Mathematics Courses

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100. Precalculus: Elementary Functions

Intended for students who plan to continue in the calculus sequence, this course involves the study of basic functions: polynomial, rational, exponential, logarithmic, and trigonometric. Topics include a review of the real number system, equations and inequalities, graphing techniques, and applications of functions. Includes problem-solving laboratory sessions. Permission of instructor is required. This course does not count toward the major or minor in mathematics. (Offered annually)

110. Discovering in Mathematics

A study of selected topics dealing with the nature of mathematics, this course has an emphasis on its origins and a focus on mathematics as a creative endeavor. This course does not normally count toward the major or minor in mathematics. (Offered each semester)

130. Calculus I

This course offers a standard introduction to the concepts and techniques of the differential calculus of functions of one variable. A problem-solving lab is included as an integral part of the course. This course does not count towards the major in mathematics. (Offered each semester)

131. Calculus II

This course is a continuation of the topics covered in MATH 130 with an emphasis on integral calculus, sequences, and series. A problem-solving lab is an integral part of the course. Prerequisite: MATH 130 or permission of the instructor. (Offered each semester)

135. First Steps into Advanced Mathematics

This course emphasizes the process of mathematical reasoning, discovery, and argument. It aims to acquaint students with the nature of mathematics as a creative endeavor, demonstrates the methods and structure of mathematical proof, and focuses on the development of problem-solving skills. Specific topics covered vary from year to year. MATH 135 is required for the major and minor in mathematics. Prerequisite: MATH 131 or permission of the instructor. (Offered each semester)

204. Linear Algebra

This course is an introduction to the concepts and methods of linear algebra. Among the most important topics are general vector spaces and their subspaces, linear independence, spanning and basis sets, solution space for systems of linear equations, linear transformations and their matrix representations, and inner products. It is designed to develop an appreciation for the process of mathematical abstraction and the creation of a mathematical theory. Prerequisite: MATH 131, and MATH 135 strongly suggested, or permission of the instructor. Required for the major in mathematics. (Offered annually)

214. Applied Linear Algebra

A continuation of linear algebra with an emphasis on applications. Among the important topics are eigenvalues and eigenvectors, diagonalization, and linear programming theory. The course explores how the concepts of linear algebra are applied in various areas, such as, graph theory, game theory, differential equations, Markov chains, and least squares approximation. Prerequisite: MATH 204. (Offered every third year)

232. Multivariable Calculus

A study of the concepts and techniques of the calculus of functions of several variables, this course is required for the major in mathematics. Prerequisite: MATH 131. (Offered annually)

237. Differential Equations

This course offers an introduction to the theory, solution techniques, and applications of ordinary differential equations. Models illustrating applications in the physical and social sciences are investigated. The mathematical theory of linear differential equations is explored in depth. Prerequisites: MATH 232 and MATH 204 or permission of the instructor. (Offered annually)

278. Number Theory

This course couples reason and imagination to consider a number of theoretic problems, some solved and some unsolved. Topics include divisibility, primes, congruences, number theoretic functions, primitive roots, quadratic residues, and quadratic reciprocity, with additional topics selected from perfect numbers, Fermat’s Theorem, sums of squares, and Fibonacci numbers. Prerequisites: MATH 131 and MATH 204 or permission of the instructor. (Offered every third year)

331. Foundations of Analysis I

This course offers a careful treatment of the definitions and major theorems regarding limits, continuity, differentiability, integrability, sequences, and series for functions of a single variable. Prerequisites: MATH 135 and MATH 204. (Offered annually)

332. Foundations of Analysis II

This course begins with a generalization of the notions of limit, continuity, and differentiability (developed in MATH 331), and extends them to the two-dimensional setting. Next, the Fundamental Theorem of Calculus is extended to line integrals and then to Green's Theorem. The course culminates with a brief introduction to analysis in the complex plane. Prerequisites: MATH 232 and MATH 331. (Offered occasionally)

350. Probability

This is an introductory course in probability with an emphasis on the development of the student's ability to solve problems and build models. Topics include discrete and continuous probability, random variables, density functions, distributions, the Law of Large Numbers, and the Central Limit Theorem. Prerequisite: MATH 232 or permission of instructor. (Offered alternate years)

351. Mathematical Statistics

This is a course in the basic mathematical theory of statistics. It includes the theory of estimation, hypothesis testing, and linear models, and, if time permits, a brief introduction to one or more further topics in statistics (e.g., nonparametric statistics, decision theory, experimental design). In conjunction with an investigation of the mathematical theory, attention is paid to the intuitive understanding of the use and limitations of statistical procedures in applied problems. Students are encouraged to investigate a topic of their own choosing in statistics. Prerequisite: MATH 350. (Offered alternate years)

353. Mathematical Models

Drawing on linear algebra and differential equations, this course investigates a variety of mathematical models from the biological and social sciences. In the course of studying these models, such mathematical topics as difference equations, eigenvalues, dynamic systems, and stability are developed. This course emphasizes the involvement of students through the construction and investigation of models on their own. Prerequisites: MATH 204 and MATH 237 or permission of the instructor. (Offered every third year)

360. Foundations of Geometry

An introduction to the axiomatic method as illustrated by neutral, Euclidean, and non-Euclidean geometries. Careful attention is given to proofs and definitions. The historical aspects of the rise of non-Euclidean geometry are explored. This course is highly recommended for students interested in secondary-school teaching. Prerequisite: MATH 331 or MATH 375. (Offered every third year)

371. Topics in Mathematics

Each time this course is offered, it covers a topic in mathematics that is not usually offered as a regular course. This course may be repeated for grade or credit. Recent topics include combinatorics, graph theory, and wavelets. Prerequisite: MATH 135 and MATH 204 or permission of instructor. (Offered alternate years)

375. Abstract Algebra I

This course studies abstract algebraic systems such as groups, examples of which are abundant throughout mathematics. It attempts to understand the process of mathematical abstraction, the formulation of algebraic axiom systems, and the development of an abstract theory from these axiom systems. An important objective of the course is mastery of the reasoning characteristic of abstract mathematics. Prerequisites: MATH 135 and MATH 204 or permission of the instructor. (Offered annually)

376. Abstract Algebra II

This course is a continuation of the study of algebraic systems begun in MATH 375. Among the topics covered are rings, fields, principal ideal domains, unique factorization domains, Euclidean domains, field extensions, and finite fields. The latter portion of the course emphasizes applications of group, ring, and field theory drawn from such areas as error-correcting codes, exact computing, crystallography, integer programming, cryptography, and combinatorics. Prerequisite: MATH 375. (Offered occasionally)

380. Mathematical Logic

First order logic is developed as a basis for understanding the nature of mathematical proofs and constructions and to gain skills in dealing with formal languages. Topics covered include propositional and sentential logic, logical proofs, and models of theories. Examples are drawn mainly from mathematics, but the ability to deal with abstract concepts and their formalizations is beneficial. Prerequisite: MATH 204, PHIL 240, or permission of instructor. (Offered every third year)