Linear Algebra Done Right, Axler. Don't learn Linear Algebra without it.
Ask HN: Good Reading/Immersion in Mathematics
11–20 of 32 posts
Re: Ask HN: Good Reading/Immersion in Mathematics
#12You may find this useful: http://math-blog.com/mathematics-books/ (DISCLAIMER: It's my site.)
Re: Ask HN: Good Reading/Immersion in Mathematics
#13I'm working through Calculus by Michael Spivak. If you want a thorough knowledge of calculus(who doesn't?) then I wholeheartedly recommend it. While it's more deep than broad, it will surely help you learn to start thinking more like a mathematician.
Re: Ask HN: Good Reading/Immersion in Mathematics
#14Potentially related threads :
Math for hackers : http://news.ycombinator.com/item?id=672067
Good books on mathematics for somebody who's only taken high school math? : http://news.ycombinator.com/item?id=299687
Recommendation for (re)learning Math Skills : http://news.ycombinator.com/item?id=1449799
Re: Ask HN: Good Reading/Immersion in Mathematics
#15You might want to have a look at the "Princeton Companion to Mathematics". It's goals seem close to your "broad but not too deep" objective.
Re: Ask HN: Good Reading/Immersion in Mathematics
#16Pick up a discreet mathematics book. Learn logic, set theory, and writing mathematical proofs (induction, etc.) I really wish they'd put a class like that right after basic symbolic algebra in normal school curriculum - it's far more useful in the modern world than trigonometry.
Can't agree more about the value of Discrete Math. Any programming worth his salt can wax about combinatorics and counting problems at a moment's notice. I'm thoroughly convinced I'd be a few years further along as a programmer had I learned discrete math at an early age.
But anyway, the Teaching Company offers a phenomenal course on Discrete Math, taught by none other than the "Math Magician" Arthur Benjamin (seriously, this guy is magic. He can do 5 digit squares in his head!). It's easily torrent-able / available through more traditional means.
Re: Ask HN: Good Reading/Immersion in Mathematics
#17Related to this, I've found most text books aren't the best way to learn the material since they don't actually provide answers to solutions. You get the theory but little followup practice to apply your understanding of that theory.
Are there any good texts that are more problem workbook style? One example that comes to mind is "Exercises in Probability", or some of the 3000 Problems books as published by Schaum.
Re: Ask HN: Good Reading/Immersion in Mathematics
#18"want to be acquainted with all of the different fields" may actually be quite hard - you can't do complex analysis, differential equations in multiple dimensions etc. without having a very firm grip on standard analysis (including all the proofs and definitions that they normally skip in high school). If you want to build up your math muscles (as a good preparation for actually studying maths), you should have a loo…
Is there dependency graph of mathematical fields somewhere? That would be useful.
Re: Ask HN: Good Reading/Immersion in Mathematics
#19Here's my list:
Basic
1. Chapter Zero (Carol Schumacher) 2. Naive Set Theory (Paul Halmos)
Linear Algebra
1. Finite-Dimensional Vector Space (Paul Halmos) 2. Linear Algebra Done Right (Steven Axler)
Real Analysis
1. Real Mathematical Analysis (Charles Pugh) 2. Introduction to Analysis (Maxwell Rosenlicht)
Algebra
1. A first course in abstract algebra (John Fraleigh)
These books are better for self-directed reading compared to some of the classics like Rudin or Herstein. These should keep you busy for a while.