- Intro Courses
- Analysis
- Algebra
- Geometry
- Discrete Math
- Number Theory
- Topology
- Probability and Statistics
- Logic

Choosing math courses is one of the most important aspects of being a math major, though these choices are often quite difficult. Upon entering Princeton, many math majors do not know which areas of math to explore. Even for those who have decided this question, it is often not apparent which courses to take and in what order. Moreover, there are always questions of which courses it is feasible to take simultaneously, which courses overlap in material covered, what knowledge does one need before taking a course, and many others.

The goal of this course guide is to provide information to help math majors make these decisions. Before this course guide was compiled,

Two important sources of information are the registrar’s Course Offerings and the math department’s undergraduate courses page; every math major should consult them. This course guide supplements these sources by bringing in the student’s perspective. All of the information presented here is taken from the experiences math majors have had taking these courses.

Contents

#### Content

The guide is split up into nine sections. One section is on introductory courses, while the other eight correspond to major branches of math. Each section starts with an overview, which discusses the subject covered by the section as well as how the subject is taught at Princeton. Following the overview is a listing of relevant courses in the subject. Most courses will have a detailed description of the course content that goes beyond the descriptions provided by the registrar or the math department. In addition to this, most overviews and course descriptions will also provide useful commentary and advice. You will find that many topics in math spill over into other departments, most notably COS, ORF, and PHI. We have provided descriptions of the relevant courses in these other departments as well.

#### Limitations

Although we hope that this guide is a major step forward in helping students select their courses, it has its inherent limitations as well.

One of these limitations is that some courses, especially at the higher levels, can change from year to year in terms of subject matter or format. For example, the content of advanced topics courses can depend on the professor. Another type of variability that can occur is a decision by the math department to change some aspect of its curriculum. This guide deals with variable-content courses by indicating this within the course description. For these courses, it is best to check Course Offerings or the math department page for the exact content of the course. As for the math department’s changing of its curriculum, Math Club will do its best to keep this guide current by announcing impending changes and updating sections affected by the changes.

Another limitation of this guide is that since it is based on experiences of other math majors, it is vulnerable to some degree of subjectivity. We have tried to give as much general-purpose advice as possible, while avoiding making too many statements classifying courses as “bad” or “good”, “easy” or “difficult.” This guide should shed a lot of light on math courses at Princeton, but ultimately it your responsibility to choose courses according to your own interests and abilities.

#### Contacts

Another limitation to this guide is that it cannot be exhaustive. However, at the bottom of each section is a list of people who are experienced in that particular subject, and who are willing to answer your questions or help you decide which courses to take. Before this guide was made, the best way to get more information was to find experienced upperclassmen and ask them questions. Now, in addition to documenting much of this information, this guide provides you with a direct link to upperclassmen or recent graduates with expertise in exactly the topics you would like to know more about. We encourage you to take advantage of this great opportunity.

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