# Mathematics

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 (10 Credits)

- MATH 251W Foundations of Advanced Mathematics (1)
- MATH 253 (QA) Linear Algebra (1)
- MATH 499W Senior Seminar in Mathematics (1)
- CS 125 Problem Solving with MATLAB (1)
**or** - CS 141 (QA*) Introduction to Programming (1)
**or** - CS 154 Introduction to Functional Programming (1)
**or** - One Computer Science course numbered 200 or higher (1)
- Three additional credits in Mathematics at the 400 level (3), including at least one of:
- MATH 446 Real Analysis I (1)
**or** - MATH 456 Abstract Algebra I (1)

### Three additional credits in Mathematics (3)

- One credit in Mathematics numbered 300 or above (1)
- Two credits in Mathematics numbered 200 or above (2)

## Requirements For The Mathematics Minor (6 Credits)

- Five credits in Mathematics numbered 142 or higher (5)
- CS 125 Problem Solving with MATLAB (1)
**or** - CS 141 (QA*) Introduction to Programming (1)
**or** - CS 154 Introduction for Functional Programming (1)
**or** - One Computer Science course numbered 200 or higher (1)

## Indicators of Achievement

### Student Learning Outcomes for the Mathematics Major

- Exposure to breadth and depth of mathematical knowledge
- Mathematical thinking, proof reading and writing (abstraction; combining creative and analytical thinking; problem-solving; making connections; formulating conjectures, including correct use of mathematical notation; appreciation of aesthetics in mathematics (style and beauty))
- Inquisitiveness and enthusiasm (thirst for knowledge and understanding, membership in a community of scholars)
- Familiarity with technological tools

## Faculty

**Josh Laison**, Associate Professor of Mathematics; Department Chair**Colin Starr**, Associate Professor of Mathematics**Mark Janeba**, Associate Professor of Mathematics**Inga Johnson**, Associate Professor of Mathematics; Advisor for Mathematical Contest in Modeling**Erin McNicholas**, Associate Professor of Mathematics**Kathryn Nyman**, Associate Professor of Mathematics**Peter Otto**, Associate Professor of Mathematics

## Part-Time and Visiting Faculty

**Naveed Ali****Jordan Purdy****Noel Spencer Sitton**

## Course Listings

### MATH 102X Problem-Solving (.25)

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.

**Offering:**Fall**Instructor:**Staff

### MATH 130 (QA*) Contemporary Mathematics (1)

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:**Quantitative and Analytical Reasoning (*)**Offering:**Every semester**Instructor:**Staff

### MATH 138 (QA*) Statistics (1)

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.

**Prerequisite**: 0.5 credits if taken after MATH 266, ECON 230, PSYC 253, SOC 401 or IDS 138**General Education Requirement Fulfillment:**Quantitative and Analytical Reasoning (*)**Offering:**Every semester**Instructor:**Staff

### MATH 140 (QA*) Modeling with Calculus (1)

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:**Quantitative and Analytical Reasoning (*)**Prerequisite:**Not to be taken after MATH 152, or MATH 249. 0.5 credits if taken after MATH 151.**Offering:**Every semester**Instructor:**Starr, Janeba, Otto, McNicholas, Johnson, Laison, Nyman

### MATH 151 (QA*) Accelerated Calculus (.5)

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.

**Prerequisite**: Not to be taken after AP Calculus credit, MATH 152, MATH 153, MATH 249**General Education Requirement Fulfillment**: One-half Quantitative and Analytical Reasoning***Offering:**Every semester**Instructor:**Staff

### MATH 152 (QA*) Accelerated Calculus II (.5)

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.

**Prerequisite**: Prior Calculus experience with derivatives. Not to be taken after AP Calculus credit, MATH 153, or MATH 249**General Education Requirement Fulfillment:**One-half Quantitative and Analytical Reasoning***Offering:**Every semester**Instructor:**Staff

### MATH 153 (QA*) Sequences and Series (.5)

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:**One-half Quantitative and Analytical Reasoning***Prerequisites:**Prior calculus experience with integrals**Offering:**Every semester**Instructor:**Staff

### MATH 163 (QA*) Discrete Mathematics (1)

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.

**Prerequisites**: Not to be taken after MATH 251W**General Education Requirement Fulfillment:**Quantitative and Analytical Reasoning***Offering:**Spring**Instructor:**Staff

### MATH 249 (QA*) Multivariable Calculus (1)

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:**Quantitative and Analytical Reasoning (*)**Prerequisite:**Prior calculus experience with integrals**Offering:**Every semester**Instructor:**Staff

### MATH 251W Foundations of Advanced Mathematics (1)

This course is intended as the first course after calculus for those students intending to major or minor in mathematics. It 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, the real number system, elementary number theory and other basic areas of mathematics.

**General Education Requirement Fulfillment:**Writing-centered**Prerequisite:**AP Calculus credit, MATH 152, or consent of instructor**Offering:**Every semester**Instructor:**Staff

### MATH 253 (QA) Linear Algebra (1)

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

**General Education Requirement Fulfillment:**Quantitative and Analytical Reasoning**Prerequisite:**MATH 251W**Offering:**Every semester**Instructor:**Staff

### MATH 256 (QA) Differential Equations (1)

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

**General Education Requirement Fulfillment:**Quantitative and Analytical Reasoning**Prerequisite:**MATH 249. MATH 253 recommended.**Offering:**Fall**Instructor:**Staff

### MATH 266 (QA*) Probability and Statistics (1)

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:**Quantitative and Analytical Reasoning (*)**Prerequisite:**AP Calculus credit or MATH 152.**Offering:**Spring**Instructor:**Staff

### MATH 345 Complex Variables (1)

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

**Prerequisite:**MATH 249**Offering:**Alternate years in fall**Instructor:**Staff

### MATH 356 Number Theory (1)

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.

**Prerequisite:**MATH 251W**Offering:**Alternate years in spring**Instructor:**Staff

### MATH 376 Topics in Mathematics (1)

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.

**Offering:**Alternate years**Instructor:**Staff

### MATH 425 Mathematics Meetings (.25)

In this course students will be exposed to the professional culture of mathematics and a wide variety of mathematical topics. The class will travel to the national Joint Mathematics Meetings conference in the week before the start of the spring semester. During the semester, students will each design a presentation based on one of these talks for the mathematics department colloquium. Travel funds may be available.

**Prerequisite:**Mathematics major and consent of instructor.**Offering:**On demand**Instructor:**Laison

### MATH 446 Real Analysis I (1)

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.

**Prerequisite:**MATH 253 or consent of instructor**Offering:**Twice every five semesters**Instructor:**Staff

### MATH 447 Real Analysis II (1)

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.

**Prerequisite:**MATH 446**Offering:**Alternate years**Instructor:**Staff

### MATH 456 Abstract Algebra I (1)

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.

**Prerequisite:**MATH 253 or consent of instructor**Offering:**Alternate years**Instructor:**Staff

### MATH 457 Abstract Algebra II (1)

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..

**Prerequisite:**MATH 456 or consent of instructor**Offering:**Alternate years**Instructor:**Staff

### MATH 470 Topology (1)

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

### MATH 476 Modern Geometry (1)

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

**Prerequisite:**MATH 253 or consent of instructor**Offering:**Twice every five semesters**Instructor:**Staff

### MATH 486 Topics in Mathematics (1)

This course offers timely exposure to topics in mathematics which are not part of the regular curriculum. Examples of topics which might be offered: Cryptology, Differential Geometry, Vector Analysis, Topology.

**Offering:**On demand**Instructor:**Staff

### MATH 490 Independent Research (.5)

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.

**Prerequisite:**Consent of instructor**Offering:**On demand**Instructor:**Staff

### MATH 491 Advanced Independent Study (.5)

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.

**Prerequisite:**Consent of instructor**Offering:**On demand**Instructor:**Staff

### MATH 499W Seminar in Mathematics (1)

Study selected in consultation with the mathematics faculty and presented to the class. The seminar serves as the Senior Year Experience and involves oral and written presentation of research and reading topics. Required for Mathematics majors.

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