Book recommendation for help with Higher Math

September 20, 2006 12:23 PM

Could someone suggest book(s) that deal with tips/tricks/methods of performing mathematical calulations faster. I mean higher mathematics and not just elementary operations like addition/multiplication/finding the root etc. What I am looking for are hints and shortcuts that would help me with stuff like calculus, linear albegra, vectors and such. Thanks!
posted by sk381 to science & nature (7 comments total)

When you reach a certain level of study, the number crunching tends to get offloaded to programs like Matlab. This is not useful if you are doing these problems to learn mathematics, in which case you have to do them by hand - I'm not sure from your question if this is the case.

If you're looking for learning aids I unfortunately don't know of any. Have you tried googling for "calculus shortcuts"?
posted by PercussivePaul at 12:54 PM on September 20, 2006

You could try Numerical Recipes in C, it's been a while since I dealt with any of this stuff, but I remember that name being bandied around a lot. It seems to have what you want (Linalg, numerical integration etc).

For symbolic manipulation, like Maple or Mathematica, I can't think of anything offhand, other than those two packages.
posted by claudius at 12:59 PM on September 20, 2006

Your question is not completely clear.

To speed up electronic computation, you want to optimize your algorithms and optimize how they're implemented. Check out the books by Donald Knuth.

To quickly obtain a result manually for real world applications, use a first or second order approximation. E.g. sin(i) ~= i for small i expressed in radians.

To quickly integrate, differentiate, cross-multiply, etc. manually and from first principles, unfortunately there are no shortcuts. You just have to practice, practice and practice.
posted by randomstriker at 1:20 PM on September 20, 2006

From what I gather, you're looking for something to help yourself do the math, not a computer. Is that right?

There are several books on more basic algebra, like Hilomath's Inner Algebra.

For more advanced material, the tricks will inevitably diverge. I would suggest getting a textbook that is more of a "Schaum's Outlines"-type book than a textbook. The former tend to be concerned more with getting you to understand the math through quick tricks than with being formal and deriving everything.
posted by lunchbox at 1:25 PM on September 20, 2006

Ooh Ooh (raises hand) I have the answer for this one!

What you are looking for is the wisdom of India, in the form of Vedic Mathematics. You may have heard of this for things like multiplication, division, etc. And for that stuff it is fantastic. It literally takes long division to a level of joy that is unspeakable.

But, its for much more than that. Allow me to sample the table of contents:

9. Factorisation of Cubics
15. Simultaneous Simple Equations
21. Simultaneous Quadratic Equations
24. Integration by Partial Fractions
26. Recurring Decimals
36. Cube Roots
39. Analytical Conics

So... there's more there than arithmetic, I assure you. And it takes it all to a new level of simplicity (once you figure it out).

That last thing I said is the one failing of the book I have. You really have to munge on this stuff to figure out what they are doing half the time. There are some things in the book that you just can't grok from the description, you have to do a sort of decoding of the process to figure it out in an understandable way.

That being said, it's not a quick fix, but something that could eat up a lot of time over a long period, but in the end you will be very glad you did it if you plan on doing mathematics on a regular basis.
posted by zhivota at 3:10 PM on September 20, 2006 [1 favorite has favorites]

I have a bunch of books on doing math in your head. The most unusual one is Dead Reckoning: Calculating Without Instruments. The book covers techniques for calculating roots, logarithms, and trigonometric functions. The guy who wrote it also has a webpage.

(After years of lurking, I just joined to answer this question)
posted by Jasper Friendly Bear at 8:58 PM on September 20, 2006

Table method factorization
posted by Sharcho at 8:20 AM on November 16, 2006