Discrete mathematics

What Hacker News says

1. impendiaOct 2020
   I am a math professor. In my observation, there is a huge amount of material available on the web, but it isn't very centralized -- especially at the upper levels.

   My advice would be to get a book on any topic which interests you, read through it, and do a significant number of the exercises. You might try Epp's Discrete Mathematics, Hefferon's Linear Algebra, Colley's Vector Calculus, Dudley's Elementary Number Theory, Spivak or Apostol's Calculus (these go far beyond ordinary freshman calculus), Pinter's A Book of Abstract Algebra, among many others. Some of these books are expensive to buy new, but just buy older editions.

   Resources like Khan Academy and 3blue1brown are also fantastic, and I have shared some of these with my students. I'd recommend using these as a supplement; if you rely on them solely then you'll develop vague intuition but not much else.

   Also, with the pandemic, there are a huge number of traditional university courses that have moved online, and you could probably enroll in one for not too much money. Check the RateMyProfessor reviews -- you want a mix of positive reviews claiming the prof inspired them, and negative reviews complaining that work was expected. I have a RateMyProfessor review which complains bitterly that "homework is graded for accuracy and not completion". :)

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2. imakecommentsFeb 2017
   Read "Discrete Mathematics" by Epp. Probably the easiest Discrete Math intro I came across.
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3. oskarkvApr 2012
   I think this book is very good. Lots of exercises and very clear. http://www.amazon.com/Discrete-Mathematics-Norman-L-Biggs/dp...
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4. sqrt17Nov 2010
   "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 look at some discrete mathematics books (the one I had was "Discrete Mathematics" by Norman Biggs) as they teach you to think in terms of proofs.

   If you want to get a thorough foundation for non-discrete maths, you should start with a good (university math) analysis textbook (No idea what's a good one in English).

   Another approach you could take is to take a math book that is targeted at physicists and EE people - those usually skimp on the proofs and don't contain enough detail to understand the fundamentals behind it all, but bring you to the interesting (to physicists and EE people) stuff much quicker than a real math course would.

   Oh, and if you hang out on Youtube, be sure to watch the catsters - this is category theory, presented by actual working mathematicians, at an accessible level (and with a cute UK accent too).

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