Based on my experience, if I were to study for the subject test in 2013 I would study in expectation of:
* 1-2 graph theory and/or combinatorics questions, sometimes written in abstract algebra, rather than graph theory, jargon
* 4 questions revolving around the textbook definition of continuity (i.e. here is strange function, where is it continuous?)
* 2 questions on continuity/compactness in mappings
* 1 question about integrability
* 1 question utilizing the definition of a Hausdorff space
* 1 question on complex arithmetic. (for instance (1+3i)^32 ---not an actual test question, but the type one might expect)
* 1-2 question on complex analysis (perhaps complex integration, residue, Cauchy integral formula, something about analytic functions, etc.)
* 1 question of the form "Here is some pseudo-code. What is the output?"
* 1 question "Order the following from least to greatest..." - computational methods
* 2-3 questions on groups
* 2 questions on rings and fields
* 1-2 questions on "how many zeros (over field X, or over the reals)?"
* 4-5 questions linear algebra (know the inside and out of the invertible matrix theorem. also know about diagonalizable matrices.)
* 1 question on Green's Theorem
* 1-2 question related to flux, conservative fields, incompressible fields, etc.
* 4-5 questions about calculating the derivative (including calculate the derivative of a definite integral with strange bounds)
* 1 question about an iterative sequence, convergence, etc.
* 3 questions on convergence (of non-iterative functions)
* 3 questions about calculating the integral
* 1 question from numerical analysis---i.e. what is the bound of the error for the approximation?
* 1 question about "How many intersections do these equations have?"
* 1 question: ODEs: know about characteristic polynomials
* 3 questions: "here is f(0) and f'(0). Which graph (Cartesian) possibly represents f?" Or "what is the limit as it approaches infinity?"
i) This is based on a small sample size of practice questions.
ii) My memory is good, but not perfect.
iii) The boundary between Calculus and non-Calculus questions is always ambiguous. Classify them how you like.
Forum for the GRE subject test in mathematics.
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