Federal Way Public Schools Graduates of Note

Scott Novotney - Email to Teacher

From:              SCOTT NOVOTNEY
Subject:           You Win
To:                   Tom-Norris –TJ

Well Norris, I hate to admit it but you were absolutely right.

I'm graduating from Johns Hopkins this May with a B.A. in Mathematics. I'm admitted into the Computer Science masters program at JHU and then the year after that I'm aiming for Stanford, Carnegie Mellon, or Cornell for a PhD in Computer Science. I'll have a year of abstract algebra, a year of analysis, number theory, topology, complex analysis, linear algebra, and many other random math courses.

Every single one of these courses relied on something I learned in high school --math.

Let me repeat that: Every single course needed something from the Pythagorean Theorem to the Fundamental Theorem of Calculus.

Let me give you an example. I finished complex analysis this Fall, which is the study of complex functions f(z) with z = a+bi.  Here are some things that I needed to know for this ONE course that I learned under your dictatorship.

Geometric series: a function can be expanded into a form k/(1-c)
Trig functions: cos and sin are closely related to many functions and the exponential
Trig rules: every one of them cos(2z), sohcahtoa, cos^2 + sin^2 = 1
Unit circle: cos(z) = pi/2, what is z?
Polar coordinates: converting between them and also using spherical coordinates
Exponential: e^(a+bi) = e^a(cos(b) + isin(b))
Pi: e^i*pi = -1
Taylor series: used to evaluate functions
Derivatives, integrals, Fundamental Theorem of Algebra, (without knowing one dimensional calculus, I'd never learn multivariable)
Limits: When is a function continues and differentiable at a point?
Definitions of continuity, differentiable, and the definition of a limit f'(x) = lim f(x-h) 

Plus everything else I learned in multivariable calculus.

When I was in high school, I didn't see the point of all the skill drills and stupid rules that I'd never use and had to do just because you put it on the test.  I knew there were theoretical reasons for it, but I was never taught them.

I now understand that high school math is just like learning how to write. No one likes it, but you gotta practice writing your capital G's, P's and Q's until they're perfect. Only once you know how to write can you produce something beautiful.

High school math seems boring and dry because it is.  The fascinating and amazing theorems started to appear only once I was 100 percent comfortable with the basic definitions that are found throughout mathematics. Some of the things I'm learning now, like p-forms, topological surfaces, and algebraic number theory all require an intense familiarity with the basics of calculus.

I only wish I could have learned more. It's tough work, without a doubt. It is boring, it is no fun, but man oh man is it necessary! I hope you can give this to each of your students to let them hear what it is like on the other side of graduation.

To Norris’ students:

I hated Skill Drills. I detested them. I'd always come in fourteenth or something in Norris's dumb race to see who could get the most done. It was the same boring problems over and over again and none of them applied to the real world. I hated his tests, how that one little mistake could ruin the whole problem.  I hated the boring material. Don't even get me started on Math Team.

And Norris used to read letters from college students to us saying how great mathematics was and how right Norris was. I thought what you're thinking right now, "Whatever, Norris is just trying to brainwash us. That guys a math major, it doesn't count."  Surprise surprise, one of your kin has discovered the other side. Think of it as a wall. I hopped on the other side and I'm now trying to tell you what it's like. You can't see on the other side, you have no idea how amazing and fabulous it is (wow, I'm a nerd) I'm scribbling these little notes to pass through a crack in the wall and you scan it and ignore it, he doesn't know what he's talking about.

Wait until you get over the wall. I'm not talking about the "real world" - life doesn't start at graduation. You're in the "real world". The things you do now, in tenth, eleventh, and twelfth grade (ninth, who cares, it doesn't count) will affect your success and position when you get to the "real world".  (Believe me, though, college is still playtime. I don't have to get up till 10, I do lots of entertaining things that you'll learn about when you're older and generally have a fun time when I'm not stressing over problem sets.)

Luckily I had to take calc I, I wish I would have stuck all the way with Calc II, it makes college so so so much easier. Because you know what? Every science uses at LEAST Calc I material. Economics, biology, chemistry, sociology (where do you think the bell curve comes from?).  Computer Science, Electrical Engineering (wait till you learn about Poisson Equations)

Math right now IS boring, but you need to stick with it. It is the same as practicing ball handling each day. Doing scales for hours on end. Doing one hundred pushups before you go to bed. It is the training for the real stuff. You stick with it and it will be amazingl Wonderful. It sucks, I agree. It's boring, it's hard, it's pointless and you have to do soooo much. But in college, you have to do soooooooooooooo much more.

A quick word to those students who memorize, memorize, memorize. Good job, but you aren't going to get far after High School. You need to UNDERSTAND the definition of an integral (the integral of f(z) from a to b = F'(b) - F'(a) where F' = f).  What is f? What is a and b? What does it mean for F' = f. You need to KNOW what is going on behind the scenes.

Memorization is a useless ability. It will get you your A's on tests, but you don't stand a chance to apply these things when you need it. If you get your A's now, you'll get into Harvard, MIT, Highline, whatever dream school you want. But the moment you step into Calc 102 and sit down for the first lecture, YOU ARE SCREWED!!!!! All the memorization will be useless, you can spout off all the theorems in the world, but who cares, the book has them written down. Then when you're asked to prove anything, or heaven forbid APPLY anything you know, you don't stand a chance. Take the B+ now, actually UNDERSTAND a few things and you will be much better prepared.

I know I sound like a weird math convert. I was once the cynical anti-mathematician that you all want to be.

I'll finish with this. Math is not a bunch of facts. These aren't laws or truths of nature. Everything you learn, from addition to anti derivatives, was thought up by some guy. He didn't "discover" them, he invented them as tools to accomplish tasks. And for every successful theorem or identity that was discovered, hundreds were discarded and forgotten. None of these theorems are "true" in the sense that the sky is blue. A proof is a convincing argument. No other mathematician could find something wrong with the proof, so it is accepted and used.  But then some other day in the future a smarter dude discovers a flaw and the theorem is discarded.  Math evolves and changes. The most random and pointless theorem can reach into the deepest reaches of math.

e^z = e^x(cos(y) + isin(y)). That doesn't make much sense right? Well it is one of the most useful and amazing theorems invented by Euler. Because of that proof, biologists can predict how fast a disease will spread.

Taylor Series/ Maclauren Series? These were invented in the 1500's. THE FIFTEEN HUNDREDS! This was before electricity, the polio vaccine, even indoor plumbing. Think the plague, Kings, and conquistadors. The Scottish Monk Maclauren sat around and invented one of the most useful methods for calculating the value of a function. How do you think your calculator spits out sin(2) = 0.90929742?

Math is a tool to get things done. All the great mathematicians, Gauss, Leibnitz, Lagrange, Euler, Euclid, Newton, guys you don't give a crap about, they invented new theorems to accomplish tasks. The anti derivative was invented to predict the distance a cannon ball would travel.  All of the things you learn have a point, it may take a while to get to it, but it DOES have a point.