# Buying Physics And Math Books

1. Jan 30, 2010

### Leptos

I want to buy some physics and math books, my parents gave me 2500 dollars to spend on books I want. Non-textbooks preferable. I want to read books that cover material that won't be covered in physics and math classes in college.

Example: By the end of college I will have completed the 3 calc and physics courses required + 8 math and 8 physics more advanced classes by the end of my undergraduate study.

My question is: What are some decent books that aren't too basic but that won't cover material required for those courses(i.e non-academic but informative books). As long as the book has an explanation for the math involved I should be fine as long as it's not a "year x, course y for dummies" book which is what I want to avoid.

All suggestions are welcome.

2. Jan 30, 2010

### Pengwuino

Hmm you want a non-textbook that teaches you a subject at a college level including the actual mathematics? Not sure that's gonna work out...

3. Jan 31, 2010

I have to agree with Pengwuino. Given that you have 2500 to spend, I'd spend it over time on academic works that give you a firm, formal understanding of the studies which you want to pursue. It tends to be the case that books that treat a topic at a higher level of sophistication will give you an advantage in the long run by providing you with much-needed academic discipline which cannot be conveyed through non-academic sources. Unfortunately, popular books tend not to cut it, as they are often simplified to the point of being misleading (as in many popular descriptions of Godel's Second Incompleteness Theorem) or blatantly dishonest (such as Michio Kaku's claims that string theory has, in fact, already reached universal acceptance). This is not to say, though, that they are completely useless; rather, without a background in the field they can often be misleading and give you a hard-to-correct misalignment in your understanding of academic studies. They can surely give intuition or alternative viewpoints to a topic already understood and provide a more practical motivation, but they should NOT form the basis of your education. One thing you could do is supplement your undergraduate books with books that describe the same material but at a far more sophisticated level. For example, most schools will teach Calculus through Stewart's textbook. This book teaches the rudiments of the calculation of integrals and derivatives, but it does not provide an accurate view of the methodology of higher mathematics; that is, proof. To supplement your education in this regard, you could purchase Spivak's "Calculus," Apostol's "Calculus," or (my personal favorite), Rudin's "Principles of Mathematical Analysis" in order to learn what is not covered in the class but is indispensable to a mathematician's training. 4. Jan 31, 2010 ### Goldbeetle I agree with the other replies but still there are books that you can read: Courant-What Is Mathematics? An Elementary Approach to Ideas and Methods How to Solve It: A New Aspect of Mathematical Method Thinking Physics: Understandable Practical Reality Mathematics: Its Content, Methods and Meaning There are also two other ones on combinatorics and group theory that may be interesting for you. I'll post the link asap. It is also very important in order not to be scared away by university math to understand to approach the abstract way of mathematics: sets, functions, definition-proof etc 5. Jan 31, 2010 ### Goldbeetle I agree with the other replies but still there are books that you can read: Courant-What Is Mathematics? An Elementary Approach to Ideas and Methods How to Solve It: A New Aspect of Mathematical Method Thinking Physics: Understandable Practical Reality Mathematics: Its Content, Methods and Meaning There are also two other ones on combinatorics and group theory that may be interesting for you. I'll post the link asap. It is also very important in order not to be scared away by university math to understand to approach the abstract way of mathematics: sets, functions, definition-proof etc 6. Jan 31, 2010 ### Truecrimson The Princeton Companion to Mathematics and the Feynman's Lectures on Physics. The latter may overlap a lot with formal classes though, but both are must-have. Last edited: Jan 31, 2010 7. Jan 31, 2010 ### jasonRF I agree with others, that you should spend this money over the next handfull of years. I would also save some for after graduation. As you learn more, you will know better what topics and approaches you are interested in. Also, if you are interested in getting books on topics that your undergrad curriculum doesn't cover, then the choice certainly depends upon the details of your undergrad curriculum! Given that, I would second the suggestion of buying the Feynman lectures on physics, as the set is truly excellent and worth reading and thinking about for anyone remotely interested in physics. good luck, jason 8. Feb 1, 2010 ### kuahji The answer really depends on you, & what you're looking to take.2500 seems like an awful lot of reading on top of what you'll be doing for school. The absolute most important thing to remember is the # of books & the amount of money you spend on them does not equate into knowledge. I've seen way too many people blow tons of money on books then never read them... thinking that through osmosis they'd absorb the knowledge.

As for what books to get, it depends on what math & physics classes you take. If there is a subject that interests you outside of that class, go to Amazon or another book store & see what others are saying about it. Usually, but not always a book with a lot of good reviews is a great choice. As others have said, spend the money over a period of time, & not all at once as at the moment you don't know what you'll be interested in or need down the line. My advice is also to save money for supplemental texts. It's always nice two read about two different approaches to a subject.

I'll recommend just one book that I recently read & enjoyed. Euler's Gem. Yes it's dumbed down topology, but it does go through the equations & gives rough proofs. It's essentially a very good introduction to the subject that most people with basic calculus can grasp.

9. Feb 2, 2010

### Leptos

That's actually what I went by. Ultimately I bought around 34 books for leisure but I don't necessarily plan to read them all at once. It's the sort of "must have in your library if..." type of collection I'm trying to build, for example books like "The Principia" by Isaac Newton and "The Road To Reality" by Roger Penrose, etc.

I already own that book. I'm currently reading "The Elegant Universe" by Brian Greene and "Why Does E=mc²?" by Brian Cox.

10. Feb 2, 2010

I agree - and admit that I myself have fallen into this trap on occasion. I really love to read technical books, and get carried away sometimes. I have found that being fully employed, with a house/yard and wife/kids, that I can seriously work through just a few books a year if they involve serious learning of new material (working through all the proofs/derivations, doing a large number of exercises, etc.). Books that are just extensions of what I know, or new, interesting approaches for familiar material, can be much less time consuming, but even then $2500 would last me a lifetime! 11. Feb 2, 2010 ### Phyisab**** 12. Feb 2, 2010 ### Fredrik Staff Emeritus "QED: The strange theory of light and matter", by Richard Feynman "Black Holes and time warps: Einstein's outrageous legacy", by Kip Thorne "Lectures on quantum theory: Mathematical and strutural foundations", by Chris Isham. "The road to reality", by Roger Penrose. (His other books are good too. Just keep in mind that his "proof" that conscious thought is non-algorithmic is flawed. No such proof exists). "Classic set theory: for guided independent study", by Derek Goldrei. Any or all of Richard Feynman's autobiographies. They are surprisingly entertaining. By the way, if they gave you that much money, you might want to think about getting an electronic book reader, like the Kindle DX, or maybe that Skiff thing when it comes out. Last edited: Feb 2, 2010 13. Feb 2, 2010 ### CFDFEAGURU WOW, would your parents adopt me. lol I love the book by Penrose - "Road to Reality" Thanks Matt 14. Feb 2, 2010 ### Dembadon Calculus by Michael Spivak Hardcover: 670 pages Publisher: Publish or Perish; 3 edition (September 1, 1994) ISBN-10: 0914098896 ISBN-13: 978-0914098898 15. Feb 2, 2010 ### snipez90 There seems to be little merit in actually owning the books mentioned in this thread if you could just borrow them. But I guess this opinion harks back to whether you actually want to learn from these books or whether you think they would look nice in a "must have" collection. 16. Feb 2, 2010 ### CFDFEAGURU Yeah, I hear you there. I know a guy who has a "collection" and if you ask him to solve something from them, he looks at you as if lobsters are crawling out your ears. Thanks Matt 17. Feb 3, 2010 ### kuahji The Elegant Universe was the first book I read on the subject of physics, very good indeed. Haven't read Brian Cox's book yet. I think that for popular science books, my all time favorite was Lee Smolin's Life of the Cosmos. It was pretty dense, & I swear the average word length was 10 letters, but it was worth the read. In fact, his other books, Three Roads to Quantum Gravity, & The Trouble with String Theory was also really good. Janna Levin's How the Universe Got It's Spots was a decent laid back book on topology. 18. Feb 3, 2010 ### Sankaku Lots of interesting suggestions so far. I would put in a vote for Lee Smolin's "The Trouble with Physics" - although I am not sure if that might make me unpopular around here. There are lots of classic textbooks (like Spivak) but you might have to discover them as you go along, depending on your direction. I don't have as much time to read light books these days, but I am currently reading "General Relativity from A to B" by Robert Geroch which is easy to read and a good intro. Popular stuff I read recently (all very lightweight, none very earth-shattering, get from the library instead of buying): Poincare's Prize by George Szpiro The Math Gene: How Mathematical Thinking Evolved by Keith Devlin Outliers: The Story of Success by Malcolm Gladwell Surely You're Joking, Mr. Feynman by Richard Feynman Why Beauty Is Truth: A History of Symmetry by Ian Stewart The Golden Ratio: The Story of PHI by Mario Livio Not all math or physics, but I would give a plug to the following stuff for anyone interested in the sciences (all worth owning): Godel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter Guns, Germs, and Steel by Jared Diamond The Collapse of Complex Societies by Joseph Tainter A Short History of Nearly Everything by Bill Bryson Hmm. Now I will have to go home and stare at my book-case. 19. Feb 3, 2010 ### Leptos I have it, it's probably the second longest popular book/non-textbook I've come across(after Stephen Hawking's God Created The Integers). I own and I've read all of Lee Smolin's books. I have the original version of his "The Trouble With Physics" with the blue cover. I've read(and own) all the books I put in bold. Technical book suggestions are fine but let's say you suggest something regarding upper level mathematics, I would prefer it to be a book that supplements a corresponding mathematics course(as opposed to a book that is used for the course itself). 20. Feb 4, 2010 ### Reedeegi If you want to begin studying mathematics right now, I would recommend some very inexpensive books published by Dover; though I'd recommend not trying to read them all at the same time. How to Prove It: A Structured Approach Velleman (A splurge at$21 =P, read AND DO before the others)
Elementary Real and Complex Analysis by Georgi Shilov (~$14) Introduction to Analysis by Maxwell Rosenlicht (~$9)
Introduction to Topology: Third Edition by Bert Mendelson (~$8) Elements of Abstract Algebra Axiomatic Set Theory by Patrick Suppes (~$9)

After studying all of these, you may be interested in some more advanced topics including

Abstract and Concrete Categories: The Joy of Cats by Adamek et al.
Topoi: The Categorial Analysis of Logic Goldblatt

Of course, after this many graduate texts are readily available, often with a hefty price tag.
As others have said, don't merely create a "collection;" actually learn from them.