<p>I’m willing to order mathbooks from any country, be it Singapore, Canada, Ireland, Russia, etc etc as long as they’re good and available in english. Linear algebra, discrete math, calculus, differential equations, complex analysis. And so on. High level math basically. Thanks in advance!</p>
<p>Hmmm…</p>
<p>The “best” textbook is very subjective because each reader can view a textbook differently.</p>
<p>Having said that, I have Strang’s Calculus book and I think it is great…even though Strang is known more for his Linear Algebra books which I have also. I did not have Strang books as an undergrad but I had his Linear Algebra book in grad school.</p>
<p>I WISHED I had his Calculus book back when I was an undergrad.</p>
<p>It would help us if you gave us a few “good” books as references. Otherwise we won’t know what you are looking for:</p>
<ul>
<li>a concise introduction or an in-depth treatment?</li>
<li>completely rigorous or with some intuitive explanations?</li>
<li>definition-theorem-proof style or expository style?</li>
<li>as preparation for a PhD in pure math, for applied mathematics or for a “terminal” Bachelor’s degree in math?</li>
<li>self-contained or intermingling with other areas of math? </li>
<li>minimum prerequisites or a richer treatment of the material?</li>
</ul>
<p>and so forth…</p>
<p>Stewart’s Calculus book I give a C grade</p>
<p>Rosen’s Discrete book I’d give a B grade</p>
<p>Complex Analysis: Theodore Gamelin
Topology: Munkres (best math text ever written imo)
Real Analysis: Frank Morgan (great introduction, not thorough enough for advanced students)</p>
<p>Munkres seems to be the standard text for topology but I don’t like it. I think it gets so caught up in details that it’s easy to lose sight of the big picture. I very much prefer Janich’s text, but Janich leaves a lot of routine proofs to the reader.</p>
<p>Walter Rudin’s Principles of Analysis is a classic for real analysis, but its definition-theorem-proof style with no pictures or explaining words may not appeal to you. I agree that Frank Morgan’s book is great for a first exposure to the material, but not through enough to replace a standard-level analysis course.</p>
<p>Dummit and Foote is a popular text for undergraduate abstract algebra. Some professors (and students) don’t like their expository style though. Lang’s text is more concise and often used for an introductory graduate abstract algebra course (treating the same material in a shorter amount of time and with a bit more depth than undergraduate algebra). Some of the professors here swear on Fraleigh’s A First Course in Abstract Algebra. I haven’t read it and cannot comment on the quality.</p>
<p>I guess I am trying to say that there are many good books on the market, but no single book appeals to every reader. Maybe you can go to a college library or use Amazon/Google preview to decide which texts you like.</p>
<p>^ I agree Walter Rudin’s Principles of Analysis is a good book and its only like 20 something dollars shipped from India. [Amazon.com:</a> Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) (9780070856134): Walter Rudin: Books](<a href=“http://www.amazon.com/Principles-Mathematical-Analysis-International-Mathematics/dp/0070856133/ref=tmm_pap_title_0]Amazon.com:”>http://www.amazon.com/Principles-Mathematical-Analysis-International-Mathematics/dp/0070856133/ref=tmm_pap_title_0)</p>
<p>I also agree with Rudin being the “standard” for Real Analysis.</p>
<p>As far as Discrete Mathematics goes, I like (and have) “Combinatorics and Graph Theory” by John Harris. You will get great background on Combinatorics and “decent” on Graph Theory.</p>
<p>To sharpen the Graph Theory skills, I like (and have) “Graph Theory” by Bela Bollobas</p>
<p>I found Maxwell Rosenlicht’s analysis book to be really good. I read a bunch of it for fun over the summer. The Munkres topology book is good. There is also the Willard topology book which is way cheaper, and is considered to be another classic. There is a pretty good on linear algebra by georgi shilov. He also has a pretty good book on analysis. Shilov is highly recommended by one of the math professors at my school. </p>
<p>Also, another author close to the realm of Rudin worth checking out is Apostal. His calculus book is similar to Spivak’s book, but I just liked it more. </p>
<p>As for abstract algebra there is a good book by charles pinter. There is also another book by allan clark called elements of abstract algebra, this book has a TON of exercises, so its good if you know theory but are looking for practice problems. I don’t think its a good book to learn from. The pinter one is though.</p>
<p>I’ve yet to find a really good book for vector calculus. The book I used in my class was Vector Calculus by Susan Jane Colley, it was ok, but I feel my geometric understanding of a lot of concepts is just completely lacking. There is also Advanced Calculus by widder, but I have yet to look through it. </p>
<p>Generally I don’t think you can go wrong with dover books for math. Just check the reviews on amazon. Many of them are good.</p>
<p>Why don’t you try MAA’s Basic Library List?</p>
<p>[MAA</a> Reviews | The Basic Library List](<a href=“http://mathdl.maa.org/mathDL/19/?nodeId=959&pa=content&sa=viewDocument]MAA”>http://mathdl.maa.org/mathDL/19/?nodeId=959&pa=content&sa=viewDocument)</p>