Note: All cadets must have at least six hours of mathematics. MA 114 does not fulfill a mathematics requirement. MA 114 is acceptable as elective credit only with approval of a cadet’s curricular head.
MA 103. MATRIX ALGEBRA
Introduction to matrices. Matrix determinant and inverse. Elementary transformations and systems of linear equations: existence and uniqueness of solution, Cramer’s Rule, Gaussian elimination with back-substitution. Introduction to linear transformations: eigenvalues and eigenvectors, matrix trace.
MA 105. INTRODUCTION TO PROBABILITY AND STATISTICS I
A study of problem solving skills, counting principles, finite probability theory, descriptive statistics and the binomial and normal distributions. Computer/calculator applications will be chosen to enhance understanding of the topics.
MA 106. INTRODUCTION TO PROBABILITY AND STATISTICS II
A continuation of MA 105. Topics include random variables, correlation, regression, confidence intervals, and hypothesis testing. Computer/calculator applications will be chosen to enhance understanding of the topics. Prerequisite: MA 105.
MA 108. INTRODUCTION TO PROBABILITY & STATISTICS
This course introduces all of the important topics that will be needed to begin a serious study of probability and statistics. Descriptive statistics; counting techniques and basic rules of probability; binomial and normal distributions and the sampling distribution of the sample mean; basics of inference on the population mean using interval estimates and tests of hypotheses. Incoming cadets with credit for AP Statistics do not need to take this course.
MA 110. MATHEMATICAL SOFTWARE
Introduction to the use of mathematical software packages Matlab and Mathcad in applied mathematics, engineering and physics.
MA 114. PRE-CALCULUS MATHEMATICS
Equations and inequalities; functions and their graphs; polynomial and rational functions; exponential and logarithmic functions; trigonometric functions. Recommended only for those cadets who plan to take MA 123. See note above.
MA 123. CALCULUS & ANALYTIC GEOMETRY I
Plane analytic geometry with single variable differential calculus. Limits, derivatives, applications of derivatives, and derivatives of transcendental functions and basic integration formulas. Prerequisites: Placement Test or Pass Grade in MA 114.
MA 124. CALCULUS & ANALYTIC GEOMETRY II
A continuation of MA 123. Integration and its applications, methods of integration, L’Hopital’s Rule, improper integrals, infinite sequences and series, Taylor Polynomials. Prerequisite: A grade of C or higher in MA 123.
MA 125. QUANTITATIVE METHODS I
A study of functions, linear and nonlinear models, systems of linear equations, matrices and applications, and an introduction to the mathematics of finance.
MA 126. QUANTITATIVE METHODS II
A study of the basic concepts of differentiation and integration to include partial derivatives and the Method of Lagrange emphasizing the techniques and applications relevant to business and economics. Prerequisites: C or better in MA 125.
MA 133. MATHEMATICAL MODELING I
A series of mathematical models are introduced by different faculty members. Each model is developed over several periods. The content will vary from semester to semester but instructors will focus on the modeling and problem solving aspects of their topics.
MA 134. MATHEMATICAL MODELING II
A continuation of MA 133. More examples of mathematical modeling and problem formulation and solution techniques.
MA 215. CALCULUS WITH ANALYTIC GEOMETRY III
A continuation of MA 124; Conic sections, parametric equations, polar coordinates, vectors, vector-valued functions, partial derivatives, improper and multiple integrals. Prerequisite: A grade of C or higher in MA 124.
MA 220. PROBABILITY & STATISTICS FOR ENGINEERS & SCIENTISTS
This is a calculus-based treatment of probability and statistics designed for scientists and engineers. Topics would include: classification of data by graphical and numerical methods; intro to probability to include definitions and theorems; discrete random variables including binomial and Poisson distributions, expectation and variance calculations; continuous random variables to include uniform, exponential, normal, Weibull, Gamma, and Chi-squared distributions; hypothesis testing and least-squares linear regression. Prerequisite: MA 124.
MA 301. HIGHER MATHEMATICS FOR ENGINEERS AND SCIENTISTS
Vector analysis, infinite series convergence, Taylor and Maclaurin Series, Fourier Series and series solutions to differential equations. Prerequisites: MA 215 and MA 311.
MA 303. ADVANCED CALCULUS I
A rigorous treatment of the following topics: limits, continuity, derivatives of real valued functions of a single real variable, Rolle’s Theorem and the mean value theorem, L’Hopital’s rule, sequences and series. Prerequisite: MA 124.
MA 304. ADVANCED CALCULUS II
Implicit-function theorems; Jacobians; vector and scalar point functions; gradient; divergence; line, surface and volume integrals. Prerequisite: MA 303.
MA 305. ELEMENTARY LINEAR ALGEBRA
Vectors; matrices; determinants; systems of linear equations; linear transformations. A study of the theoretical and computational aspects pertaining to matrices and vector spaces, including: systems of linear equations, Gaussian elimination, LU decomposition, determinants, eigenvalues and eigenvectors, linear independence, span, bases, linear transformations, inner product spaces and least square approximation. Computer software packages will be introduced and utilized as part of the course. Prerequisite: MA 103 or permission of the instructor.
MA 306. ELEMENTARY NUMBER THEORY
Properties of integers, prime numbers, number theoretic functions, congruencies. Diophantine equations. Prerequisite: Permission of the instructor.
MA 307. APPLIED STATISTICS FOR THE SOCIAL SCIENCES
Treatment of categorical data, contingency tables, analysis of variance, and distribution-free methods. The course will use a statistical software package. Prerequisite: Either MA 106 or MA 108 or MA 220.
MA 310. MATLAB PROGRAMMING
Advanced MATLAB functionality, geometric techniques (Monte Carlo, random walks, and Levy Flights), and the brute force, nearest neighbor, simulated annealing, and genetic algorithms applied to the Traveling Salesman Problem (TSP). The course concludes with the development of a TSP graphical user interface (GUI) that integrates these algorithms. Prerequisite: MA 110, ME 203, or PY 223.
MA 311. ELEMENTARY DIFFERENTIAL EQUATIONS
Ordinary differential equations; applications; Laplace transforms; Systems of ODEs. Prerequisite: MA 124.
MA 319. MATHEMATICAL METHODS OF OPERATIONS RESEARCH
Mathematical modeling, linear programming, allocation models, network models, scheduling models. Prerequisites: MA 103 and MA 124.
MA 326. PROBABILITY AND STATISTICS
Simple, discrete, and continuous probability distributions. Sampling from probability distributions and finite populations. Prerequisite: MA 215 and MA 108 or MA 220.
MA 330W. HISTORY OF MATHEMATICS
This is a topics course in the history of mathematics beginning with the ancients. This is a guided tour of the most important aspects from the beginnings of recorded mathematical activity through the development of calculus. Topics beyond the development of the calculus will be covered as time permits. Coverage includes the motives, influences, and methods affecting the development of algebra, geometry, trigonometry, and calculus in Mesopotamian, Egyptian, Greek, Islamic, Indian, and European civilizations. Prerequisites: One semester of calculus or permission of the instructor. Prerequisite: MA 123 or MA 126 (Preference is given to AM Majors).
MA 401. MODERN ALGEBRA
Basic algebraic properties of groups, rings and fields.
MA 405. STATISTICS
A continuation of MA 326; probability distributions, estimation, hypothesis testing, regression analysis and techniques of experimental design. Prerequisite: MA 326.
MA 407. COMPLEX VARIABLES
Properties of complex numbers; analytic functions; power series, residues and poles; Laurent series. Prerequisite: MA 301, MA 304, or consent of department head.
MA 422. GRAPH THEORY
Graphs, digraphs trees, connectivity, cycles and transferability, and planar graphs. Prerequisite: Permission of the instructor.
MA 432. NUMERICAL ANALYSIS
Numerical interpolation; error analysis; numerical solution of ordinary and partial differential equations and simultaneous linear equations. Recommended for cadets contemplating a career in computing. Prerequisites: MA 110, MA 215 and MA 311.
MA 433. NUMERICAL SOLUTIONS OF DIFFERENTIAL EQUATIONS
Introduction to MATLAB. Numerical methods for ordinary differential equations: Taylor series, Euler and Modified Euler, Runge-Kutta. Multi-step methods, Milne’s method, Adams-Moulton method. Convergence criteria and comparison of methods. Numerical methods for partial differential equations. Convergence, stability and consistency. Prerequisite: MA 311 or consent of instructor.
MA 451-459. INDEPENDENT STUDY
1—0—1 TO 3—0—3
Selected areas such as topology, geometry, algebra, real analysis. Recommended for cadets contemplating doctoral programs in mathematics. Prerequisite: consent of department head.
MA 490W. RESEARCH PRACTICUM IN APPLIED MATHEMATICS
An undergraduate research experience in an area of applied mathematics under the tutelage of a member of the Math & CS faculty. Projects are agreed to by cadet and faculty member and culminate with an oral presentation and with a publishable (not necessarily published) paper as determined by the faculty member. Prerequisite: 28 credit hours in Math coursework or First Class Standing. Writing Intensive (W).
MA 471-479. TOPICS IN MATHEMATICS
Selected topics in mathematics such as graph theory, topology, dynamic systems, partial differential equations, spline approximation and operator theory. Prerequisite: Permission of Department Head.