I'll be looking to start preparing for the mathematics GRE in a month's time. To that end, I am devising a study plan to cover the material in the span of approximately 4 months.
I have decided to keep the following textbooks with me:
Calculus: Tom Apostol's Calculus I and II and James Stewart's Calculus: Early Transcendentals. I have kept Apostol's textbook(s) to go through the units very quickly, enabling me to revise the theory. I am thinking of skipping the portions on Linear Algebra; I'm not too sure about the portion on differential equations. I can also use the textbook for some pracrice questions. I'll use Stewart's textbook to simply practice, practice and practice.
Question: It'd be great if someone could recommend a text to prepare for the differential equations portion of the GRE. More so, is going through Tom Apostol's textbook (or Micheal Spivak's textbook) going to be an overkill for the GRE? I would like to revise the theory to refreshm my memory though.
Linear Algebra: I intend to revise Friedberg, Insel and Spence's Linear Algebra.
Question: I am not sure if this will be enough. Should I consider keeping some other problem book on the side, which'll prepare me for the more 'GRE-esque' linear algebra questions.
Algebra: Unfortunately, I haven't covered algebra in detail thus far. I intend to work out Anthony Knapp's Basic Algebra starting summer. I may perhaps keep some textbook as an aid on the side; for instance, Fraleigh's Abstract Algebra.
Question: I am not at all sure of the difficulty and breadth of the problems on abstract algebra that show up on the exam. For instance, the handbook mentions that topics on "group theory, theory of rings and modules, field theory, and number theory" may be tested. This gives me the impression that one should thoroughly prepare for this portion of the exam. More so, should I consider keeping Dummit and Foote's Algebra on the side as well?
Introductory Real Analysis: I'll try and revise Bartle and Sherbet's Real Analysis.
Question: There are loads of good books on introductory real analysis. But which textbook should one use for the purposes of the GRE, given the types of questions that pop up on the GRE?
Also, I think Tom Apostol Mathematical Analysis, Walter Rudin's Principles of Mathematical Analysis and Karl Stromberg's Introduction to Classical Real Analysis may be an over kill. Is this the case?
Discrete Mathematics: Blank!
Question: I'm blank over here. I haven't had much exposure to discrete mathematics. What textbooks should I read, along with a list of topics I should be studying?
Other Topics: This section includes general topology, geometry, complex variables, probability and statistics and numerical analysis.
Questions/comments: Mixed feelings over here. For instance, I have had a course in point-set topology, so I can perhaps just revise some of the chapters from Munkres' Topology. I haven't studied complex analysis or numerical analysis, however. Suggestions on this front? Also, what about geometry.
It'd be great if someone could offer some advice on this tentative plan.