What Are Good Non-Textbook Physics and Math Books for an Advanced Reader?

[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.

 

[Pengwuino]

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

 

[Reedeegi]

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.

 

[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

 

[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

 

[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.

 

[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

 

[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.

 

[Leptos]

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.

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'll recommend just one book that I recently read & enjoyed. Euler's Gem.

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

 

[jasonRF]

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.

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!

 

[Phyisab****]

https://www.amazon.com/dp/0486689220/?tag=pfamazon01-20

https://www.amazon.com/dp/0486406830/?tag=pfamazon01-20

$24 total, will keep you occupied for a long long time.

 

[Fredrik]

"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.

 

[CFDFEAGURU]

..2500 dollars to spend on books...

WOW, would your parents adopt me. lol

I love the book by Penrose - "Road to Reality"

Thanks
Matt

 

[Dembadon]

Calculus by Michael Spivak
Hardcover: 670 pages
Publisher: Publish or Perish; 3 edition (September 1, 1994)
ISBN-10: 0914098896
ISBN-13: 978-0914098898

 

[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.

 

[CFDFEAGURU]

...want to learn from these books or whether you think they would look nice in a "must have" collection.

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

 

[kuahji]

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.

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.

 

[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.

 

[Leptos]

WOW, would your parents adopt me. lol

I love the book by Penrose - "Road to Reality"

Thanks
Matt

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).

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.

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.

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.

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).

 

[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.

 

[Leptos]

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.

I was asking for book suggestions for books that I would find of use or interesting even after I master the topics in them. For example: say I master a topic such as Riemann Geometry(or at least in the academic sense) I want books that would be good to use as a reference for RG regardless of skill level and especially if the book holds equal value before and after mastery of related subjects.

 

[Sankaku]

I was asking for book suggestions for books that I would find of use or interesting even after I master the topics in them.

That is a bit of a strange request. For something like Riemannian Geometry, there is no "regardless of skill level." There are very few "non-course" books left once you have completed your studies of a topic. As you said, there are some good reference books, but really you are on to reading papers or monographs after that.

There are some general things like "Proofs from THE BOOK":

https://www.amazon.com/dp/3642008550/?tag=pfamazon01-20

But, unless you know what fields you will "master" ahead of time, I think that it is pretty much impossible to give you recommendations. We will run out of useful suggestions unless you can be more specific about the fields you are interested in. Even then, much of the valuable material is in textbooks, which you don't seem to want unless (if I am reading your post right) it will NOT be assigned in some future course you might take?

Sorry if I have misinterpreted, but you might attempt to narrow things down a bit...

 

[Reedeegi]

I was asking for book suggestions for books that I would find of use or interesting even after I master the topics in them. For example: say I master a topic such as Riemann Geometry(or at least in the academic sense) I want books that would be good to use as a reference for RG regardless of skill level and especially if the book holds equal value before and after mastery of related subjects.

The books I listed were quite good, often more pedagogical than most texts, and are successful at accompanying much harder texts usually used in courses or bridging the gap between numerical and proof-based mathematics. Also, while it is good to think ahead, you give no indication that you've actually mastered the subjects yet, nor have you learned them from a more technical perspective; your interest in many topics may wane after seeing what professionals in the field do as their work and research. Also, you've given two incredibly broad topics- mathematics and physics, both of which have a vast amount of resources available, making it quite hard to compile a suitable list for your purposes. If you provide us with that, you'll probably get more answers regarding what you want.

Also, when you "master" a subject in mathematics or physics, you'll already have been acquainted with the standards of the field, so mostly research journals and as-of-yet-unpublished monographs and texts would /truly/ suit your request.

 

[Leptos]

The books I listed were quite good, often more pedagogical than most texts, and are successful at accompanying much harder texts usually used in courses or bridging the gap between numerical and proof-based mathematics. Also, while it is good to think ahead, you give no indication that you've actually mastered the subjects yet, nor have you learned them from a more technical perspective; your interest in many topics may wane after seeing what professionals in the field do as their work and research. Also, you've given two incredibly broad topics- mathematics and physics, both of which have a vast amount of resources available, making it quite hard to compile a suitable list for your purposes. If you provide us with that, you'll probably get more answers regarding what you want.

Also, when you "master" a subject in mathematics or physics, you'll already have been acquainted with the standards of the field, so mostly research journals and as-of-yet-unpublished monographs and texts would /truly/ suit your request.

I suppose I'll see what my needs are over time since I couldn't judge this early in my academic career. Thanks for the advice, Reed. Excellent post by the way; so far you've made the only posts that left me satisfied.

 

[Winter Flower]

Sometimes to supplement my studies I try reading non-textbook-form books about various subjects. I just go to the book store and look at the science/physics section until I find something I think looks interesting and relevant. Usually I choose based on whether I think the author seems like they have a reputable knowledge of the subject, and their credentials. Maybe save the money and buy the ones you need when you have the time.

 

[Winter Flower]

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.

I'm confused about the misalignment that could result from reading such books. Surely we should use textbooks as references rather than popular books, but if you find some disagreement with popular literature in a textbook, isn't that exciting?

 

[Leptos]

Alright, sorry about the earlier confusion. Consider this post over the others in this thread.

I'm currently considering the following books:

How to Prove It: A Structured Approach - Daniel J. Velleman
How to Solve It: A New Aspect of Mathematical Method - G. Polya
What Is Mathematics? An Elementary Approach to Ideas and Methods - Richard Courant
Introduction to Analysis - Maxwell Rosenlicht
Introduction to Topology: Third Edition - Bert Mendelson
Elements of Abstract Algebra - Allan Clark
Axiomatic Set Theory - Patrick Suppes
Principles of Mathematical Analysis, Third Edition - Walter Rudin

Do you guys have any suggestions for what else I should consider(feel free to express your opinion regarding books I've listed).

 

[Reedeegi]

Definitely get "How to Prove It." After going through the book in detail, any of the books you listed on algebra, analysis, and topology should be within your grasp (though do not expect it to be necessarily easy!)