Paul Orland - Math for Programmers: 3D graphics, machine learning, and simulations with Python MEAP V10

MEAP Edition

Manning Early Access Program

Math for Programmers

3D graphics, machine learning, and simulations with Python

Version 10

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Thank you for purchasing the MEAP of Math for Programmers. Ive been a math enthusiast my whole life, and only accidentally stumbled into software engineering as a career. I first taught myself how to code on a TI-84 graphing calculator, writing programs to do my high school math homework for me. Ever since then Ive been excited by how complementary the disciplines of math and programming can be. I look forward to sharing what Ive learned with you!

Now more than ever, knowing some math can accelerate your career as a developer. As evidence, look at the recent prevalence of the job title Data Scientist, and what people with this title get paid. I joke with my coworkers about what a Data Scientist really is, but the best answer is probably someone who knows statistics, linear algebra, and calculus, and how to turn them into code. Beyond data analysis, these fields of math are useful in graphics, game design, simulation, optimization, and many other software development domains.

In this book, well start by exploring vectors, which are the mathematical tool for representing multidimensional data. Computer graphics in 2D and 3D are built with vectors, and youll learn how to render your own 3D animations using matrix transformations. Part 1 culminates by showing you how these geometric lessons extend to higher dimensions within the framework of linear algebra.

Part 2 focuses on calculus, which is the study of continuous change. Youll learn that many of the laws of physics can be expressed in terms of calculus equations called differential equations. By solving these in Python, you can create realistic simulations of the physical world.

With a working knowledge of calculus and linear algebra, youll be ready to learn some of the math behind machine learning in Part 3. Machine learning algorithms are often used to draw conclusions about vector data, and the learning is often accomplished using an operation from calculus called the gradient.

With a title as broad as Math for Programmers, theres more content than Ill be able to cover. I look forward to hearing your feedback on what I have included as well as what I havent. Please post your questions and comments in the forum, and I will take them seriously to make this book as useful as possible. Happy reading!

Paul Orland

This chapter covers

Making money by implementing mathematical ideas in code

Avoiding common pitfalls in math learning

Thinking like a programmer to understand math

Using Python as a powerful and extensible calculator

Math is like baseball or poetry or fine wine. Some people are so fascinated by math that they devote their whole lives to it, while others feel like they just dont get it. Youve probably already been forced into one camp or another by twelve years of compulsory math education in school.

What if we learned about fine wine in school like we learn math? I dont think Id like wine at all if I got lectured on grape varietals and fermentation techniques for an hour a day. Maybe in such a world, Id need to consume three or four glasses for homework, as assigned by the teacher. Sometimes this would be a delicious and educational experience, but sometimes I wouldnt feel like getting loaded on a school night. My experience in math class went something like this, and it turned me off of the subject for a while. Like wine, mathematics is an acquired taste, and a daily grind of lectures and assignments is no way to refine ones palate.

If you miss this, its easy to think youre either cut out for math or you arent. If you already believe in yourself and youre excited to start learning, thats great! Otherwise, this chapter is designed for you. Feeling intimidated by math is so common, it has a name: math anxiety. I hope to dispel any anxiety you might have, and show you that math can be a stimulating experience rather than a frightening one. All you need are the right tools and the right mindset.

The main tool for learning in this book is Python programming. Im guessing when you learned math in high school, you saw it written on the blackboard and not written in computer code. This is a shame, because a high-level programming language is a far more powerful than a blackboard, and far more versatile than whatever overpriced graphing calculator you may have used. An advantage of meeting math in code is that the ideas have to be precise enough for a computer to understand, theres never any hand-waving about what new symbols mean.

As with learning any new subject, the best way to set yourself up for success is to want to learn it. There are plenty of good reasons. You could be intrigued by the beauty of mathematical concepts or enjoy the brain-teaser feel of math problems. Maybe theres an app or game youve been dreaming of building that needs some math to make it work. For now, Ill try to motivate you with an even lower common denominator: solving mathematical problems with software can make you filthy rich.

A classic criticism you hear in high school math class is when am I ever going to use this stuff in real life? Our teachers told us that math would help us succeed professionally and make money. I think they were right about this, even though their examples were off. For instance, I dont calculate my compounding bank interest by hand (and neither does my bank). Maybe if I became a construction site surveyor, as my trigonometry teacher suggested, Id be using sines and cosines every day to earn my paycheck.

It turns out the real world applications from high school textbooks arent that useful. Still, there are real applications of math out there, and some of them are mind-bogglingly lucrative. Many of them are solved by translating the right mathematical idea into usable software. Ill share some of my favorite examples.

Weve all heard legends of stock traders making millions of dollars by buying and selling the right stocks at the right time. Based on the movies Ive seen, I always pictured a trader as a middle-aged man in a suit yelling at his broker over a cell phone while driving around in a sports car. Maybe this stereotype was spot-on at one point, but the situation is different today. Holed up in back-offices of skyscrapers all over Manhattan are thousands of people called quants. Quants, otherwise known as quantitative analysts, design mathematical algorithms that automatically trade stocks and earn a profit. They dont wear suits and they dont spend any time yelling on their cell phones, but Im sure many of them still own very nice sports cars.

So how does a quant write a program that automatically makes money? The best answers to this question are closely-guarded trade secrets, but you can be sure they involve a lot of math. We can look at a toy example to get a sense of how an automated trading strategy might work.