Textbook Suggestions for Math Subject GRE

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Posted

I was wondering: What textbooks have everyone found useful in prepping for the subject GRE? Are there any textbooks particularly helpful in prepping for the subject GRE and if so, which chapters of the texts should be gone through when prepping for the exam?

I was thinking of using Stewart to practice Calculus problems and possibly Rudin (or Pugh) for Analysis, but I am not sure which texts to use to prep for Linear Algebra, Number Theory, Abstract Algebra, Discrete Math, Geometry, Numerical Analysis, etc.

I will have 4 months to prep for the exam and a month and a half as well (but at that time I will be busy with grad courses).

I have taken upper div classes: Number Theory (withdrew, but took most of the class), Probability, Statistics, Ordinary Differential Equations, Real Analysis I at Berkeley, Abstract Algebra, Math for Physics/Engineers (mostly applied PDEs, a bit of complex analysis, and Fourier Analysis) and am currently taking Real Analysis II and Linear Algebra (second course).

I haven't taken Complex Analysis, Discrete Math, Geometry, Numerical Analysis, and Topology.

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Posted

here is my two cents on the matter:

doing well on the test is more about how fast you can pump out answers and sometimes if you can narrow down to making a very educated guess on other stuff vs knowing advanced topics.

i liked the Princeton Review book, I think it's called "Cracking the Math Subject GRE" or something like that. if you search these on google, it will know which one, I'm not 100% on any of the names, but I'll get you close enough for google to do the rest.

the REA book "The Best Mathematics GRE Test Prep" does not live up to its name. I found a copy for a dollar on amazon or half or something, so I figured, why not. the tests are a bit out there and unrealistic of the actual exam. having taken almost the entire gambit of undergraduate mathematics at two very good schools (one being a top private school honors college & the other an ivy league), there is loads of vocab that is esoteric to the point that, even with my background, i've never heard of some stuff and had no clue how to go about answering. I basically used it to do 4-5 problems out of each day for a few months before the test. At least all the answers are explained and solved in the book, but I love how it always says "It's a well known fact that ..." or "It's obvious and elementary that ..." uhh, maybe to whoever is writing this but not to a normal Joe studying for the GRE. I do think the book is valuable, just not as a resource to sit down and take practice tests from. Solving problems slowly over a couple months is fine since it'll give you a chance to look stuff up and learn as you go, but totally unrealistic prep for the real thing.

your best bet is to find PDFs of past exams / practice exams to take. They are out there on the web if you look hard enough and don't mind going to sketchy sites ... I ran a scan of my system after every place I looked for old exams.

Other than that, review your pre-calc / trig, calc / analysis, and algebra / linear algebra and you'll be fine. The test doesn't really cover advanced stuff, maybe a question or two about rings or topological spaces, but not enough to really devote time to those areas rather than drilling pre-calc, calc/analysis, and algebra/linear algebra.

I made a few flash cards to help prep too. they were mainly meant to accelerate my response time by cutting out things I normally just work out via substitution / looking up / taylor expansion / etc... What I'm referring to is memorizing things like:

integrals of cot x, csc x, sec x (which I normally just look up), all kinds of trig identities that, again, I normally just look up quickly, law of sines / cosine, 5-10 of the most common Laplace transforms / inverse transforms, etc...

I think I had about 40 cards total and I did end up using a few of the identities / laws / whatever on the test. It probably obviated 5-10 minutes of busy work that I was able to devote to other questions. I'm quite certain I've forgotten most of them now, but it's worth the time I spent memorizing them. To be honest, I kept them beside the toilet so I would flip through them for a min or two each day for a couple months and it never really set me back in "real" study time, haha.

if you have the above stuff covered and are sick of reviewing, learn the basic counting formulas from combinatorics, basic distribution stuff from probability, and make sure you can do all the basic stuff with complex numbers (like polar form and taking powers and division). you can probably bet on there being at least 1-2 of each of those questions on the test, so spending a couple days going over that may get you 3-5 more points if you didn't already know those basic topics.

not sure what else to say. good luck? hope this post helped a bit.

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Posted

I also found the Princeton book very helpful, because it knew how much detail I needed to know about the various extra areas (complex analysis, for example).

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Posted

Thank you Tominkini, very helpful!

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Thank you Tominkini, very helpful!

\

You're Welcome Mate :)

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Posted

Btw, how did you do? You can message me details if it's personal.

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Posted

The one by Princeton review is very good. Three-fourths of Subject test is calculus and linear algebra. Also, try to take a few timed mock tests to get a 'feel' of the real thing. In my experience, speed is very crucial. The questions are easy enough. But like majority of objective based exams, this one also demands speed.

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Far better served just researching introductory material of topics beyond Calculus. They are not going to ask about extension fields, or splitting fields, or characteristic polynomials or pointwise convergence, etc. Any of the advanced stuff is going to be the basics. So if you've had a first semester in Analysis, Algebra some Complex and Linear Algebra you'll be fine. If you want books (that can also be found online. . .winkwink):

Analysis -Rudin (first chapter reviews of basic topology)

Algebra - Gilbert & Gilbert

Linear Algebra - Friedberg

Calculus - Stewart

Beyond that, depending on what you are going for, you should have enough. Half the test is Calculus so you should at least get a 50%. . .right? RIGHT?!

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^I hope so....

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here is my two cents on the matter:

doing well on the test is more about how fast you can pump out answers and sometimes if you can narrow down to making a very educated guess on other stuff vs knowing advanced topics.

i liked the Princeton Review book, I think it's called "Cracking the Math Subject GRE" or something like that. if you search these on google, it will know which one, I'm not 100% on any of the names, but I'll get you close enough for google to do the rest.

the REA book "The Best Mathematics GRE Test Prep" does not live up to its name. I found a copy for a dollar on amazon or half or something, so I figured, why not. the tests are a bit out there and unrealistic of the actual exam. having taken almost the entire gambit of undergraduate mathematics at two very good schools (one being a top private school honors college & the other an ivy league), there is loads of vocab that is esoteric to the point that, even with my background, i've never heard of some stuff and had no clue how to go about answering. I basically used it to do 4-5 problems out of each day for a few months before the test. At least all the answers are explained and solved in the book, but I love how it always says "It's a well known fact that ..." or "It's obvious and elementary that ..." uhh, maybe to whoever is writing this but not to a normal Joe studying for the GRE. I do think the book is valuable, just not as a resource to sit down and take practice tests from. Solving problems slowly over a couple months is fine since it'll give you a chance to look stuff up and learn as you go, but totally unrealistic prep for the real thing.

your best bet is to find PDFs of past exams / practice exams to take. They are out there on the web if you look hard enough and don't mind going to sketchy sites ... I ran a scan of my system after every place I looked for old exams.

Other than that, review your pre-calc / trig, calc / analysis, and algebra / linear algebra and you'll be fine. The test doesn't really cover advanced stuff, maybe a question or two about rings or topological spaces, but not enough to really devote time to those areas rather than drilling pre-calc, calc/analysis, and algebra/linear algebra.

I made a few flash cards to help prep too. they were mainly meant to accelerate my response time by cutting out things I normally just work out via substitution / looking up / taylor expansion / etc... What I'm referring to is memorizing things like:

integrals of cot x, csc x, sec x (which I normally just look up), all kinds of trig identities that, again, I normally just look up quickly, law of sines / cosine, 5-10 of the most common Laplace transforms / inverse transforms, etc...

I think I had about 40 cards total and I did end up using a few of the identities / laws / whatever on the test. It probably obviated 5-10 minutes of busy work that I was able to devote to other questions. I'm quite certain I've forgotten most of them now, but it's worth the time I spent memorizing them. To be honest, I kept them beside the toilet so I would flip through them for a min or two each day for a couple months and it never really set me back in "real" study time, haha.

if you have the above stuff covered and are sick of reviewing, learn the basic counting formulas from combinatorics, basic distribution stuff from probability, and make sure you can do all the basic stuff with complex numbers (like polar form and taking powers and division). you can probably bet on there being at least 1-2 of each of those questions on the test, so spending a couple days going over that may get you 3-5 more points if you didn't already know those basic topics.

not sure what else to say. good luck? hope this post helped a bit.

I don't have any idea what to buy so i searched for this one. It's a big help. Thank you for the input. I would gladly send feedback after buying the books.

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