## Core Classes

We currently have three year-long core sequences. They are **Algebra** (MATH 504-506), **Analysis** (MATH 524-525 and MATH 534), and** Manifolds** (MATH 544-MATH 546).

During their thirst two years in the program, students are expected to take seven quarters of core courses, at least five of them in their first year.

Below is some information about each of the sequences including the list of topics that are usually covered.

**Algebra (MATH 504-506):** list of topics

Our **Analysis** sequence consists of** Real Analysis (Math 524-525)** and** Complex Analysis (Math 534)**; these two subsequences are independent of each other and can be take in any order.

**Real Analysis (Math 524-25)**:

The course follows the book "Real Analysis: Modern Techniques and Their Applications", Folland, 2nd Edition (see also "Real Analysis", Stein and Shakarchi). Math 524 essentially covers all of Chapters 1 through 3 of Folland's book. Math 525 covers Chapter 5, and parts of Chapters 6 - 7. If time permits, there is also a quick review of point set topology along the way, depending on whether students have seen it.

**Complex Analysis (Math 534)**: list of topics

**Manifolds or "Geometry and Topology" (Math 544-546)**: list of topics

Please note that our Manifolds sequence assumes knowledge of basic set topology. If you would like to take this sequence but have not taken an undergraduate topology class, we recommend starting with Math 441 or at least being concurrently enrolled in Math 544 and Math 441.