# Mathematics

## MATH 111. Precalculus (4F)

Functions and graphs. Transformations, compositions, inverses, and combinations of functions. Exponentials and logarithms. Trigonometric functions and their inverses. Polynomial and Rational functions. This course is designed to prepare students for further studies in mathematics and the sciences; in particular, for an in-depth study of calculus. The course does not satisfy the Core Curriculum requirement in Mathematics.

## MATH 131. Survey of Mathematics (4E)

This course will include study of both theoretical and applied aspects of mathematics. Topics will vary from section to section and may include the following: number systems, mathematical modeling, Euclidean and non-Euclidean geometry, projective geometry, group theory, graph theory, mathematical logic, sets and infinity, topology, the concepts of calculus and the history of mathematics. The course is recommended for students of the liberal arts who wish to obtain a general view of contemporary mathematics. This course satisfies the Core Exploration requirement in Mathematics.

## MATH 151. Calculus I (4E)

The differential and integral calculus of functions of one variable: limits and continuity, the derivative, curve sketching, applications of the derivative, indefinite integrals and differential equations, definite integrals and the fundamental theorem, integration methods, applications of the integral, the convergence of sequences and series, power series, Taylor’s theorem and analytic functions, polar coordinates and parametric equations. This course satisfies the Core Exploration requirement in Mathematics. *Prerequisite: Familiarity with high school trigonometry is expected.*

## MATH 152. Calculus II (4E)

The differential and integral calculus of functions of one variable: limits and continuity, the derivative, curve sketching, applications of the derivative, indefinite integrals and differential equations, definite integrals and the fundamental theorem, integration methods, applications of the integral, the convergence of sequences and series, power series, Taylor’s theorem and analytic functions, polar coordinates and parametric equations. This course satisfies the Core Exploration requirement in Mathematics. *Prerequisite: Familiarity with high school trigonometry is expected.* *MATH 151 is a prerequisite for MATH 152*.

## MATH 161. Math for Teachers I (4F)

The foundations of arithmetical reasoning including general problem-solving skills; sets and operations; the use of manipulatives to model arithmetic; arithmetic in other bases; standard, alternative and invented algorithms; fractions and proportional reasoning; basic number theory. Student-centered pedagogies will be modeled and discussed.

## MATH 162. Math for Teachers II (4S)

Geometry (including constructions and proofs), tessellations and tilings of the plane, polyhedra, measurement, basic probability and statistics. Student-centered pedagogies will be modeled and discussed. *(MATH 161 is not a prerequisite for this course.)*

## MATH 181. Emerging Scholars Program (1E)

Supplemental problem-solving workshop for calculus (MATH 151, 152) students in the Emerging Scholars Program. Enrollment by permission of instructor. May be repeated for credit.

## MATH 191. General Problem Solving (1S)

Problem-solving methods in higher mathematics, with an emphasis on how different strategies are used across different areas of math. May be repeated for credit. *Prerequisites: MATH 151 or permission of the instructor.*

## MATH 199/299/399/499. Independent Study (1-4E)

This course consists of an independent creative or research project designed by the student and supervised by a mathematics faculty member. The nature of the project, the schedule for accomplishment, and the means of evaluation must be formalized in a learning contract prior to registration. May be repeated for credit if the topic is not repetitive.

## MATH 200. Discrete Mathematics (4S)

Set theory, elementary logic, sequences and mathematical induction, functions and relations, counting techniques, matrix theory, graphs and trees. This course satisfies the Core Exploration requirement in Mathematics. MATH 200 assumes more mathematical preparation than MATH 131.

## MATH 201. Psychological Statistics (4E)

The analysis of experimental data, including data from both laboratory and natural settings. Parametric analysis through two-way analysis of variance and nonparametric statistics. This course is cross-listed as PSYC 201.

## MATH 221. Introduction to Statistics (4S)

Introduction to the concepts and methods of statistics, including descriptive statistics (measures of central tendency, dispersion and shape, as well as data organization), probability theory, probability distributions, confidence intervals, hypothesis testing, types of error, correlation and regression, and analysis of variance. Computer software which provides statistical capabilities is used to apply the concepts covered to realistic data sets from the biological and/or social sciences. This course satisfies the Core Exploration requirement in Mathematics.

## MATH 255. Vector Calculus (4E)

The differential and integral calculus of scalar and vector-valued functions in one and several variables. This course satisfies the Core Exploration requirement in Mathematics. Prerequisite: MATH 152.

## MATH 256. Linear Algebra (4E)

Vectors in the plane and in space, vector spaces, linear transformations, matrices and determinants, systems of linear equations, characteristic values and vectors, inner product spaces and orthogonality. This course satisfies the Core Exploration requirement in Mathematics. Prerequisites: MATH 255; or MATH 152 and permission of the instructor.

## MATH 281. Foundations of Mathematics (4E)

Mathematical logic; proof techniques and proof writing; set theory (including Cantor’s theory of the infinite); relations and functions; theoretical foundations of number systems including the natural numbers, integers, rationals, reals, and complex numbers. This course satisfies the Core Exploration requirement in Mathematics. *Prerequisite: MATH 152.*

## MATH 293. Field Studies in Mathematics Education (1-4E)

This course provides experience in a school setting for students seeking teacher certification and for others interested in learning more about the nature of the school, the nature of children, the nature of mathematics education, and about teaching/learning processes within school settings. Students may take at most two of the following courses for a total of up to four credit-hours: ILCC 293, ILCS 293, IlLCF 293, ILCG 293, EDUC 293, MATH 293. *Prerequisite: MATH 256; or MATH 152 and permission of the instructor*.

## MATH 307. Classroom Assistantship (1-3E)

This course provides a credit-based experience for classroom assistants. The students serving as classroom assistants will attend their assigned classes, hold review sessions and assist faculty members during in-class assignments, among other duties. This course will follow the general college policies for classroom assistantship courses. This course may be repeated once. Prerequisites: Permission of the instructor, minimum 2.5 GPA and at least 8 credits of 200-level or above coursework in Mathematics.

## MATH 312. Differential Equations (4S)

Solution methods for first-order differential equations; existence and uniqueness theorems; solutions of second-order linear differential equations; power series methods; Laplace transformations; applications. *Prerequisite: MATH 256; or MATH 152 and permission of instructor*.

## MATH 321. Abstract Algebra I (4F)

Groups, subgroups, symmetry groups, homomorphisms, quotient groups, isomorphism theorems. Additional topics may include classification of finitely generated abelian groups, group actions, series of groups, Sylow theory, group presentations. *Prerequisite: MATH 281*

## MATH 351. Analysis I (4F)

The real number system, convergence and summability, compactness, connectedness and other topological aspects of the real line, limits and continuity. May also include differentiation and integration. *Prerequisite: MATH 281.*

## MATH 391. Putnam Seminar (1F)

Preparation for the Putnam Exam, an annual math competition held in December. Topics include general problem-solving strategies and previous exam problems which typically integrate knowledge from different areas of mathematics. May be repeated for credit.

## MATH 398/498. Off-Campus Internship (4-16E)

A variety of off-campus learning opportunities can be arranged through the Career Development Center. The off-campus internship is an individually designed experience that allows the student to explore the relationship between learning in the classroom and the practical application of knowledge in everyday work situations. *Prerequisites: Admission to the Internship Program and approval of the academic adviser and department chair. **Credit/no credit grading*.

## MATH 411. Partial Differential Equations (4AF)

Solution methods for basic partial differential equations, with a detailed study of the heat and wave equations. Topics include Fourier series solutions, integral transform methods, numerical methods for elliptic, parabolic and hyperbolic equations. *Prerequisite: MATH 312; or MATH 152 and permission of the instructor.*

## MATH 421. Combinatorics (4AF)

Topics may include the following: permutations, combinations, partitions, counting principles, generating functions, partially ordered sets, designs and codes, graphs and trees, planarity, networks, Hamiltonian cycles, Eulerian tours, combinatorial designs, games of complete information, asymptotic methods, combinatorial existence theorems and Ramsey theory. *Prerequisites: MATH 281 or permission of the instructor*.

## MATH 422. Abstract Algebra II (4S)

Rings, fields, vector spaces, homomorphisms, ideals, quotient rings, polynomial rings, extension fields. Additional topics may include PIDs, UFDs, compass and straightedge constructions, algebraic number theory, Galois theory. *Prerequisite: MATH 321.*

## MATH 444. Mathematical Modeling (4F)

The course provides a systematic approach to mathematical modeling, including construction and analysis of continuous and discrete mathematical models inspired by real life problems. Existing models and their mathematical concepts (such as Statistics, Differential Equations and Stochastic Processes) are studied. Using examples from a variety of fields such as physics, biology, engineering and economics, students will learn how to develop and use mathematical models of realworld systems. *Prerequisite: MATH 312 or the permission of the instructor.*

## MATH 451. Complex Analysis (4AS)

Complex numbers and functions, differentiability, integration, Cauchy theory, power series, and analytic continuation. *Prerequisite: MATH 281*.

## MATH 452. Analysis II (4S)

Metric spaces, topological spaces, fixed point theorems, convergence of sequences and series of functions; additional topics may include functional analysis, measure theory, Fourier series. *Prerequisite: MATH 351.*

## MATH 461. Topology (4AS)

Topological spaces, separation axioms, compactness and connectedness, continuity, metrizability, an introduction to algebraic topology. *Prerequisite: MATH 281*.

## MATH 490. Senior Topics Seminar in Mathematics (4E)

The Senior Topics Seminar is a capstone course for the Mathematics major centered around an in-depth study of an important field and/or open question in mathematics. Each seminar will have a small number of students who will work together to investigate an advanced topic that builds on their prior mathematics courses. Every student in the course will generate, either in a group or individually, two final products from the seminar: a public presentation in a form designated by the instructor, and a written report on the work to be kept by the department for the benefit of future students.

A detailed topic description will be available in the online “Schedule of Classes” before registration. May be repeated for credit if the topic is not repetitive. *Prerequisite: Consent of the instructor.*

## MATH 493/494. St. Mary’s Project in Mathematics (1-8E)

The St. Mary’s Project in mathematics is one of the culminating experiences in the mathematics major. It usually is completed in the two semesters of the student’s senior year. The project draws on and extends knowledge, analytical skills, and creative thought developed through previous work in an area or areas of mathematics or mathematics education. Usually, it is initiated by the student; however, the student may peruse lists of project ideas developed by the mathematics faculty or draw on other sources. The student shall select a faculty mentor and a topic with the advice of the department chair. A project proposal must be submitted, identifying the area to be explored and the methods of inquiry to be used. While working on the project, the student should learn a significant amount of mathematics beyond that learned in previous course work. Upon completion, the project shall be presented to the public in a way agreed upon by the student, the mentor, and the department chair. *Prerequisite: Consent of mentor and department chair*.

## MATH 495. Senior Project in Mathematics (4E)

Together with a 400-level mathematics course, the Senior Project in mathematics can be a component of the capstone experience in the major. Normally, a student will complete the project during the senior year. It draws on previous course work and study and should expand the student’s horizon in mathematics and develop his or her thinking skills. The idea should come from the student, but lists of project ideas developed by the mathematics faculty are available, and other sources may be used. The student shall select a faculty mentor and a topic with the advice of the department chair. A project proposal must be submitted, identifying the area to be explored and the methods of inquiry to be used. While working on the project, the student should learn a significant amount of mathematics beyond that learned in previous course work. Upon completion, the project shall be presented to the public in a way agreed upon by the student, the mentor and the department chair. May be repeated for credit if the topic is not repetitive. *Prerequisite: Consent of mentor and department chair*.