(Part 2) Top products from r/mathbooks

Not a book, but I can share a few videos that I've found inspirational during some rough times with mathematics...

Fermat's Last Theorem -- This is a documentary on Andrew Wiles' proof of Fermat's last theorem. It's also probably the most emotional video I've ever watched about math. Highly recommended.

Fractals -- This is a neat NOVA documentary on fractals. In particular, it provides some inspiring history regarding Mandelbrot's discovery and journey with this subject.

Everything is relative, Mr. Poincare -- Another exceptional and inspiring documentary.

The only book I can recommend is Journey Through Genius by William Dunham, which provides an excellent treatise on the history of mathematics. From the book description

> Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics.

It's a very good read, and not too gigantic. Good wishes your way, mate.

I passed exam P and exam FM earlier this year.


The textbook that covered the exam P material was This One It did an ok job and covered all the exam P material. I assume any mathematical Statistics book would be similar.


I did use the Kellison Theory of Interest book a bit. However, an interest theory book will not cover all the material on the syllabus for exam FM. roughly 2/3 of the syllabus is interest theory while the other third (roughly) is financial derivatives covered in This Book which is also used in the syllabus for exam MFE/3F.


Now, these textbooks are great for learning the material but your goal is to be able to pass the exams. To do this I HIGHLY recommend you get a study manual and use it as your primary method of study.


Some good study manuals for exam P are either from ASM or ACTEX.


The best manual for Exam FM is ASM. Many people I have talked to have passed the exam in the first sitting using only this manual as their study material.


Also, if you are interested there is a site called The Infinate Actuary that has video lessons available.

I hope this was helpful.

I think it depends what kind of PDEs you're going to be doing really. If you're just looking at physicsy things like Laplaces equation, the heat equation and the wave equation then a methods book might be good. My personal choice would be this one but there is a lot of choice out there.

If it's a slightly higher level PDEs course (doing stuff like method of characteristics and conservation laws) then either this dover book or this book were the two recommended texts for my upper undergrad course on PDEs. The second is also recommended on a grad course I'm doing come september, and has loads of material in the book.

If you could give some more details of the course I could probably help you pick one of these easier. :)

There's no single book that's right for everyone: a suitable book will depend upon (1) your current background, (2) the material you want to study, (3) the level at which you want to study it (e.g., undergraduate- versus graduate-level), and (4) the "flavor" of book you prefer, so to speak. (E.g., do you want lots of worked-out examples? Plenty of exercises? Something which will be useful as a reference book later on?)

That said, here's a preliminary list of titles, many of which inevitably get recommended for requests like yours:

1. Undergraduate Algebra by Serge Lang
   
   
2. Topics in Algebra, 2nd edition, by I. N. Herstein
   
   
3. Algebra, 2nd edition, by Michael Artin
   
   
4. Algebra: Chapter 0 by Paolo Aluffi
   
   
5. Abstract Algebra, 3rd edition, by David S. Dummit and Richard M. Foote
   
   
6. Basic Algebra I and its sequel Basic Algebra II, both by Nathan Jacobson
   
   
7. Algebra by Thomas Hungerford
   
   
8. Algebra by Serge Lang
   
   Good luck finding something useful!

The book Ideals, Varieties and Algorithms by Cox, Litle and O'Shea is a very good undergraduate level algebraic geometry book. It has the benefit of teaching you the commutative algebra you need along the way instead of assuming you know it.

I'm not really aware of any algebraic topology books I'd consider undergraduate, but most of them are accessible to first year grad students anyway, which isn't too far away from senior undergrad. Some of my favorite sources for that are Munkres' book and Fulton's Book.

For knot theory, I haven't really studied it myself, but I've heard that The Knot Book is quite good and quite accessible.

Is your objective to build a comprehensive understanding of the underlying topics of Calculus or is your objective to master quick problem solving, tricks, etc? If it is the latter I would suggest you pick this up as an auxiliary resource; Stuart is good but mastery of the mechanics of solving the problems will come only through ardent practice. You will need to see, and solve, a wider set of examples than is typically found in Stewart.

If your objective is the former I would grab this instead. Probably look for it on a used book seller's site like abebooks.com, though.

Linear programming:

• Vanderbei, Linear Programming: Foundations and Extensions
  
  Combinatorial optimization:
  
  
• Papadimitriou and Steiglitz, Combinatorial Optimization: Algorithms and Complexity
  
• Cook, Cunningham, Pulleyblank, and Schrijver, Combinatorial Optimization
  
  Game theory:
  
  
• Fudenberg and Tirole, Game Theory
  
• Osborne and Rubinstein, A Course in Game Theory
  
  Combinatorial game theory:
  
  
• Berlekamp, Conway, and Guy, Winning Ways for Your Mathematical Plays (volume 1, volume 2, volume 3, volume 4)
  
• Berlekamp, The Dots and Boxes Game: Sophisticated Child's Play
  
• Albert, Nowakowski, and Wolfe, Lessons in Play: An Introduction to Combinatorial Game Theory
  
• Conway, On Numbers and Games

A few Suggestions:

• Kostrikin - Linear algebra and Geometry: The best there is. This book is solid and you can go far with it, it's a book for life. But beware that some of it's exercises are really difficult.
  
  
• Hoffman - Linear Algebra: This one has lots of examples and is particularly good on the eingenvectors part you want, but sometimes the notation is bad.
  
  
• Lang - Linear Algebra
  
  All this books can easily be found. Good luck.

The following are all really good and all very different. Check out the reviews and decide what fits you best. If I had to pick only one, I would pick one of the first three listed.

http://www.amazon.com/gp/product/0471530123

http://www.amazon.com/gp/product/1592577229

http://www.amazon.com/The-Humongous-Book-Calculus-Problems/dp/1592575129

http://www.amazon.com/gp/product/0817636773

http://www.amazon.com/gp/product/0760706603

http://www.amazon.com/gp/product/B000ZEC19Y

http://www.amazon.com/gp/product/0070293317

I'd recommend Mathematics: A Very Short Introduction by Tim Gowers if you'd like a fairly serious but informative book describing what mathematics is really about.

For a more fun, coffee-table kind of book, have a look at The Math Book by Clifford Pickover.

For synthetic planar geometry I can recommend the Millman-Parker, it's really good and you only need a little bit of calculus to understand it.

I think "Mathematical Proofs: A Transition to Advanced Mathematics (2nd Edition)" is a solid book.

It starts off with what I would expect in a discrete math course (which is generally a first proofs course) and ends with a few chapters that would begin a second step writing intensive proofs course: number theory, calculus (real analysis), and group theory (algebra).

There are also many resources online that will help you once you've gotten through the basic notions in the book.

I just finished an ODE course and we used Differential Equations: Computing and Modeling. It was straight forward, fairly cheap used on amazon and has an available (and helpful) solutions manual.

http://www.amazon.com/gp/aw/d/0306812835/ref=mp_s_a_1_1?qid=1449385131&sr=8-1&pi=SY200_QL40&keywords=structures+or+why+things+don%27t+fall+down&dpPl=1&dpID=516rxXknhsL&ref=plSrch

I just ordered a copy for me and my just off to college wannabe engineer brother in law. Thanks!

My favorite intro to the subject is still A First Course in Real Analysis by Protter & Morrey.

I liked this one by Munkres

http://www.amazon.co.uk/Topology-Featured-Titles-James-Munkres/dp/0131816292