# Mathematics: Course Descriptions

#### MATH-122 College Algebra

Offers students the opportunity to polish their general algebra skills in preparation for precalculus, statistics and other courses where a working knowledge of algebra without trigonometry is a prerequisite. Throughout the course, students are asked to translate information back and forth between grammatical and mathematical forms. Topics include modeling, graphing, and analysis with linear, quadratic and general polynomial expressions, solving linear, quadratic and general polynomial equations and inequalities and functions. 4 credits.
*Credits: 4.00*

#### MATH-125 Precalculus

Most science and mathematics courses require that students be comfortable working with functions symbolically, graphically, and numerically. Precalculus offers students the background they need to pursue these courses. An integral component of the course is translating information back and forth between grammatical and mathematical forms. Concentrating on functions and their properties, the course includes the study of several classes of functions including polynomial, rational, exponential, logarithmic, and trigonometric functions. The conic sections are also studied. Prerequisite: MATH 122 with a minimum grade of C or placement. 4 credits.
*Credits: 4.00*

#### MATH-155 Special Topics in Mathematics

See department for course description.
*Credits: 1.00*

#### MATH-165 Modern Topics in Mathematics

This course exposes students to abstraction and problem solving with mathematical constructs. Elements of descriptive and inferential statistics give students the foundation to understand visual and numerical representations of data and to make informed judgments about survey and experimental study results. Various topics chosen from among management science, finance, voting theory, game theory, symmetry, proportionality, or other modern topics offer the opportunity to see connections of mathematics to business, political science, art and other fields. 4 credits.
*Credits: 4.00*

#### MATH-195 Independent Study

See department for details. Independent study contract required.
*Credits: 1.00*

#### MATH-207 General Elementary Statistics

This course covers the basic theory and practice of descriptive and inferential statistics including the presentation and structure of data sets, histograms, correlation, and regression analysis. Sampling distributions, binomial, normal, and chi-square probability distributions, confidence intervals, estimation, and hypothesis testing including t-tests and analysis of variance will also be discussed. Includes an introduction to a statistical software package. Prerequisite: MATH 122 with a minimum grade of C or placement. 4 credits.
*Credits: 4.00*

#### MATH-212 Language and Logic

A survey of formal syntactic and semantic features of language, including topics such as sentential logic, predicate logic, axiomatic systems and set theory, and nonclassical extensions such as multivalued logics. Also listed as PHIL 212. Offered annually. 4 credits.
*Credits: 4.00*

#### MATH-221 Mathematics for Elementary Teachers I

Designed for future elementary teachers. Elements of logic, numeration, the number systems of arithmetic, elementary number theory, the algorithms of arithmetic, introductory concepts of statistics and probability. Alternate years 2012-2013. 4 credits.
*Credits: 4.00*

#### MATH-223 Mathematics for Elementary Teachers II

Designed for future elementary teachers. Intuitive geometry in two and three dimensions, systems of measurement, estimation and approximation. Alternate years 2013-2014. 4 credits.
*Credits: 4.00*

#### MATH-226 Calculus I

The study of functions and their rates of change. Topics include the concept of derivative as rate of change, limits and continuity, differentiation and its applications, Intermediate, Extreme and Mean Value Theorems, introduction to integrals, and the Fundamental Theorem of Calculus. Prerequisite: MATH 125 with a minimum grade of C or placement. 4 credits.
*Credits: 4.00*

#### MATH-227 Calculus II

Investigation of single variable integration including techniques of symbolic integration, numerical integration and error analysis, applications of integration, and improper integrals. Infinite sequences, infinite series, and Taylor series will be introduced. Prerequisite: MATH 226 with a minimum grade of C or placement. 4 credits.
*Credits: 4.00*

#### MATH-228 Calculus III

The study of calculus of several variables. Topics include visualization techniques, vectors and solid analytic geometry, vector arithmetic, partial differentiation and its applications, gradients, optimization techniques, iterated integrals, line integrals, divergence, curl and related theorems. Prerequisite: MATH 227 with a minimum grade of C. 4 credits.
*Credits: 4.00*

#### MATH-240 Discrete Mathematics

This course introduces the fundamentals of number systems, sets, functions and relations, logic and proof, elementary combinatorics, Boolean algebra and graph theory. It plays the role of a transition course for mathematics majors, moving them from calculus to the upper division courses in mathematics, and as an important course in logic for computer science majors. Prerequisite: MATH 226 with a minimum grade of C or placement. 4 credits.
*Credits: 4.00*

#### MATH-255 Special Topics

See department for course description.
*Credits: 1.00*

#### MATH-275 Internship

See department for details. Internship contract required.
*Credits: 1.00*

#### MATH-301 Mathematical Modeling

A wide variety of physical and social systems can be described and analyzed using mathematics. In this course, students will learn about the mathematical modeling process through examination and analysis of frequently used models in physics, chemistry, biology and other sciences. Students will also experience generating and testing new models. Prerequisite: MATH 226 with a minimum grade of C or placement. Offered alternate years 2012-2013. 4 credits.
*Credits: 4.00*

#### MATH-306 Linear Algebra

Systems of linear equations, vector spaces, dependence, basis, dimension, linear transformations, determinants, eigenvalues, eigenvectors, orthogonal matrices, curves of best fit, quadratic forms. Attention to computational, and graphical applications and argumentation. Prerequisite: MATH 226 and MATH 240 each with a minimum grade of C. 4 credits.
*Credits: 4.00*

#### MATH-311 Ordinary Differential Equations

Topics include the theory of linear equations, investigations of non-linear equations, systems of equations, numerical methods, stability, long-term behavior and Laplace transforms. Emphasis is placed on both quantitative and qualitative descriptions of solutions and applications. Prerequisite: MATH 227 with a minimum grade of C. Offered alternate years 2013-2014. 4 credits.
*Credits: 4.00*

#### MATH-316 Mathematical Probability and Statistics

This course covers the fundamentals of mathematical probability and statistics, including the axioms of probability, conditional probability, discrete and continuous random variables, multivariate distributions, moment generating functions, the binomial, geometric, Poisson, normal, and exponential distributions and the Central Limit Theorem. Additional topics from statistical inference theory such as order statistics, confidence intervals, and Chi-Square tests in addition to estimation of parameters using maximum likelihood methods will also be covered as time permits. Prerequisite: MATH 228 (may be taken concurrently) and MATH 240 each with a minimum grade of C. Alternate years 2013-2014. 4 credits.
*Credits: 4.00*

#### MATH-321 Higher Geometry

A rigorous study of both Euclidean and non-Euclidean geometries. Prerequisite: MATH 240 with a minimum grade of C. Offered alternate years 2012-2013. 4 credits.
*Credits: 4.00*

#### MATH-326 Introduction to Analysis

Provides a transition from calculus to real and complex analysis. Focuses on rigorous development of fundamental concepts in calculus including limits, convergence of sequences and series, compact sets, continuity, uniform continuity and differentiability of functions. Prerequisite: MATH 227 and MATH 240 each with a minimum grade of C. 4 credits.
*Credits: 4.00*

#### MATH-355 Special Topics

See department for course description.
*Credits: 1.00*

#### MATH-360 Special Topics in Mathematics

The topic of this course will change from year to year, and will depend on the interests and judgment of the math department faculty. Examples of topics may include the history of mathematics, dynamical systems, foundations and logic, mathematical biology, topology, graph theory, number theory, and differential geometry. Prerequisite: MATH 240 with a minimum grade of C; additional prerequisites may apply depending on the topic. May be repeated once for credit. 4 credits.
*Credits: 4.00*

#### MATH-385 Junior Seminar

This course is designed to help students learn how to read mathematics, to communicate it through mathematical writing and speaking, and to prepare students for careers in mathematics and related fields. Students will read and present two journal articles. Contents will further include the mathematical writing package Latex and presentation software Beamer, as well as career planning and graduate school preparation. Students will also attend mathematical colloquia and mathematics projects presented during senior project day. Prerequisite: Junior standing or above (60 or more completed credits) and 6 credits of 300-level MATH courses with a minimum grade of C. 2 credits.
*Credits: 2.00*

#### MATH-395 Independent Study

See department for details. Independent study contract required.
*Credits: 1.00*

#### MATH-400 Number Theory

Studies the theory of numbers with an emphasis on algebraic structures. Topics may include modular arithmetic, quadratic fields, Pell's equations, quadratic reciprocity, sums of squares, unit groups, factorization in number rings, ideals, diophantine equations, and the geometry of numbers. Prerequisite: MATH 306 with a minimum grade of C. Offered alternate years 2013-2014. 4 credits.
*Credits: 4.00*

#### MATH-402 Abstract Algebra

A survey of fundamental concepts in abstract algebra. Topics may include Group theory, including quotient groups, fundamental results on group homomorphisms and the study of finite groups; Ring theory, including fundamental homomorphism theorems, quotient rings and Euclidean rings, vector spaces and modules; Field theory including field extensions, Galois theory and classical results concerning constructability and solvability. Prerequisite: MATH 240 and MATH 306 each with a minimum grade of C. Offered alternate years 2012-2013. 4 credits.
*Credits: 4.00*

#### MATH-405 Real Analysis

A rigorous treatment of the limit concept, continuity, differentiation and integration. Sequence and series convergence. Uniform and pointwise convergence of sequence and series of functions. Prerequisites: MATH 326 with a minimum grade of C. 4 credits.
*Credits: 4.00*

#### MATH-410 Discrete Topics

This course will provide advanced study of a topic in discrete mathematics. Topics may include graph theory, combinatorics, discrete optimization, or set theory. Prerequisite: MATH 227 and MATH 240 with a minimum grade of C; other prerequisites as required by the topic. Offered alternate years 2012-2013. 4 credits.
*Credits: 4.00*

#### MATH-411 Partial Differential Equations

Addresses solution methods for the three basic partial differential equations of mathematical physics: the heat, wave and potential equations. Methods covered will include power series, Fourier series, Laplace transform methods, separation of variables, and the method of characteristics. Initial and boundary data will also be covered, as well as physical applications and numerical simulations of solutions. Special topics as time permits. Prerequisite: MATH 228 and MATH 311 each with a minimum grade of C. Offered alternate years 2013-2014. 4 credits.
*Credits: 4.00*

#### MATH-412 Complex Analysis

Complex numbers, analytic functions, elementary functions, mapping by elementary functions, integrals, series, residues and poles, conformal mapping. Prerequisites: MATH 228 and MATH 240 both with a minimum grade of C. Offered alternate years 2012-2013. 4 credits.
*Credits: 4.00*

#### MATH-455 Special Topics

See department for course description.
*Credits: 1.00*

#### MATH-475 Internship

See department for details. Internship contract required.
*Credits: 1.00*

#### MATH-490 Senior Capstone

Students will have the opportunity to use their mathematical skills and knowledge to investigate projects of their choice under the supervision of faculty in mathematics. The project will result in a final paper and senior capstone presentation. Prerequisite: Senior standing (90 or more completed credits), a declared Mathematics major, and 9 credits of upper division MATH courses with a minimum grade of C. 1 credit.
*Credits: 1.00*

#### MATH-492 Senior Capstone II

This is a continuation of MATH 490. Prerequisite: MATH 490 with a minimum grade of C. 1 credit.
*Credits: 1.00*

#### MATH-495 Independent Study

See department for details. Independent study contract required.
*Credits: 1.00*