### Major

170, 171, 211, 262, 270, 351, 361

One math course having 351 or 361 as a prerequisite

One additional math course numbered 301 or higher

Two mathematics electives numbered 201 or higher. One elective may be replaced by COMP 132 or by the professional semester for students pursuing certification in mathematics, or, upon prior approval by the department, a mathematics-intensive course from another department.

### Minor

171 and 211, one of the three courses 325, 351 or 361 and two other courses numbered 201 or higher. Possible tracks include: Track 1: 170, 171, 211, 262, 270, 361; Track 2: 170, 171, 211, 262, 351, elective; Track 3: 170, 171, 211, 225, 270, 325. Tracks 1 and 2 focus on theoretical mathematics. Track 3 focuses on statistics.

### Suggested curricular flow through the major

There are many possible paths through the mathematics major. Which path to take depends on the student’s prior coursework and placement. We present four models here. With careful planning, all four models allow the possibility for students to spend a semester or a year abroad.

**Model 1** - MATH 151 as entry point (for students who place into 151)

*First Year:* 151, 170

*Sophomore Year:* 171, 211, 270, 262

*Junior and Senior Years:* 351,361, MATH electives

**Model 2** - MATH 170 as entry point (for students with suitable pre-calculus preparation)

*First Year:* 170, 171

*Sophomore Year:* 211, 262, 270

*Junior and Senior Years:* 351,361, MATH electives

**Model 3** - MATH 171 as entry point (for students with 170 credit)

*First Year: *171, 270

*Sophomore Year:* 211, 262

*Junior and Senior Years: *351,361, MATH electives

**Model 4** - MATH 171 as entry point (for students with 170 and 270 credits)

*First Year *[Option 1]: 171, 211

*First Year* [Option 2]: 211, 262

*Sophomore Year* [Option 1]: 262, MATH elective

*Sophomore Year *[Option 2]: 171, MATH elective

*Junior and Senior Years:* 351,361, MATH electives

Students who are interested in applied mathematics should consider the electives 225, 241, 325, and 331 during their third and fourth years.

**Note: Mathematics and Computer Science are one department but have been filed individually and alphabetically for ease of access.**

### Honors

Departmental honors is the highest distinction that the Department can award to a Major. Majors who receive departmental honors will be those who demonstrate a broad mastery of the discipline as well as an ability to complete and present high quality research. A broad mastery of the discipline is demonstrated by a GPA of 3.40 or higher in all courses related to the major. The ability to complete high quality research is demonstrated by the completion of a yearlong research project. This project will be characterized by an independent and in-depth study of an advanced topic including a literature search, reading of original sources and a novel formulation of results. Finally, the ability to present such research is demonstrated by the preparation of an honors thesis, a public presentation and a successful defense of the work to the department faculty. Detailed guidelines can be found on the departmental web page.

### Courses

121 Elementary Statistics

An introduction to the science of collecting, organizing, analyzing, and interpreting data. The focus is on data presentation and statistical reasoning based upon the analysis of data sets. Topics include the study of sampling methods, observational and experimental studies, graphical and numerical summaries of data, probability, sampling distributions, significance testing, estimation, and simple linear regression. Does not count toward the major or minor in mathematics.*Students cannot take this course concurrently with 225. Students who have received credit for 225 cannot take this course for credit. Offered every semester. *

Attributes: ARCH Area A Elective, ARCH Area B Elective, Appropriate for First-Year, ES Foundations of Env Sci Crs, LPPM Empirical Social Analysis, Quantitative Reasoning

151 Introduction to Calculus

An introduction to limits and derivatives together with a review of polynomial, rational, trigonometric, exponential, and logarithmic functions.*Three hours of classroom and one and a half hour of lab per week. Prerequisite: departmental placement. Offered every semester.*

Attributes: Appropriate for First-Year, ES Foundations of Env Sci Crs, Quantitative Reasoning

170 Single Variable Calculus

The study of real-valued functions, including transcendental functions, limits, derivatives and their applications, the definition of the Riemann integral, and the Fundamental Theorem of Calculus.*Three hours of classroom and one and a half hour of lab per week. Prerequisite: 151 or departmental placement. Offered every semester.*

Attributes: Appropriate for First-Year, ES Foundations of Env Sci Crs, Quantitative Reasoning

171 Multivariable Calculus

Multivariable calculus including parametric and polar equations, vectors, three-dimensional analytic geometry, vector-valued functions, functions of several variables, partial derivatives, and multiple integrals. Additional topics if time permits.*Three hours of classroom and one and a half hour of lab per week. Prerequisite: 170 or departmental placement. Offered every semester. *

Attributes: Appropriate for First-Year, ES Foundations of Env Sci Crs, Quantitative Reasoning

201 Special Topics

Topics to be announced when offered.

*Prerequisite: permission of the instructor. One-half or one course credit.*

202 Special Topics

Topics to be announced when offered.

*Prerequisite: permission of the instructor. One-half or one course credit.*

211 Discrete Mathematics

An introduction to fundamental mathematical concepts used in mathematics as well as computer science, with an emphasis on writing mathematical arguments. The course presents the principles of mathematical logic and methods of proof such as direct and indirect proofs and mathematical induction. Other topics include sets, functions, relations, matrix algebra, and techniques from elementary combinatorics and graph theory. *Prerequisite: 170 or COMP 131 or departmental placement. Offered every semester.*

Attributes: Appropriate for First-Year, ES Foundations of Env Sci Crs, Writing in the Discipline

225 Probability and Statistics I

An introduction to the core topics of probability and statistics. Topics include discrete and continuous random variables, joint distributions, expectation, variance, random sampling from populations, hypothesis tests, and confidence intervals.*Prerequisite: 171. Offered in even numbered fall semesters.*

Attributes: ARCH Area A Elective, ARCH Area B Elective, ES Foundations of Env Sci Crs

241 Numerical Methods

An introduction to numerical methods for solving mathematical problems. Topics chosen from interpolation, numerical differentiation and integration, solutions to linear and nonlinear systems, numerical solutions to differential equations and related topics.*Prerequisite: Completion of two of the following courses: 170, 171, 211 and 270. This course is cross-listed as COMP 241. Offered in even numbered spring semesters.*

Attributes: ES Foundations of Env Sci Crs

262 Introduction to Linear Algebra

An introduction to matrix algebra and abstract vector spaces with an emphasis on writing mathematical arguments. Topics include linear systems and matrices, vector spaces, linear independence, eigenvalues and eigenvectors.*Prerequisite: 211 or permission of the instructor. Offered every semester.*

Attributes: ES Foundations of Env Sci Crs

270 Integration and Infinite Series

The study of methods of integration, applications of the integral, elementary differential equations, and infinite sequences and series.*Prerequisite: 171 or departmental placement. Offered every spring. *

Attributes: Appropriate for First-Year, ES Foundations of Env Sci Crs

271 Differential Equations

Elementary methods of solutions of selected types of differential equations; solutions of systems of linear differential equations with constant coefficients; and a brief introduction to numerical methods and series solutions. Includes a strong emphasis on applications.*Prerequisite: 171 and 270. Offered in odd numbered fall semesters.*

301 Special Topics

Topics to be announced when offered.*Prerequisite dependent upon topic. One-half or one course credit. *

302 Special Topics

Topics to be announced when offered.*Prerequisite dependent upon topic. One-half or one course credit. *

311 Applied Combinatorics

An advanced course in discrete mathematics introducing the basic tools of combinatorics and their applications. The course will consider the three basic problems of combinatorics; counting, existence and optimization. *Prerequisite: 211. Offered even numbered spring semesters.*

314 Theoretical Foundations of Computer Science

An introduction to the theory of computation. Topics include formal language theory (grammars, languages, and automata including Turing machines), and an introduction to the concept of undecidable problems, including the halting problem.

* Prerequisite: COMP 132 and MATH 211. This course is cross-listed as COMP 314. Offered every spring.*

325 Probability and Statistics II

A continuation of Introduction to Probability and Statistics I. Topics include additional discrete and continuous distributions, conditional distributions, additional hypothesis tests, simple linear regression and correlation, multiple linear regression, analysis of variance, and goodness of fit tests. Special topics may include nonparametric tests, nonlinear regression, and time series analysis.*Prerequisites: 171, 225 and completion of, or concurrent registration in 270. Offered in odd numbered spring semesters.*

Attributes: ES Foundations of Env Sci Crs

331 Operations Research

An introduction to deterministic operations research, including linear programming, sensitivity analysis, and duality. Special topics may include transportation and assignment problems, network models, integer programming, and game theory.*Prerequisite: 262. This course is cross-listed as COMP 331. Offered in odd numbered fall semesters.*

Attributes: ES Foundations of Env Sci Crs

351 Abstract Algebra

An introduction to axiomatic formalism using algebraic structures as paradigms. Topics chosen from groups, rings, integral domains, fields and vector spaces. *Prerequisite: 262. Offered every spring.*

361 Real Analysis

A theoretical development of the basic ideas and concepts of real analysis. Topics include a study of real numbers, sequences, limits and continuity, differentiation and integration. Optional topics include infinite series, sequences and series of functions, and an introduction to point-set topology.*Prerequisite: 171, 262 and 270. Offered every fall.*

401 Special Topics

Topics to be announced when offered.*Prerequisite dependent upon topic. One-half or one course credit.*

402 Special Topics

Topics to be announced when offered.*Prerequisite dependent upon topic. One-half or one course credit.*

472 Complex Analysis

An introductory study of functions in the complex plane. Topics include: complex numbers and functions, the theory of differentiation and integration of complex functions; Cauchy's integral theorem; the Residue theorem. *Prerequisite: 361 and completion of, or concurrent registration in 351. Offered in odd numbered spring semesters.*

481 Topology

An elementary study of topological spaces. Topics include open and closed sets, the Hausdorff property, compactness, connectedness, continuity, homeomorphisms, product spaces, and the classification of spaces. Optional topics include metric spaces, identification spaces, manifolds, and the fundamental group. *Prerequisite: 361 and completion of, or concurrent registration in 351. Offered in even numbered spring semesters. *