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Anyone have good reading material about 'how to reason mathematically' on a basic level? I mean, not going too deep into any specific topic, but how to get better at interpreting equations and grokking relationships.
http://www.amazon.com/Mathematics-Nonmathematician-Dover-Boo...
I have not read it, but I have heard it recommended many times by knowledgeable educators.
Anyone have good reading material about 'how to reason mathematically' on a basic level? I mean, not going too deep into any specific topic, but how to get better at interpreting equations and grokking relationships.
I think Gödel, Escher Bach does a good job imparting the "mathematical mindset", albeit indirectly. It's a great read even if it's quite long and a bit repetitive. Definitely worth a read if you're not already familiar with abstract mathematics and formal logic.
Anyone have good reading material about 'how to reason mathematically' on a basic level? I mean, not going too deep into any specific topic, but how to get better at interpreting equations and grokking relationships.
Anyone have good reading material about 'how to reason mathematically' on a basic level? I mean, not going too deep into any specific topic, but how to get better at interpreting equations and grokking relationships.
Love and Math: The Heart of Hidden Reality
by Edward Frenkel
It's definitely my favorite book of 2013.
http://www.amazon.com/Love-Math-Heart-Hidden-Reality/dp/0465...
2. 'How to Solve It' by G. Polya (http://www.amazon.com/How-Solve-It-Mathematical-Princeton/dp...)
I am interested in pure mathematics mainly including logic, set theory, category theory, etc.
[1] An excellent example not mentioned by others here is also The Road to Reality by Roger Penrose. The sections on mathematics are very good, but ultimately leave the topic open-ended too soon.
Anyone have good reading material about 'how to reason mathematically' on a basic level? I mean, not going too deep into any specific topic, but how to get better at interpreting equations and grokking relationships.
Does someone have a recommendation for a book that get deeper into mathematics by teaching actual mathematics rather than teaching about it? Many of the books I have come across leave me with more questions than answers [1]. I am interested in pure mathematics mainly including logic, set theory, category theory, etc. [1] An excellent example not mentioned by others here is also The Road to Reality by Roger Penrose. T…
If you're comfortable with calculus as a subject, for example, and want a "pure mathematics" approach, I recommend Michael Spivak's Calculus. If you've never worked through a pure math textbook from start to finish, that's a good start.
There's not that much interesting in the three subjects you listed — logic, set theory, and category theory — that doesn't depend on other subjects or a prior level of mathematical maturity. Category theory was originally invented to solve and categorize problems in algebraic topology, for example.
For example, I rather like mathematical logic and model theory, but you're going to have a rough time if you don't have a visceral, intuitive understanding of countability arguments and at least a handful of subjects you'd be reasoning "about." Unless you know the standard model of arithmetic, for example, how can you think about non-standard models? Without that, important results like the Löwenheim–Skolem theorem will likely seem contextless.
Does someone have a recommendation for a book that get deeper into mathematics by teaching actual mathematics rather than teaching about it? Many of the books I have come across leave me with more questions than answers [1]. I am interested in pure mathematics mainly including logic, set theory, category theory, etc. [1] An excellent example not mentioned by others here is also The Road to Reality by Roger Penrose. T…
What are you looking for that isn't simply a math textbook? Honestly, that's how mathematicians learn "actual" mathematical subjects, too. If you're comfortable with calculus as a subject, for example, and want a "pure mathematics" approach, I recommend Michael Spivak's Calculus . If you've never worked through a pure math textbook from start to finish, that's a good start. There's not that much interesting in the th…
You are right in bringing countability arguments into the picture; I understand them only to some level. I would love to read a book that gives it a formal treatment. The following has been great for example:
https://news.ycombinator.com/item?id=6838917
Another one showed up on HN recently that I am still to read in full:
https://news.ycombinator.com/item?id=6966695
Thanks
Finally, cannot help but mention in praise, Colin Wright here on HN has been a good help before in clearing some of my doubts on the subject.