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Ask HN: Math books like SICP?

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Re: Ask HN: Math books like SICP?

#51

Post by tel »

decasteve wrote: post #34

If you've already covered Vector Spaces, Groups, and Rings in your studies, I would suggest checking out Bill Lawvere's "Conceptual Mathematics: A First Introduction to Categories". i.e. An introduction to category theory through the category of sets. His "Sets for Mathematics" is also good but it's a more concise presentation of the topic but a less than gentle introduction than the former book.

I was going to recommend this one. Conceptual Mathematics is wonderful in that it provides a narrative of intuition instead of just the proofs. It's kind of like seeing How It Is Made for algebra.

Re: Ask HN: Math books like SICP?

#52

Post by kenferry »

nextos wrote: post #17
zodiac wrote: post #9

Math is a much, much broader field than the part of Computer Science than SICP covers, so it's really hard to search for "consistent and broad knowledge throughout all areas". Do you really need to learn analytic number theory? category theory? axiomatic set theory? tensor calculus? My suggestion would be to narrow it down to a specific field you're interested in like abstract algebra and ask for suggestions about th…

I was planning to structure my learning around linear algebra and real analysis, sort of like Harvard's Math 55 does. Apart from that I wanted to expand on basic set theory, geometry, combinatorics and probability theory to have a well-rounded basic education. My ultimate goal is to be able to digest advanced probability and statistics books.

I don't know an answer to your original question.

Re: statistics and such though, I have heard very good things about http://www.indiana.edu/~kruschke/DoingBayesianDataAnalysis/

If you are interested in a Math 55 approach (yikes! I took 25), you could consider using their syllabus. http://abel.math.harvard.edu/~elkies/M55a.02/index.html

Re: Ask HN: Math books like SICP?

#53

Post by Jugurtha »

jimmaswell wrote: post #50
Jugurtha wrote: post #35

Well, I don't know how it goes over there, but here in Algeria, Engineers go through two common years (after which they chose a specialty in the third year, and then, in the fourth and fifth year, a specialty of specialty). All Engineers go through both years, except Computer Science who don't do the common second year and they directly go to Computer Science. In these two years, everyone goes through this (maybe it'…

you have to retake Algebra even if you did it in high school?

Well, it's more advanced and in depth than Algebra you take in High-School.

Re: Ask HN: Math books like SICP?

#54

Post by Derander »

jimmaswell wrote: post #50
Jugurtha wrote: post #35

Well, I don't know how it goes over there, but here in Algeria, Engineers go through two common years (after which they chose a specialty in the third year, and then, in the fourth and fifth year, a specialty of specialty). All Engineers go through both years, except Computer Science who don't do the common second year and they directly go to Computer Science. In these two years, everyone goes through this (maybe it'…

you have to retake Algebra even if you did it in high school?

I'd be surprised if the average high school algebra course covered group theory :-).

Re: Ask HN: Math books like SICP?

#56

Post by elviejo »

zodiac wrote: post #9

Math is a much, much broader field than the part of Computer Science than SICP covers, so it's really hard to search for "consistent and broad knowledge throughout all areas". Do you really need to learn analytic number theory? category theory? axiomatic set theory? tensor calculus? My suggestion would be to narrow it down to a specific field you're interested in like abstract algebra and ask for suggestions about th…

Precisely my interes what is the SICP equivalent for: Discrte Math ? And for Linear Algebra?

Re: Ask HN: Math books like SICP?

#57

Post by biot »

This might be along the lines of what you're looking for: http://www.amazon.com/Mathematics-Birth-Numbers-Jan-Gullberg...

  "This extraordinary work takes the reader on a long and
   fascinating journey--from the dual invention of numbers
   and language, through the major realms of arithmetic,
   algebra, geometry, trigonometry, and calculus, to the
   final destination of differential equations, with
   excursions into mathematical logic, set theory, topology,
   fractals, probability, and assorted other mathematical
   byways. The book is unique among popular books on
   mathematics in combining an engaging, easy-to-read
   history of the subject with a comprehensive mathematical
   survey text."

Re: Ask HN: Math books like SICP?

#60

Post by Grothendieck »

SICP doesn't really cover very much in the grand scheme of CS, so "like SICP" might mean ...

... something covering "how to do math". This might be an introductory real analysis or linear algebra book, or (alas, I haven't read much in this area) you could do no wrong looking for books on problem solving, contests, and inequalities, say by Polya or Andreescu.

... a higher-level view of day-to-day mathematical practice. There probably isn't one book for this, but I'd recommend Loomis and Sternberg's Advanced Calculus as a summation of linear algebra and calculus on manifolds; you'd also need to read on complex and functional analysis, algebra (Lang and the unofficial companion volume?), topology ...

... a broad but shallow introduction to several fields and applications unified but a common underlying approach (abstraction and programming language design). I'd recommend Geroch's Mathematical physics, which, as the name implies, studies algebra, algebraic topology, and functional analysis through the common lens of category theory.

... a somewhat quirky book on foundations? You could look for a book on naive or axiomatic set theory, categories, or type theory.

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