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    Thread: Math book suggestions

    1. #1
      DEATH TO FANATICS! StonedApe's Avatar
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      Math book suggestions

      I want to start doing math again. I was always very good at it. My calculus teacher had always annoyed me(abstinence only advocate, I can't stand whiny self righteous morons), so when she said we would have homework every night, even when we had tests, I dropped the class. It didn't seem like something I'd ever need and I was sick of school at that point.

      I want to get some books. I'm going to go to the University's library tomorrow to see what I can find. Does anyone have any they think are particularly good? I wanna brush up on some algebra first but I think in a month or so I'll start teaching myself calculus. I mainly need problems to work out, I can find resources to learn from online.
      157 is a prime number. The next prime is 163 and the previous prime is 151, which with 157 form a sexy prime triplet. Taking the arithmetic mean of those primes yields 157, thus it is a balanced prime.

      Women and rhythm section first - Jaco Pastorious

    2. #2
      Consciousness in the Void Universal Mind's Avatar
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      Glencoe's math textbooks are generally really good, but their most recent Algebra II book sucks. Their previous edition is awesome.

      If you look up math topics on YouTube, look for khanacademy and/or patrickJMT. They are usually listed near the top for each topic, and they are the two best math teachers on YouTube, as far as I know. Watching both of them teach the same topic is extremely helpful. Math Warehouse and Purple Math are really good websites.
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    3. #3
      DEATH TO FANATICS! StonedApe's Avatar
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      Yeah, I've watched some Khan Academy stuff. It's good, but until I get to calculus I really just need problems to refresh my memory. Been doing long division in my head to try to get the rust off the gears, KA is a good source for those. I'll look into patrickJMT.
      157 is a prime number. The next prime is 163 and the previous prime is 151, which with 157 form a sexy prime triplet. Taking the arithmetic mean of those primes yields 157, thus it is a balanced prime.

      Women and rhythm section first - Jaco Pastorious

    4. #4
      DuB
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      Distinct among snowflakes DuB's Avatar
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      StonedApe, have you seen MIT's free, self-contained online courses, under the "OCW Scholar" label? They have a course "Single Variable Calculus" that I worked through about a year ago and I can tell you that it is wonderful.

      Link to course list:
      OCW Scholar | MIT OpenCourseWare | Free Online Course Materials

      At many U.S. universities, the calculus sequence is divided into 3 courses: "Calc 1" (mainly differentiation in one variable), "Calc 2" (mainly techniques of integration in one variable), and "Calc 3" (differentiation and integration in multiple variables). The MIT course is basically the equivalent of Calc 1 and 2. It moves at a pretty brisk pace but is very rewarding if you take the time and actually do all the work.

      I don't know that an algebra review would be necessary to begin this, but I would instead recommend brushing up on basic trigonometry. It would probably suffice just to go through the Trig videos on Khan Academy first.
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      Xei
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      Seconding the MIT course. Multivariable calculus was even better.

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      Read Godel, Escher, Bach If you're math-minded, it's a fantastic book. It can be a challenging read, but will really get your brain spinning in the way you like if you enjoy math.
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    7. #7
      Xei
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      It won't help with calculus, but definitely a beautiful book and one which'll actually teach you some pretty high level stuff in logic, for a popsci book.

      Personally I couldn't make much headway in it until I had a year of undergraduate studies under my belt though. It's hard work if you're not used to formal thinking.

    8. #8
      DEATH TO FANATICS! StonedApe's Avatar
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      I'm watching the lecture for the MIT course now. It seems really good, but I definitely need to review trigonometry.

      I've read about halfway through GEB twice. I really like it. It took me about a month to get halfway through it, it's a little bit daunting. But that was a few years ago. I have a better understanding of a lot of what the book talks about now and could probably read it faster now. I remember stopping after almost every section and thinking about it for a while.

      I'm reading Flow by Mihaly Csikszentmihalyi right now and his anatomy of consciousness makes me think that he's read GEB.
      157 is a prime number. The next prime is 163 and the previous prime is 151, which with 157 form a sexy prime triplet. Taking the arithmetic mean of those primes yields 157, thus it is a balanced prime.

      Women and rhythm section first - Jaco Pastorious

    9. #9
      Xei
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      Maybe you should also consider reading some first year undergraduate mathematics? Mathematics at school basically only covers a small section of what mathematics really is - basically applied things, such as calculus, which is used largely in physics. Don't get to thinking that this section is representative of mathematics as a whole. There's an entire new continent of mathematics (arguably a much more beautiful and interesting one), which you start studying the (very) simple beginnings of when you start a degree. This includes things like abstract algebra ("group theory", to start off with), number theory and set theory (you'll have glimpsed some set theory in GEB in the section about Cantor), and analysis. The approach is very different, emphasising a building up of layers of abstraction and a discovery of structure, critically based on the notion of proof - contrasted with stuff at school which is more about techniques for getting answers to various mundane problems. If your interest is recreational then I'd definitely recommend you explore it, rather than or at least in addition to calculus.
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    10. #10
      DEATH TO FANATICS! StonedApe's Avatar
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      I took a basic undergraduate math course I needed for my music degree a few years ago, but it was really bad. It was all review of things I'd learned in high school. We learned the very basics of set theory.

      But that would probably be more of what I'm interested in. I'll look for some books on those topics next time I'm at the library.

      My main motivation for this is just brain exercise. I've noticed that when I've been doing math I can think about music more quickly and play better. I don't really think I'll be using much of this, but I am considering going back to school in a year or two and getting a degree in one of the sciences.
      157 is a prime number. The next prime is 163 and the previous prime is 151, which with 157 form a sexy prime triplet. Taking the arithmetic mean of those primes yields 157, thus it is a balanced prime.

      Women and rhythm section first - Jaco Pastorious

    11. #11
      DuB
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      Xei, do you have book suggestions for an introduction to the kind of abstract mathematics you have in mind?

      I have Eccles - Introduction to Mathematical Reasoning (recently bought it and haven't worked through it yet) but would welcome other suggestions.

    12. #12
      Xei
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      Oh look, it's my signature!

      Pretty much all of my degree was learned from the lecture notes, so I can't really recommend any books. In addition, we weren't really "introduced" to anything, as such. In one course, the lecturer spent about twenty minutes at the very start, talking generally about proof, but beyond that there was no explicit focus on proof as a subject in itself (as seems to be the case in American universities). We simply started the various subjects, at their absolute beginnings, and then worked upwards, picking it up as we went. But in my experience this is the best approach - the kind of skills that you need (namely being able to work with abstraction, rigour, and proof), are best learned simply by doing.

      In fact there is a similar book to yours recommended on that Amazon page, "How To Think Like a Mathematician", which I've read through. But it was just casual skimming out of curiosity, long after I was comfortable with its concepts. Such books may be helpful, but only as companion pieces to study of an actual pure course. In themselves, I think it would be kind of hard for a newcomer to understand the general ideas they talk about, without having some experience with the actual substance it's generalising from.

      In respects to which, I'm happy to email my first year notes for Numbers and Sets, Group Theory, and Analysis, to anybody who'd like them. The elements of this list are independent, but probably ordered according to increasing difficulty. I'd also argue that they're ordered according to decreasing levels of fun. And also, Numbers and Sets is probably the course most concerned with introducing the reader to concepts of proof and rigour.

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