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Mathematics Courses

### Mathematics

Initial course placements in mathematics and computer science are generally determined by the Mathematics Placement Test. After students take their first course, they must take courses in sequence as determined by the departmental prerequisites. Any exceptions must be approved by the course instructor and department chair.

**104 Mathematics for Elementary Teachers (1)**

Prerequisite: Three years of college-preparatory mathematics (or its equivalent). Priority given to students in the elementary education program.

An investigation of mathematics (arithmetic, geometry, algebra, problem solving) for elementary school teachers. Topics are selected from: sets, relations and functions; numeration systems; whole numbers and their operations; number theory; rational numbers and fractions; decimals and real numbers; geometry and measurement; and probability and statistics. Emphasizes doing mathematics, using manipulatives, and developing intuition and problem-solving skills. Laboratory. *Bollman.*

**119 Finite Mathematics for Decision Making (1)**

An introduction to discrete mathematics. Applications are drawn from diverse areas including biological sciences, economics, political science and personal finance. Topics typically include graph theory, management science, statistics, the mathematics of social choice, game theory and the logical foundations of mathematics. Investigation and creation of mathematical models. Intended for non-majors. *Staff.*

**123 Mathematics for the Liberal Arts (1)**

Prerequisite: Permission of department.

A study of selected topics in mathematics drawn from among algebra, geometry, statistics, probability, discrete mathematics, and other fields of mathematics as determined by the instructor.* Staff.*

**125 Precalculus (1) **

Prerequisite: Permission of department.

A modern, unified approach to algebra, trigonometry, logarithms and analytical geometry based on the concept of a function. Linear equations and inequalities, quadratic equations and inequalities, polynomials and rational functions, logarithms and exponential functions, trigonometric and inverse trigonometric functions, and analytic geometry (the circle, the parabola, the ellipse and the hyperbola) are normally covered. Emphasizes the use of graphing calculators and the use of mathematics as a problem-solving tool. Covers applications in natural science, social science and business. Serves as a preparation for calculus. Well-prepared students who already have a strong working knowledge of algebra, trigonometry and logarithms should elect Mathematics 141 in place of Mathematics 125. A graphing calculator is required. *Staff.*

**141 Calculus of a Single Variable I (1)**

Prerequisite: Mathematics 125 or permission of department.

Mathematics 141 and 143 constitute a thorough introduction to calculus for students who intend to continue in mathematics and for those who will use calculus in other fields such as science and engineering. Mathematics 141 covers limits, continuity, derivatives and a brief introduction to integration, as well as applications to problems in related rates, optimization, solid geometry and elementary mechanics. Requires a strong working knowledge of algebra and trigonometry. Students who are weak in these areas should elect Mathematics 125. A graphing calculator is required. *Staff.*

**143 Calculus of a Single Variable II (1)**

Prerequisite: Mathematics 141 or permission of department.

Second half of the standard one-year calculus sequence (see Mathematics 141 above). Mathematics 143 covers techniques of integration, applications of the integral, simple differential equations with their associated mathematical models, and sequences and series. Requires a strong working knowledge of algebra, trigonometry, derivatives, and some familiarity with integration, including Riemann sums and the Fundamental Theorem of Calculus. Students with a calculus background who are weak in these areas should elect Mathematics 141. A graphing calculator is required. *Staff.*

**209 An Introduction to Statistics (1)**

Prerequisite: Permission of instructor.

Statistics is the art/science of collecting and interpreting data. Topics include probability, probability distributions which include the binomial and normal distributions, the central limit theorem, sampling distributions, confidence interval estimation, and hypothesis testing. Students will then advance to linear regressions, goodness-of-fit tests, and analysis of variance. Emphasis is placed on multiple applications in the life and social sciences. *Anderson, Bollman.*

**239 Discrete Structures (1)**

Prerequisite: Mathematics 141.

A survey of discrete mathematics with topics selected from set theory, functions and relations, number theory, combinatorics, graph theory, logic (predicate calculus, quantifiers), introduction to proof techniques, and probability. *Staff.*

**245 Multivariate Calculus (1) **

Prerequisite: Mathematics 143.

Vectors, inner and cross products, and vector-valued functions including parametric representations of curves and surfaces in space. Partial differentiation, the chain rule, function gradients, implicit differentiation, multivariate optimization, and Lagrange multipliers, multiple integrals and vector analysis, including divergence and curl of vector fields, as well as the theorems of Green, Stokes and Gauss. *Mason. *

**247 Differential Equations and Linear Algebra (1) **

Prerequisite: Mathematics 245.

First-order differential equations and numerical algorithms of Euler and Runge-Kutta. Linear algebraic systems, Gaussian elimination, row-echelon form matrix algebra, inverses and determinants. Vector spaces, subspaces, linear independence, bases, span, dimension, linear mappings and function spaces. Second and higher-order linear differential equations. Eigenvectors, eigenvalues and spectral decomposition methods. First-order linear differential systems, including solutions methods using matrix exponentials. Applications focus on problems in physics, chemistry, biology, economics and engineering. Additional topics may include nonlinear dynamical systems, stability theory, transform theory and power series solutions. *Mason. *

**309 Mathematical Statistics (1)**

Prerequisite: Mathematics 245. Mathematics 247 is recommended.

A mathematical study of probability distributions, random sampling, and topics selected from statistical theory: estimation, hypothesis testing and regression. *Anderson.*

**310 Actuarial Statistics (1)**

Prerequisite: Mathematics 309.

A continuation of Mathematics 309 that covers many of the diverse methods in applied probability and statistics for students aspiring to careers in insurance, actuarial science, and finance. Covers loss distributions, multivariate distributions, conditional expectation, mixture distributions, risk theory, and generalized linear models. The course is organized specifically to meet the needs of students preparing for the Society of Actuaries and Casualty Actuarial Society qualifying examination P/1. *Anderson.*

**311 Regression and Time Series Models**

Covers two topics in detail: multiple linear regression analysis and time series analysis. Inherent to both topics: parsimonious linear models, parameter estimation, diagnostic checking, and forecasting. Uses the matrix approach for multiple linear regression, and the Box-Jenkins methodology for constructing autoregressive-integrated moving average (ARIMA) models for time series analysis. Employs the statistical package MINITAB for analyzing all real-world data sets. *Anderson.*

**316 Numerical Analysis (1) **

Prerequisites: Mathematics 247 and Computer Science 171.

Methods of obtaining numerical solutions to mathematical problems. Stresses the implementation and error analysis of algorithms. Topics include solution of non-linear equations, systems of equations, interpolating polynomials, numerical integration and differentiation, numerical solution to ordinary differential equations, and curve fitting. Offered in alternate years. Same as Computer Science 316. *Mason. *

**326 Operations Research (1) **

Prerequisites: Mathematics 247.

An introduction to computational methods in mathematical modeling including linear programming and Markov chains. Applications in business, economics and systems engineering. Knowledge of probability is helpful. Offered in alternate years. Same as Computer Science 326. *Mason.*

**331 Real Analysis (1)**

Prerequisites: Mathematics 245 and 239.

A study of the concepts underlying calculus of a single variable: The completeness property of the real number system, convergence, continuity, properties of elementary functions, the derivative and the Riemann integral. *Bollman.*

**333 Complex Analysis (1) **

Prerequisites: Mathematics 239 and 245.

An introduction to complex variable theory. Specific topics to be covered include elementary and analytic functions, differentiation and integration in the complex plane, series representations, residues and poles, transform theory, and conformal mapping. Offered in alternate years. *Bollman.*

**335 Abstract Algebra (1)**

Prerequisites: Mathematics 239 and 247.

Properties of the integers, real number system and other familiar algebraic entities are viewed abstractly in structures such as groups, semigroups, rings and fields. Homomorphisms and isomorphisms (functions compatible with the algebraic operations) illuminate the underlying similarities among these structures. Students will develop their skills in mathematical writing and presentations. *Bollman.*

**342 Geometry (1) **

Prerequisites: Mathematics 143 and 239.

The logical foundation of Euclidean geometry, including the axiom systems of Euclid and Hilbert, and their philosophical implications. An introduction to hyperbolic, elliptic and projective geometry. Employs software such as *Geometer’s Sketchpad* to illustrate course topics. *Bollman.*

**345 History of Mathematics (1)**

Prerequisite: Mathematics 141.

A study of the history and evolution of mathematical ideas and their significance, from approximately 3500 B.C.E. to the present. Topics include number systems, arithmetic, Euclidean and non-Euclidean geometry, algebra, calculus, probability, number theory and applied mathematics. Offered in alternate years. *Bollman.*

**349 Advanced Linear Algebra (1)**

Prerequisites: Mathematics 239 and 247.

A continued study of linear algebra as begun in 247. Topics may include abstract vector spaces, dimension, normed linear spaces, inner product spaces, canonical forms, unitary and Hermitian matrices, factorization, eigenvector analysis, and infinite-dimensional spaces. Offered in alternate years.* Bollman.*

**360 Mathematical Modeling (1) **

Prerequisites: Mathematics 247 and Computer Science 171.

An introduction to analytical methods in mathematical modeling, including nonlinear optimization, dynamical systems and random processes. Applications in physics, biology, economics and systems engineering. Knowledge of probability and statistics is helpful. Same as Computer Science 360. *Mason.*

**368 Topology (1)**

Prerequisites: Mathematics 239 and 245.

An introduction to the basic concepts of point set topology. Fundamental concepts of topological spaces including open and closed sets, limit points, continuous functions, as well as the product, subspace, metric, and quotient topology. Connectedness and compactness with applications to the real line. Countability and separation axioms including Hausdorff, regular, and normal spaces. Urysohn’s Lemma and Metrization Theorem. Tychonoff’s Theorem. Topics from algebraic topology if time permits*. Mason, Bollman.*

**370 Partial Differential Equations (1) **

Prerequisites: Mathematics 239 and 247. Mathematics 331 recommended.

A study of the theory and applications of partial differential equations (PDEs). Linear and nonlinear PDEs, including quasilinear first order equations, conservation laws, discontinuous solutions, classification of PDEs, wave propagation in multiple space dimensions, Fourier analysis and separation of variables, Sturm-Liouville theory, fundamental solutions for equations of parabolic and elliptic type, including the maximum principle. Applications in biology, chemistry, engineering and physics. Offered in alternate years. *Mason.*

**375 Introduction to Solid Mechanics (1)**

Prerequisites: Physics 167 and 168; Math 245.

Statics: Forces, moments and couples; equilibrium of particles and rigid bodies; trusses and frames; distributed loads. Mechanics: Stress/strain, classification of material behavior, generalized Hooke's law. Engineering applications: Axial loads, torsion of circular rods and tubes, bending and shear stresses in beams, deflection of beams, combined stresses, stress and strain transformation, Mohr's circle, elastic stability/buckling of columns. Same as Physics 375. *Mason.*

**380 Mathematical Physics (1)**

Same as Physics 380. *Staff.*

### Computer Science

The Department of Mathematics and Computer Science reserves the right to deny enrollment to students taking courses out of sequence as determined by prerequisites.

**151 Information Technology (1) **

Intended for the liberal arts student who wants to understand and better use information technology. Topics include how computers work, the Internet and World Wide Web, new trends in computing such as mobile computing and peer-to-peer networks, how software development differs from traditional manufacturing, how computing is changing our culture and laws, current trends in computer crime, security, and privacy. Additional topics are drawn from current events and issues. Laboratory. Does not count toward the computer science major or minor. *Staff.*

**171 Introduction to Computer Science I (1) **

Prerequisite: Mathematics 125 (or equivalent) or permission of instructor.

Designed to be the first computer science course taken by students in mathematics and computer science. Topics include fundamentals of computation and algorithmic problem-solving, data types, control structures, the object-oriented programming paradigm and applications. Introduces a high-level programming language such as Java or Python. *Reimann. *

**172 Accelerated Introduction to Computer Programming (1/2)**

Prerequisite: Permission of instructor.

Intended for students receiving AP or transfer credit for CS 171. It is recommended that such students take this course prior to enrolling in additional computer science courses. An overview of programming in the same high-level language used in CS 171. *Reimann.*

**173 Introduction to Computer Science II (1) **

Prerequisite: Computer Science 171.

A continuation of Computer Science 171. Emphasizes advanced object-oriented programming (interfaces, multiple inheritance, reflections), abstract data types (stacks, queues, lists, strings, trees, graphics, etc.) and analysis of algorithms. Other topics include recursion, searching and sorting, simulation and an introduction to some of the advanced areas of computer science, e.g., computer organization, artificial intelligence and user interfaces. Students refine their programming skills in a high-level programming language such as Java or Python. *Reimann. *

**256 Practicum in Programming Languages (1/4)**

Prerequisite: Computer Science 171 or permission of instructor.

Designed to teach an additional computer language beyond those currently used in the computer science courses. Emphasizes writing and debugging programs that use the special features of the language. FORTRAN and C are the languages that have been taught most recently. Special sections of this course have been offered that are devoted to developing problem-solving skills in computer programming. *Staff.*

**261 Computers, the User and Society (1) **

Prerequisite: Computer Science 171.

An examination of how computers are used and how computers fit into society. Topics include user interface design, human-centered software development and evaluation, software reliability, social context of computers, professional and ethical responsibilities for technology professionals, intellectual property rights, privacy and civil liberties, computer crime. Offered every third year. *Reimann, Staff. *

**263 Operating Systems and Networks (1) **

Prerequisite: Computer Science 173.

The role of operating systems, concurrency and deadlock avoidance, memory management, client-server models, device management, networking, LANs and WANs, TCP/IP, network architectures, security, trends in networks such as wireless networks and the Internet. Offered every third year. *Reimann. *

**265 Database Programming (1) **

Prerequisites: Computer Science 173 and Mathematics 239.

Fundamental concepts of database management systems: the relational data model, relational algebra, and normal forms, file organization and index structures, and the query language SQL and embedded SQL. Offered every third year. *Reimann, Staff.*

**271 Artificial Intelligence (1) **

Prerequisites: Mathematics 239 and Computer Science 173.

Basic techniques of artificial intelligence including knowledge representation and reasoning, problem-solving and planning, game playing, and learning. Covers AI programming and languages. Offered every third year. *Staff.*

**273 Computer Graphics and Image Processing (1) **

Prerequisites: Computer Science 173 and Mathematics 236 or 247.

A unified introduction to image synthesis and image analysis aimed at students with an interest in computer graphics, computer vision or the visual arts. Covers the basics of image generation, image manipulation and digital special effects. Includes a significant programming project using the OpenGL programming interface. Offered every third year. *Reimann. *

**275 Software Development (1) **

Prerequisite: Computer Science 173.

An introduction to the techniques of developing large software projects including unit testing, version control and build management. Covers the popular industrial languages C and C++ and includes a large-group programming project. Offered every third year. *Reimann, Staff.*

**316 Numerical Analysis (1) **

Prerequisites: Mathematics 247 and Computer Science 171.

Methods of obtaining numerical solutions to mathematical problems. Stresses the implementation and error analysis of algorithms. Topics include solution of non-linear equations, systems of equations, interpolating polynomials, numerical integration and differentiation, numerical solutions to ordinary differential equations, and curve fitting. Offered in alternate years. Same as Mathematics 316. *Mason. *

**326 Operations Research (1) **

Prerequisites: Mathematics 247.

An introduction to computational methods in mathematical modeling including linear programming and Markov chains. Applications in business, economics and systems engineering. Knowledge of probability is helpful. Offered in alternate years. Same as Mathematics 326. *Mason. *

**352 Algorithms (1) **

Prerequisites: Mathematics 239 and Computer Science 171.

Focuses on the design and efficiency of algorithms. Covers the basic algorithm paradigms including graph traversals, greedy algorithms, divide and conquer, dynamic programming and flow algorithms. Introduces complexity theory, NP-completeness and polynomial-time reductions. Additional topics may include approximation algorithms, randomized algorithms and linear programming. Offered in alternate years. *Reimann. *

**354 Computer Organization (1) **

Prerequisite: Computer Science 173.

Organization of digital computers: digital logic, arithmetic, assembly language, data paths, memory, input-output, secondary storage devices, multiprocessors and computer performance. Programming tools and techniques are also discussed with emphasis on their application in assembly language. Offered in alternate years. *Reimann. *

**356 Programming Languages (1) **

Prerequisite: Computer Science 173.

A survey of the structure of programming languages and programming as an abstract concept. Topics include syntax and semantics, scope rules, environments, types, procedures, parameters, overloading, parametric polymorphism and inheritance. Projects include programming in the functional paradigm using the Scheme programming language and development of a language interpreter. Offered in alternate years. *Reimann. *

**358 Foundations of Computing (1) **

Prerequisites: Mathematics 239 and Computer Science 171.

The theoretical underpinnings of computer science: models of computation including automata, Turing machines, circuits, the Chomsky language hierarchy, Church’s thesis, computable and noncomputable functions, recursive and recursively enumerable sets, reducibility and introduction to complexity theory. *Bollman.*

**360 Mathematical Modeling (1) **

Prerequisites: Mathematics 247 and Computer Science 171.

An introduction to analytical methods in mathematical modeling including nonlinear optimization, dynamical systems and random processes. Applications in physics, biology, economics and systems engineering. Knowledge of probability and statistics will be helpful. Same as Mathematics 360. *Mason. *

### Special Studies

**187, 188, 189 Selected Topics (1/4, 1/2, 1)**

An examination of subjects or areas not included in other courses. *Staff.*

**287, 288, 289 Selected Topics (1/4, 1/2, 1)**

An examination of subjects or areas not included in other courses. *Staff*

**299 Colloquium in Mathematics and Computer Science (1/4) **

Prerequisite: Mathematics 143 or Computer Science 173.

Selected topics in mathematics and computer science as presented by students, departmental faculty and visiting speakers. Requirements include written summaries of each presentation and a paper on a mathematics/computer science topic of personal interest. Same as Computer Science 299. *Staff. *

**387, 388, 389 Selected Topics (1/4, 1/2, 1)**

Prerequisite: Permission of instructor.

An examination of subjects or areas not included in other courses. *Staff.*

**391, 392 Internship (1/2, 1)**

Offered on a credit/no credit basis. *Staff.*

**399 Colloquium in Mathematics and Computer Science (1/4) **

Prerequisites: Mathematics 299 and senior standing.

Selected topics in mathematics and computer science as presented by students, departmental faculty and visiting speakers. Requirements include written summaries of each presentation, a departmental major assessment examination and an oral presentation on a mathematics/computer science topic of personal interest. Offered only on a credit/no credit basis. Same as Computer Science 399. *Staff.*

**401, 402 Seminar (1/2, 1)**

*Staff.*

**411, 412 Directed Study (1/2, 1)**

*Staff.*