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Comment by jonnybgood | Hacker News Reader

There are some decent intro books for adults out there if you don’t care about the branch. Honestly, if you’re looking for intro math books you really shouldn’t care too much about the branch. I think what’s more important is to develop mathematical thinking.

Here’s some off the top of my head. I really think these will help you build a good foundation for mathematical thinking.

Concrete Mathematics by Graham, Knuth, Patashnik

Spivak’s Calculus

How to Prove It by Velleman

Polya’s How to Solve It

E.T. Jaynes’ Probability Theory

Conceptual Mathematics by Lawvere and Schanuel

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Gil Strang's books are probably even better for an adult with little math background.

Intro to Linear Algebra: http://math.mit.edu/~gs/linearalgebra/

Strang does a GREAT job explaining the intuition behind linear algebra. The book is targeted at first-year undergrads and an adult with just high-school math could work through it.

Bonus: if you're interested in machine learning, you must learn linear algebra.

More advanced is this Strang masterpiece: Intro to Applied Mathematics. http://bookstore.siam.org/wc02/ It covers a lot of the applied math that we focused on pre-AI and pre-cloud computing. Diff eqs, diffusion equations, Fourier analysis, numerical methods, phase plane analysis, optimization, complex anlaysis.

I can't recommend Strang enough. I tend to learn better when I can visualize math concepts, and had such a hard time understanding Linear Algebra until I finally bought a copy of that book. I love that thing, and it still sits in my bookshelf years later.

There are also complete lecture series on linear algebra with Gilbert Strang on Youtube, highly recommended.

Concrete Mathematics
Spivak

Jaynes

All good books, all pitched at a level that is very ill suited for what is being asked for.

To the GP, "math for English majors" is a common enough course schema that I think looking at a few syllabi might score you something.

I specifically mentioned those because they have little to no prerequisites other than high school math which I interpret can be read by any non-math major. They’re very self-contained but have very little hand-holding. I think just absorbing a little of these books will establish a decent foundation.

Concrete Mathematics is pitched at graduate students in computing. Spivak’s Calculus is an introductory real analysis book pitched at undergraduates who have gone through a computational calculus course already and want to study the subject more formally and rigorously; it has many difficult problems and would generally benefit greatly from the structure and expert feedback of a university course. Jaynes’s book is probably most relevant to science students who are at least at the advanced undergraduate level. How to Solve It is a dictionary of heuristic problem-solving techniques which is most useful to someone who is already (deeply) familiar with mathematical problem solving, and wants to codify their existing methods. Even advanced undergraduate math students who read it aren’t going to fully understand the book IMO; I would recommend Pólya’s other books (Mathematics and Plausible Reasoning, Mathematical Discovery), or maybe start with a gentler book like Mason, Burton, & Stacey, Mathematical Thinking.

Concrete Mathematics is solidly an undergraduate text. Much of the material in it would already be taught well before graduate school. The preface actually states the book takes comes course material taught to graduates and junior/senior undergraduates and presents it for a “wider audience (including sophomores).”

Otherwise I basically agree with your comment. I just take issue with calling Concrete Mathematics a graduate textbook, because I hear people say that as though it’s not an appropriate recommendation for learning. That gives me the impression they’ve not actually opened up a graduate textbook in math or computer science. Concrete Mathematics might not be year one material, but you can do it after a calculus course and maybe an algorithms course. Contrast this with an actual graduate course, like convex analysis and optimization. Textbooks at that level would definitely not be accessible for most undergrads.

Fair enough. It’s still not an easy book for someone to self-study after having no university-level mathematics, just as a side hobby.

I would certainly recommend giving it a shot for anyone interested, as it’s a lovely book full of fun problems. As you say, it’s accessible to well prepared undergraduates.

> Spivak’s Calculus

Took me 3 yrs of evenings and weeekendw to get through this :\.

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