I recent bought a hardcover book titled "Dr. Euler's Famous formula - cures many mathematical ills". Sorry Borders, I found this book at your store but bought it at Amazon to save some money.
As you can see from the title it demonstrates the witty side of (some) mathematicians. Math is not all boring abstract discussions and calculations. In fact, it takes a lot of writing/communication skills to communicate math. Your heavy accent professor that you've had just isn't sophisicated enough to do that. The author is very articulate and this is a very well written book: packed with enthusiasm and applications of the Euler's formula eix=cos x + i sin x. It is jammed packed with clever derivations of many gems from all over mathematics and engineering.
Most of us were told π is irrational but were told not to worry about the proof. Maybe you have heard the "prince of mathematics" Gauss showed a 17-gon can be constructed when he was 18. This book tells you the glorious details which involves the Euler's formula. And you will know why you weren't told the details because it is gosh, quite involved. You will have some idea what sort of genius was Gauss and Euler after reading a couple chapters.
The prerequisite of this book is a couple years of calculus and differential equations. Ok I had that, and so do most college students. We are talking the very motivated 'A' or 'B+' math students here and not those who barely passed. I am not sure if I will ever understand all of this book. But it will be proudly displayed in my bookshelf after I understand all that I can.
I think this book can gain broader audience if author can start with an introduction of each of the important constants involved in the Euler's formula: e, i, π, derive this formula from the Taylor series. Ok, he actually did that by showing a page in Feyman's teenage notebook in the introduction.
2 comments:
I was never fortunate enough to have a motivated math prof. I took lots of math in college to get a so-called engineering degree. (Calculus I, II, III, DiffEq and Linear Albegra) I didn't do well in any of the classes, I barely passed. I had so much pain with math that I suppressed all the bad memories.
10 years after college, I don't think I can do any simple Calculus problem.
The first problem with math is the homework problems are damn hard and pointless. The chapters only have like 4 examples, the homework problems are not like the examples at all.
The second problem with higher math is there is no real reason to learn any of it, if you are not a physics or math major. I don't care! I don't care! I don't care the area under the curve. I don't even care how the curve look the way it is. Pi? doesn't that belong to a circle , what are they doing all over the place in harder math?
I made myself care enough to pass the exams. I did pass, count them 5 super hard calculus classes, no one can dare say I'm dumb.
Most people will need to understand how money compound over time; and how valuables depreciate over time. Every student need to learn personal finance. Let the genius student study the Euler Method (I think I studied that in Calculus 2 circa 1994)
One reason for π to enter aspects in math is trig ratios, and that radians is compatible with real numbers. Trig functions (sin, cos, tan) are considered well understood elementary functions.
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