(Part 2) Best products from r/mathbooks

you're going to struggle with mathematics until you get a better handle on stuff like proofs. it gets a little better once you've paid your dues.

book wise i'd recommend Linear Algebra and Its Applications by Peter Lax really just because i'm a huge fan of his. additionally, i'd recommend reading (or trying to read) every book you can get your hands on.

I've worked with a handful of standard calc texts, and my favorite is Calculus: Early Transcendentals Anton - Bivens - Davis. The eighth edition can be found super cheap as it's not used much anymore. There are a lot of good algebra and trig books out there to get you where you'd need to be in order to start studying calc. If you're particularly interested in the physical side of things The Mathematical Mechanic is a neat book with many interesting problems.

Hang out at a community college and talk to professors. Often, they don't mind someone just sitting in on lectures. This could be especially helpful if you haven't worked with algebra/trig in a while.

Edit-- also MIT opencourseware lectures kick ass.

For the Mathematics for the Millions there are two books. Is it this one or this [one?] (https://www.amazon.com/Mathematics-Million-Lancelot-Hogben/dp/1291585451). Also, I read the Amazon description for Mathematics for the Nonmathematician and the book itself seems a bit advanced for me. However, it does seem like a fascinating read. You've had this book so tell me, is great for even a beginner or is designed for someone with more advanced mathematics skills?

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!

Whatever book you purchase, make sure that you also purchase a book of problems for you to solve to go along with it. For the book you have asked about, this book is the companion.

http://www.amazon.ca/Basic-Math-Pre-Algebra-Workbook-Dummies/dp/1118828046/ref=pd_bxgy_b_text_y

The best way to become good at math is to solve a lot of problems.

I would recommend Khan Academy. They have videos for all levels of math, and a lot of problems to go with them.

More information on what you want to learn, and about you, would be good. What level of education do you have? Are you a student right now? What is your first/best language? What kind of science do you want to do? A strong understanding of mathematics is very important for some parts of science, like physics, but less important for others, like biology.

These are, in my opinion, some of the best books for learning high school level math:

• I.M Gelfand Algebra {[.pdf] (http://www.cimat.mx/ciencia_para_jovenes/bachillerato/libros/algebra_gelfand.pdf) | Amazon}
  
• I.M. Gelfand The Method of Coordinates {Amazon}
  
• I.M. Gelfand Functions and Graphs {.pdf | Amazon}
  
  These are all 1900's Russian math text books (probably the type that /u/oneorangehat was thinking of) edited by I.M. Galfand, who was something like the head of the Russian School for Correspondence. I basically lived off them during my first years of high school. They are pretty much exactly what you said you wanted; they have no pictures (except for graphs and diagrams), no useless information, and lots of great problems and explanations :) There is also I.M Gelfand Trigonometry {[.pdf] (http://users.auth.gr/~siskakis/GelfandSaul-Trigonometry.pdf) | Amazon} (which may be what you mean when you say precal, I'm not sure), but I do not own this myself and thus cannot say if it is as good as the others :)
  
  
  I should mention that these books start off with problems and ideas that are pretty easy, but quickly become increasingly complicated as you progress. There are also a lot of problems that require very little actual math knowledge, but a lot of ingenuity.
  
  Sorry for bad Englando, It is my native language but I haven't had time to learn it yet.

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.