<p>What classes do math majors aiming for grad school in math take? What subjects beyond calculus and analysis generally need to be studied?</p>
<p>The three "big" sections of modern mathematics are topology, algebra, and analysis. You should have at least basic knowledge of each of the fields, i.e., common structures, theorems, etc. If you're aiming for a good grad program here are the subjects I'd be at least familiar with:[ul]
[<em>]Measure theory
[</em>]Point-set topology
[<em>]Functional analysis
[</em>]Group, ring, and field theory, especially Galois theory
[<em>]Algebraic topology
[</em>]Complex analysis
[<em>]Linear algebra
[</em>]Differential equations
[/ul]That about covers it, I'd say. If you have a solid working knowledge of the fundamentals of these subjects then you're well off. In addition it might be worth studying the following, depending on your interests:[ul]
<a href="Algebraic,%20analytic,%20or%20just%20regular%20old">*</a> number theory
[<em>]Discrete mathematics, particularly graph theory
[</em>]Manifolds
[<em>]Modern geometry and associated topics, e.g., algebraic curves
[</em>]Commutative algebra
[<em>]Probability theory
[</em>]Category theory
[/ul]That's about all I can think of right now. Hope that helps.</p>