Mathematics began with roots in the basic concepts of space and number and has flowered into many wonderful forms. The creation and discovery of new mathematics have never been more active or vital than they are today. Mathematics is sometimes called the science of pattern and order. It relies on logic as a standard of truth, but uses observation and even experimentation as means of discovering truth. Mathematicians think of their work as a blend of science and art, sometimes elegant and beautiful, describing deep and useful creations. In addition to theorems and theories, mathematics offers distinct modes of thought which are both versatile and powerful for understanding the world.

Courses serve those who wish to make mathematics a part of a liberal arts education, those who desire a mathematics background for other disciplines, such as Computer Science, Economics or the natural sciences, those who wish to minor in Mathematics, and those who wish to major in Mathematics.

Mathematics majors choose careers in education, industry, business, banking and insurance serving as teachers, statisticians, industrial mathematicians, computer programmers or analysts, actuaries and research workers in the biological, management or social sciences. Their training can also serve as a stepping stone to professional training or graduate work in a variety of fields.

## Requirements for the Mathematics Major (40 semester hours)

- MATH 251W Foundations of Advanced Mathematics (4)
- MATH 253 Linear Algebra (4)
- MATH 446 Real Analysis I (4)
**or**MATH 456 Abstract Algebra I (4) - One Computer Science course (numbered CS 125, CS 141, CS 151, CS 354, or anything at the 200-level or higher) (4)
- MATH 499W Senior Seminar in Mathematics (4)

### Twenty additional semester hours in Mathematics (20)

- Eight semester hours in Mathematics numbered 200 or above (8)
- Eight semester hours in Mathematics numbered 300 or above (8)
- Four semester hours in Mathematics numbered 400 or above (4)

## Requirements For The Mathematics Minor (24 semester hours)

- Twenty semester hours in Mathematics, 16 semester hours numbered at the 200-level or above (20)
- One Computer Science course (numbered CS 125, CS 141, CS 151, CS 154, or anything at the 200-level or higher) (4)

# Indicators of Achievement

## Student Learning Outcomes for the Mathematics Major

- Develop content depth and breadth of knowledge in mathematics and related subjects
- Communicate ideas clearly both in oral presentations and in written expository or argument driven work
- Gain independence as a reader and writer of mathematical proofs and/or quantitative arguments
- Use technology to solve problems and use appropriate tools for applications
- Collaborate in group problem solving and participate in a community of scholars

## Faculty

**Inga Johnson**, Professor and Chester F. Luther Chair of Mathematics, Advisor for Mathematical Contest in Modeling, , Department Chair,**Josh Laison**, Professor of Mathematics**Erin McNicholas**, Professor of Mathematics**Kathryn Nyman**, Professor of Mathematics**Peter Otto**, Professor of Mathematics,**Colin Starr**, Professor of Mathematics

## Course Listings

### MATH 102X Problem-Solving (1)

The course will offer students the opportunity to solve challenging mathematical problems unlike standard homework problems in any course. Class time will be spent studying problems, discovering solutions, writing up solutions formally, and discussing the important ideas of each solution. Most problems will be of the kind appearing on the Putnam Exam, an annual international mathematics competition. This course may be repeated for credit.

**Course is offered as Credit/No Credit****General Education Requirement Fulfillment:**Mathematical Sciences**Offering:**Fall**Instructor:**Staff

### MATH 130 Contemporary Mathematics (4)

A survey of contemporary topics in mathematics such as: voting systems and power, apportionment, fair division of divisible and indivisible assets, efficient distribution, scheduling and routing, growth and decay in nature and economics, symmetry and fractal geometry, probability and statistics.

**General Education Requirement Fulfillment:**Mathematical Sciences**Offering:**Every semester**Instructor:**Staff

### MATH 138 Introduction to Applied Statistics: Statistics and Applications (4)

This course is an introduction to descriptive and inferential statistical analysis. The following topics will be examined: scales of measurement; frequency distributions; graphing data; measures of central tendency, dispersion and skewness; sampling distributions; probability distributions; the binomial, Poisson and normal distributions; hypothesis testing; confidence intervals and interval estimation; t-tests; analysis of variance; correlational analysis; regression analysis; and analysis of nominal-level data.

**General Education Requirement Fulfillment:**Mathematical Sciences**Prerequisite**: Cannot take after ECON 230, PSYC 253, IDS 138 or AP Stat credit**Offering:**Every semester**Instructor:**Staff

### MATH 140 Modeling with Calculus (4)

Modeling with Calculus introduces and applies the concept of calculus to solve open-ended, real-word problems, especially those in the natural and social sciences. The emphasis is on developing and interpreting mathematical models. Topics include differential calculus, linear algebra, and differential equations. This course takes advantage of computational tools so that the focus can be on calculus concepts useful in applied work. This course is appropriate for students with no prior calculus experience.

**General Education Requirement Fulfillment:**Mathematical Sciences**Prerequisite:**Not to be taken after MATH 152, or MATH 249. 2 semester hours if taken after MATH 151.**Offering:**Every semester**Instructor:**Starr, Otto, McNicholas, Johnson, Laison, Nyman

### MATH 150 Differential Calculus with Precalculus (4)

MATH 150 is an introduction to differential calculus that includes some review of algebra and trigonometry. Topics covered include limits, the definition of the derivative, rules of differentiation, applications of the derivative, the definition of the definite integral, and the Fundamental Theorem of Calculus. Review of algebra and trigonometry will be included.

**General Education Requirement Fulfillment:**Mathematical Sciences**Prerequisite:**No credit if taken after AP Calculus credit, MATH 151, or MATH 152**Offering:**Annually**Instructor:**Staff

### MATH 151 Accelerated Calculus (2)

A first course in calculus for students with some previous exposure to the subject. Topics covered include limits; continuity; derivatives of algebraic, trigonometric, and exponential functions; implicit differentiation; the Mean Value Theorem; and optimization.

**General Education Requirement Fulfillment**: Mathematical Sciences**Prerequisite**: Not to be taken after AP Calculus credit, MATH 152, MATH 153, MATH 249**Offering:**Every semester**Instructor:**Staff

### MATH 152 Calculus II (4)

A second course in Calculus. Topics covered include definite and indefinite integrals, the Fundamental Theorem of Calculus, volume, arc length and surface areas, integration techniques, improper integrals, polar coordinates and parametric equations, sequences and series, Taylor Polynomials, Taylor Series, convergence, and Fourier Series.

**General Education Requirement Fulfillment**: Mathematical Sciences**Prerequisite**: Prior Calculus experience with derivatives. Not to be taken after AP Calculus credit, MATH 153, or MATH 249**Offering:**Every semester**Instructor:**Staff

### MATH 153 Sequences and Series (2)

A half-semester course on sequences and series. Topics covered include sequences and series, Taylor Polynomials, Taylor Series, convergence, and Fourier Series.

**General Education Requirement Fulfillment:**Mathematical Sciences**Prerequisites:**Prior calculus experience with integrals**Offering:**Every semester**Instructor:**Staff

### MATH 163 Discrete Mathematics (4)

Introduction to basic techniques and modes of reasoning in combinatorial problem-solving. Topics will be chosen from combinatorial mathematics, logic and Boolean algebra, difference equations, graph theory and applied algebra.

**General Education Requirement Fulfillment:**Mathematical Sciences**Prerequisites**: Not to be taken after MATH 251W**Offering:**Spring**Instructor:**Staff

### MATH 199 Topics in Mathematics (1-4)

A semester-long study of topics in Mathematics. Topics and emphases will vary according to the instructor. This course may be repeated for credit with different topics. See the New and Topics Courses page on the Registrar’s webpage for descriptions and applicability to majors/minors in other departments.

**General Education Requirement Fulfillment:**Topic dependent**Prerequisite:**Topic dependent**Offering:**Occasionally**Professor:**Staff

### MATH 239 Statistical Learning with R (4)

The general linear model is a fundamental tool frequently implemented by statisticians to describe the relationship between a quantitative response variable and one or more qualitative and/or quantitative explanatory variables. In this course, we will explore the implementation of the general linear model which will ultimately lead us to common model fitting techniques, including one-sample t-tests, two-sample t-tests, simple and multiple linear regressing, ANOVA, and ANCOVA. While theoretical results will occasionally be covered to provide necessary justification, the primary focus of the class will be on applying the aforementioned model fitting techniques to real data sets. The statistical software R will be used throughout the course to perform data analysis. Students enrolled in this course are presumed to have strong quantitative backgrounds and/or previous statistics experience.

**General Education Requirement Fulfillment:**Mathematical Sciences**Prerequisite:**AP Statistics or MATH 138 or IDS 138 or ECON 230 or instructor approved equivalent**Offering:**Annually**Instructor:**Staff

### MATH 249 Multivariable Calculus (4)

Three-dimensional analytic geometry; partial differentiation; maxima-minima problems; multiple integrals; vector fields, curl and divergence; line and surface integrals; applications.

**General Education Requirement Fulfillment:**Mathematical Sciences**Prerequisite:**Prior calculus experience with integrals**Offering:**Every semester**Instructor:**Staff

### MATH 251W Foundations of Advanced Mathematics (4)

This course provides an introduction to logic and the methods of proof commonly used in mathematics. Applications covered in the course are the foundations of set theory, equivalence relations, elementary number theory and other areas of mathematics.

**General Education Requirement Fulfillment:**Writing-centered; Mathematical Sciences**Prerequisite:**Any 100-level Math course (or higher, statistics, or computer science course; or any AP math, statistics, or computer science) or Instructor consent**Offering:**Every semester**Instructor:**Staff

### MATH 253 Linear Algebra (4)

Systems of linear equations, matrices, vector spaces and linear transformations.

**General Education Requirement Fulfillment:**Mathematical Sciences**Prerequisite:**MATH 152 (including AP credit), MATH 249, or instructor consent. MATH 251W recommended, but not required.**Offering:**Every semester**Instructor:**Staff

### MATH 256 Differential Equations (4)

Elementary differential equations; linear differential equations of second order; Laplace transformations; infinite series solutions; systems of linear differential equations.

**General Education Requirement Fulfillment:**Mathematical Sciences**Prerequisite:**MATH 249; MATH 253 recommended.**Offering:**Fall**Instructor:**Staff

### MATH 266 Probability and Statistics (4)

A calculus-based introduction to probability and statistics. Topics include summary statistics, probability theory, discrete and continuous random variables, distribution, limit theorems, estimation, hypothesis testing, and linear regression.

**General Education Requirement Fulfillment:**Mathematical Sciences**Prerequisite:**AP Calculus credit or MATH 152.**Offering:**Alternate years**Instructor:**Staff

### MATH 280 Math for Data Science (4)

An Introduction to the basic mathematical theory that underlie current data science methods. Students will gain an appreciation for the value of the mathematical theory as well as their limitations. Topics covered in the course will include: 1) Linear modeling and matrix computation (e.g., matrix algebra and factorization, eigenvalues/eigenvectors, and projection/least squares), 2) Optimization (e.g., calculus concepts related to differentiation), 3) Multivariate thinking (e.g., concepts and numerical computation of multivariate derivatives and integrals), and 4) Probabilistic thinking and modeling (e.g., counting principles, univariate and multivariate distributions, and independence). The connection between the mathematical theory and data science applications will be emphasized and the presentation of the theory will be driven by specific data science models and algorithms.

**General Education Requirement Fulfillment:**Mathematical Sciences**Prerequisite:**MATH 150 or MATH 151, or high school equivalent**Offering:**Fall**Instructor:**Otto

### MATH 299 Topics in Mathematics (1-4)

A semester-long study of topics in Mathematics. Topics and emphases will vary according to the instructor. This course may be repeated for credit with different topics. See the New and Topics Courses page on the Registrar’s webpage for descriptions and applicability to majors/minors in other departments.

**General Education Requirement Fulfillment:**Topic dependent**Prerequisite:**Topic dependent**Offering:**Occasionally**Professor:**Staff

### MATH 345 Complex Variables (4)

Complex numbers, limits, differentiation, analytic functions, integration, conformal mapping, Riemann surfaces and applications.

**General Education Requirement Fulfillment:**Mathematical Sciences**Prerequisite:**MATH 249 and MATH 251W**Offering:**Alternate years**Instructor:**Staff

### MATH 376 Topics in Mathematics (4)

This course offers timely exposure to topics in mathematics which are not part of the regular curriculum. Examples of topics which might be offered: Graph Theory, Advanced Linear Algebra, Operations Research.

**General Education Requirement Fulfillment:**Mathematical Sciences**Prerequisite:**MATH 251W**Offering:**Alternate years**Instructor:**Staff

### MATH 398 Junior Research Seminar (1)

In this course, students begin developing their Mathematics senior thesis projects under the mentorship of a departmental faculty member. Students will learn foundational techniques and concepts or review the relevant literature. Course meetings include discussion of research articles, peer teaching, learning about open problems, and practice with mathematical communication skills. The course culminates in a progress report that is given as a formal oral presentation.

- Prerequisite: Junior Standing and instructor consent
- Offering: Annually
- Instructor: Staff

### MATH 399 Topics in Mathematics (1-4)

A semester-long study of topics in Mathematics. Topics and emphases will vary according to the instructor. This course may be repeated for credit with different topics. See the New and Topics Courses page on the Registrar’s webpage for descriptions and applicability to majors/minors in other departments.

**General Education Requirement Fulfillment:**Topic dependent**Prerequisite:**Topic dependent**Offering:**Occasionally**Professor:**Staff

### MATH 429 Topics in Mathematics (1-4)

**General Education Requirement Fulfillment:**Topic dependent**Prerequisite:**Topic dependent**Offering:**Occasionally**Professor:**Staff

### MATH 446 Real Analysis I (4)

Rigorous study of the real numbers and real-valued functions. Topics include: limits and continuity on the real line, elementary topology of the real numbers, pathological examples. Other topics may include metric spaces, differentiation, vector-valued functions.

**General Education Requirement Fulfillment:**Mathematical Sciences**Prerequisite:**MATH 251W and MATH 253**Offering:**Alternate years**Instructor:**Staff

### MATH 447 Real Analysis II (4)

A continuation of MATH 446. Topics include: Differentiation and Riemann integration, sequences of functions. Other topics may include point-set topology of the reals, vector-valued functions, topological vector spaces, Lebesgue intetration, introductory measure theory.

**General Education Requirement Fulfillment:**Mathematical Sciences**Prerequisite:**MATH 446**Offering:**Alternate years**Instructor:**Staff

### MATH 456 Abstract Algebra I (4)

Number systems, elementary number theory, groups, rings, fields, polynomials and applications. Additional topics may be chosen from linear algebra, multilinear algebra, Sylow theory and Galois theory.

**General Education Requirement Fulfillment:**Mathematical Sciences**Prerequisite:**MATH 251W and MATH 253**Offering:**Alternate years**Instructor:**Staff

### MATH 457 Abstract Algebra II (4)

Course will build on the topics studies in MATH 456, Abstract Algebra I. In addition to Groups, Rings, and Fields, topics may include Galois Theory, Sylow Theory, Cayley Graphs, etc..

**General Education Requirement Fulfillment:**Mathematical Sciences**Prerequisite:**MATH 456**Offering:**Alternate years**Instructor:**Staff

### MATH 462 Number Theory (4)

An introduction to the theory of numbers to include such topics as divisibility, congruence, diophantine equations, quadratic reciprocity, the theory of prime numbers and analytic number theory.

**General Education Requirement Fulfillment:**Mathematical Sciences**Prerequisite:**MATH 251W**Offering:**Alternate years**Instructor:**Staff

### MATH 470 Topology (4)

Elementary point-set topology with an introduction to combinatorial topology and homotopy.

**General Education Requirement Fulfillment:**Mathematical Sciences**Prerequisite:**MATH 251W and MATH 253**Offering:**Alternate years**Instructor:**Staff

### MATH 476 Modern Geometry (4)

A modern approach to geometry. Topics will be chosen from Euclidean, non-Euclidean, affine, projective and differential geometry.

**General Education Requirement Fulfillment:**Mathematical Sciences**Prerequisite:**MATH 251W and MATH 253**Offering:**Alternate years**Instructor:**Staff

### MATH 490 Independent Research (2)

Directed research to investigate topics of special interest under the guidance of a faculty member. Topics chosen on the basis of the background and interests of the individual student.

**General Education Requirement Fulfillment:**Mathematical Sciences**Prerequisite:**Consent of instructor**Offering:**On demand**Instructor:**Staff

### MATH 491 Advanced Independent Study (2)

A course of directed research designed to enable the exceptional student to continue the investigation of topics of special interest under the guidance of a faculty member.

**General Education Requirement Fulfillment:**Mathematical Sciences**Prerequisite:**Consent of instructor**Offering:**On demand**Instructor:**Staff

### MATH 498 Senior Research Seminar I (2)

Students begin their Mathematics senior thesis project under the mentorship of a departmental faculty member. Students will build on foundational techniques and concepts from the Junior Research Seminar. Weekly meetings include peer teaching, study of new problems, presentation of progress on the research plans, and practice with mathematical communication skills. The course culminates in a progress report that is given as a formal oral presentation.

- Prerequisite: Senior standing and MATH 398 Junior Research Seminar, or instructor consent
- Offering: Fall
- Instructor: Staff

### MATH 499W Senior Research Seminar II (4)

Students complete their Mathematics senior thesis project under the mentorship of a departmental faculty member. Weekly meetings include peer teaching, study of new problems, presentation of progress on the research plans, and practice with mathematical communication skills. The course culminates in a written paper and a formal oral presentation

**General Education Fulfillment Requirement:**Writing-centered; Mathematical Sciences**Prerequisite:**Senior standing and consent of instructor**Offering:**Spring**Instructor:**Staff