
(MATH) MATHEMATICS Department of Mathematical Sciences Irene Lasiecka, 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 20112019. Special Topics in Mathematics. (13). Topics are varied and in online class listings. PREREQUISITE: permission of instructor. MATH 401019. Special Topics in Mathematics and Statistics. (13). 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. PREREQUISITE: a minimum score of 14 on the ALEKS Math Assessment.
MATH 1420  Foundations of Mathematics (3) Algebra review and applications; functions, graphs, permutations, combinations; introduction to probability and statistics; problem solving. PREREQUISITE: MATH 1100 or MATH 1710 with a minimum grade of C or a minimum score of 30 on the ALEKS Math Assessment. Special sections of MATH 1420 that meet 4 days a week require a minimum score of 14 on the ALEKS Math Assessment. [G]
MATH 1421  Honors Calculus I (4) 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 I (3) Examination of mathematics taught in grades K6 focusing on the Common Core Domains of Counting and Cardinality, Operations and Algebraic Thinking, Number and Operations in Base 10, Number and Operations  Fractions, and Expressions and Equations. PREREQUISITE: MATH 1100 or MATH 1420 or MATH 1710 with a minimum grade of C or a minimum score of 46 on the ALEKS Math Assessment.
MATH 1481  Math/Elem School Teachers II (3) Examination of mathematics taught in grades K6 focusing on the Common Core Domains of Ratios and Proportional Reasoning, Number System, Measurement and Data, Expressions and Equations, Geometry, and Statistics and Probability. PREREQUISTE: MATH 1480 with a minimum grade of C.
MATH 1530  Prob/Statistics/Non Calculus (3) 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 pvalues, basic concepts of correlation and regression analyses; MINITAB. NOTE: Math majors may not use this course as part of the major. PREREQUISITE: MATH 1100 or MATH 1420 or MATH 1710 with a minimum grade of C or a minimum score of 46 on the ALEKS Math Assessment. [G]
MATH 1710  College Algebra (3) 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: A minimum score of 46 on the ALEKS Math Assessment. Special sections of MATH 1710 that meet 4 days a week require a minimum score of 30 on the ALEKS Math Assessment. [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: MATH 1710 with a minimum grade of C or a minimum score of 61 on the ALEKS Math Assessment.
MATH 1730  PreCalculus (4) 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, halfangle and doubleangle 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: MATH 1710 with a minimum grade of C or a minimum score of 61 on the ALEKS Math Assessment. [G]
MATH 1830  Elementary Calculus (3) 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 or MATH 1730 with a minimum grade of C or a minimum score of 61 on the ALEKS Math Assessment. [G]
MATH 1900  Experience/Calculus (1) Indepth 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) 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 or MATH 1730 with a minimum grade of C or a minimum score of 76 on the ALEKS Math Assessment. [G]
MATH 1920  Calculus II (4) 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 2110  Calculus III (4) Multivariable calculus including threedimensional 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) Differential and integral calculus with emphasis on theory; antiderivatives, 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 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) Introduction to ordinary differential equations; first order differential equations; linear differential equations of all orders; series methods for linear equations; Lapalce transform; systems of differential equations; applications. PREREQUISITE: MATH MATH 1920 or MATH 2421.
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 2702, COMP 2700 with a minimum grade of C 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 2702, COMP 2700 with a minimum grade of C or permission of instructor.
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 Theorem, 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 one of MATH 2702, COMP 2700 with a minimum grade of C.
MATH 4001  Math Connect/Function/Model (3) Use of mathematics as an aid to understand problems from social and life sciences; insightful understanding of powerful mathematical modeling techniques. PREREQUISITE: Enrollment limited to students in the Tigers Teach program and MATH 1910, 1920, 2702
MATH 4017  Intro/Math Quantum Mechanics (3) Hilbert space; Spectral Theorem and associated functional calculus, Newtonian and Hamiltonian classical mechanics with examples from Schroedinger's equation, simple harmonic motion, simple relativistic versions; Dirac equations and Quantum Chemistry. PREREQUISITE: 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 4022  Fin Math I/Theory of Interest (3) Preparation for SOA Exam FM, CAS Exam 2. Interest rates and time value of money, annuity valuation, loan repayment, bond valuation and amortization, internal rates of return, the term structure of interest rates, asset liability management, duration and immunization. PREREQUISITE: MATH 1920.
MATH 4025  Fin Math II/Derivatives (3) Preparation for SOA Exam FM, CAS Exam 2. Financial risk concepts; derivatives, forwards, futures, short and long positions, call and put options, spreads, collars, hedging, arbitrage, swaps. Definitions and evaluations of basic derivatives contracts and trading strategies. PREREQUISITE: MATH 1920
MATH 4028  Models for Fin Econ/Options (3) Various aspects of theory and practice of options pricing and related topics: putcall parity, binomial trees, arbitrage, riskneutral pricing, random walk model, lognormality and the binomial model, estimating volatility, BlackScholes formula, option Greeks, market making, delta hedging, Asian, barrier, compound, gap and exchange options. PREREQUISITE: MATH 4025.
MATH 4030  Model Fin Econ/Adv Pre Thry (3) Continuation of MATH 4028; lognormal model of stock prices, distribution of asset prices, risk neutral valuation, true valuation, simulated stock prices, Monte Carlo valuation, geometric Brownian motion, Sharpe ratio, Ito's lemma, BlackScholes equation, allornothing options, measurement and behavior of volatility, bond price models, BlackDermanToy model. PREREQUISITE: MATH 4028.
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 4083  Dynamical Systems/Chaos (3) Examples of dynamic systems, one dimensional maps (periodic points, stability of fixed points, sensitivity dependence on initial conditions), two dimensional maps (sinks, sources and saddles, linear and nonlinear maps, Julia and Mandelbrot sets), chaos (Lyapunov exponents, chaotic orbits, basins of attraction), fractals (probabilistic and deterministic constructions, fractals dimension), differential equations (one and higher dimensional linear equations, periodic orbits and limit sets). COREQUISITE: MATH 3120 or MATH 3242.
MATH 4084  Introduction to Graph Theory (3) Applications, connectivity, trees, paths and cycles, factors, matching and coverings, vertex and edge colorings, planar graphs, directed graphs, maxflow mincut theorem, basic algorithms. PREREQUISITE: MATH 2702 or COMP 2700 with a minimum grade of C and MATH 3221 or MATH 3581, or permission of instructor.
MATH 4085  Introduction to Combinatories (3) Convexity and fundamental theorems (Radon's Theorem, Helly's Theorem), geometric incidences, geometric graphs (planar graphs, proximity graphs), Pick's Theorem, distance problems in the plane, geometric transversals and covers. PREREQUISITE: One of MATH 2702, COMP 2700 with a minimum grade of C and MATH 3221 or MATH 3581.
MATH 4086  Analytic Number Theory (3) Partial summation, EulerMaclaurin summation formula, basic arithmetic functions and their mean values; Dirichlet series, Euler products; Meilin function and prime number theorem; characters and primes in arithmetic progressions, basic sieve methods. PREREQUISITE: MATH 3221. COREQUISITE: MATH 4361
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 2702, COMP 2700 or permission of instructor.
MATH 4171  Special Problems in Math (13) 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, directsum 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; RiemannStieltjes integration, series of functions. PREREQUISITE: MATH 2110, 2702 and 3242.
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; CauchyRiemann conditions; Taylor and Laurent series; integration. PREREQUISITE: MATH 2110.
MATH 4391  Partial Diffrntl 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 4396  Perturbation Methods (3) Asymptotic approximations, boundary layers, matched asymptotic expansions, multiple scales, geometric optics approximation (WKB), homogenization, application to differential equations. PREREQUISITE: MATH 2110 and MATH 3120.
MATH 4402  Senior Honors Seminar (3) Indepth 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 builtin 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, chisquare test, ttest. Ftest, 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.
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 one of MATH 2702, COMP 2700 with a minimum grade of C.
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. chisquare, 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  Intro/Stat Models/Analysis (3) Basic concepts of statistical modeling and analysis with extensive us of R; topics include hypothesis testing, 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 MATH 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 4643  Intro Regression/Time Ser Anyl (3) Hypothesis testing and confidence intervals for linear regression models, examination of residuals, calculation of elasticities and partial correlations, heteroscedasticity, serial correlation, multicolinearity, nonlinearity, deterministic and stochastic time series models, stationary time series and autocorrelation functions, diagnostic checks, forecasting using ARIMA models. PREREQUISITE: MATH 4636.
MATH 4721  Numerical Analysis (3) Derivation and application of computeroriented, numerical methods for functional approximation, differentiation, quadrature, and solution of ordinary differential equations. PREREQUISITE: MATH 1920 and knowledge of some structured programming language.
