I love Calculus Made Easy by Silvanus Thompson (updated by Martin Gardner).
This is an absolute must. You can get it free (the original version) here : http://www.gutenberg.org/ebooks/33283
Ask HN: Good Reading/Immersion in Mathematics
21–30 of 32 posts
Re: Ask HN: Good Reading/Immersion in Mathematics
#22Check out The Unapologetic Mathematician "blath":
Re: Ask HN: Good Reading/Immersion in Mathematics
#23You may find this useful: http://math-blog.com/mathematics-books/ (DISCLAIMER: It's my site.)
I like this list; thank you for taking the time to compile and annotate it.
Re: Ask HN: Good Reading/Immersion in Mathematics
#24"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.
i'm not able to dig it up right away - but just a couple of days back there was a blog post by someone who gave a long, very comprehensive listing of topics that take you all the way from basic to postgraduate level math.
It was organized in a dependency graph kind of way.
Re: Ask HN: Good Reading/Immersion in Mathematics
#25Pick 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.
I can't believe no one has mentioned Concrete Mathematics by Knuth & friends yet.
It's incredibly well-written. Very challenging, yet totally approachable and accessible to someone with even just a rather basic (even foggy) understanding of "high-school" math.
Re: Ask HN: Good Reading/Immersion in Mathematics
#26I'd definitely recommend Godel, Escher, Bach by Doug Hofstadter. Not just about mathematics, but fascinating. Also, anything by Martin Gardner.
GEB is excellent as a pop-science/pop-philosophy book, but (like most pop-sci books) it's terrible for actually learning any subject. You need more than one proof every 200 pages.
Yup. It gave me a nice intro to formal systems / number theory iirc. Intro only though, and it was only a small part of the book.
Re: Ask HN: Good Reading/Immersion in Mathematics
#27Pick 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.
I can't believe no one has mentioned Concrete Mathematics by Knuth & friends yet. It's incredibly well-written. Very challenging, yet totally approachable and accessible to someone with even just a rather basic (even foggy) understanding of "high-school" math.
What is the prerequisite for reading this book. Can I read this book effectively with basic knowledge of high school algebra and some calculus?
Re: Ask HN: Good Reading/Immersion in Mathematics
#28Earlier quoted context omitted.
I can't believe no one has mentioned Concrete Mathematics by Knuth & friends yet. It's incredibly well-written. Very challenging, yet totally approachable and accessible to someone with even just a rather basic (even foggy) understanding of "high-school" math.
What is the prerequisite for reading this book. Can I read this book effectively with basic knowledge of high school algebra and some calculus?
Yes. I did. It will be very challenging.
I, quite a few times, spent more than four hours with a pencil and paper making my way through 2-4 pages of material, as since my background was lacking, there were parts where I had to figure out how they got from A to B. IIRC, I spent multiple days on a few paragraphs at one point.
That said, it is written how I think math books should be written, is considered part of the start of Discrete Mathematics, and is conversational, illuminating, well-layed-out, and approachable despite it's level of difficulty.
I can't recommend it enough.
Don't view it as something where if you're not making progress you're failing. Take the time to ensure you understand every bit of what you read before moving on, and do all the exercises you can muster.
Re: Ask HN: Good Reading/Immersion in Mathematics
#29It may be helpful if you state your mathematical background, though I'm guessing that, if you had taken any proof-based math course, you wouldn't be asking this. I recommend The Art of Problem Solving I and II. On the one hand, they're intended for (mathletic) middle and high-schoolers. On the other hand, some of their problems are quite challenging, and much of the material therein is what my school teaches in its i…
I'm currently a junior in high school. I am doing some summer work in math and considering doing it as a degree in college, but so far I have only taken basic Algebra, Geometry, Trigonometry, and currently in Statistics (as well as in a math-focused Computer Science track). I'm looking at Calculus I next year.
Re: Ask HN: Good Reading/Immersion in Mathematics
#30If youre looking to learn mathematics as a tool rather than an end goal the list above seems far too abstract. A good foundation in analysis is probably as abstract as you'll need for a majority of applied fields. For computational science and learning you need to know (albeit very well):
linear algebra (strang, trefethen, golub and van loan) optimization (nocedal, bertsekas) probability (rice, casella & berger, grimmett) statistical learning (tibshirani, bishop)
A good free online book was recently an HN topic: http://news.ycombinator.com/item?id=1738670