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 physical sciences and engineering, but also the quantitative side of economics, biology, the behavioral sciences, business and architecture. Even parts of the humanities rely on analytic modeling and 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 quantitative training is a valuable asset in many jobs. Others simply view mathematics as an interesting concentration in their liberal arts training, even though they plan to enter professional fields such 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:
- IRS Investigator
- Private Practice (CPA)
- Business Manager
- Computer Scientist
- Industrial Mathematician
- Investment Counselor
- Market Researcher
- Mathematical Analyst/Consultant
- Physics Researcher
- Securities Analyst
- Spacecraft Design Consultant
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 the tracks have room for some flexibility, each has its own flavor:
- Traditional Mathematics—a broad, more theoretical major that is a useful preparation 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 back-ground in traditional mathematics combined with economics. This track provides good preparation for advanced work in economics or finance.
Help and Flexibility to Choose Your Direction
As a math major, you will be assigned a faculty advisor who will help you shape 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 receive a lower score, contact your advisor about other possible ways to earn advanced placement.
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 40 years, our team’s record has been one of the best in the nation, placing among the top ten in 21 of those years and in the top five in 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 study groups for beginning calculus courses, or through grading papers.
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:
- Algorithms for Reducing the Complexity of High- Dimensional Data Sets
- Quantal Response: Models of Irrationality and Correlation in Games
- Group Decision-Making with Negative Influence Actors
- Hodge Decomposition and the Shapley Value of a Cooperative Game
- Spectral Gap of a Specific Linear Operator
- Semiparametric Modeling of Train Accident Costs with Implications for the Importance of Positive Train Control
- Modeling the Spread of Amyloid in Patients with Alzheimer’s Disease
- Elements of the Mathematical Formulation of Quantum States
- Exponential Random Graph Models Under Measurement Error
- Risk Factor Analysis of Thrombocytopenia
- Stochastic Thermodynamics of Markov Chain from Billiards Model
- The Hermitian Symplectic Group, Neumann Extension Theory, and Scattering on Quantum Graphs
- A Comparison of the Lasso and Dantzig Selector in Linear Regression Models – 𝑁-Complexes and 𝑆𝑛 Representations
- Schatten-class Truncated Toeplitz Operators
- Computing the Dispersion Relation of Periodic Quantum Graphs
- Modeling Air Pollution with GIS
- Polynomial Automorphisms
- An Alternative Graph Theoretic Proof of the Amitsur-Levitzki Identity
- Nash-Moser Inverse Function Theorem and its Application to Ricci Flow
- Automatic Classification of Formal and Informal Text
- The Relativistic Heat Equation
- Modifications to Nowak et al.’s Mathematical Population Genetic Model of the Evolution of Eusociality
- Categories, Groupoids, and Groupoidifications
- Aliquot Cycles for Elliptic Curves with Complex Multiplication
- On a Small Non-Shellable Lie Algebra
- Applications of Mixed Effects Models: An Analysis of fMRI Data in Anesthesiology
- Lie Groups and Lie Algebras