FeaturedAlgebra Math texts that make you fall in love all over again

1. Oct 25, 2016

ibkev

I often see textbook recommendations here that about rigour and depth of coverage. Serious books for serious people!

This question is different. I'm looking textbooks that inspire a love for mathematics. And I want to come at it from two different angles:

(1) is there a textbook that was so good, led to such beautiful insights that it was almost a religious experience and cemented your decision to be a student of mathematics?

(2) What textbooks would you recommend a casual, self-studying, student of math, that keeps them motivated and inspired to keep moving forward? Assumptions:
• student has a day job and only so much time to devote
• ideal texts have a big payoff/effort ratio (possibly sacrificing some depth in the process)
• inspires love and interest in the subject
• not discouraging, in the sense of a punishing difficulty level (we all know texts that are viewed as a right of passage!)
The form forced me to choose a prefix but please feel free to respond about any math topic/level you like!

A friend recommended this one:
https://www.amazon.com/Visual-Complex-Analysis-Tristan-Needham/dp/0198534469
He said it is full of diagrams and graphs and is incredibly clear.

Last edited by a moderator: May 8, 2017
2. Oct 27, 2016

Let'sthink

I think loving or getting inspired by maths or its application is an intellectual exercise, which involves only thinking. it is not like listening to music and dancing and watching things. Those are experiences which consume time and you experience pleasure of a different kind which does not involve much thinking. Thinking involves time so the raw material for extracting pleasure out of maths and its application is in the first instance TIME only. Time and willingness to think are the two essential internal inputs the external inputs such as discussion and books can just help!

3. Oct 27, 2016

smodak

4. Oct 28, 2016

vanhees71

5. Oct 28, 2016

Logical Dog

What is mathematics? richard courant ---> difficult book to follow for me personally but an excellent holistic introduction to mathematics fundamentals.

Book of proof. really rigourous and good intro to basic foundations of maths. FREE HEREhttp://www.people.vcu.edu/~rhammack/BookOfProof/

Elias zakon lecture notes ---> can be found free online, legally.

Discrete mathematics by Norman biggs (I ordered the Indian economy edition on amazon much cheaper).
link for you: https://www.amazon.com/Discrete-Mat...rete+mathematics+biggs+indian+economy+edition

how to think about analysis

6. Oct 28, 2016

Mondayman

I am relatively new to mathematics (I only discovered a passion for it at 23), but two books that did it for me were:

Mathematics and the Physical World - Morris Kline

A First Course in Calculus - Serge Lang

I'm sure as I learn more I'll have more books to add.

7. Oct 28, 2016

jonjacson

8. Oct 28, 2016

Stella.Physics

This one is not pure Mathematics but still a book full of inspiration:

"Gravity: an introduction to Einstein's General Relativity" by James B. Hartle

9. Oct 28, 2016

Logical Dog

Principles of mathematics by allendoerfer and oakley.

Logic for dummies by mark z. (good book)

free legal link to zakons book : http://www.trillia.com/zakon1.html

hello, I would say the authors guide your thinking, when you learn from the best you get a completely different and refreshing viewpoint. :) ...and one day, maybe, you can become like them :P but reading the books is not enough, you must DO the exercises too..but without a good guide to the subject it is difficult for the less motivated people like me to study..I think this is what the op meant, there are a lot of garbage texts out there too.

Last edited: Oct 28, 2016
10. Oct 28, 2016

houlahound

Gross & Miller, mathematics a human endeavour.

Intro level text: it explained to me why highschool math is true. I just kept saying as I read it...aaaah that's why.

11. Oct 28, 2016

Krylov

Yes, I agree. High quality books have been essential for me since university, as I have always found it difficult to follow lectures or other forms of oral presentation. (I was and am quite motivated, but lectures often go too quickly for me and sometimes skip important details.)

I am still thinking about what I will reply to the OP.

12. Oct 28, 2016

Logical Dog

Not only will some lectures skip important details, but they will often not provide questions and insight like the real authors do that give you the most valuable insights into mathematical objects and mathematics in general because they don't have the time or motivation, or this type of thinking is useless for your course anyway, one must really do a lot of self learning if he wants to get under the "hood" of this subject and/or explore its philosophy. It has been a few months for me since this I found this desire, I am a bottom feeder in mathematics, hundreds or thousands of years behind the boundary of this body of knowledge, but I want to get better and maybe even do a degree, thats why I know these books. :)

Luckily I have a good lecturer who knows a lot about the subject :). If someone is really into math they should get a maths degree! One should not expect to be taught in this manner in a bachelor in engineering or other applied math heavy subjects. Same goes for physics, if you want to deal with high level physics, do physics instead and not a bachelor in other subjects.

Last edited: Oct 28, 2016
13. Oct 28, 2016

houlahound

Yeah but if you want a job do applied mathematics.

14. Oct 28, 2016

Student100

Err...???

To the OP, maybe you can give us a bit of background as to where you're actually at in terms of mathematics?

15. Oct 28, 2016

houlahound

Just a light hearted jab. My lecturers always used to make jabs where the pure science and math guys boast how smart they are and cite their papers in prestigious journals. The engineers and applied guys would cite their pay packets.

Me personally I did honours level undergraduate (4 years degree) in physics then got a job in coal as a wire logger (underground gamma spectroscopy) and nondestructive testing. The math was basic that any decent high schooler could do it. The company made millions tho and created hundreds of jobs.

Last edited: Oct 28, 2016
16. Oct 28, 2016

Simon Phoenix

My vote for a book in category (2) would be "Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics" by John Derbyshire
https://www.amazon.co.uk/dp/B004D39PGU/ref=dp-kindle-redirect?_encoding=UTF8&btkr=1

I loved it - it's aimed at a more general audience but it does a heroic job of explaining the Riemann hypothesis, its significance, and progress towards a proof (or otherwise) up to about 2003. It's a mix of maths and history and roughly speaking the chapters alternate between the two.

It's not really a textbook, sorry, but it is inspiring

17. Oct 28, 2016

Laurie K

18. Oct 28, 2016

Let'sthink

At elementary level George Gammow's "One, two, three, .... infinity" is also awe-inspiring! The idea of one to one correspondence makes impossible looking propositions become possible and proveable like the number of points on two unequal line segments are equal. When infinity is there anything is possible!

19. Oct 29, 2016

haushofer

I love the books of Tony Zee, but that's theoretical physics. Inspiring, funny, witty, with historical sidemarks and topics you don't find in other books.

20. Oct 29, 2016

jonjacson

21. Oct 29, 2016

BOAS

The book that convinced me I was capable of pursuing mathematics (physics) further, was "Calculus Made Easy" - Martin Gardner.

It isn't the best or my favourite book, but it is partly responsible for getting me this far, so it has a special place for me :)

22. Oct 29, 2016

jonjacson

23. Oct 30, 2016

vanhees71

Another one, I liked very much when I read it the first time is Weyl's "Raum, Zeit, Materie" (Space, Time, Matter), although the mathematicians of his time ahorred it. There is the famous story that Heisenberg went to the famous mathematics professor Lindemann in Munich (who proved that $\pi$ is transcendent) asking about the prospects of studying math. When he mentioned that he had read Weyl's book, Lindemann told him: "You are lost for mathematics." ;-).

24. Oct 30, 2016

Krylov

I think this is an interesting thread. Various books that I have encountered during my studies may fit your description, although my experiences were not exactly religious. Most influential was probably One-Parameter Semigroups for Linear Evolution Equations by Engel and Nagel. I never since gained more insight into the topic by reading a single book. (Please do not let the "linear" deceive you. Numerous nonlinear problems can be attacked by perturbing linear problems and, besides, linear problems are of great interest in their own right.) This book should be required reading for anyone who routinely "exponentiates" differential operators using ordinary power series.

More recently, I started reading C.D. Meyer's Matrix Analysis and Applied Linear Algebra. It reinforced my long-standing love for the subject and taught me that new things can be learnt about material that I believed I already knew inside-out. It also demonstrated that teaching LA could be fun instead of a punishment.

It depends a lot on the level and interest, of course. Meyer's book is a good option for a second course on linear algebra, or for a first course at a somewhat higher-than-usual level. In particular, it is suitable for self-study because it comes with a solution booklet by default.

Last edited: Oct 30, 2016
25. Oct 30, 2016