# Information for Mathematics Majors

Mathematics is a discipline inseparable from scientific and philosophical inquiry. The rigorous and logical thinking that characterizes mathematics is an essential tool for theory building of any kind because its clarity and precision expose hidden assumptions, inner inconsistencies and deep structural similarities in problems that seem unrelated on the surface. Our courses cover a wide variety of well-established mathematical knowledge that is actively under development by today’s mathematicians and that offers fundamental tools for scientists and engineers of all kinds.

Students begin their work in the department with a thorough training in rigorous logical reasoning and mathematical proofs in the context of analysis and linear algebra. Next, they complete a survey of the main areas of modern mathematics by completing core courses in real and complex analysis, in algebra and in geometry/topology or discrete mathematics. Then students are free to take courses exploring a wide variety of topics in both pure and applied mathematics to acquire a good general knowledge of the main areas of current mathematical work.

In the independent work, students learn how to move beyond the classical knowledge found in textbooks to explore contemporary research literature through collaboration with their peers and with active researchers in mathematics or applied fields. Through this collaboration students

- Learn how to join a scholarly discussion in progress to orient themselves in a rapidly developing area of research.
- Build on their broad general knowledge of mathematics and logical reasoning skills in order to develop a working knowledge of a significant area of contemporary mathematics via the research literature.
- Learn to identify interesting problems they want to investigate and develop their own ideas about how to carry out those investigations.
- Learn to come up with a complete argument of their own, adapting and expanding ideas and techniques from various sources, as needed.
- Develop mastery of rigorous logical thinking by constructing complete and correct arguments.
- Develop mastery of clear mathematical exposition in a manner that allows and invites dialog with other scholars in the intended audience, where important definitions and theorems are clearly explained, and contributions of other scholars are properly acknowledged.

The program produces critical and creative thinkers with a broad general knowledge of contemporary mathematics and with the analytic and expository skills needed for collaborative problem solving in any quantitative setting.

**Why Major in Mathematics?**

Mathematics is one of the most versatile majors at Princeton and students here have the opportunity to work with some of the best mathematicians in the world in a wide variety of fundamental areas of both pure and applied mathematics. The program for majors is extremely flexible, providing exciting opportunities both for students who enter with a strong background in rigorous mathematical proof as well as for novices with strong mathematical aptitude and interest. For many of our students the first proof course, typically 215 (Honors Analysis in a Single Variable), is the first serious experience with true mathematical thinking, and future majors generally find it a deeply challenging but irresistibly intriguing experience.

Our undergraduate majors form a large group of independent-minded and curious people with a rich variety of intellectual interests. In recent years we have had approximately 70-75 majors and their programs of study include advanced courses in many other disciplines such as computer science, physics, economics and finance, biology and philosophy. A substantial fraction of our majors write a senior thesis with an advisor from one of these other departments, along with a second reader from mathematics. After Princeton, many go on to graduate studies in pre-eminent mathematics programs, but others pursue their interests in these other disciplines instead, where their mathematical training is a crucial advantage.

For additional information about majoring in mathematics at Princeton, start with the Program Overview.