In Your Head

By Jim Shapiro

There are plenty of books out there that lead the reader through numerical gymnastics. If you want to know how to multiply 45 times 25 in your head, this isn't the book for you. (Hint: 25 is 100 divided by 4.; Hint 2: 45x25 = (40 + 5)(20 + 5)) Our goal is a different, and I believe, a much deeper one. This book is mostly about deriving things without paper and pencil, which is how the title arose. We'll tackle some fairly easy derivations, like why the test for even divisibility of an integer by 3 works, but we will also look at some more esoteric divisibility problems, like divisibility by 7, which you may have never seen before. Note that I am not talking about memorizing the various divisibility rules. Our goal is deriving the rules, all in our heads.A glance at the table of contents will give you an idea of the breadth of our coverage. This book covers in-your-head derivations from the fields of algebra, geometry, trigonometry, and differential and integral calculus, with even some formulas from finance thrown in for good measure. You, the reader, needn't follow the text in order, as very few of the derivations are dependent on one another, at least between chapters. On the other hand, the mental problems I present generally get more difficult as you progress through the pages and you will get more comfortable and capable as you get more derivations under your belt. Deriving the equation for the AC power factor in your head may at first sound if not impossible at least very, very hard to perform mentally, and it likely is. Stick with me and you will be able to rattle the power factor derivation off faster than you can find a pencil and paper. And it is a wonderful and confident feeling to be able to handle once complex derivations completely mentally. You might even say that it's empowering.

• Format: Paperback
• Language: English
• ISBN: 1479357235
• ISBN13: 9781479357239
• Release Date: September 2012
• Publisher: CreateSpace Independent Publishing Platform
• Length: 60 Pages
• Weight: 0.37 lbs.
• Dimensions: 10.0" x 0.1" x 7.0"