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Many of the list are pop-maths rather than fundamental texts. I do see many in software field recommend Chrystal:Algebra an Elementary Textbook. I also find D

Many of the list are pop-maths rather than fundamental texts. I do see many in software field recommend Chrystal:Algebra an Elementary Textbook. I also find Don Knuth, 'Concrete Mathematics' a interesting book for software people.

commandlinefan 8y ago
I came to a realization years ago that when it comes to math/science/computers, if I just read about it, I’m not really learning anything. I don’t learn unless I’m participating. Math books without _lots_ of exercises probably don’t really impart that much, although they can be a fun distraction if you need something to read on an airplane.
- arvinsim 8y ago
  I agree. Some things only stick by repeated application. This becomes more relevant the one older gets.
- hnuser355 8y ago
  Depending on your level of math ability you can often learn a lot by reading textbooks and proofs very carefully and closely (my opinion)
  - whatshisface 8y ago
    It depends on your definition of learning. If by learning you mean remembering how one author defined and proved various things then sure. If by learning you mean gaining the ability to do what the author did except for new problems, then at some point you will have to grapple with the fact that coming up with new ideas is a very different mental exercise from recalling things you've read. A supporting factor in the necessity of exercises for learning to actually do the math is that authors often hide important technical tricks in the exercises. Of course, a sufficiently intelligent person could learn anything by reading tea leaves and then deriving on their own whatever it was they wanted to learn, so in a sense you can learn math by doing anything.
  - throwawaymath 8y ago
    I disagree. Generally speaking students aren't able to teach themselves mathematics on their own until they hit the graduate level. That's not a hard rule, it just depends on mathematical maturity. But everyone I know who is able to teach themselves math without lectures or a professor still does the exercises in the textbook. Math isn't a spectator sport, it's really important to do active learning.
  - The_suffocated 8y ago
    This depends on the textbooks. It is very, very hard to find a textbook that is (a) well written, (b) suitable for self-study and (c) affordable.
    - hnuser355 8y ago
      Idk, I tried to self study the first two chapters of a very hated textbook (Principles of Mathematical Analysis). If you’d have asked me if I understood the material I would have said no. But by the time I took the actual class on that material I made high As on all the exams and could call out mistakes my professor made on metric sets with counter examples.
- jordigh 8y ago
  In my country we have a saying: la matemática entra por la mano, no por los ojos -- mathematics is absorbed with your hands, not with your eyes.
- kiba 8y ago
  You can't hardly learn anything by just reading or watching it.
mymythisisthis 8y ago
Any good recommendations on books that are more than pop-fluff but lighter than an academic text?
- technofire 8y ago
  Jeremy Kun, who writes the "Math ∩ Programming" blog,[1] recently published a book, "A Programmer's Introduction to Mathematics,"[2] that seems to leverage the conceptual knowledge programmers already have to help them learn serious math. There also are sections in the book on math culture which seems interesting, something I haven't seen elsewhere. [1] https://jeremykun.com/ https://jeremykun.com/ [2] https://pimbook.org/ https://pimbook.org/
- tyler- 8y ago
  I like this book: https://www.amazon.com/Fearless-Symmetry-Exposing-Patterns-Numbers/dp/0691138710 https://www.amazon.com/Fearless-Symmetry-Exposing-Patterns-N...
- bgutierrez 8y ago
  I really liked Introduction to Graph Theory by Trudeau. No upper level math required, but it got rigorous and fun at times. Mostly spatial reasoning. David Foster Wallace wrote Everything and More which included a lot of math history, while driving into transfinite numbers and set theory. Kindle typesetting is generally terrible for math, but was completely readable in this case. The forward by Neal Stephenson really sets the mood.
  - a_wild_dandan 8y ago
    > David Foster Wallace wrote Everything and More This is far and away my favorite math book. The way DFW can seamlessly transition from discussing a serious mathematical concept, to the nature of insanity, to the philosophy of abstraction all within a few pages is astounding. He somehow manages to do it while maintaining a conversational, two-folks-at-a-bar tone, teaching me dozens of new word, and being insightful/funny. Like an English professor sneaked into the math dept. I didn't know it was available on Kindle. Guess I'm buying it again...
okl 8y ago
Would also recommend 'Surreal Numbers' by Don Knut hand 'The Book of Numbers' by Conway and Guy.
masonic 8y ago
The author may have just chosen what's in stock at Amazon, given that all the links are Amazon affiliate links (tag=alikayaspor0b-20).

commandlinefan 8y ago

I came to a realization years ago that when it comes to math/science/computers, if I just read about it, I’m not really learning anything. I don’t learn unless I’m participating. Math books without _lots_ of exercises probably don’t really impart that much, although they can be a fun distraction if you need something to read on an airplane.

arvinsim 8y ago
I agree. Some things only stick by repeated application. This becomes more relevant the one older gets.
hnuser355 8y ago
Depending on your level of math ability you can often learn a lot by reading textbooks and proofs very carefully and closely (my opinion)
- whatshisface 8y ago
  It depends on your definition of learning. If by learning you mean remembering how one author defined and proved various things then sure. If by learning you mean gaining the ability to do what the author did except for new problems, then at some point you will have to grapple with the fact that coming up with new ideas is a very different mental exercise from recalling things you've read. A supporting factor in the necessity of exercises for learning to actually do the math is that authors often hide important technical tricks in the exercises. Of course, a sufficiently intelligent person could learn anything by reading tea leaves and then deriving on their own whatever it was they wanted to learn, so in a sense you can learn math by doing anything.
- throwawaymath 8y ago
  I disagree. Generally speaking students aren't able to teach themselves mathematics on their own until they hit the graduate level. That's not a hard rule, it just depends on mathematical maturity. But everyone I know who is able to teach themselves math without lectures or a professor still does the exercises in the textbook. Math isn't a spectator sport, it's really important to do active learning.
- The_suffocated 8y ago
  This depends on the textbooks. It is very, very hard to find a textbook that is (a) well written, (b) suitable for self-study and (c) affordable.
  - hnuser355 8y ago
    Idk, I tried to self study the first two chapters of a very hated textbook (Principles of Mathematical Analysis). If you’d have asked me if I understood the material I would have said no. But by the time I took the actual class on that material I made high As on all the exams and could call out mistakes my professor made on metric sets with counter examples.
jordigh 8y ago
In my country we have a saying: la matemática entra por la mano, no por los ojos -- mathematics is absorbed with your hands, not with your eyes.
kiba 8y ago
You can't hardly learn anything by just reading or watching it.

mymythisisthis 8y ago

Any good recommendations on books that are more than pop-fluff but lighter than an academic text?

technofire 8y ago
Jeremy Kun, who writes the "Math ∩ Programming" blog,[1] recently published a book, "A Programmer's Introduction to Mathematics,"[2] that seems to leverage the conceptual knowledge programmers already have to help them learn serious math. There also are sections in the book on math culture which seems interesting, something I haven't seen elsewhere. [1] https://jeremykun.com/ https://jeremykun.com/ [2] https://pimbook.org/ https://pimbook.org/
tyler- 8y ago
I like this book: https://www.amazon.com/Fearless-Symmetry-Exposing-Patterns-Numbers/dp/0691138710 https://www.amazon.com/Fearless-Symmetry-Exposing-Patterns-N...
bgutierrez 8y ago
I really liked Introduction to Graph Theory by Trudeau. No upper level math required, but it got rigorous and fun at times. Mostly spatial reasoning. David Foster Wallace wrote Everything and More which included a lot of math history, while driving into transfinite numbers and set theory. Kindle typesetting is generally terrible for math, but was completely readable in this case. The forward by Neal Stephenson really sets the mood.
- a_wild_dandan 8y ago
  > David Foster Wallace wrote Everything and More This is far and away my favorite math book. The way DFW can seamlessly transition from discussing a serious mathematical concept, to the nature of insanity, to the philosophy of abstraction all within a few pages is astounding. He somehow manages to do it while maintaining a conversational, two-folks-at-a-bar tone, teaching me dozens of new word, and being insightful/funny. Like an English professor sneaked into the math dept. I didn't know it was available on Kindle. Guess I'm buying it again...

okl 8y ago

Would also recommend 'Surreal Numbers' by Don Knut hand 'The Book of Numbers' by Conway and Guy.

masonic 8y ago

The author may have just chosen what's in stock at Amazon, given that all the links are Amazon affiliate links (tag=alikayaspor0b-20).