Best calculus text for review.

Forum for the GRE subject test in mathematics.
Itisreek
Posts: 1
Joined: Wed Jan 28, 2015 11:36 pm

Best calculus text for review.

Postby Itisreek » Wed Jan 28, 2015 11:39 pm

I'm currently studying for the mGRE that will be given in October of this year and I'm having trouble deciding which books to use for the calculus review. I'm currently brushing up in Stewart's Precalculus and was planning on moving to Spivak after. I also have Apostol's Calculus, which seems to cover a lot of relevant material like DEs, vector calc, and some linear algebra, but I'm not sure which text to devote time to. Apostol seems like it would be a good review for a lot of stuff beyond calculus so it seems like an efficient text, but I'm not completely sure. Also, I've read the comments left by other users that seem to indicate that Stewart's Calculus is important for the mGRE-type problems. I would appreciate any suggestions so I can start to study more efficiently for the test. Thanks.

catofcats
Posts: 8
Joined: Thu Jan 29, 2015 12:44 am

Re: Best calculus text for review.

Postby catofcats » Thu Jan 29, 2015 1:01 am

My favorite calculus text is Serge Lang's a complete course in Calculus. The book is written for advanced high school students, but really looks to be for undergraduates. It covers basically all the calc I-III and linear algebra you'll need for the subject test. The book is relatively cheap (I found it online for < $10) and is well written. Also, this book is unlike any of Lang's graduate texts. The writing is easy to follow and there is plenty of detail. If you have the time, I recommend working through most of the book. It will definitely help increase your subject score.

arctanX
Posts: 18
Joined: Fri Jan 23, 2015 6:31 pm

Re: Best calculus text for review.

Postby arctanX » Thu Jan 29, 2015 7:13 am

If you have a good background in calculus, and your sole objective is to get good mGRE score, you need nothing more than the review in "Cracking-GRE-Mathematics-Subject-Test". Going through a proper textbook will take you time that you can otherwise dedicate to solving test-like problems which is the best way to prepare yourself to the test.

In general, the material in the test is quite basic and repeats itself. e.g. constructing the irrational numbers using Dedekind cuts may be interesting but has less value for the test.

josephgerth
Posts: 7
Joined: Tue Sep 02, 2014 6:49 pm

Re: Best calculus text for review.

Postby josephgerth » Sat Feb 07, 2015 2:22 pm

I can vouch for Lang's A First Course in Calculus, it's really good. It contains just about all of the answers in the back of the book, and it even includes full solutions for some of the problems.

Some of it is obtuse, admittedly. I wasn't able to master some of the content (for example, Lang treats integrals that contain sqrt(1+ax^2) by using sinh(x) substitution, and I wasn't able to figure out how to deal with these efficiently. I was able to get right answers, but it leaves some really messy solutions that take forever to simplify). It is also missing differentiable equations, which most Calc textbooks have something on.

I'm in a similar boat, and am studying for the October exam as well (perhaps earlier, depending on my level of dedication). My undergrad left me woefully underprepared, and, even though I had a GRE subject test practice book, I felt it would be best to review all of the material as thoroughly as I could, and dedicate the last month or two strictly to test prep. I intend to go though all of Lang's undergrad math books, if possible. I also recommend a course I'm taking through Udemy (Entitled "GRE Subject Math April 2015 Prep").

arctanX
Posts: 18
Joined: Fri Jan 23, 2015 6:31 pm

Re: Best calculus text for review.

Postby arctanX » Sun Feb 08, 2015 9:54 am

josephgerth wrote:I also recommend a course I'm taking through Udemy (Entitled "GRE Subject Math April 2015 Prep").


Yes, that course seems to be awesome. It promises to cover all the necessary material, although only the first module out of 10 or so is published.

grad
Posts: 31
Joined: Sun Nov 09, 2014 1:02 am

Re: Best calculus text for review.

Postby grad » Tue Feb 10, 2015 6:14 pm

arctanX wrote:If you have a good background in calculus, and your sole objective is to get good mGRE score, you need nothing more than the review in "Cracking-GRE-Mathematics-Subject-Test". Going through a proper textbook will take you time that you can otherwise dedicate to solving test-like problems which is the best way to prepare yourself to the test.

In general, the material in the test is quite basic and repeats itself. e.g. constructing the irrational numbers using Dedekind cuts may be interesting but has less value for the test.


I have to say that I think for the vast majority of people "Cracking the GRE Mathematics Subject Test" won't be enough. Most of the test is calculus, sure. The majority of it will be review for most people. Still, you have to get really good at doing advanced calculus problems. "Cracking the GRE" only covers a small fraction of what you'll see on the test. And most of the problems in the book are significantly easier than the actual problems you'll get on the test.

I took the math GRE for the first time two years ago and studied mostly just by using "Cracking the GRE." That wasn't enough - I got a 700 on the test. When I took it this fall I got an 850 after thoroughly studying calculus the summer previous to the test. Of course this is just my experience. But calculus wasn't really a focus of my undergrad education and I think the same will go for a lot of people taking the test.

For what it's worth, I would recommend buying a few books from the Schaum's Outlines series. They're cheap. They cover a lot of material without very much unnecessary text. And most importantly, they contain a ton of exercises.

arctanX
Posts: 18
Joined: Fri Jan 23, 2015 6:31 pm

Re: Best calculus text for review.

Postby arctanX » Tue Feb 10, 2015 10:59 pm

Sure practice makes perfect, and doing a lot of exercises is the key to success.

However, I did not encounter a single calculus GRE problem which required theoretical knowledge beyond what is included in "Cracking the GRE". Well, there are not many questions out there, right? Only 4 known past exams which account for ~120 calculus questions. My observation is based on those questions and the questions I saw when I actually took the exam (to the best of my memory).

I studied the material exclusively from that book, after a long break from math, and scored 900.

(I have no connections what so ever to the authors of that book, I just think it is a good fit for that specific exam. No doubt, it is garbage as a mathematics textbook).

grad
Posts: 31
Joined: Sun Nov 09, 2014 1:02 am

Re: Best calculus text for review.

Postby grad » Tue Feb 10, 2015 11:57 pm

arctanX wrote:Sure practice makes perfect, and doing a lot of exercises is the key to success.

However, I did not encounter a single calculus GRE problem which required theoretical knowledge beyond what is included in "Cracking the GRE". Well, there are not many questions out there, right? Only 4 known past exams which account for ~120 calculus questions. My observation is based on those questions and the questions I saw when I actually took the exam (to the best of my memory).

I studied the material exclusively from that book, after a long break from math, and scored 900.

(I have no connections what so ever to the authors of that book, I just think it is a good fit for that specific exam. No doubt, it is garbage as a mathematics textbook).


I agree that the test requires very little "theoretical knowledge." It does require a very thorough understanding of calculus, linear algebra, and (introductory) real analysis, though. Even though every undergrad takes those courses, I don't think that everyone has the same level of familiarity with calculus, linear algebra, etc. By and large, it's not even necessary for people going into grad school to have that kind of knowledge. But still, that's what the math GRE requires and I don't think anyone will get that out of reading "Cracking the GRE."

josephgerth
Posts: 7
Joined: Tue Sep 02, 2014 6:49 pm

Re: Best calculus text for review.

Postby josephgerth » Tue Feb 17, 2015 7:39 pm

Yeah, I own Princeton's Cracking the GRE, but it's been a long time since I last took Calculus (I finished Calc III in 2007) and my undergrad institution isn't exactly "reputable." (Their minimum ACT scores for entry are an embarrassing 18, just to give you one example). I had owned Princeton's book for about a year and many of the problems I just couldn't do. So I decided it was time to make an effort to review, relearn, and (in some cases) learn for the first time, so that I could succeed on the MGRE. I benefit most - although, don't we all? - from seeing the theory, proofs, and "where stuff came from," as opposed to just seeing the recipe to answer a particular problem. In this regard, Lang's Calculus has been very helpful for me (and when it gets too theoretical, I always have my undergrad text - Stewart - to give me some basic background) Additionally, I figure that I need to be able to read theoretical texts, read and write proofs, and answer difficult, thought-provoking questions in Grad school anyway, so I decided to begin my "training" now.

Anyway, that's just my perspective. I definitely have a lot to learn, and am open to taking any advice. I do, however, think this is a very practical and effective approach and I do fully intend to do well on my MGRE come next fall.




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