49
$\begingroup$

What are some good undergraduate level books, particularly good introductions to (Real and Complex) Analysis, Linear Algebra, Algebra or Differential/Integral Equations (but books in any undergraduate level topic would also be much appreciated)?

EDIT: More topics (Affine, Euclidian, Hyperbolic, Descriptive & Diferential Geometry, Probability and Statistics, Numerical Mathematics, Distributions and Partial Equations, Topology, Algebraic Topology, Mathematical Logic etc)

Please post only one book per answer so that people can easily vote the books up/down and we get a nice sorted list. If possible post a link to the book itself (if it is freely available online) or to its amazon or google books page.

$\endgroup$
7
  • $\begingroup$ This is borderline, but I think it is a legitimate question of interest to math instructors. I think its better as a community wiki though. $\endgroup$ Oct 16, 2009 at 17:28
  • 7
    $\begingroup$ It's no longer possible to add useful answers to this question (as there are too many!) and it's unclear whether this question would be "allowed" by modern standards -- far too broad. As it's been popping back to the front page fairly frequently, we've decided to close it. $\endgroup$ Jul 11, 2010 at 13:30
  • 10
    $\begingroup$ See discussion on meta: tea.mathoverflow.net/discussion/499/… (and remember to vote this comment up, so it is visible to others) $\endgroup$ Jul 14, 2010 at 10:34
  • $\begingroup$ I don't have enough rep to rate anything and I only skimmed through the meta discussion but essentially what the mods did is bad for the website... Most websites start with one thing and then change their purpose by the will of the users... Otherwise they fail miserably as soon as some competition shows up... So the final judgment for closure "The system was created for people looking for precise answers to precise questions. Big list questions were an emergent phenomenon" is generally a flawed mindset. $\endgroup$
    – person
    Jul 16, 2010 at 23:19
  • $\begingroup$ I asked the question because I am an undergraduate student and want to learn more about math... A lot of great books were recommended here and I guess what was suggested so far is more then enough for me to read... So at this point I don't really care about the policies at MathOverflow but my friendly advice is given in the preceding comment... And NO I'm not gonna create a new account for meta just for one post ¬_¬ $\endgroup$
    – person
    Jul 16, 2010 at 23:22

95 Answers 95

1 2 3
4
1
$\begingroup$

Milnor's book "Dynamics in One Complex Variable: Introductory Lectures". An early version is available from his website. Suitable for advanced undergraduates, graduate students, and mathematicians.

http://www.math.sunysb.edu/cgi-bin/preprint.pl?ims90-5 (Wayback Machine)

$\endgroup$
1
$\begingroup$

Hugo Steinhaus https://en.wikipedia.org/wiki/Hugo_Steinhaus book "Mathematical Kaleidoscope". It is kind of mathematical trivia sometimes very deep;-) It is not for learning math but for learning how to learn math in fun way.

$\endgroup$
1
$\begingroup$

Most readers here will not be able to appreciate them for a simple reason, but my favorite beginners' Analysis text is that by Bröcker (Wayback Machine). No-nonsense, concise, with a slight orientation towards topology.

$\endgroup$
0
$\begingroup$

Real Analysis, by Frank Morgan. The chapters are short and very directed. The proofs are written well. The exercises are well-selected. The book is written at a level accessible for most students.

$\endgroup$
0
$\begingroup$

Vinogradov's Elements of Number Theory - the problems more so than the text itself.

$\endgroup$
1 2 3
4

Not the answer you're looking for? Browse other questions tagged or ask your own question.