Mathematics - MAT (53)

Administered by Department of Mathematics and Computer Science

Effective Spring, 2004

53.101 Mathematical Thinking (3) - Presents mathematical topics and applications in a context designed to promote quantitative reasoning and the use of mathematics in solving problems and making decisions. Suitable for majors in humanities, education and others seeking a broad view of mathematics. No background in algebra required.

53.111 Finite Mathematics (3) - Presents an introductory development of counting techniques, probability spaces and game theory. Prerequisite: two years of high school algebra or equivalent.

53.112 Trigonometry (3) - Studies elementary algebraic functions and relations, exponential and logarithmic functions, circular functions and inverse functions and their applications. Prerequisite: 53.109 or two years of high school algebra or high school trigonometry or their equivalent.

53.113 Pre-Calculus (3) - Studies elementary algebraic functions and relations, exponential and logarithmic functions, circular functions and inverse functions and their applications. Prerequisite: 53.109 or two years of high school algebra or the equivalent.

53.109 College Algebra (3) - Studies fundamental algebraic concepts and develops the mathematical and computation skills necessary to apply algebraic techniques to problems in business, economics, the social and natural sciences and the liberal arts. Prerequisite: 1 1/2 years of high school algebra or the equivalent. Not open to students with a C- or higher recorded for 53.113, 53,123 or 53.125.

53.118 Applied Matrix Algebra (3) - Introduces vectors, matrices, linear equations and linear programming with applications to the social and biological sciences and business. Prerequisite: two years of high school algebra or equivalent.

53.123 Essentials of Calculus (3) - Presents the basic concepts of elementary calculus in a non-rigorous approach for students who are not mathematics majors. Pertinent topics in the real number system, analytic geometry, functions and limits prepare the student for the study of the basic techniques of applications of differentiation and integration. Course is not for chemistry, mathematics or physics majors. Prerequisite: At least two years of high school algebra or 53.109 or consent of the instructor.

53.125 Calculus I (3) - Designed to meet part of the major-level mathematics requirement; first in the sequence of four calculus courses. Provides the basic tools for differentiation and the beginnings of integration for functions of a single variable. Prerequisite: placement test or 53.113. TI-89 graphical calculator is required.

53.126 Calculus II (3) - Studies techniques of integration, functions, infinite series, Taylor's theorem, some special differential equations and polar coordinates. Prerequisite: 53.125. TI-89 graphical calculator is required.

53.141 Introduction to Statistics (3) - Presents the concepts necessary to use and understand basic statistical techniques. Topics include: descriptive statistics, probability, random variables, sampling distributions, hypothesis tests, confidence intervals and analysis of variance. Prerequisite: High school algebra.

53.185 Discrete Mathematics (3) - An introduction to set theory, logic, combinatorics and graph theory for those interested in mathematics or computer science. Not usually taken during the freshman year. Prerequisite: 53.125 or consent of instructor.

53.201 Mathematics for Elementary Teachers I (3) - Presents the language of sets, the four elementary operations through the real number system and the elementary theory of numbers. Course is open only to majors in elementary education, special education or communication disorders.

53.202 Geometry and Statistics for Elementary Education Majors (3) - Presents the content of geometry and beginning probability and statistics for the elementary curriculum.

53.225 Calculus III (3) - Presents infinite sequences and series, power series, Taylor and Maclaurin series, three dimensional vector analysis and partial derivatives. Prerequisite: 53.126.

53.226 Calculus IV (3) - Presents an introduction to the differentiation and integration of real valued functions of several variables. Presents curves and parametric equations, surfaces, Taylor's, Stoke's and Green's theorems, functions between Euclidean spaces and multiple integrals. Prerequisite: 53.225.

53.231 College Geometry (3) - Presents elementary geometry from an advanced standpoint. Discusses incidence in the plane and in space, congruence, inequality and similarity concepts. Studies properties of circles, polygons and spheres. Prerequisite: High school geometry, 53.185.

53.240 Statistical Methods (Spring only) (3) - Presents common statistical techniques with emphasis on applications. Topics include: confidence intervals, hypothesis test, regression analysis and analysis of variance. Strongly encourages use of statistical software, especially SAS. Prerequisite: 53.141 or 53.241 or consent of the instructor.

53.241 Probability and Statistics (3) - Calculus-based study of probability and statistics. Topics covered include: descriptive statistics, probability, discrete and continuous random variables, common distributions, sampling destributions, estimation procedures and inferential statistics. A more rigorous course than 53.141. Prerequisites: 53.126 (or concurrent) and 53.185.

53.243 Nonparametrics Statistics (3) - Presents standard nonparametric statistical procedures. After a brief review of hypothesis testing fundamentals, topics such as goodness-of-fit tests, one and two-sample procedures for location parameter, tests of randomness and association analysis are covered. Prerequisites: 53.123 or 53.125 and 53.141 or the equivalent.

53.303 Mathematical Problem Solving for Teachers (3) - Examines mathematical problem solving, number sense, pattern recognition and mathematical reasoning. Basic problem solving, use of manipulatives and assessment are covered. Games involving mathematical problem solving are examined and designed. Requires off-campus observations and testing. For elementary and secondary education majors. Prerequisite: 53.201.

53.310 Introduction to Abstract Algebra (3) - Provides an introduction to the language and methods of abstract mathematics. Subjects include sets, relations, rings, functions, groups and fields. Prerequisites: 53.185 with a minimum grade of C- and 53.225.

53.311 Algebra for Secondary School Teachers (Fall/even-numbered years) (3) - Presents topics of elementary algebra from an advanced viewpoint. Considers topics of contemporary school mathematics programs. Intended for students in secondary education majoring in mathematics. Prerequisite: 53.310.

53.314 Linear Algebra (3) - Studies abstract vector spaces, linear transformation, matrices, determinants, inner product spaces and related topics. Prerequisites: 53.185 and 53.126.

53.322 Differential Equations (3) - Studies elementary ordinary differential equations, infinite series and power series solution, some numerical methods of solution and LaPlace transforms. Prerequisite: 53.225.

53.331 Modern Geometry (Spring/odd-numbered years) (3) - Presents non-Euclidean geometrics and their development from postulate systems and a formal approach to projective geometry. Prerequisite: 53.231.

53.340 Statistical Software (Fall, even numbered years) (3) - Provides an introduction to the most widely-used statistical software packages in government and industry. Students gain practical experience by solving real-world statistical problems encountered by various government agencies and private companies. Graphical and numerical descriptive procedures and inferential statistical techniques will be discussed. Prerequisite: 53.240.

53.342 Design and Analysis of Experiments (Fall, eve-numbered years) (3) - Basic experimental statistics including methods of estimation and hypothesis testing, analysis-of-variance procedures, principles of experimental design, completely randomized and randomized complete block designs, factorial arrangements of treatments, linear regression and correlation analysis, covariance analysis and distribution-free methods. Prerequisite: 53.141 or 53.241 or consent of the instructor.

53.343 Applied Regression Analysis (Fall, odd-numbered years) (3) - A basic course in multiple linear regression methods including weighted least squares, stepwise regression, residual analysis and applications to mathematical models. Treats problems which involve the use of computing equipment. Prerequisite: 53.141 or 53.241 or consent of the instructor.

53.360 Number Theory (Spring only) (3) - Presents the theory of numbers. Includes the topics of Euclidean algorithm, congruences, continued fractions, Gaussian integers and Diophantine equations. Prerequisites: 53.185 and 53.225.

53.361 Coding and Signal Processing (Spring only) (3) - A mathematical approach to codes and ciphers. Includes security codes, coding for efficiency in computer storage, error-correcting codes. Signal processing, including the Fourier transform and digital filters. Individual projects required. Prerequisites: 53.126 and 56.116 or 56.122.

53.373 Numerical Methods in Computing (Fall) (3) - Analysis and application of various methods of numerically solving problems in the areas of nonlinear equations; systems of equations, interpolation and polynomial approximation; numerical integration; approximation theory; and differential equations. Students design and execute algorithms on the computer for specific numerical procedures. Prerequisites: 56.121 and 53.126.

53.374 Introduction to Discrete Systems Simulation (Spring/odd-numbered years) (3) - Studies the ways that systems can be moduled for computer solution. Emphasizes stochastic behavior by discrete random processes and the simulation tools for their solution. Prerequisites: One course each in calculus, programming and statistics.

53.381 Introduction to Operations Research (Fall/odd-numbered years) (3) - A survey of the methods and models used in applying mathematics to problems of business. Topics drawn from decision making, linear and dynamic programming, networks, inventory models, Markov processes and queuing theory. Prerequisites: 53.118 and 53.123 or 53.225.

53.410 Mathematical Modeling (3) - A synthesis of mathematical methods utilized to model and solve real-world problems. The emphasis is on developing models that provide the means to analyze and answer questions posed in practical settings. A problem-solving approach toward applied problems in optimization, dynamical systems, and stochastic processes. Prerequisites: 53.241, 56.122 or higher, 53.314.

53.411 Introduction to Group Theory (3) - Continued and advanced study of theorems and applications of group theory begun in abstract algebra. Prerequisite: 53.310.

53.421, 53.521 Advanced Calculus (Spring, even numbered years) (3) - Presents a rigorous treatment of the study of functions of a single real variable. Topics include limit, continuity, derivative and integration. Some topics for multivariable calculus include partial differentiation and multiple integration. Prerequisites: Analysis IV, Permission of Instructor.

53.422 Complex Variables (Fall, odd numbered years) (3) - A rigorous treatment of complex numbers and an introduction to the theory of functions of a complex variable. Central topics are the complex number system, analytic functions, harmonic functions and conformal mappings. Additional topics may include power series, contour integration, Cauchy's formula and applications. Prerequisites: 53.226, consent of instructor.

53.441 Mathematics and Sports (Fall, even numbered years) (3) - Links between mathematics, statistics and sports; includes data analysis and modeling related to the various facets and types of sports using certain mathematical and statistical techniques. Sports used as examples include basketball, tennis, volleyball, track and weightlifting. This course counts as a Group C, Natural Sciences & Math General Education Requirements. Three hours of lecture per week. Prerequisites: 53.241 or permission of the instructor.

53.446 Biostatistics (3) - An introduction to the concepts and methods of advanced statisticsl techniques that arise in health and life sciences with emphasis on problems that are likely to be encountered by graduate researchers in biological sciences. It includes methodologies for design and analysis of multivariate data. The use of statistical software to analyze data sets is stressed.

53.451 Introduction to Topology (3) - Introduces fundamentals of general topology; elementary set theory, topological spaces, mappings, connectedness, compactness, completeness, product and metric spaces; nets and convergence. Prerequisites: 53.226, consent of instructor.

53.456 The Theory of Computation (Spring, odd-numbered years) (3) - An introduction to automata, formal languages and computability. Topics include finite automata, pushdown automata, context-free grammars, Turing machines, algorithmically unsolvable problems and computational complexity. Prerequisites: 53.185 and 56.112 or consent of the instructor.

53.461, 53.561 Probability Models and Applications (Spring, even-numbered years) (3) - An introduction to the concepts and methods of probabilistic modeling for random trials and occurrences. It covers classical models, poisson processes, Markov chains, Renewal and Braching processes and their applications to various phenomena in engineering, management, physical and social sciences. Prerequisite: 53.241.

53.462 Introduction to Mathematical Statistics (Spring, even-numbered years) (3) - An introductory study of mathematical statistics including distributions of functions of random variables, interval estimation, statistical hypotheses, analysis of variance and the multivariate normal distribution. Prerequisite: 53.241.

53.471 Numerical Analysis (3) - Provides a computer-oriented analysis of algorithms of numerical analysis. Includes the topics of non-linear equations, interpolation and approximation, differentiation and integration, matrices and differential equations. Prerequisites: 53.322 and 53.373.

53.472 Matrix Computation (Spring/odd numbered years) (3) - Presents a computer-oriented analysis of matrices. Includes Gaussian reduction, LDU factorization, special reduction techniques for tridiagonal matrices, iterative methods and a study of the matrix eigenvalue problem. Prerequisites: 53.225 and 53.373.

53.491 Special Topics in Mathematics (3) - Presents an area of mathematics which is not available as a regular course offering. Prerequisite: Consent of the instructor.

53.492 Independent Study in Mathematics (1-3) - Provides for directed study of a particular area of mathematics as mutually agreed upon by the student and the instructor. Emphasizes individual scholarly activity of the highly motivated student.

53.493 Honors in Independent Study in Mathematics (3) - For students who have demonstrated a high level of interest and ability in mathematics and have mastered the required course work. Students investigate research problems selected under the supervision of a faculty member of the Department of Mathematics and Computer Science. Prerequisite: Admission to the Honors Program in natural sciences and mathematics.

53.497 Internship in Mathematics (2-12) - Provides mathematics majors with an opportunity to acquire meaningful and professional on-site training and learning experiences in mathematics at an industrial, private or business workplace. Note: a student may, with departmental approval, apply a maximum of 3 credits of internship toward the fulfillment of the mathematics major. Each academic credit requires 40 hours of supervised work and the limit is 12 total semester hours for internships. Prerequisites: students must establish adequate course preparation for the proposed internship. Internship applications must be submitted one month before the internship begins and must be approved by the department chairperson.

53.500 Research and Communication in Applied Mathematics (3) - Practical information for scientists about research and technical writing. A study of how to prepare a manuscript and an introduction to certain basic communication principles that are accepted in most disciplines. Prerequisites: Calculus I, II, III, Probability and Statistics

53.520 Mathematical Modeling (3) - An introduction to the concepts and methods of mathematical modelling with emphasis on the problems that arise in governmental and industrial projects. It includes modelling process, model construction including numerical considerations, testing the appropriateness of the models, model analysis and model research. Prerequisites : Calculus I, II, III or permission of instructor

53.522 Applied Differential Equations (3) - Presents an advanced treatment of differential equations including systems of linear differential equations, systems of nonlinear differential equations, and boundary value problems and their solutions, asymptotic behavior and applications. Prerequisite: Analysis III

53.541 Applied Statistics (3) A comprehensive treatment of applications of statistical methodology in practice, and development of statistical techniques for real world problem solving. Prerequisite: A first course in statistics.

53.542 Design and Analysis of Experiments (3) - Basic experimental statistics including analysis-of variance procedures, principle of experimental design, completely randomized and randomized complete block designs, factorial arrangements of treatments, linear regression and correlation analysis, covariance analysis and distribution-free methods and the Taguchi approach to parameter design.

53.543 Regression (3) - An in-depth, modern, applied approach to the study of multiple linear regression analysis. Topics include simple linear regression, inferences in regression analysis, examination of residuals, multiple regression, and model selection procedures. Prerequisites: Calculus I, II, III, Probability and Statistics

53.544 Statistical Quality Control (3) - Presents the modern practice of statistical quality control with a strong engineering and management orientation. Prerequisite: Probability and Statistics, Applied Statistics

53.545 Time Series Analysis and Its Application (3) - A survey of time series models, their statistical analysis and applications. It includes investigation of trend, seasonal variations, serial dependency and stationarity, and covers estimation, forecasting, and identification techniques for stationary and nonstationary autoregressive, moving average, and mixed models and related computational problems.

53.546 Biostatistics (3) - An introduction to the concepts and methods of advanced statisticsl techniques that arise in health and life sciences with emphasis on problems that are likely to be encountered by graduate researchers in biological sciences. It includes methodologies for design and analysis of multivariate data. The use of statistical software to analyze data sets is stressed.

53.563 Nonparametric Statistics (3) - Presents a comprehensive account of statistical inference using nonparametric approaches. Attempts to provide modern nonparametric techniques for data analysis with a view towards application. Prerequisite: Applied Statistics

53.572 Operations Research (3) - Presents the principles of mathematical modeling applied to man-machine systems. Special emphasis will be given to mathematical programming models including linear and integer programming. Optimal decision models will be a focus of the course Mathematical Software. Prerequisite: Graduate Standing

53.574 Advanced Discrete Mathematics (3) - Includes discussion of topics such as combinatorial analysis (enumeration of various types of objects), discrete structures (for example, sets, relations, graphs, and finite state machines), algorithmic thinking (development, implementation, and verification of algorithms) and applications of these ideas to diverse fields (such as business, linguistics and the sciences). Prerequisites:56.121 (Computer Science 1), 53.125 (Calculus 1), 53.185 (Introduction to Discrete Mathematics), 53.310 or 53.314 or 53.360

53.576 Computer Graphics for Instructional Applications (3) - Sequel to 53.375 where techniques for creating color, graphics, and sound are examined and applied to the development of instructional computing programs.

53.592 Special Topics (3)

53.471, 56.571 Numerical Analysis (3) - A graduate level course in numerical analysis in the areas of nonlinear equation and systems of equations, interpolation theory, numerical integration, differential equations, numerical solution of linear systems, and the matrix eigenvalue problems. The original problems to be solved and the numerical methods will be studied, including the derivation of the method, error analysis, convergence analysis, and computational implementations. Prerequisites: Calculus III, Fortran, and an elementary numerical method course (or permission of instructor)