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I overcame my math illiteracy by reading How To Prove It. The book is so simple and narrow in scope and yet it gave me a feeling that ultimately no math is beyo

I overcame my math illiteracy by reading How To Prove It. The book is so simple and narrow in scope and yet it gave me a feeling that ultimately no math is beyond my grasp, even the papers on arxiv. Now I would say my math skills are still rather low because I know how much is out there, but at least I am competent. At this point I wouldn't want to read books that avoid math for mathematical topics. Algorithms are mathematical, so it's silly to seek books for math illiterate. It's like looking to copypaste a large chunk of code without reading and understanding it while caring about code quality of your system, it just doesn't make sense. It is not a good decision.

westoncb 8y ago
I wonder if there is just a big split between what folks are looking for in mathematics. I cannot understand how "How to Prove It" is so frequently praised. I tried reading after finishing my CS degree, while I was searching for books that would do math 'right,' being especially inspired by Paul Lockhart (and others), and it was one of the first books I picked up. I found it to be so much more of the same, focused on all these small things I didn't care about, pedantic, written in a cold detached tone, still no suggestion of why I should care about the things being talked about. I had a much better time with "What is Mathematics?" (aka "Courant and Robbins"), though it still suffers from some similar problems (I remember being baffled by all the attention paid to these properties like commutativity, associativity, etc.—"why should I care about this!?"). Really, I still can't think of a single book that was great for overcoming my own "math illiteracy," it was mostly just a haphazard process of trying enough different things that eventually various parts started falling into place etc. But I guess part of what's going on is that what works for one person is gonna be awful for another. So I just want to say, maybe "How to Prove It" will be great for you (other readers)—but don't feel bad if it isn't.
- paulriddle 8y ago
  Truth be told, at the time I was also reading around 20 other books, it's just that I completed 90% of How To Prove It and around 10-15% of the other books. I was so captivated by math after discovering blogs of rather opinionated math professors and students that I downloaded literally over a hundred books (for free) and started designing the perfect curriculum. I would start over many times, over and over, study most of the free time I had between college and programming, watch dozens of lectures, seek lecture notes and additional exercise sheets, and try to solve everything. This particular period lasted about 8 months, after which I stopped studying math and took a long break to resolve some life issues and prepare myself for my first job as a software engineer. I remember reading a few sections from What is Mathematics too. Some chapters on topology and the preface. So, yeah, I also succeeded because I drowned myself in everything possible until I got used to it. It's just that I never felt any frustrations with Velleman's book, so I knew that every time I open it I will learn something new, won't get confused, and the level of difficulty will be just right. That's why I kept coming back to this book and completed most of it, while didn't make much progress in others.
  - westoncb 8y ago
    Oops! My bad! I just realized that you're talking about a different book. I thought you were referring to the book's namesake, Polya's "How to Solve it." I have not had any contact with how "How to Prove it"! Also, interesting how much of a similar way we seem to have gone about learning math. I kept it as my main focus for a similar amount of time, then for as a secondary focus while working on a big software side project for another 7 months or so (I was working at a grocery store for money the whole time), then got my first software engineering job and largely dropped any focused study in mathematics. But now I'm in a position where I'll learn bits of math as I need them for projects or whatever, so it definitely wasn't a waste (and like you mentioned in being able to read stuff off of arxiv, it expanded the range of ideas I can understand). I've actually started getting interested in continuing study again, getting more into applied math this time since I really focused on pure last time. First goal is to get a clear understanding of Maxwell's Equations :)

westoncb 8y ago

I wonder if there is just a big split between what folks are looking for in mathematics. I cannot understand how "How to Prove It" is so frequently praised. I tried reading after finishing my CS degree, while I was searching for books that would do math 'right,' being especially inspired by Paul Lockhart (and others), and it was one of the first books I picked up. I found it to be so much more of the same, focused on all these small things I didn't care about, pedantic, written in a cold detached tone, still no suggestion of why I should care about the things being talked about. I had a much better time with "What is Mathematics?" (aka "Courant and Robbins"), though it still suffers from some similar problems (I remember being baffled by all the attention paid to these properties like commutativity, associativity, etc.—"why should I care about this!?"). Really, I still can't think of a single book that was great for overcoming my own "math illiteracy," it was mostly just a haphazard process of trying enough different things that eventually various parts started falling into place etc. But I guess part of what's going on is that what works for one person is gonna be awful for another. So I just want to say, maybe "How to Prove It" will be great for you (other readers)—but don't feel bad if it isn't.

paulriddle 8y ago
Truth be told, at the time I was also reading around 20 other books, it's just that I completed 90% of How To Prove It and around 10-15% of the other books. I was so captivated by math after discovering blogs of rather opinionated math professors and students that I downloaded literally over a hundred books (for free) and started designing the perfect curriculum. I would start over many times, over and over, study most of the free time I had between college and programming, watch dozens of lectures, seek lecture notes and additional exercise sheets, and try to solve everything. This particular period lasted about 8 months, after which I stopped studying math and took a long break to resolve some life issues and prepare myself for my first job as a software engineer. I remember reading a few sections from What is Mathematics too. Some chapters on topology and the preface. So, yeah, I also succeeded because I drowned myself in everything possible until I got used to it. It's just that I never felt any frustrations with Velleman's book, so I knew that every time I open it I will learn something new, won't get confused, and the level of difficulty will be just right. That's why I kept coming back to this book and completed most of it, while didn't make much progress in others.
- westoncb 8y ago
  Oops! My bad! I just realized that you're talking about a different book. I thought you were referring to the book's namesake, Polya's "How to Solve it." I have not had any contact with how "How to Prove it"! Also, interesting how much of a similar way we seem to have gone about learning math. I kept it as my main focus for a similar amount of time, then for as a secondary focus while working on a big software side project for another 7 months or so (I was working at a grocery store for money the whole time), then got my first software engineering job and largely dropped any focused study in mathematics. But now I'm in a position where I'll learn bits of math as I need them for projects or whatever, so it definitely wasn't a waste (and like you mentioned in being able to read stuff off of arxiv, it expanded the range of ideas I can understand). I've actually started getting interested in continuing study again, getting more into applied math this time since I really focused on pure last time. First goal is to get a clear understanding of Maxwell's Equations :)