120. Appreciation of Mathematics
An exploration of topics which illustrate the power and beauty of mathematics, with a focus on the role mathematics has played in the development of Western culture. Topics differ by instructor but may include: Fibonacci numbers, mathematical logic, credit card security, or the butterfly effect. This course is designed for students who are not required to take statistics or calculus as part of their studies.
An introduction to statistical thinking and the analysis of data using such methods as graphical descriptions, correlation and regression, estimation, hypothesis testing, and statistical models.
160. Calculus for the Social Sciences
A graphical, numerical and symbolic introduction to the theory and applications of derivatives and integrals of algebraic, exponential, and logarithmic functions, with an emphasis on applications in the social sciences. Note: A student may not receive credit for both MATH 160 and MATH 181.
181. Calculus 1
A graphical, numerical, and symbolic study of the theory and applications of the derivative of algebraic, trigonometric, exponential, and logarithmic functions, and an introduction to the theory and applications of the integral. Suitable for students of both the natural and the social sciences. Note: A student may not receive credit for both MATH 160 and MATH 181.
182. Calculus 2
A graphical, numerical, and symbolic study of the theory, techniques, and applications of integration, and an introduction to infinite series and/or differential equations. Prerequisite: MATH 181 or permission of instructor.
201. Modeling and Simulation for the Sciences
A course in scientific programming, part of the interdisciplinary field of computational science. Large, open-ended, scientific problems often require the algorithms and techniques of discrete and continuous computational modeling and Monte Carlo simulation. Students learn fundamental concepts and implementation of algorithms in various scientific programming environments. Throughout, applications in the sciences are emphasized. Cross-listed as COSC 201. Prerequisites: MATH 181 or permission of instructor.
210. Multivariable Calculus
A study of the geometry of three-dimensional space and the calculus of functions of several variables. Prerequisite: MATH 182.
212. Vector Calculus
A study of vectors and the calculus of vector fields, highlighting applications relevant to engineering such as fluid dynamics and electrostatics. Prerequisite: MATH 182.
220. Linear Algebra
The theoretical and numerical aspects of finite dimensional vector spaces, linear transformations, and matrices, with applications to such problems as systems of linear equations, difference and differential equations, and linear regression. Prerequisite: MATH 182.
235. Discrete Mathematical Models
An introduction to some of the important models, techniques, and modes of reasoning of non-calculus mathematics. Emphasis on graph theory and combinatorics. Applications to computing, statistics, operations research, and the physical and behavioral sciences. Prerequisite: MATH 182.
240. Differential Equations
The theory and application of first- and second-order differential equations including both analytical and numerical techniques. Prerequisite: MATH 182.
250. Introduction to Technical Writing
An introduction to technical writing in mathematics and the sciences with the markup language LaTeX, which is used to typeset mathematical and scientific papers, especially those with significant symbolic content.
260. Introduction to Mathematical Proof
An introduction to rigorous mathematical argument with an emphasis on the writing of clear, concise mathematical proofs. Topics will include logic, sets, relations, functions, and mathematical induction. Additional topics may be chosen by the instructor.
Prerequisite: MATH 182.
280. Selected Topics in Mathematics
Selected topics in mathematics at the introductory or intermediate level.
310. History of Mathematics
A survey of the history and development of mathematics from antiquity to the twentieth century. Prerequisite: Math 260.
320. Mathematical Modeling
The study of problem-solving strategies to solve open-ended, real-world problems. Prerequisite: MATH 210, 220, or 240.
330. Numerical Methods
A study of the theory and computer implementation of numerical methods. Topics include error analysis, zeros of polynomials, numerical differentiation and integration, and systems of linear equations. Prerequisites: MATH 220 and computer programming ability.
A study of the foundations of Euclidean geometry with emphasis on the role of the parallel postulate. An introduction to non-Euclidean (hyperbolic) geometry and its intellectual implications. Prerequisite: MATH 260.
An introduction to topological spaces. Topics will include examples of topological spaces, standard constructions of topological spaces, continuous maps, topological properties, homotopies, homeomorphisms, and simplicial complexes. Prerequisite: MATH 260.
421-422. Probability and Statistics
A study of probability models, random variables, estimation, hypothesis testing, and linear models, with applications to problems in the physical and social sciences. Prerequisite: MATH 210 and 260.
424. Advanced Game Theory
This advanced class is intended to provide a more rigorous introduction to the main concepts and techniques of the field. These techniques will be used to investigate relevant social phenomena, such as evolutionary games, auction theory, the "prisoner's dilemma," the "tragedy of the commons," tacit collusion, competition among firms, and strategic interactions in labor, credit, and product markets. The most important classes of games will be analyzed (zero-sum games, cooperation problems, coordination games, bayesian games, signaling games, etc.), as well as the most important solution concepts (rationalizability, nash equilibrium in pure and mixed strategies, bayesian nash equilibrium, and evolutionarily stable strategies). This course also will introduce students to the main techniques of game-theoretic mathematical modeling. Cross-listed with ECO 424. Prerequisite: MATH 210.
431-432. Abstract Algebra
The axiomatic development of abstract algebraic systems, including groups, rings, integral domains, fields, and vector spaces. Prerequisite: MATH 220 and 260.
An introduction to cryptology and modern applications. Students will study various historical and modern ciphers and implement select schemes using mathematical software. Cross-listed with COSC 435. Prerequisites: MATH 220 and either MATH 235 or 260.
439. Elementary Number Theory
A study of the oldest branch of mathematics, this course focuses on mathematical properties of the integers and prime numbers. Topics include divisibility, congruences, diophantine equations, arithmetic functions, primitive roots, and quadratic residues.
Prerequisite: MATH 260.
441-442. Mathematical Analysis
A rigorous study of the fundamental concepts of analysis, including limits, continuity, the derivative, the Riemann integral, and sequences and series. Prerequisites: MATH 210 and 260.
445. Advanced Differential Equations
This course is a continuation of a first course on differential equations. It will extend previous concepts to higher dimensions and include a geometric perspective. Topics will include linear systems of equations, bifurcations, chaos theory, and partial differential
equations. Prerequisite: MATH 240.
448. Functions of a Complex Variable
An introduction to the analysis of functions of a complex variable. Topics will include differentiation, contour integration, power series, Laurent series, and applications.
Prerequisite: MATH 260.
470. Independent Study in Mathematics
Independent study of selected topics in Mathematics at an advanced level. Specific topics vary from semester to semester. Prerequisite: Permission of instructor.
480. Advanced Topics in Mathematics
Advanced topics in undergraduate mathematics offered occasionally to meet special needs. Typical topics include number theory, foundations of mathematics, topology, and complex variables