What is Mathematics?

Mathematics is a central subject in academic studies, prized for its beauty and logical patterns, but also powerful in its applications. It is the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions. It is also the study of spatial configurations and their structure, measurement, transformations, and generalizations.

When you study mathematics, you are really exploring the “language of science”—not just the traditional engineering, physical sciences, business, or architecture—but all of the social, economic, biological, and behavioral sciences, as well as those parts of the humanities that employ analytic modeling techniques or rely heavily on data analysis.

Why Major in Mathematics?

You may have many reasons for majoring in mathematics. Mathematics has come to play a growing, prominent role in society at large. You may be planning an academic career in mathematics, involving teaching or research. Or, you may plan to work in industry or government.

Many math majors do not intend to become “mathematicians” at all, but realize that in many jobs quantitative training is a valuable asset. Others simply view mathematics as an interesting concentration in their liberal arts training, even though they plan to enter such professional fields as law, medicine, psychology, or social work.

You Can Do a Lot with a Math Major

Mathematics allows you to combine your major with your other interests in chemistry, physics, engineering, pre-med, or other disciplines in the humanities and social sciences.

Here are some examples of careers toward which you could apply your degree in mathematics.

• Accountant Business
• Government
• IRS Investigator
• Private Practice (CPA)
• Actuary
• Architect
• Business Manager
• Computer Scientist
• Economist
• Engineer
• Industrial Mathematician
• Investment Counselor
• Market Researcher
• Mathematical Analyst/Consultant
• Physics Researcher
• Securities Analyst
• Spacecraft Design Consultant
• Statistician
• Stockbroker
• Teacher/Professor

Mathematics at Washington University

Our primary goal is to provide you with an outstanding educational foundation for productive and creative careers in mathematics and related fields.

Flexible Ways to Complete Your Major
You can use one of several possible “tracks” to complete your major. While each track has room for some flexibility, each has its own flavor:

• Traditional Mathematics—a broad, more theoretical major that is a useful emphasis for graduate study in math or in combination with other subjects such as physics, biophysics, computer science, and geophysics.
• Probability and Statistics—the route chosen by those interested in actuarial work and many with interests in business or economics, using methods of probability and statistics to analyze data and assess what data are appropriate to certain questions.
• Applied Mathematics—with emphasis toward a career working (often in a team) with engineers, physicists, or programmers on problems to improve quality, design, productivity, or to decrease costs.
• Secondary Education Mathematics—a major which, together with a major in secondary education, can lead to a career in teaching.
• Mathematics with Economics Emphasis—a strong background in traditional mathematics combined with economics. This track provides good preparation for additional work in finance and related areas.

Help and Flexibility to Choose Your Direction
As a math major, you will be assigned a faculty advisor who will guide you in the construction of your program according to your personal interests and abilities. Your advisor will make sure that maximum opportunities are afforded you in using your electives to explore and define your path. If you have interdisciplinary interests and abilities in more than one field, a double major or a major and a minor is possible.

Possible Advanced Placement
You can receive Advanced Placement (AP) credit in calculus on the basis of earlier work. Students who receive a score of 5 on the Advanced Placement Calculus Exam (AB version) are automatically awarded credit for Calculus I; students who receive a 5 on the BC version automatically receive credit for Calculus I and II. If you do not take an AP exam, or received a lower score, contact your advisor about other possible ways to earn advanced placement.

Senior Honors
You are encouraged to work toward Honors or do a senior project. You must have a superior academic record and must successfully complete an Honors project under the guidance of a faculty member. In addition, you will make an oral presentation of your project to a faculty Honors committee. Check with your advisor for details and deadlines.

Research and Special Opportunities
You will have access to several different ways to enhance your study of mathematics at Washington University, such as:

• Conducting research directed by faculty members, or through the Research Experiences for Undergraduates (REU) programs sponsored each summer by the National Science Foundation.
• Participating in the undergraduate math club, where you might present a talk at one of the regular meetings on your own work and reading.
• Taking part in the annual William Lowell Putnam Mathematical Competition, a nationwide collegiate mathematics competition each December involving about 4,500 students from 500 schools. During the past 35 years, our team’s record has been one of the best in the nation, placing among the top ten in 19 of those years and in the top five for 11 of those years.
• Taking part in the annual Missouri Collegiate Mathematics Competition, sponsored by the Missouri Section of the Mathematical Association of America.
• Arranging independent work with a faculty member, perhaps leading to an Honors project during your senior year.
• Including (with advanced undergraduate standing) introductory graduate level courses in algebra, complex variables, functional analysis, or geometry into your program.
• Getting experience in teaching (with advanced undergraduate status) through supervised leading of discussion sessions in beginning calculus courses, study groups, or through grading papers.

The Minor
You also have the option to minor in mathematics to enhance your major in another field. There are seven math courses required in the core curriculum for this option, plus you must complete at least one additional course in advanced mathematics.

Examples of Recent Undergraduate Student Honors Projects:

• The Hough Transform
• Stochastic Methods for the Lotka-Volterra Model with Migration
• A Symmetric Function Invariant for Graphs
• Ramsey Theory: From Finite to Infinite
• An Elementary Proof of a Generalization of Brun's Theorem
• Explorations of a Generalization of the Descent Statistic
• An Inquiry into the Optimality of Diseases
• On the Row Sums of the Character Tables of GL(2,q)
• Randomly Generated Covering and Almost-Covering Arrays
• Polygonal Billiards and Markov Chains
• On the Algebraic Topology of Finite Spaces
• An Application of Harmonic Function in Estimating the Conversion Rate of a Heterogeneous Catalyst
• Refinable Functions in L^2(R) with Composite Symmetry
• The Complexity of Pebbling and Cover Pebbling
• Methods for Characterizing Doubly Invariant Subspaces
• Use of the Pigeonhole Principle in an Attempt to Solve a Problem of Moreto
• Finite Groups Associated with Composition Dilation Wavelets
• Patterns of Progression from Psychiatric Disorders to Alcohol Use Disorders: A Unique Method of Analysis
• Studies of Dependence and Asymptotic (In)dependence in a New Family of Bivariate Distributions
• Approaches to the Virtual Positive Betti Number Conjecture
• A New Framework for Removing Gaussian and Impulse Noise
• The Algebraic Structure of OP(P)
• Utilization of Census Data 2000 in California
• Differentiable Paths in the "Hawaiian Earring"

For Additional Information Contact:

Professor Ronald Freiwald
Department of Mathematics
Washington University
Campus Box 1146
One Brookings Drive
St. Louis, MO 63130-4899
Phone: (314) 935-6839
Fax: (314) 935-5799
Email: rf@math.wustl.edu
Website: http://www.math.wustl.edu/
(Use the link to “Undergraduate Programs”)