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.*

**109** **Statistical Methods** **(1)**

Prerequisite: Permission of instructor.

Descriptive statistics, probability, sampling distributions, hypothesis testing, parameter estimation, confidence intervals, linear regression, curve fitting and analysis of variance are discussed. Uses the Minitab statistics package to display and analyze data. Students may not receive credit for both Mathematics 109 and 210. Usually not open to students who have had Mathematics 141. *Anderson.*

**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.*

**125** **Functions** **(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.

**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.*

**210** **Introduction to Statistical Analysis** **(1)**

Prerequisite: Mathematics 141 or equivalent.

Topics include descriptive statistics, principles of probability, random variables, sampling distributions, point and interval estimation, hypothesis testing, analysis of variance, regression and non-parametric statistics. Uses Minitab statistics program to analyze data. Students may not receive credit for both Mathematics 109 and 210. *Anderson.*

**236** **Linear Algebra** **(1)**

Prerequisite: Mathematics 143 or 239, or permission of instructor.

Vector spaces, matrices, Gauss-Jordan reduction, products, dimension, linear transformations, eigenvalues and eigenvectors, and a selection of applications of linear algebra to other disciplines. Develops skills in mathematical writing and creating mathematical proofs. Properties of equality, logical implication, proof by contradiction, quantification and proof by induction are illustrated in context. *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. *

**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. *

**309** **Mathematical Statistics** **(1)**

Prerequisite: Mathematics 236 or 245.

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

**310** **Applied Mathematical Statistics** **(1)**

Prerequisite: Mathematics 309.

A continuation of Mathematics 309. In-depth studies of regression analysis, analysis of variance, experimental design and nonparametric statistics. Covers topics pertinent to actuarial mathematics. Offered in alternate years. *Anderson.*

**316 Numerical Analysis (1) **

Prerequisites: Mathematics 236 or 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 236 or 247, and Mathematics 245.

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 either 236 or 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 236 and 239.

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 Geometerâ€™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.*

**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.*

**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.*

**380** **Mathematical Physics** **(1)**

Same as Physics 380. *Staff.*

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

Prerequisite: Permission of instructor.

Topics chosen to fit departmental interests, such as complex analysis, mathematical logic, geometric topology, chaos and fractals, algebraic coding theory, experimental design, nonparametric statistics and stochastic processes. Offered on demand. *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.*