COURSE  TITLE  CREDIT HOURS  
MA100 20161  PRECALCULUS MATHEMATICS  3.5 (BS=0.0, ET=0.0, MA=3.5) 

Scope  Offerings  
SCOPE This course prepares cadets with background deficiencies in algebra and trigonometry for the core mathematics program. The course develops fundamental skills in algebra, trigonometry, and functions, through an introduction to mathematical modeling and problem solving. Since this course does not count toward graduation requirements; cadets enrolled in MA100 will forfeit an elective opportunity. 


COURSE  TITLE  CREDIT HOURS  
MA103 20161  MATH MODELING/INTRO CALCULUS  4.5 (BS=0.0, ET=0.0, MA=4.5) 

Scope  Offerings  
SCOPE MA103 is the first course of the mathematics core curriculum. It emphasizes applied mathematics through modeling. Students develop effective strategies to solve complex and often illdefined problems. The course exercises a wide array of mathematical concepts while nurturing creativity, critical thinking, and learning through activities performed in disciplinary and interdisciplinary settings. The course introduces calculus using continuous and discrete mathematics while analyzing dynamic change in applied problems. Students employ a variety of technological tools to enhance the ability to visualize concepts, to explore ideas through experimentation and iteration, to complete complex and timeconsuming computations, and to develop numerical, graphical, and analytical solutions that enhance understanding. 


COURSE  TITLE  CREDIT HOURS  
MA104 20232  CALCULUS I  4.5 (BS=0.0, ET=0.0, MA=4.5) 

Scope  Offerings  
SCOPE This is the second semester of the mathematics core curriculum. It provides a foundation for the continued study of mathematics and for the subsequent study of the physical sciences, the social sciences, and engineering. MA104 covers topics in single variable differential and integral calculus, parametric equations, 3dimensional geometry, and vectors. Throughout the course, mathematical models motivate the study of topics such as optimization, accumulation, change in one variable, motion in space, 1st order differential equations, and other topics from the natural, social, and decision sciences. An understanding of course material is enhanced through the use of computer algebra systems. 


COURSE  TITLE  CREDIT HOURS  
MA153 20161  MATH MODELING/INTRO DIF EQ  4.5 (BS=0.0, ET=0.0, MA=4.5) 

Scope  Offerings  
SCOPE This is the first course of a twosemester advanced mathematics sequence for selected cadets who have validated single variable calculus and demonstrated strength in the mathematical sciences. It is designed to provide a foundation for the continued study of mathematics, sciences, and engineering. This course emphasizes the interaction between mathematics and the physical sciences through modeling with differential equations. Topics may include a study of first order differential equations, first order difference equations, second order linear equations, systems of first order linear and nonlinear equations, numerical methods, and nonlinear equations and stability. An understanding of course material is enhanced through the use of a computer algebra system. 


COURSE  TITLE  CREDIT HOURS  
MA204X 20242  CALCULUS I AND II  4.5 (BS=0.0, ET=0.0, MA=0.0) 

Scope  Offerings  
SCOPE An alternative version of the second semester of the mathematics core curriculum. This course, intended for students who have had a full year of high school calculus, provides a short review of singlevariable calculus before progressing into multivariable differential and integral calculus. It will also cover vectors and geometry of Euclidean space, vector functions, and vector calculus. Throughout the course mathematical models motivate the study of topics such as optimization, accumulation, change in several variables, and other topics from the natural, social, and decision sciences. Students who successfully complete the course will receive validation credit for MA104 and equivalency credit for MA205. **This is a pilot course and must be approved by the Curriculum Committee NLT AY251 to continue.** 


COURSE  TITLE  CREDIT HOURS  
MA205 20231  CALCULUS II  4.0 (BS=0.0, ET=0.0, MA=4.0) 

Scope  Offerings  
SCOPE This course provides a foundation for the continued study of mathematics and for the subsequent study of the physical sciences, social sciences, and engineering. MA205 covers topics in multivariable differential and integral calculus, vectors and geometry of Euclidean space, vector functions, and vector calculus. Throughout the course mathematical models motivate the study of topics such as optimization, accumulation, change in several variables, and other topics from the natural, social, and decision sciences. An understanding of course material is enhanced through the use of computer algebra systems. 


COURSE  TITLE  CREDIT HOURS  
MA206 20192  PROBABILITY & STATISTICS  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This is the final course in the mathematics core curriculum. The course develops cadet ability to structure their reasoning under conditions of uncertainty and presents fundamental probability and statistical concepts that support the USMA core curriculum. Coverage includes data analysis, probabilistic models, independence, simulation, random variables and their distributions, hypothesis testing, confidence intervals, and linear regression. The course also introduces engineering applications of probability and statistics techniques. Applied problems motivate concepts, and technology enhances understanding, problem solving, and communication. 


COURSE  TITLE  CREDIT HOURS  
MA255 20162  ADV MULTIVARIABLE CALCULUS  4.5 (BS=0.0, ET=0.0, MA=4.5) 

Scope  Offerings  
SCOPE This is the second course of a twosemester advanced mathematics sequence for selected cadets who have validated single variable calculus and demonstrated strength in the mathematical sciences. It is designed to provide a foundation for the continued study of mathematics, sciences, and engineering. This course consists of an advanced coverage of topics in multivariable calculus. Topics may include a study of infinite sequences and series, vectors and the geometry of space, vector functions, partial derivatives, multiple integrals, and vector calculus. An understanding of course material is enhanced through the use of a computer algebra system. 


COURSE  TITLE  CREDIT HOURS  
MA256 20232  ADV PROBABILITY AND STATISTICS  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This is the advanced version of the final course in the mathematics core curriculum. The course develops cadet ability to structure their reasoning under conditions of uncertainty and presents fundamental probability and statistical concepts that support the USMA core curriculum. Coverage includes data analysis, probabilistic models, independence, simulation, random variables (including jointly distributed random variables) and their distributions, hypothesis testing, confidence intervals, linear regression and analysis of categorical data. Emphasis will be on model based approaches and significant time will be spent on selecting an appropriate model and assessing its validity. Applied problems illustrate concepts, and technology enhances understanding, problem solving, and communication. 


COURSE  TITLE  CREDIT HOURS  
MA289 20242  INTRO IND STUDY IN MATH (1CR)  1.0 (BS=0.0, ET=0.0, MA=0.0) 

Scope  Offerings  
SCOPE This course is an individually supervised research and study program. The scope of the course is tailored to the needs of the project and interests of the cadet in consultation with a faculty member. Activities vary by project, but the primary purpose is for the cadet to engage in independent study and produce a work of scholarship. With the approval of one of the Program Directors in the Department of Mathematical Sciences, the cadet chooses a project of interest and is supervised by a faculty member. Cadets are expected to perform a total of 40 hours of work for the semester. A final presentation and final project deliverable are required. 


COURSE  TITLE  CREDIT HOURS  
MA289A 20242  INTRO IND STUDY IN MATH (1CR)  1.0 (BS=0.0, ET=0.0, MA=0.0) 

Scope  Offerings  
SCOPE This course is an individually supervised research and study program. The scope of the course is tailored to the needs of the project and interests of the cadet in consultation with a faculty member. Activities vary by project, but the primary purpose is for the cadet to engage in independent study and produce a work of scholarship. With the approval of one of the Program Directors in the Department of Mathematical Sciences, the cadet chooses a project of interest and is supervised by a faculty member. Cadets are expected to perform a total of 40 hours of work for the semester. A final presentation and final project deliverable are required. 
No Course Offerings 

COURSE  TITLE  CREDIT HOURS  
MA289B 20242  INTRO IND STUDY IN MATH (1CR)  1.0 (BS=0.0, ET=0.0, MA=0.0) 

Scope  Offerings  
SCOPE This course is an individually supervised research and study program. The scope of the course is tailored to the needs of the project and interests of the cadet in consultation with a faculty member. Activities vary by project, but the primary purpose is for the cadet to engage in independent study and produce a work of scholarship. With the approval of one of the Program Directors in the Department of Mathematical Sciences, the cadet chooses a project of interest and is supervised by a faculty member. Cadets are expected to perform a total of 40 hours of work for the semester. A final presentation and final project deliverable are required. 
No Course Offerings 

COURSE  TITLE  CREDIT HOURS  
MA363 20232  ORDINARY DIFFERENTIAL EQUATION  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course introduces the mathematical theory of ordinary differential equations and its application to problems in science and engineering. The course emphasizes the conceptual and theoretical understanding of differential equations necessary for advanced study in mathematical sciences. The course covers first and second order differential equations, systems of differential equations, and infinite series. Students will utilize a range of fundamental solution techniques  analytical, qualitative, and numerical. Special focus will be placed on the theory of existence and uniqueness of solutions. 


COURSE  TITLE  CREDIT HOURS  
MA364 20232  ENGINEERING MATHEMATICS  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course provides additional mathematical techniques and deepens the understanding of concepts in mathematics to support continued study in science and engineering. Emphasis is placed upon using mathematics to gain insight into natural and manmade phenomena that give rise to problems in differential equations and infinite series representations of functions. Analytic and numerical solutions to differential equations and systems of differential equations are found using a variety of techniques. Linear algebra topics include solutions to homogeneous and nonhomogeneous systems of equations. An introduction to classical partial differential equations is also included. 


COURSE  TITLE  CREDIT HOURS  
MA365 20192  ADV MATH FOR ENGRS/SCIENTISTS  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This is a course designed for the advanced mathematics student that has completed courses in differential equations and vector calculus (those that have completed MA153 and MA255) and will study ME, EE, NE, Physics or Space Science. MA365 begins where the advanced mathematics program ends. The advanced engineering course offering includes topics in linear algebra, complex variables, Fourier series, partial differential equations, and computational mathematics. 


COURSE  TITLE  CREDIT HOURS  
MA367 20202  MATH FOR THE SOCIAL SCIENCES  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE MA367 is a required course for those majoring in economics and is available to any who would like to develop their understanding of the mathematical tools applied to common methods of inquiry in several of the social sciences including, but not limited to, psychology and political science. The course develops student ability to use and develop mathematical models to quantify the relationship between variables, actors, and outcomes. The course helps formalize and quantify the properties of these relationships. The course continues to develop math skills introduced in the core math program, and it introduces more advanced math topics that serve as fundamental skills required for modeling in upper level microeconomics, macroeconomics, and econometrics courses. Specific topics include multivariable optimization, including linear and nonlinear programming, differential equations, stochastic modeling, and an introduction to dynamic programming. This course is designed to demonstrate the relevance of mathematics to the modem practice of analysis in the social sciences and to help prepare future Army leaders to use sound logic and relevant evidence to make convincing arguments. 


COURSE  TITLE  CREDIT HOURS  
MA371 20131  LINEAR ALGEBRA  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course emphasizes both the computational and theoretical aspects of linear algebra one encounters in many subjects ranging from economics to engineering. The course covers solutions of linear systems of equations and the algebra of matrices. The foundational aspects of vector spaces and linear transformations to include linear dependence and independence, subspaces, bases and dimension, inner products, and orthonormalization are developed. This is rounded out with a detailed investigation of eigenvalues and eigenvectors as they relate to diagonalization, quadratic equations, and systems of differential equations. The Invertible Matrix Theorem is explored as the conceptual/theoretical thread of the course. A computer algebra system is used to explore concepts and compute solutions to problems. Applications of the course material are included in the form of special problems to illustrate its wide scope. 


COURSE  TITLE  CREDIT HOURS  
MA372 20131  INTRODUCTION TO DISCRETE MATH  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE The purpose of this course is to introduce topics in Discrete Mathematics, providing a foundation for further study and application. The topics covered are useful to both the applied mathematician and the computer scientist. They include propositional logic, elements of set theory, combinatorics, relations, functions, partitions, methods of proof, induction and recursion, digraphs, trees, finite state machines, and algebraic systems. Specific applications to computer science are presented. 


COURSE  TITLE  CREDIT HOURS  
MA376 20201  APPLIED STATISTICS  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course builds on the foundations presented in the core probability and statistics course to provide a broad introduction to some of the most common models and techniques in applied statistics. The mathematical basis for each of the models and techniques is presented with particular emphasis on the development of the required test statistics and their distributions. Topics covered include hypothesis testing, analysis of variance, categorical data analysis, regression analysis, and nonparametric methods. 


COURSE  TITLE  CREDIT HOURS  
MA381 20131  NONLINEAR OPTIMIZATION  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course provides an undergraduate presentation of nonlinear topics in mathematical programming that builds on multivariable Calculus II. The emphasis of this course is on developing a conceptual understanding of the fundamental topics introduced. These topics include general convexity, convex functions, derivativebased multivariable search techniques, minima and maxima of convex functions, gradients, hessian matrices, Lagrange Multipliers, FritzJohn and KuhnTucker optimality conditions, and constrained and unconstrained optimization. Computer software is used to explore and expose various key ideas throughout the course. 


COURSE  TITLE  CREDIT HOURS  
MA383 20131  FOUNDATIONS OF MATH  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course introduces the student to the methods and language of upper division mathematics. It presents formal set theory, and introduces the student to the methods of formulating and writing mathematical proofs. Finally, it provides the student a rigorous introduction to the theory of relations, functions, and infinite sets. 


COURSE  TITLE  CREDIT HOURS  
MA385 20132  CHAOS AND FRACTALS  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course introduces topics in fractal geometry and chaotic dynamical systems, providing a foundation for applications and further study. The topics from fractal geometry include the military applications of image analysis and data storage. The chaotic dynamical systems studied in the course are one, two, and threedimensional, nonlinear, discrete and continuous dynamical systems. Topics include the logistics equation, the Henon attractor, the Lorenz equations, bifurcation theory, Julia sets, and the Mandelbrot set. These topics have applications in many fields of science, and examples from biology, meteorology, engineering, and the social sciences are studied. The course integrates concepts introduced in the core mathematics courses. 


COURSE  TITLE  CREDIT HOURS  
MA386 20201  INTRO TO NUMERICAL ANALYSIS  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course develops an understanding of the methods for solving mathematical problems using a digital computer. Algorithms leading to solution of mathematical problems will be examined for consistency, stability, and convergence. After a brief review of calculus theory, a study of error analysis and computer arithmetic will provide the framework for the study of the following topics: solutions of equations of one variable, solutions of linear and nonlinear systems of equations, the use of polynomials to approximate discrete data, curve fitting, numerical integration and differentiation, and the approximation of continuous functions. Special problems will incorporate computer graphics and the use of mathematical software libraries to produce numerical solutions of applied problems. 


COURSE  TITLE  CREDIT HOURS  
MA387 20132  MATHEMATICAL ANALYSIS I  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE A one semester course providing a rigorous introduction to the calculus of a single variable. The course is designed to introduce the student to the foundations of the calculus necessary for advanced undergraduate and graduate studies in applied mathematics and engineering. Course coverage includes a treatment of the structure of the real number system, sequences, continuous functions, and differentiation. 


COURSE  TITLE  CREDIT HOURS  
MA388 20222  SABERMETRICS  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course builds on the statistical foundation of the core mathematics sequence by exploring the application of statistical concepts to sports analytics. Students develop skills and apply statistical techniques appropriate for baseball and other sports including: regression, forecasting, and stochastic processes. Guest lectures and a course trip section to discuss Sabermetrics at the baseball Hall of Fame in Cooperstown, NY are part of this course (when available). Software packages (Mathematica, Excel) are used as decision support tools to investigate application problems and augment understanding of course material. 


COURSE  TITLE  CREDIT HOURS  
MA389 20171  INDIV STUDY IN MATHEMATICS  2.0 (BS=0.0, ET=0.0, MA=0.0) 

Scope  Offerings  
SCOPE This course is intended for individually supervised research and study, in order to familiarize cadets with techniques used in advanced scientific study. The primary purpose is to prepare students for independent research in mathematics with the essential skills required. With the approval of the Head of the Department, the cadet chooses a research project of interest and is supervised by a faculty member conducting the research. 


COURSE  TITLE  CREDIT HOURS  
MA389A 20241  INDIV STUDY IN MATHEMATICSA  2.0 (BS=0.0, ET=0.0, MA=0.0) 

Scope  Offerings  
SCOPE This course is intended for individually supervised research and study, in order to familiarize cadets with techniques used in advanced scientific study. The primary purpose is to prepare students for independent research in mathematics with the essential skills required. With the approval of the Head of the Department, the cadet chooses a research project of interest and is supervised by a faculty member conducting the research. 


COURSE  TITLE  CREDIT HOURS  
MA389B 20241  INDIV STUDY IN MATHEMATICSB  2.0 (BS=0.0, ET=0.0, MA=0.0) 

Scope  Offerings  
SCOPE This course is intended for individually supervised research and study, in order to familiarize cadets with techniques used in advanced scientific study. The primary purpose is to prepare students for independent research in mathematics with the essential skills required. With the approval of the Head of the Department, the cadet chooses a research project of interest and is supervised by a faculty member conducting the research. 


COURSE  TITLE  CREDIT HOURS  
MA391 20222  MATHEMATICAL MODELING  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course is designed to give cadets the opportunity to develop skills in model construction and model analysis while addressing interesting scenarios with practical applications from a wide variety of fields. This course serves as the entry point for both the Mathematical Sciences major and the Operations Research major. The course addresses the complex process of translating realworld events into mathematical language, solving the resulting mathematical model (iterating as necessary), and interpreting the results in terms of real world issues. Topics include model development from data, regression, general curve fitting strategies, and deterministic and stochastic model development. Interdisciplinary projects based on actual modeling scenarios are used to integrate the various topics into a coherent theme. 


COURSE  TITLE  CREDIT HOURS  
MA391 20251  MATHEMATICAL MODELING  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course is designed to give cadets the opportunity to develop skills in model construction and model analysis while addressing interesting scenarios with practical applications from a wide variety of fields. The course addresses the complex process of translating realworld events into mathematical language, solving the resulting mathematical model (iterating as necessary), and interpreting the results in terms of realworld issues. Topics may include model development from data, optimization, dynamic models, and deterministic and stochastic model development. Interdisciplinary projects based on actual modeling scenarios are used to integrate the various topics into a coherent theme. 


COURSE  TITLE  CREDIT HOURS  
MA394 20231  FUNDAMENTALS/NETWORK SCIENCE  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE MA394 exposes cadets to the basic concepts of networks and gives them an opportunity to apply techniques learned in the course to realworld problems. Students will develop skills and problemsolving strategies for modeling complex networks associated with physical, informational, and social phenomena. Software packages are used as decision support tools to investigate application problems and augment understanding of the course material. 


COURSE  TITLE  CREDIT HOURS  
MA396 20132  NUM METH SOLUTIONS DIFF EQNS  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE The focus of this course is to find numerical solutions of differential equations that result when modeling physical phenomena. The numerical solution of both initial value problems and boundaryvalue problems that arise with ordinary differential equations are covered. Techniques for solving partial differential equations are introduced. Software packages (Mathematica, Maple, Matlab, etc.) have proved to be very useful tools for many numerical techniques and are used to augment an understanding of course material. 


COURSE  TITLE  CREDIT HOURS  
MA461 20131  GRAPH THEORY AND NETWORKS  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course introduces the student to the techniques, algorithms, and structures used in graph theory and network flows in order to solve real world discrete optimization problems. Basic definitions relating to graphs and digraphs, together with a large number of examples and applications are provided. Cadets learn to implement new graph theory techniques in their area of study. Emphasis is on modeling, algorithms, and optimization. 


COURSE  TITLE  CREDIT HOURS  
MA462 20132  COMBINATORICS  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course introduces the basic techniques and modes of combinatorial problemsolving important to the field of computer science and mathematical sciences such as operations research. Applications of combinatorics are also related to fields such as genetics, organic chemistry, electrical engineering and political science. Combinatorial enumeration and logical structure are stressed. Applications and examples provide the structure of progression through topics which include counting methods, generating functions, recurrence relations, and enumeration techniques. 


COURSE  TITLE  CREDIT HOURS  
MA464 20132  APPLIED ALGEBRA W/ CRYPTOLOGY  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE We study the underlying algebra of computer science structures as well as sets, set functions, Boolean algebra, finite state machines, groups, and modular arithmetic. We introduce and study mathematical aspects of cryptology with an emphasis on cryptanalysis of encryption ciphers. We study early paperandpencil systems through current computer algorithms for encryption. We employ algebraic principles in both design and analysis of encryption systems, be it matrix, linear feedback shift register sequence, or linear congruential random number generator sequence efforts. Further, we investigate the mathematics of breaking machine ciphers and of designing modern publickey crypto systems. 


COURSE  TITLE  CREDIT HOURS  
MA466 20132  ABSTRACT ALGEBRA  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This is an introductory course in modern algebra for cadets who plan to do graduate work in mathematics or theoretical work in the physical sciences or engineering. The emphasis of the course is on group theory, considering such topics as cyclic and abelian groups, normal subgroups and factor groups, series of groups, and solvable groups. Selected applications are interspersed with the material on group theory. The course concludes with an introduction to rings and fields. One special problem is provided to allow the student to do independent research in an area of the student's interest. 


COURSE  TITLE  CREDIT HOURS  
MA476 20132  MATHEMATICAL STATISTICS  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course builds on the foundation presented in the core probability and statistics course to provide a mathematical presentation of the important topics in mathematical statistics. The course begins with a review of probability concepts from the core course, adding additional topics such as transformations of random variables and moment generating functions. To provide the mathematical basis for much of statistical practice, certain limit theorems and sampling distributions are proven. The central focus of the course is distribution theory, to include the theory of estimation and the theory of hypothesis testing. 


COURSE  TITLE  CREDIT HOURS  
MA477 20241  THEORY & APPL OF DATA SCIENCE  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course builds on the foundations presented in the core probability and statistics course and the applied statistics course to develop a broad base of Advanced Data Science to some of the most common techniques in the field. The mathematical basis for each method is presented with focus on both the statistical theory and application. Topics covered may include classification and regression trees, regularization methods, splines and localized regression, and model validation. 


COURSE  TITLE  CREDIT HOURS  
MA478 20222  GENERALIZED LINEAR MODELS  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course provides an introduction to statistical modeling beyond that gained in MA376. Students will learn statistical models for analyzing quantitative and qualitative data. Methods will generally be taught in the generalized linear model framework and may include binomial and multinomial regression models, models for count data and models for survival data. Students will also be exposed to techniques for handling problems that arise when analyzing real data: for example missing data, unstructured data and influential observations. 


COURSE  TITLE  CREDIT HOURS  
MA481 20201  LINEAR OPTIMIZATION  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course emphasizes the applications of optimal solutions to linear algebraic systems using the simplex method of linear programming. This includes an indepth development of the simplex method, the theory of duality, an analysis of the dual problem, convex hull concepts, integer programming, sensitivity analysis and the revised simplex procedure. Additional computational techniques that are applicable to specific mathematical models such as the transportation problem, assignment problem and network problems are also studied. Problems illustrating applications are emphasized throughout the course. Use of existing computer software to solve problems is also emphasized. 


COURSE  TITLE  CREDIT HOURS  
MA484 20201  PARTIAL DIFF EQUATIONS  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE The course is devoted to the solution of the classical partial differential equations of mathematical physics and most engineering fields. For example, these equations describe such diverse phenomena as the flow of heat in a metal plate, the gravitational field of the solar system, the vibration of a structural beam, and the energy levels of the hydrogen atom. The subject matter has application in many fields and should be of interest to mathematics, science, and engineering concentrators. Specific topics covered are the heat, wave, and potential equations, Fourier series, series solutions to ordinary differential equations, special functions, and boundary value problems. 
No Course Offerings 

COURSE  TITLE  CREDIT HOURS  
MA485 20132  APPLIED COMPLEX VARIABLES  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course presents a logical development of complex variable theory sufficient for the development and solution of a number of interesting and practical problems. Residue theory is developed and applied to problems in integration and in the solution of partial differential equations via transform techniques. Conformal mapping theory is used to solve partial differential equations for which the solution is a harmonic function satisfying prescribed boundary conditions. These classical DirichletNeumann problems model phenomena arising in the study of electrostatic potential, equilibrium thermodynamics, incompressible fluids, elasticity, and other areas of continuum mechanics. 


COURSE  TITLE  CREDIT HOURS  
MA486 20191  MATHEMATICAL COMPUTATION  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course provides an undergraduate presentation of computational problem solving that builds on math and science classes from USMA. The emphasis of this course is on developing a conceptual understanding of the fundamental topics in algorithm development as well as developing an understanding of a high level programming language. MA486 exposes students to mathematical applications best understood through computational analysis. Contemporary topics of application may include linear algebra, numerical analysis, statistics, data analytics and visualization, simulation, optimization, and machine learning. Students will be exposed to topics in computer science including data structures, object oriented programming, debugging, complexity, as well as testing and verification. We will use a high level computer programming language such as R or Python to explore and expose various topics. 


COURSE  TITLE  CREDIT HOURS  
MA487 20131  MATHEMATICAL ANALYSIS II  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE Continuation of MA387. Course coverage includes Riemann and Stieltjes integration, infinite series, sequences and series of functions, uniform convergence, and power series. 


COURSE  TITLE  CREDIT HOURS  
MA488 20192  SPECIAL TOPICS IN MATHEMATICS  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course provides an indepth study of a special topic in mathematics not offered elsewhere in the USMA curriculum. Course content will be based on the special expertise of the visiting professor or a senior mathematical science faculty member. 


COURSE  TITLE  CREDIT HOURS  
MA488A 20201  SPECIAL TOPICS IN MATHEMATICS  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course provides an indepth study of a special topic in mathematics not offered elsewhere in the USMA curriculum. Course content will be based on the special expertise of the visiting professor or a senior mathematical science faculty member. 
No Course Offerings 

COURSE  TITLE  CREDIT HOURS  
MA489 20131  ADV INDIV STUDY IN MATH  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This is essentially a tutorial course or an individual project, offered only to a limited number of highly qualified cadets who have completed available mathematics elective courses and have expressed a wish to pursue advanced study in a field of mathematics. The course work will be tailored to suit the individual needs. 


COURSE  TITLE  CREDIT HOURS  
MA489A 20241  ADV INDIV STUDY IN MATHA  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This is essentially a tutorial course or an individual project, offered only to a limited number of highly qualified cadets who have completed available mathematics electives courses and have expressed a wish to pursue advanced study in a field of mathematics. The course work will be tailored to suit the individual needs. 


COURSE  TITLE  CREDIT HOURS  
MA489B 20241  ADV INDIV STUDY IN MATHB  3.0 (BS=0.0, ET=0.0, MA=0.0) 

Scope  Offerings  
SCOPE This is essentially a tutorial course or an individual project, offered only to a limited number of highly qualified cadets who have completed available mathematics elective courses and have expressed a wish to pursue advanced study in a field of mathematics. The course work will be tailored to suit the individual needs. 


COURSE  TITLE  CREDIT HOURS  
MA490 20242  ETHICS IN MATH, DATA SCI & ENG  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course is intended to serve as an integrative experience for cadets of all majors and FOSs. Cadets having completed the core math program will be given the opportunity to explore ethical issues including legitimate data use, algorithmic fairness, and further develop skills in model construction and analysis while addressing problems and scenarios with practical applications from science, social sciences, engineering, computer science and/or mathematics. Interdisciplinary projects based on actual modeling scenarios are used to explore ethical issues and integrate the various topics into a coherent theme. 


COURSE  TITLE  CREDIT HOURS  
MA491 20131  RESEARCH SEMNRAPPLD MATH  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE The student integrates the mathematical concepts and techniques learned in previous courses with the principles developed throughout the whole USMA Curriculum to solve a current problem of interest to the individual, to the Academy, or to agencies in the Department of the Army. Cadets may select problems from a list of suitable projects provided by the Department of Mathematical Sciences. Cadets choose a faculty advisor who has an interest and background in the problem. Cadets may work individually or in small teams, depending on the nature of the research. Regular workshop sessions will be held. Cadets will be given an opportunity to present their research at the Service Academies Student Mathematics Conference and/or other undergraduate conferences. Research reports will be reviewed, edited, and compiled into the USMA Transactions on Cadet Mathematical Research. 


COURSE  TITLE  CREDIT HOURS  
MA493A 20131  OPNL CALC AND TRANSFORMS  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course is the logical extension and synthesis of MA484 and MA485. It employs the integral calculus of complex functions and the theory of residues to investigate solutions to a number of partial differential equations arising from electrostatics, thermostatics, elasticity, gravitation, and other fields of continuum mechanics. The PoissonIntegral Formula is applied to the solution of boundaryvalue problems. Fourier and Laplace transforms are studied in detail and are used to develop general techniques for the solution of many ordinary, partial, and integral equations which result from the above applications. 
No Course Offerings 

COURSE  TITLE  CREDIT HOURS  
MA493B 20131  REAL VARIABLE THEORY  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE Continuation of MA487. Topics include sequences and series of functions, equicontinuity power series, Fourier series, the exponential and logarithmic function, and the Gamma function. The last portion of the course will be devoted to individual research projects. 
No Course Offerings 

COURSE  TITLE  CREDIT HOURS  
MA493C 20131  TOPICS IN NUMERICAL ANLYSIS  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE A continuation of MA396. Topics include boundaryvalue problems for ordinary and/or partial differential equations. 


COURSE  TITLE  CREDIT HOURS  
MA493D 20131  INTRODUCTION TO TOPOLOGY  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE The course begins with cardinality and the modern definition of a function. Then the basic properties of topological spacescompactness, connectedness, and continuitywill be emphasized. Special attention will be given to metric topologies on Euclidean spaces. Complete metric spaces and function spaces will be introduced. 


COURSE  TITLE  CREDIT HOURS  
MA493E 20131  TOPICS IN ANALYSIS  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course provides cadets the opportunity to pursue in detail subjects of special interest. 


COURSE  TITLE  CREDIT HOURS  
MA498 20131  SR THESIS I: RSCRCH & PROPOSAL  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE The purpose of the Senior Thesis is to provide cadets with an unique opportunity to create a scholarly product that is academically, professionally, and personally meaningful to them and that reflects their thinking and abilities as developed at West Point and in the Department of Mathematical Sciences. Cadets will choose a faculty advisor with whom they will collaborate over two semesters. Cadets will meet on a regular basis with their advisor to discuss mathematics, progress on their research and thesis, and developmental issues. The objectives of the research are: (1) to synthesize and cohere the cadet's studies; (2) to apply methodological skills of research design, conceptual reasoning, analysis, and research gained to a selected area of substantive interest; (3) to extend the cadet's indepth study of the selected area of interest beyond the level obtained in the Mathematical Sciences Major; (4) to design and conduct focused research beyond the constrained opportunities in elective courses; and (5) to develop cadet skills in conceptual reasoning, critical analysis, and effective writing. 


COURSE  TITLE  CREDIT HOURS  
MA499 20132  SR THESIS II: PAPER & DEFENSE  3.0 (BS=0.0, ET=0.0, MA=3.0) 

Scope  Offerings  
SCOPE This course continues the work on the thesis commenced in MA 498. At the end of the course, cadets will submit a written thesis to the Department of Mathematical Sciences. In addition, cadets will defend that thesis before a faculty committee. Cadets will be given an opportunity to present their research at the Service Academies Student Mathematics Conference and/or other undergraduate conferences. Theses will be reviewed, edited, and compiled into the USMA Transactions on Cadet Mathematical Research. 

