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I started off with abstract algebra, and found in the next 3 pages that I needed a bit more of matrices, since I had no idea how functions could also be represented by matrices, so I dipped next into a book about matrices, but again the book says I'm expected to have a background knowledge of calculus, and I figure that same would be for calculus rotating me through a series of nought. Just as programming in a concrete sense is a series of electrical impulses guided by codes, I would like to put mathematics from the very concrete level and come to all these developed topics not rotating from here and there. It's not that high school maths didn't teach me even a bit on calculus but with more knowledge I believe it is true that we can solve complex calculus problems with general logic than the rules we step on to solve those problems regardless of the effort, that would be more understable thoroughly.

Editing my question, where is that--- I can start with learning that operations such as--- change in signs with positions in an equation are proved?

lind
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  • You have to be more specific with what you want out of this book. Are you looking to know more about the history of mathematics? Are you looking for the math which is typically learned directly after high school? What are you trying to get out of studying math? Are you more interested in math that is useful for "real world problems", or math that is just interesting in and of its own right? – Ben Grossmann May 31 '16 at 09:00
  • @Omnomnomnom, I edited my question – lind May 31 '16 at 09:22
  • If you want the fastest route to understanding abstract algebra: take calculus up to integration techniques, then linear algebra, then abstract algebra. That, however, requires getting several textbooks or online resources that you would have to work through. – Ben Grossmann May 31 '16 at 09:30
  • You might also be interested in number theory or discrete mathematics, which you can probably start without becoming familiar with other topics first. – Ben Grossmann May 31 '16 at 09:31
  • @Omnomnomnom, do you know what the concrete level of mathematics is, I mean what maths started off with, was it number theory, algebra? – lind May 31 '16 at 09:45
  • @lind just because a topic came first historically first, doesn't mean that it's easier to start off with that topic. Number theory is an older topic than basic (not abstract) algebra, but a good understanding of basic algebra is necessary in order to take a modern course on number theory. – Ben Grossmann May 31 '16 at 09:53
  • @Omnomnomnom, the point is not the level of difficulty, it is to understand everything the way it was developed. Ex: several proofs are available for Euclid's algorithm to calculate GCD(one was an abstract proof) but the way euclid did it was with mere logical arguments, though it was lengthy, more complex, symbolically lacking, it was the orgin. Likewise, I want to get to the origin and start off from there. – lind May 31 '16 at 10:00
  • @lind That does not strike me as a particularly effective way to learn things, but good luck with that. – Ben Grossmann May 31 '16 at 10:02

3 Answers3

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I'm not aware of one book or one summary that has everything there is to know about mathematics, since it's such a broad topic. My recommendation is to start from some first year undergraduate mathematics, like calculus and linear algebra, and continue from there. What mathematics do you know already

AnonymouseCat
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  • I'm just a high schooler, and none of the books that i have spent over 17 yrs of life studying taught me anything useful, ex: only common logs are taught in high school, though I'll edit my question to be a bit more specific – lind May 31 '16 at 09:18
  • Ok. Thanks for that information. If that's the case, my recommendation is to start with basic linear algebra. Here's an online book you can start with http://linear.ups.edu/download/fcla-3.40-tablet.pdf. Let me know if you have any questions here. – AnonymouseCat May 31 '16 at 09:37
  • Thanks a lot! I really appreciate it. – lind May 31 '16 at 09:43
  • do you know what the concrete level of mathematics is, I mean what maths started off with, was it number theory, algebra? – lind May 31 '16 at 09:46
  • I wouldn't recommend you to learn math historically, only because many proofs were very complicated, since they didn't use many useful tools that exist today. It's tough to say where exactly math started, since many fields evolved separately. – AnonymouseCat May 31 '16 at 11:04
  • could you look at my edit please, is this something included in linear algebra? – lind May 31 '16 at 15:28
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There is absolutely no such book, mathematics are way to broad. If you want to learn about a specific field in mathematics, there is top books in those categories. However, you will not find a book to learn about them all. It is simply not possible to feat mathematics in a single book. It would be like asking if there is a book about physic. You would have to say first if you want to learn about quantum physic, astronomy, relativity, mechanic...

E. Joseph
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From your question I interpret that you did not pay attention to maths in high school and want to catch up. So probably the first step would be to start from the beginning of high school material and do the work. After that you will have a better picture.

user343547
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