I am looking to buy a good Calculus and a good Linear Algebra book, so as to teach myself.
The problems I have had, looking before, is a presentation that pretty much shows each new method as a black box. For instance, they will take matrixes and say, "Well so you got these numbers, you plop them in, multiply and voila you’ve got a new set of numbers! Without knowing at least what the numbers I put into the matrix were meant to represent, or what the end result number means, I just can’t visualise anything and I’m fairly sucky at rote memorization.
So what I am hoping for are some books that are very long, don’t go into advanced topics (or if so do so by adding another 1000 pages in later chapters), are fine to show lots of n-degree graphs of everything that for every step in progression of a single calculation, are fine to show the development of the black boxes like matrix multiplication to show why they work and such, and otherwise very clearly advance in complexity in a linear fashion regardless of how many more pages it might take to do it.
For instance, in Linear Algebra, I was trying to do 3D math for game programming and once I found out that the numbers I was putting in to the matrix were the positions of points (0,0,1), (0,1,0), and (1,0,0) would be after the transformation I independentally figured out why 3D math requires work in a fourth dimension, since you need that to move an object, rather than just rotate and distort. So I’m fairly confident that I could learn the math and be good at it, I just need something that shows me what the numebrs represent and what exact effect I am supposed to be attaining by working the various forumlas on them.
My son taught himself calculus using Calculus the easy way. (Amazon link) It explains everything in a very hands on way using an ongoing story about some residents of a fantastical town who try to solve everybody’s problems using math, but keep on having to invent new methods to deal with increasingly thorny problems.
Calculus: Early Transcendentals by Stewart is what I have. It goes from the very beginning to some quite advanced stuff. There’s loads of worked examples taken from science i.e. physics, chemistry, computer science and biology.
The recommended book for our machine learning course for Linear Algebra is Linear Algebra with applications. Of course, if you wanted to learn what the numbers meant in a computer graphics context, I’d pick up Foley and Van Damme, which is the recommended book for our computer graphics course.
The classic introductory book is still Calculus Made Simple by Silvanus P. Thompson back in the Pleistocene, and still in print. I used it, and my friends used it, and I highly recommend it:
Then there’s George B. Thomas’ college text Calculus, which was, and maybe still is, one of the top ten college text best-sellers. I used it in high school, then used it in college, where Thomas as my professor. Very clear and straightforward presentation with excellent drawings.
This is the textbook that I used for two and a half years of calculus in high school, and I found it to be quite good. I’ve also found it to be good for reference since then.
Alas, there seems to be no Algebraic Topology for Dummies, Partial Differential Equations for Dummies, Galois Theory for Dummies, or anything really fun like that.
One of the best general math books I’ve ever used was Allyn J Washington’s Basic Technical Mathematics with Calculus–it’s the one we used in electronics school back in '84 and it’s still in print now, many editions later. It takes the reader from ‘how to count’ to basic integral and differential calculus (of one variable). It covers trig, algebra, matrices, and all sorts of things. It’s not cheap–$140 canadian, but worth it.
I’ll second (third?) the suggestion for Schaum’s Outlines - pick up the Mathematical Handbook, too, since it has a lot of the stuff you might look up frequently. I’ve not used the Linear Algebra or Matrices volumes, and mine date from the 60’s so they might have changed anyway.
For linear algebra, I have Strang, which is nice and modern, and an old copy of “Linear Algebra with Applications” by Agnew & Knapp, which I happen to like for its simplicity (although some sections are quite dated).
BTW, looking on Amazon, there seems to be a bunch of books all titled “Linear Algebra with Applications” - I noted ones by Bretscher, Leon, Nicholson, and Williams, and that was only the first page of the search. Good luck.
For a unified approach I’d recommend Corwin & Szczarba if you can find it, I think it’s out of print. As a fallback, Hubbard & Hubbard is good, but I have my misgivings about using it as a class text. Maybe for personal use it’s better.
By the way, I saw in yesterday’s paper an obituary for George B. Thomas, whose calculus boomk I recommended above. Sorry to see him go (and right below was the obit for SF great Jack Williamson. They were both in their nineties, but it’s weiird they both died at the same time. )
One time in class he told us to look up “Whales” in the index of his Calculus book.
Whales? Damned if it wasn’t there. What do whales have to do with calculus?
You flip to the page, and there’s a graph of two loopy curves, with the space between them colored in, illustrating the calculation of areas between two curves or something. It kinda sorta looked like a whale, if you squinted at it. I think Thomas and his editor were getting a little punchy by then, and threw it in for a gag.
I’m firmly convinced that Schaum’s Outlines (at least in the technical fields) offer clearer, more pithy explanations and have vastly fewer errors than the vast majority of hardbound textbooks out there. Although you’ll pry my Shigley and Mischke Mechanical Engineering Design from my cold dead hands (unless you were going to replace it with Standard Handbook of Machine Design, which I just purchased 'cause MED is falling apart) for the most part $100+ textbooks are a major scam. Don’t even get me started on my undergraduate controls text, or the signals text I purchased for a graduate class which was so rife with errors that the publisher sent along a 50 page addenda booklet to try to cover some of the most egregious errors in the text.
Calculus Made Easy is a great text for introductory calculus. For matrix/linear algebra, I’d opt either for the Schaum’s Outline of Linear Algebra or the classic (Russian) Shilov Linear Algebra, reprinted as part of Dover’s Science & Mathematics series. These are, for the money, some of the best texts around; while they’re generally classic texts from backintheday and don’t have four color diagrams or referencing the most modern hardware and computer tools (no MATLAB scripts or Objective-C algorithms, I’m afraid) they’re usually clear and concise. I got far more out of Den Hartog’s Mechanical Vibrations, despite the fact that it was first published by hand on papyrus (well almost) than the supermodern (as of 1994) Vibrations with Computer Applications (including a disk of then-cutting edge C++ programs which no one could get to work properly on PCs). Shiny and new is not always better.
