# Math, Better Explained

## Kalid Azad

Language: English

Pages: 144

ISBN: 1479186724

Format: PDF / Kindle (mobi) / ePub

You could never forget what a circle is for, right? I want you to have that same realization about e, the natural log, imaginary numbers, and more.

What's inside the final ebook?

12+ Chapters covering exponents, logarithms, radians, the pythagorean theorem and other subjects essential to any student

A bonus chapter on Euler's Formula, tying the above concepts together

PowerPoint slides for all diagrams used in the chapters

Who's it for?

Students: Save hours of frustration -- get things as I wish they were explained to me!

Teachers: Get high-quality educational materials & ideas for your lesson plans.

Self-learners: Understand subjects at a conceptual level that is rarely discussed in textbooks

What's the benefit?

Get a professionally designed, easy-to-read PDF

Browse chapters on your iPhone, Kindle or other PDF-reading device (no DRM!)

Learn for yourself, or as a gift for your favorite student, teacher, or autodidact.

Save hours/years of frustration when learning math:

Never before have I heard such a clear and concise explanation of the fundamentals... I seriously could have saved hours of hair-pulling in university had I had access to this article years ago.

I have several books on calculus (Calculus for Dummys, Math for the Millions, etc. etc. - never was able to read them) but your explanation is what I have needed all these years.

This is a great explanation! I am 49 years old and have never known what e is all about. It is thanks to your article that I get it and now can explain it to my son who is 13 years old...

Mathematical Apocrypha Redux: More Stories and Anecdotes of Mathematicians and the Mathematical

Concentration of Measure for the Analysis of Randomized Algorithms

Axiomatic Fuzzy Set Theory and Its Applications (Studies in Fuzziness and Soft Computing)

The Number Mysteries: A Mathematical Odyssey through Everyday Life

mistake. As children, we learn the “caveman” definition of a circle (a really round thing), which gives us a comfortable intuition. We can see that every point on our “round thing” is the same distance from the center. x2 + y2 = r2 is the analytic way of expressing that fact (using the Pythagorean theorem for distance). We started in one corner, with our intuition, and worked our way around to the formal definition. Other ideas aren’t so lucky. Do we instinctively see the growth of e, or is it

Functions and e 95 of 144 Explained After 3 years, we’ll have 10 * e^(-1 * 3) = .498 kg. We use a negative exponent for decay — we want a fraction (1/ert) vs a growth multiplier (e(rt)). [Decay is commonly given in terms of “half life”, or non-continuous growth. We’ll talk about converting these rates in a future article.] More Examples If you want fancier examples, try the Black-Scholes option formula (notice e used for exponential decay in value) or radioactive decay. The goal is to see

grows. • Compounding lets you adjust your “speed” as you earn more interest. The APR is the initial speed; the APY is the actual change during the year. • Man-made growth uses (1+r)^n, or some variant. We like our loans to line up with years. • Nature uses e^{rt}. The universe doesn’t particularly care for our solar calendar. • Interest rates are tricky. When in doubt, ask for the APY and pay debt early. Treating interest in this funky way (trajectories and factories) will help us

finds new equations, and algebra solves them. Like evolution, calculus expands your understanding of how Nature works. An Example, Please Let’s walk the walk. Suppose we know the equation for circumference (2*pi*r) and want to find area. What to do? Realize that a filled-in disc is like a set of Russian dolls. Here are two ways to draw a disc: Math, Better 11 Introduction To Calculus 119 of 144 Explained • Make a circle and fill it in • Draw a bunch of rings with a thick marker

Theorem We agree the theorem works. In any right triangle: If a=3 and b=4, then c=5. Easy, right? Well, a key observation is that a and b are at right angles (notice the little red box). Movement in one direction has no impact on the other. It’s a bit like North/South vs. East/West. Moving North does not change your East/West direction, and vice-versa — the directions are independent (the geek term is orthogonal). The Pythagorean Theorem lets you use find the shortest path distance