Math GRE study books
Posted: Sat Mar 07, 2020 6:14 pm
I'm writing a little reflection in my profile post on math GRE. Thought I'd make a separate post with my favorite studying/training books and link to it in my profile reflection. Please feel free to add.
Background: I mostly do analysis and tutor calc/diffeq/linear so my background is weak in topology/geometry/algebra [hence my 71]. But I think I have good suggestions on those fronts even if I didn't exhaust those resources.
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~ G R E A T B O O K S ~
Some people will say YOu ShOUlDn'T sTuDY fOr tHe MAth GRE or that It'S A supER easY test aNyWAY, so don't be like those people ¯\_(ツ)_/¯
Background: I mostly do analysis and tutor calc/diffeq/linear so my background is weak in topology/geometry/algebra [hence my 71]. But I think I have good suggestions on those fronts even if I didn't exhaust those resources.
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- Calculus & ODEs Stewart is a good resource. Key sections are 7.5 and 11.7; make sure to do all of the problems in those sections once or twice. For ODEs, I like Schaum's Outline of Differential Equations by Bronson since it condenses the material and has a ton of problems.
- Analysis A Problem Book in Analysis, Aksoy & Khamsi; Understaning Analysis, Abbot.
- Algebra Easy problems in A First Course in Abstract Algebra by Fraleigh. Harder problems in Abstract algebra, Dummit \& Foote. For linear algebra, study Linear Algebra: Challenging Problems for Students by Zhang.
- Combinatorics Two types of combo should be studied. First is enumerative combinatorics; see the associated chapter in Problem Solving Strategies by Engel. The other type is graph theory, see Graph theory: a problem oriented approach by Marcus (great book).
- Probability For a gentle introduction, see A first course in probability by Ross. Some good problems, especially at the beginning over counting/discrete probability.
- Geometry & Topology For Topology, I like Elementary Topology Problem Book by Viro, Ivanov, et al.. For geometry, I like Euclidean Geometry in the Mathematical Olympiads by Chen (IMO god). Be warned: those problems are hard as ____, but a few hours spent in the first part attempting them pays off.
- Number Theory The number theory section of Problem Solving Strategies by Engel is a great resource. Very accessible and challenging. Also there's an old one by Minkowski(?) that I don't remember the title of.
- Statistics Don't rule out a random stats question on this exam, but again, don't try to master something new; some good general stuff can be found in Schaum's Outline of Statistics by Spiegel.
~ G R E A T B O O K S ~
- Linear Algebra: Challenging Problems for Students, Zhang
- Problem Solving Strategies, Engel
- Elementary Topology Problem Book, Viro, Ivanov, et al..
Some people will say YOu ShOUlDn'T sTuDY fOr tHe MAth GRE or that It'S A supER easY test aNyWAY, so don't be like those people ¯\_(ツ)_/¯