Hi toopham,
I planned to take the exam in this November.
Well I'll follow the content page of 'Cracking the GER Maths Sub Test 4th ed' as my guide of topic revision.
For the abstract algebra, I think "Sylow Theorem" may be a bit advanced for the test. And almost all easier topics in group theory are needed: eg. Cyclic groups, subgroups, cyclic subgroup and generators, isomorphisms and homomorphisms. Topics needed on RING and FIELD may be less advanced: e.g Definition of Ring, Ring homomorphisms, integral domains, finite extension of field.
Probably you know 25% of the questions are on elementary, abstract and LINEAR ALGEBRA, which you did not mention.
Other additional topics include: NUMBER THEORY (primes, division algorithm, Euclidean algorithm, Diophantne eqn, congruence eqn, etc.) ODE (no need to study numerical methods) DISCRETE MATHS (Logic, permutations, combinations, algorithms, graph theory, probability and statistics) COMPLEX ANALYSIS (someone in this forum mentioned: "... need to know arithmetic with complex numbers, the residue theorem and Cauchy's integral formula")
I'll also use the Schaum's outline series for revision purpose (Calculus, Advanced Calculus, Linear Algebra, General Topology, Discrete Maths, ODE, Prob and Stat). The series on Abstract Algebra, Group Theory (and PDE, not needed in the GRE test) are not very good.
