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Two or three years ago I decided to re-learn math from scratch, I did some research on what to read, made a list of books. I started from a Sawyer, it opened my eyes a little bit on the fact that math isn't that cryptic if you study it right, and that in fact it's quite interesting. But, for some reason I dropped it. Now I'm almost finished re-reading "Mathematician's Delight", but I look at the list I made several years ago and it scares and confuses me. I would be grateful if you guys could tell me in what order I should read this books (I own every book but the ones marked "don't have it"), should I buy the ones missing etc.

A little background: my school was math-focused and I kinda did well, but only because I learned by heart formulas and patterns of when to use them. I'm trying to do things right this time. I'd like to go through school program in a year, then spend summer learning Discreete math and Calculus (trying to apply for CS undergrad next year), so I could be month or two ahead of the program. Why I wanna be ahead? Because I found out that I can't at all absorb knowledge in class, mainly because there is always someone who spits answers faster then I get that precious insight on how things work, and why exactly they work this way.

So, here's the list of books with notes to myself:

Basics

  • "Mathematician's Delight" by W. W. Sawyer
  • "Journey through Genius: The Great Theorems of Mathematics" by William Dunham

Algebra

Geometry

  • "Euclid's Elements"
  • "Geometry: Euclid and Beyond" (Undergraduate Texts in Mathematics) by Robin Hartshorne

Trigonometry (prerequisite: geometry)

  • "Trigonometry" by I.M. Gelfand

Pre-calculus/Analytical Geometry

  • "Functions and Graphs" by I. M. Gelfand
  • "Pre-Calculus Demystified" by Rhonda Huettenmueller

Calculus (prerequisite: pre-calculus)

  • "Calculus: The Elements" by Comenetz
  • "Calculus and Analytic Geometry (9th Edition)" by Thomas, Finney (blue hardcover w/ lighthouse) *don't have it
  • "Calculus" by Spivak (read "How to prove it" first)
  • Paul's Notes http://tutorial.math.lamar.edu
  • Linear algebra is needed for cacl III

Linear Algebra (prerequisite: calculus 1,2)

  • "Elementary Linear Algebra, 2nd Edition" by Paul Shields
  • "Linear Algebra, 4th Edition" by Friedberg, Insel, Spence *dont have it
  • "Linear Algebra Done Right" (Undergraduate Texts in Mathematics) by Sheldon Axler *don't have it

Discrete Math

  • "Discrete Mathematics with Applications" by Susanna S. Epp (2nd edition) hardcover
  • "Concrete Mathematics: A Foundation for Computer Science" (2nd Edition) by Ronald L. Graham *dont have it
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closed as off-topic by Daniel W. Farlow, user296602, Henrik, user99914, Chill2Macht Jul 30 '16 at 21:13

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  • $\begingroup$ I don't know about "Mathematician's Delight", but "Journey Through Genius" is, IMHO, not something to learn math from. It is mostly history there, and the author arguably assumes a large set of math skills and a good level of familiarity with proof structures in the audience. It is also poorly structured because the author makes big jumps towards the end. It is just a good read when you have acquired enough knowledge and if you have some interest in the history of Maths. $\endgroup$ – user258700 Jul 30 '16 at 19:45
  • $\begingroup$ Take an online course offered by universities. Learning only from books isn't so ideal I find. $\endgroup$ – RonaldB Jul 30 '16 at 20:31
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The order is generally right the way you have it more or less: basics, then algebra, then geometry, then calculus and linear algebra, then advanced calculus.

I'd strongly advise against locking yourself in a room with all these books you bought and forcing yourself to read every sentence. That's generally a terrible learning model.

You'd make better progress if you make a friend or two who's as passionate about math as you. Join a community or group. Lots of schools offer free turoring. The best progress you will make is going to be when you are interacting with people and are fully engaged.

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    $\begingroup$ (except him) nobody buy books anymore $\endgroup$ – reuns Jul 30 '16 at 20:32
  • $\begingroup$ I wouldn't say that I'm forcing myself. I like spending time experimenting with things all by myself, I may feel that I got the material, yet spend another 3-4 hours trying to explain it from different angles just to find the one that feels the most natural to me. And if I don't feel like it I switch to another activity that day. Between "how to solve/prove it" which one do you think I should try first? I saw people suggesting studying discrete math before "prove it", which is a bit weird to me, since geometry has a lot of proofs and discrete math starts only in university. $\endgroup$ – Renox92 Jul 30 '16 at 21:04
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    $\begingroup$ The "all by myself" part may be what's screwing you over. There's a saying, go alone, go fast, go together, go far. I'd instead of spending four hours trying to understand a concept, try and talk to a few friends or peers and get them to explain how it works. Also, in explaining to someone, you solidify your own understanding. $\endgroup$ – darksky Jul 30 '16 at 23:04
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    $\begingroup$ Regarding your other question, solving and proving are two different proccesses, but are fundementally the same thing: in both you try to reason abstractly, search for a solution or proof, try things, and eventually reach your logical destination. One is not more important than the other. $\endgroup$ – darksky Jul 30 '16 at 23:07

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