**MATH**

**(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 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. 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 Combo 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 K-6 focusing on the Tennessee Academic Standards 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 K-6 focusing on the Tennessee Academic Standards 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 p-values, 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 Combo 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 - Pre-Calculus (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, 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: 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)**

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)**

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 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)**

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 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. NOTE: incoming students who have had a lower-division differential equations course may receive credit for MATH 3120 by passing the Departmental Examination outlined in the Credit by Exam policy. 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 MATH 2702, or 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)**

Explorations of basic and advanced Euclidean geometry and hyperbolic geometry using dynamic geometry software. PREREQUISITE: MATH 1910 and one of MATH 2702, COMP 2700 with a minimum grade of C-.

**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: put-call parity, binomial trees, arbitrage, risk-neutral pricing, random walk model, lognormality and the binomial model, estimating volatility, Black-Scholes 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, Black-Scholes equation, all-or-nothing options, measurement and behavior of volatility, bond price models, Black-Derman-Toy model. PREREQUISITE: MATH 4028.

**MATH 4080 - Math/Sec School Teachers I (3)**

Examination of mathematics taught in grades 9-12 focusing on the Tennessee Academic Standards conceptual categories of Number and Quantity and Algebra. Credit earned for this course may not be applied toward requirements for the Mathematical Sciences major. PREREQUISITE: MATH 4082. COREQUISITE: ICL 4080.

**MATH 4081 - Math/Sec School Teachers II (3)**

Examination of mathematics taught in grades 9-12 focusing on the Tennessee Academic Standards conceptual categories of Functions and Statistics and Probability. Credit earned for this course may not be applied toward requirements for the Mathematical Sciences major. PREREQUISITE: MATH 4080. COREQUISITE: ICL 4081

**MATH 4082 - Math/Mid School Teacher (3)**

Examination of mathematics taught in grades 7 and 8 focusing on the Tennessee Academic Standards Domains of Ratios and Proportional Reasoning, Number System, Functions, Expressions and Equations, and Statistics and Probability. Credit earned for this course may not be applied toward requirements for the Mathematical Sciences major. 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, max-flow min-cut theorem, basic algorithms. PREREQUISITE: MATH 2702 or COMP 2700 with a minimum grade of C-.

**MATH 4085 - Introduction to Combinatories (3)**

Combinations and permutations, counting techniques, recurrence relations, generating functions, block designs, finite planes, and coding theory. PREREQUISITE: MATH 2702 or COMP 2700 with a minimum grade of C-.

**MATH 4086 - Analytic Number Theory (3)**

Partial summation, Euler-Maclaurin 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.

**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.

**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 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)**

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, 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 2110, or MATH 1920 and one of MATH 2702 or COMP 2700 or permission of instructor 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. 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 4635.

**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, non-linearity, 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 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.