Mathematics

(MATH) MATHEMATICS
Department of Mathematical Sciences
James E. Jamison, Ph.D., Chair
Room 373, Dunn Hall
http://www.msci.memphis.edu/

In addition to the courses below, the department may offer the following Special Topics courses:
MATH 2011-2019. Special Topics in Mathematics. (1-3). Topics are varied and in online class listings. PREREQUISITE: permission of instructor.
MATH 4010-19. Special Topics in Mathematics and Statistics. (1-3). Topics are varied and announced in online class listings. PREREQUISITE: permission of instructor.

MATH 1100 - Basic Algebra (3)
Review of Real number system; exponents; rational roots; graphs using graphing calculators; partial fractions; synthetic division; theory of equations; inequalities; applications. NOTE: does not satisfy any part of mathematics requirements for any degree; not applicable toward fulfilling credit hour minimum for degrees in The College of Arts and Sciences. PREREQUISITE: two years of high school algebra or DSPM 0850 with C- or better.

MATH 1420 - Foundations of Mathematics (3)
(1182). Algebra review and applications; functions, graphs, permutations, combinations; introduction to probability and statistics; problem solving. PREREQUISITE: two units of high school algebra or DSPM 0850. [G]

MATH 1421 - Honors Calculus I (4)
(1401). Concepts of differential calculus with emphasis on theory; limits, continuous functions, applications of the derivative. NOTE: students may not receive credit for both MATH 1421 and MATH 1910. PREREQUISITE: permission of instructor.

MATH 1480 - Math/Elem School Teachers (3)
Examination of mathematics taught at the elementary school level; problem solving, sets, algebraic thinking, number theory, rational numbers, real numbers. PREREQUISITE: two units of high school algebra or DSPM 0850.

MATH 1530 - Prob/Statistics/Non Calculus (3)
(1601). Underlying ideas of statistical and quantitative thinking; randomization in sample survey methods and design of experiments; double blind experiments and observational studies; descriptive and summary statistics; measurement errors; probability models; normal approximation; tests of significance and p-values, basic concepts of correlation and regression analyses; MINITAB. NOTE: Math majors may not use this course as part of the major. PREREQUISITE: Two years of high school algebra or DSPM 0850. [G]

MATH 1710 - College Algebra (3)
(1211). Analysis of functions (linear, quadratic, polynomial, root, rational, exponential, logarithmic) using graphing calculators; partial fractions; synthetic division; conic sections; theory of equations; inequalities; applications. NOTE: only one of MATH 1710 or MATH 1730 may be used to satisfy degree requirements. PREREQUISITE: two years of high school algebra , or DSPM 0850. [G]

MATH 1720 - Trigonometry (3)
(1212). Circular functions; inverse circular functions, graphs of circular and inverse functions, identities, equations, angles, trigonometric functions, solution of triangles, elementary application of vectors; trigonometric form of complex numbers. NOTE: MATH 1720 and MATH 1730 will not satisfy a six semester hour degree requirement. PREREQUISITE: placement test recommended but not required; MATH 1710.

MATH 1730 - College Algebra/Trig (4)
(1213). Exponents, radicals, quadratic functions, inequalities; relations and functions; inverse, exponential and logarithmic functions; solution of algebraic systems; trigonometric functions, identities, equations and graphs; angle measurements; sum, difference, half-angle and double-angle formulas; solution of triangles, laws of sines and cosines. NOTE: MATH 1710 and 1730, or 1720 and 1730 will not satisfy a six semester hour degree requirement. PREREQUISITE: two units of high school algebra, or DSPM 0850. [G]

MATH 1830 - Elementary Calculus (3)
(1312). Introduction to concepts and methods of elementary calculus of one real variable as related to rational, exponential, and logarithmic functions; nature of derivatives; differentiation; application of derivative; nature of integration: definite integral; applications of definite integral. NOTE: only one of MATH 1830 or 1910 may be used to satisfy degree requirements. PREREQUISITE: MATH 1710 (with a minimum grade of C), ACT Math subscore of at least 24, or equivalent SAT Math score. [G]

MATH 1900 - Experience/Calculus (1)
In-depth study of concepts introduced in MATH 1830 with focus on use of transcendental function. Students completing both MATH 1830 and 1900 will fulfill the required prerequisites for MATH 1920. PREREQUISITE: MATH 1830 with a grade of "A", and permission of instructor.

MATH 1910 - Calculus I (4)
(1321). Introduction to calculus of one real variable; limits; continuity; derivatives; applications of derivatives including Newton's method, graphing techniques, optimization, indeterminate forms and l'Hospital's rule; antiderivatives; includes transcendental functions. NOTE: only one of MATH 1830 or MATH 1910 may be used to satisfy degree requirements. Students may not receive credit for both MATH 1910 and MATH 1421. PREREQUISITE: MATH 1720 (with a minimum grade of C) or MATH 1730 (with a minimum grade of C), or satisfactory score on placement exam. [G]

MATH 1920 - Calculus II (4)
(2321). Integration and applications of the definite integral; techniques of integration and improper integrals; curves defined by Parametric equations; arc length and surface area; polar coordinates; infinite series, Taylor and McLaurin series. NOTE: students may not receive credit for both MATH 1920 and MATH 2421. PREREQUISITE: MATH 1910 or both MATH 1830 and 1900.

MATH 2000 - Experiences in Mathematics (3)
Introduction to selected areas of mathematical sciences through application to modeling and solution of problems involving networks, circuits, trees, linear programming, random samples, regression, probability, inference, voting systems, game theory symmetry and tilings, geometric growth, conics, comparison of algorithms, codes and data management. PREREQUISITE: three years of high school mathematics, including two years of algebra and one year of geometry. [G]

MATH 2015 - Math/Elementary Teacher II (3)
Topics and material include improved mathematical peoblem solving abilities, thinking skill, content to provide a deeper understanding of mathematical concepts related to measurement, goemetry, and statistics as they are used at the K-8 grade levels.

MATH 2015 - Math/Elementary Teacher II (3)
Topics and material include improved mathematical problem solving abilities, thinking skills, content to provide a deeper understanding of mathematical concepts related to measurement, geometry, and statistics as they are used at the K-8 grade levels.

MATH 2110 - Calculus III (4)
Multivariable calculus including three-dimensional analytic geometry and vectors, quadratic surfaces, arc length and curvature, limits and continuity, partial derivatives and their applications, tangent planes, optimization problems and Lagrange multipliers, multiple integrals, vector fields, line and surface integrals, Green's theorem, Stokes' theorem, the divergence theorem. PREREQUISITE: MATH 1920.

MATH 2421 - Honors Calculus II (4)
(1402). Differential and integral calculus with emphasis on theory; anti-derivatives, definite integrals, techniques of integration, sequences, and series. NOTE: Students may not receive credit for both MATH 2421 and 1920. PREREQUISITE: MATH 1421 or MATH 1920, and permission of instructor.

MATH 2422 - Honors Calculus III (4)
Multivariable calculus; vectors and matrices, partial derivative and applications, multiple integrals, line and surface integrals, Green's and Stokes' theorem. NOTE: Students may not receive credit for both MATH 2422 and 2110. PREREQUISITE: MATH 2421.

MATH 2701 - Discrete Structures (3)
Elementary logic; sets, relations, functions, orderings, equivalence relations, partitions: finite sets, modular arithmetic; natural numbers, mathematical induction, strings, string programs, connectedness, traversals, graph algorithms. NOTE: students may not receive credit for both MATH 2701 and MATH 2702. PREREQUISITE: MATH 1910. COREQUISITE: COMP 2701.

MATH 2702 - Intro Proof/Fundamental Math (3)
Logic, algebra of sets; forms of proof including mathematical induction; elementary combinatorics and binomial theorem; paradoxes, basic number theory, cardinality. PREREQUISITE: MATH 1910.

MATH 3120 - Differential Equations (3)
(3391). Ordinary differential equations including series solutions. PREREQUISITE: MATH 2110.

MATH 3221 - Elementary Number Theory (3)
Divisibility properties of integers; prime numbers; congruences; Diophantine equations; quadratic residues; number theoretic functions; Fermat's theorem and Euler's generalization; applications to cryptography; quadratic reciprocity law. PREREQUISITE: MATH 3242 , or one of MATH 2701, MATH 2702, or permission of instructor.

MATH 3242 - Intro Linear Algebra (3)
Systems of linear equations, matrices, elementary row and column operations, determinants; vector spaces and subspaces; linear transformations. PREREQUISITE: MATH 2110, or MATH 1920 and one of MATH 2701, 2702, or permission of instructor. [C]

MATH 3402 - Honors Mathematics IV (4)
Linear algebra and differential equations; vector spaces, bases, linear transformations, matrices, first and second order ordinary differential equations, systems, phase plane methods. NOTE: students with credit for this course cannot receive credit for MATH 3242 or MATH 3120. PREREQUISITE: MATH 2422.

MATH 3410 - Honors Seminar in Math I (1)
Exploration of origin and evolution of important mathematical ideas through examination of lives and work of famous mathematicians. PREREQUISITE or COREQUISITE: enrollment in one of the Honors Calculus courses (MATH 1421, 2421, 2422, or 3402), or admission to departmental or University Honors Program, or permission of instructor.

MATH 3411 - Honors Seminar in Math II (1)
Investigation of major topics in field of mathematics, such as Fundamental Theorem of Arithmetic, Prime Number Theorim, van der Waerden's Theorem, and nowhere differentiable functions. PREREQUISITE or COREQUISITE: enrollment in one of the Honors Calculus courses (MATH 1421, 2421, 2422, or 3402), or admission to departmental or University Honors Program, or permission of instructor.

MATH 3581 - College Geometry (3)
Axiomatic systems; major results from plane geometry; affine, projective, elliptic, and hyperbolic geometry; applications of differential calculus. PREREQUISITE: MATH 1910 and 2702.

MATH 4013 - Intro Combinatorial Geometry (3)
Combinatorial/structural properties of geometric objects; convexity, fundamental theorems, incidences, geometric graphs, distance, traversals and covers.

MATH 4015 - Intro to Hilbert Spaces (3)
Subspaces, projections, Riesz representation theorem, bounded linear operators, spectra, and compact operators. PREREQUISITE: MATH 3242, or permission of instructor.

MATH 4020 - Actuarial Mathematics (3)
Preparation for SOA Exam P, CAS Exam 1. Conditional probability, dependence, combinatorial principles, random variables, discrete and continuous probability distributions, expectation, marginal distributions, risk management concepts. COREQUISITE: MATH 4635.

MATH 4082 - Math/Mid School Teacher (3)
Capstone course consisting of more thorough study of fundamental concepts involving numbers, operations, functions, spatial relationships, data analysis; Excel, graphing calculators, modern software. PREREQUISITE: permission of instructor.

MATH 4151 - History of Mathematics (3)
Development of mathematics from earliest times to present; problem studies; parallel reading and class reports. PREREQUISITE: 21 hours in MATH courses including MATH 2110 and one of MATH 2701, MATH 2702, or permission of instructor. [I]

MATH 4171 - Special Problems in Math (1-3)
Directed individual study in selected area of mathematics chosen in consultation with instructor. Repeatable by permission of department chair. PREREQUISITE: permission of instructor.

MATH 4242 - Linear Algebra (3)
Linear transformations, polynomials, determinants, direct-sum decompositions, diagonalizable operators, rational and Jordan forms, inner product spaces, the spectral theorem. PREREQUISITE: MATH 3242.

MATH 4261 - Abstract Algebra (3)
Groups; homomorphisms; rings; integral domains; polynomials; fields. PREREQUISITE: MATH 2702 and 3242, or permission of instructor.

MATH 4350 - Intro Real Analysis I (3)
Real number system, functions and sequences, limits, continuity, differentiation; Riemann-Stieltjes integration, series of functions. PREREQUISITE: MATH 2110, 2702 and 3242. [W]

MATH 4351 - Intro Real Analysis II (3)
Integration theory; Riemann and Lebesgue integrals; partial differentiation, implicit function theorem. PREREQUISITE: MATH 4350, or permission of instructor.

MATH 4361 - Complex Variables (3)
Complex numbers; analytic functions; Cauchy-Riemann conditions; Taylor and Laurent series; integration. PREREQUISITE: MATH 2110.

MATH 4391 - Partial Diffrntial Equation I (3)
Laplace transforms; Fourier series; introduction to partial differential equations. PREREQUISITE: MATH 3120.

MATH 4392 - Partial Diffrntl Equation II (3)
Methods of characteristics; Green's functions; existence and regularity of solutions of boundary value; Cauchy problems. PREREQUISITE: MATH 4391.

MATH 4402 - Senior Honors Seminar (3)
In-depth study of one or more topics in mathematical sciences; emphasis on individual research and problem solving techniques; student writes and presents an Honors Thesis. PREREQUISITE: open only to senior Honors Students in mathematical sciences with permission of instructor.

MATH 4411 - Topology (3)
Introductory set theory; metric spaces; topological spaces; continuous functions; separation axioms; separability and countability axioms; connectedness and compactness. PREREQUISITE: MATH 2702 and either 3242 or 4350.

MATH 4607 - Intro SAS Programming (3)
SAS program statement syntax and flow control; selecting and summarizing observations; combing, dividing and updating SAS dataset; input tailoring and output customization; SAS built-in functions SAS Macro Language Programming and other SAS packages such as SAS/GRAPH and SAS/IML. PREREQUISITE: Introductory course in statistics.

MATH 4611 - Intro Applied Statistics (3)
Binomial, hypergeometric, Poisson, multinomial and normal distributions, test of hypotheses, chi-square test, t-test. F-test, etc, nonparametric tests; correlation analysis. Credit earned for this course may not be applied toward requirements for the Mathematical Sciences major. Students who have a calculus background are encouraged to take MATH 4635 instead of this course. PREREQUISITE: 6 hours in mathematics at level of MATH 1710 or above (except MATH 1601).

MATH 4614 - Probability/Statistics (3)
Probability distribution; statistical methods of parameter estimation and hypothesis testing; comparisons of two population means, proportions, and variances; analysis of variance, linear models and multiple regression. Students may not receive credit for both MATH 4614 and MATH 4635. PREREQUISITE: MATH 1920 and 2701.

MATH 4635 - Intro Probability Theory (3)
Basic probability theory, random variables, expectation, variance, covariance, moment generating functions; binomial, hypergeometric, Poisson, geometric, negative binomial, uniform, normal, exponential, Cauchy. chi-square, t, and F distributions; central limit theorem. functions of a random variable; bivariate, marginal, and conditional distributions. NOTE: Students may not receive credit for both MATH 4614 and MATH 4635. PREREQUISITE: MATH 1920.

MATH 4636 - Intro Statistical Theory (3)
Functions of two random variables; gamma, beta, multinomial, and bivariate normal distributions; Bayes estimators; maximum likelihood and methods of moments estimators; sufficient statistics, unbiasedness, confidence intervals, and hypothesis testing. PREREQUISITE: MATH 4335.

MATH 4637 - Statistical Methods (3)
Basic concepts of hypothesis testing; comparisons of two population means, proportions, and variances; analysis of variance; completely randomized designs, randomized block designs, Latin square designs; multiple comparisons; simple linear model and multiple regression; analysis of covariance. PREREQUISITE: MATH 4611 or 4635.

MATH 4640 - Intro Probability Models (3)
Basic concepts of discrete Markov chains; branching processes; Poisson processes; applications to modeling of population growth; applications to modeling of spread of infectious disease. PREREQUISITE: MATH 4635.

MATH 4721 - Numerical Analysis (3)
Derivation and application of computer-oriented, numerical methods for functional approximation, differentiation, quadrature, and solution of ordinary differential equations. PREREQUISITE: MATH 1920 and knowledge of some structured programming language.