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Are there books in other branches in the similar fashion of Golan's "The Linear Algebra a Beginning Graduate Student Ought to Know"?

Martin Sleziak
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Under-stu
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    Golan's book is good but its title is misleading. A whole chapter is devoted to the Moore-Penrose pseudoinverse and I'm willing to bet that most professional mathematicians including, say, Grothendieck have no idea what it is about, and have never been the worse for that! – Georges Elencwajg Feb 16 '13 at 19:49
  • @GeorgesElencwajg I can't comment on US grad schools, but the Moore-Penrose pseudoinverse is certainly taught in undergraduate 1st/2nd year "basic linear algebra for economists/business students" courses (for non-math majors) at some UK universities. It wouldn't surprise me if at some institutions it is regarded as a staple of the undergrad math curriculum and at others it as seen as a more advanced curiosity! – Silverfish Oct 05 '16 at 23:15

2 Answers2

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I think there are many books that claim this (not exactly by title), so there are many.

For example, almost all math programs and colleges require courses in Calculus, Linear Algebra and Complex Variables, so you could seek out titles along those lines.

However, here are some of that ilk that you might be interested in:

  • All the Mathematics You Missed: But Need to Know for Graduate School, Thomas A. Garrity, Lori Pedersen

  • Analysis for Applied Mathematics, Ward Cheney

  • A Mathematician's Survival Guide: Graduate School and Early Career Development, Steven G. Krantz (Not Technical)

  • You might also have luck in finding things on websites dedicated to resources for graduate students, for example Resources for Graduate Students.

  • Lastly, you might want to peruse the answers for fun but serious mathematics books to gift advanced undergraduates.

Regards

Community
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Amzoti
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  • Great recommendations, Amzoti! – amWhy May 02 '13 at 01:02
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    I found Garrity's book to be full of tiny typos. As it is the first edition at the time of this comment, it is to be expected. I wonder if he will publish a second edition. – Gabriel Fair Dec 29 '13 at 22:00
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    I would certainly try to find out if there is an online or emailable errata just in case they are going to publish another one. The date might give away if there is any chance, but one never knows. Regards – Amzoti Dec 29 '13 at 22:01
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There are many books like that. I will mention my favorite. I will update my answer later since there are many of them:

Linear algebra:

Problems In Linear Algebra And Matrix Theory by Fuzhen Zhang Problems and Theorems in Linear Algebra by V. V. Prasolov

Galois theory:

Galois Theory Through Exercises by Juliusz Brzeziński

Analisys:

Problems in Mathematical Analysis 3 vols by W. J. Kaczor, M. T. Nowak

Lie groups:

Lie Groups and Algebraic Groups by Arkadij Onishchik and Ernest Vinberg

Aleksandr Kalinin
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