
1304. Precalculus Mathematics. Graphs, functions, basic analytic geometry, exponentials, logarithms, trigonometry, inverse functions. Prerequisites: High school algebra and trigonometry. No credit given if taken after any calculus course. Credit not given for both MATH 1303 and 1304. Intended for students planning to take MATH 1337.
1307. Introduction to Mathematical Sciences. Permutations and combinations, probability, Markov chains, linear programming, elementary statistics, and mathematics of finance. Prerequisite: High school algebra.
1309. Introduction to Calculus for Business and Social Science. Derivatives and integrals of algebraic, logarithmic, and exponential functions with applications to the time value of money, curve sketching, maximum-minimum problems, and computation of areas. Applications to business and economics. (Natural science and engineering students must take MATH 1337. Credit not allowed for both MATH 1309 and 1337.) Prerequisite: Placement out of MATH 1303 or a grade of C or higher in MATH 1303.
1337. Calculus with Analytic Geometry I. Differential and integral calculus for algebraic, trigonometric functions, and transcendental functions, with applications to curve sketching, velocity, maximum-minimum problems, areas, and volumes. (Credit not allowed for both MATH 1309 and 1337.) Prerequisite: Placement out of MATH 1304 or a grade of C or higher in MATH 1304.
1338. Calculus with Analytic Geometry II. A continuation of MATH 1337 through differential and integral calculus, techniques of integration, improper integrals, and infinite sequences and series, including Taylor series. Prerequisite: A grade of C or higher in MATH 1337 (or MATH 1309 and departmental permission).
2339. Calculus with Analytic Geometry III. A continuation of MATH 1338 including parametric equations, polar coordinates, partial differentiation, multiple integrals, and vector analysis. Prerequisite: A grade of C or higher in MATH 1338.
2343. Elementary Differential Equations. First order equations, linear equations, Laplace transforms, power series solutions, and applications. Prerequisite: A grade of C or higher in MATH 1338.
3308. Introduction to Discrete Mathematics. An introduction to logic, set theory, graph theory, recurrence relations, and combinatorics. Mathematical foundations and applications of these subjects are presented. (Credit not allowed for both CSE 2353 and MATH 3308.) Prerequisite: A grade of C or higher in MATH 1338.
3315 (CSE 3365). Introduction to Scientific Computing. An elementary survey course that includes techniques for root-finding, interpolation, functional approximation, linear equations, and numerical integration. Special attention is given to FORTRAN or C programming, algorithm implementations, and library codes. Prerequisites: CSE 1340 or 1341; and a grade of C or higher in MATH 1338. Students registering for this course must also register for an associated computer laboratory.
3334. An Introduction to Applied Mathematics. Formulation, solution, and interpretation of mathematical models used in populations dynamics and traffic flow. Equilibrium, stability, and phase-plane analysis of nonlinear ordinary differential equations from ecology. Method of characteristics for nonlinear partial differential equations of traffic flow yielding density waves and shocks. Prerequisite: A grade of C or higher in MATH 2343.
3337. Advanced Mathematics for Science and Engineering. Elements of vector integral calculus, Fourier series, and boundary-value problems in partial differential equations. (No credit given if taken after MATH 5334.) Prerequisites: Grades of C or higher in MATH 2343 and 2339.
3353. Introduction to Linear Algebra. Matrices and linear equations, Gaussian elimination, determinants, rank, geometrical notions, eigenvalue problems, and coordinate transformations, norms, inner products, orthogonal projections, Gram-Schmidt and least squares. (No credit given if taken after MATH 5353.) Prerequisite: A grade of C or higher in MATH 1338.
4300. Independent Study in Math. Independent study of a selected topic in mathematics. Prerequisite: By arrangement with faculty sponsor and with departmental approval.
4335. Mathematical Biology. Introduction of mathematical models of biological systems. Population dynamics, infectious diseases, population genetics, molecular and cellular biology. Prerequisites: MATH 2343 and MATH 3353.
4338. Analysis. Sequences and series of real numbers and functions, properties of continuous functions, differentiation and integration with some attention paid to higher dimensions. Prerequisite: MATH 2339.
4351. Theory of Numbers. Classical number theory, including divisibility, congruencies, quadratic reciprocity, Diophantine equations, and number theoretic functions. Prerequisite: MATH 3308 or 3353.
4355. Groups and Rings. Basic properties of groups, rings and fields, homomorphisms, normal subgroups, integral domains, ideals, algebraic extension fields, geometric constructions. Prerequisite: MATH 3308 or 3353.
5315 Introduction to Numerical Analysis. Numerical solution of linear and nonlinear equations, interpolation and approximation of functions, numerical integration, floating point arithmetic, and the numerical solution of initial value problems in ordinary differential equations. Student use of the computer is emphasized. Prerequisites: MATH 3315/CSE 3365 and MATH 2343; a programming course (e.g., C, FORTRAN, or MATLAB).
5316. Numerical Linear Algebra. The efficient solution of linear systems by both direct and iterative methods and least-squares problems by direct methods. Elementary and orthogonal matrix transformations provide a unified treatment of direct methods. Stationary and conjugate direction methods for efficiently solving sparse linear systems. Prerequisites: A programming course (e.g., C, FORTRAN, or MATLAB); MATH 3353; and MATH 3315/CSE 3365 or MATH 5315.
5331. Functions of a Complex Variable. Complex numbers, analytic functions, mapping by elementary functions, complex integration. Cauchy-Goursat theorem, Cauchy integral formulas. Taylor and Laurent series, residues, evaluation of improper integrals. Applications of conformal mapping and analytic functions. Prerequisite: MATH 3337.
5332. Wavelet Transforms. A mathematical introduction to sampling, data compression, multiresolution analysis, Fourier analysis and wavelet theory, including biorthogonal wavelets and spline wavelets. Prerequisites: MATH 3337, 3353, and 3315/CSE 3365.
5334. Introduction to Partial Differential Equations. Elementary partial differential equations of applied mathematics: heat, wave, and Laplace's equations. Topics include physical derivations, separation of variables, Fourier series, Sturm-Liouville eigenvalue problems, Bessel functions, Fourier transforms. Prerequisite: MATH 3337.
5353. Linear Algebra. Norms, inner products, orthogonal projections, Gram-Schmidt, and least squares. Linear transformations. Eigenvalues and eigenvectors, similarity and unitary transformations, Schur and diagonal forms, singular value decomposition, and Jordan form. Discrete and continuous systems, matrix exponentials. Quadratic forms, Rayleigh's principle, and a minimum-maximum principle. Prerequisites: MATH 2343 and 3353, or permission of instructor.
5381. Introduction to General Topology. Elementary topology of the line and plane, metric spaces, and general topological spaces; continuity of mappings, connectedness, compactness, completeness, and fixed-point theorems. Prerequisite: MATH 3353.