## Mathematics

We are delighted that you are considering a major in mathematics! The information below will help you get started thinking about which courses to take first. You don't need to have taken any advanced courses in high school to be a math major - just make sure you follow our placement advice so that you start in the right place. If you are interested in learning more about the mathematics major, we recommend you come to Seeley Mudd to talk with a math professor. We are all happy to discuss the course requirements with you, and we can advise you on appropriate pathways through the major given your experience and interests.

**To declare the Mathematics major**, there are two steps:

- Complete this Google Form for the department records;
- Submit a request through Workday to add a major (via "Academics" and "Overview" on your student profile page).

### Calculus Sequence

Most students interested in majoring in mathematics at Amherst start with calculus courses (Math 111, 121 and 211). These courses are part of the major requirements, and some of them are prerequisites for other majors too. If you are unsure which course is appropriate for you, look at our page on Placement Advice. Because these courses build on one another, we recommend that you start them as early as possible, so that you have time to complete the calculus sequence before moving on to higher-level courses. See Pathways through the Major for example schedules depending on when you start the major.

### Recommended Courses for Exploring the Major

To get additional experience with mathematics before declaring the major, we recommend you take a 200-level course. Some of the following courses have no prerequisites and can be taken without previous experience in calculus. All will give you exposure to the themes of higher mathematics, such as writing mathematical proofs.

Note that it is a requirement for the major to take either Math 271 or Math 272. These two courses cover most of the same material though with slightly different emphasis, so you can take either.

- Math 220 (Mathematical Reasoning and Proof): an introduction to logic, proof-writing and other fundamental ideas in mathematics (no prerequisites)
- Math 225 (Fractal Geometry): an introduction to the beautiful area of fractals (prerequisite: Math 211 or permission of instructor)
- Math 250 (Number Theory): a study of the theory of the integers (prerequisite: Math 121 or permission of instructor)
- Math 255 (Geometry): an axiomatic approach to geometry starting from Euclid's axioms (no prerequisites)
- Math 260 (Differential Equations): a central course in applied mathematics (prerequisite: Math 211 or permission of instructor)
- Math 271 (Linear Algebra): linear algebra is a central topic in both pure and applied mathematics (prerequisite: Math 121 or permission of instructor)
- Math 272 (Linear Algebra with Applications): covers the same material as Math 271, but with more emphasis on applications and including a weekly computer lab (prerequisite: Math 121 or permission of instructor)

### For Students with Previous Proof Experience

If you have taken courses before, either at Amherst or elsewhere, that involve writing formal proofs, then you may be ready for one of our more advanced 200- or 300-level courses. The following courses are suitable for any students that have some previous experience of writing proofs, e.g. in one of the courses listed in the previous section, though we usually recommend taking Linear Algebra (either Math 271 or Math 272) first.

- Math 252 (Mathematics of Public Key Cryptography): a course addressing security issues in computer communication using ideas from number theory and abstract algebra. Involves programming, though no previous experience is required (prerequisites: Math 220/221 or 271/272, or consent of the instructor)
- Math 280 (Graph Theory): a study of fundamental and general aspects of the important mathematical structures known as combinatorial graphs (prerequisite: Math 271 or 272 or consent of the instructor)
- Math 281 (Combinatorics): a classical subject in mathematics related to the theory of counting (prerequisite: Math 121 and experience writing proofs, such as Math 220/221, or consent of the instructor)
- Math 310 (Introduction to the Theory of Partitions): a fundamental branch of combinatorics and number theory pertaining to enumerative properties and patterns of the integers (prerequisite: Math 121 and experience writing proofs, such as Math 220/221, or consent of the instructor)

### For Students Interested in Applied Mathematics

Courses in applied mathematics aim to give you tools for developing and analyzing mathematical problems in various scientific disciplines. To prepare students for real-world practices and challenges, most of these courses have programming components (with no coding prerequisite) and collaborative projects. To explore the underlying theory of the techniques, some of the courses require previous experience in writing proofs.

- Math 140 (Mathematical Modeling): an introduction to the process of formulating a real-world problem as a mathematical problem (no prerequisites)
- Math 142 (Mathematical Modeling with Environmental Applications): a course about principles of mathematical modeling in the context of environmental problems (no prerequisites)
- Math 150 (Voting and Elections: A Mathematical Perspective): a mathematical analysis of different voting systems (no prerequisites)
- Math 284 (Numerical Analysis): a study of the theoretical foundations of numerical algorithms used to solve problems arising in scientific applications (prerequisites: Math 211 and Math 271/272 or consent of instructor)
- Math 294 (Optimization): a branch of applied mathematics focused on algorithms to determine maxima and minima of functions, often under constraints (prerequisites: Math 211, and Math 271/272 or consent of instructor)
- Math 320 (Wavelet and Fourier Analysis): this course covers various aspects of the decomposition of functions or real-life data into oscillatory building blocks such as sine and cosine functions (prerequisites: Math 211, and Math 271/272 or consent of instructor)
- Math 333 (The Structure of Networks): an exploration of the mathematical and machine learning techniques used to reveal underlying network structures found in various fields (prerequisites: Math 271/272 or consent of instructor)
- Math 365 (Stochastic Processes): a study of processes that model the evolution of a system over time and involve an element of uncertainty (prerequisites: Math 360 or consent of instructor)