# ESP Biography

## MILO BRANDT, Enthusiast of math and music; often found outside.

Major: Mathematics and Music

College/Employer: Yale

## Brief Biographical Sketch:

Hailing from the far away land of Massachusetts and the strange ways of progressive education, I have come to Yale to learn everything. I am about half way done with this task, if you don't account for the things that I don't know about.

## Past Classes

(Look at the class archive for more.)

Listening Carefully: An Brief Taste of Musical Analysis in Splash Spring 19 (Apr. 06, 2019)
How is music put together? What structures does it obey? Why does it make us feel the way it does? We will not come even close to answering any of these questions (sorry), but we'll listen to some music with an ear to understanding it at a practical level.

Arithmetic Trickery in Splash Spring 19 (Apr. 06, 2019)
While it can sometimes be tedious to add, subtract, multiply, and divide, there are some amazing hidden patterns that appear... sometimes? We will do some math around this. At the very least, you'll leave this class knowing a few things that you can ask your calculator to get surprising results.

How To Win (Easy) Games in Sprout Spring 19 (Feb. 16 - Mar. 02, 2019)
We will use logic to figure out the winning strategies for some simple games. (...and the only obstacle to solving more complex games will be that there is insufficient time in a Sprout class)

Arithmetic on a Clockface in Splash Fall 2018 (Oct. 27, 2018)
Did you know that an even number times an odd number is always even? That an even plus an odd is odd? That $2=0$ and $3=1$? We will explore the slightly suspiciously looking mathematics of modular arithmetic, where we forget about numbers and consider descriptions like "even" and "odd" or "has last digit 5" and build a new theory of adding and multiplying around it.

Listening Carefully: An Brief Taste of Musical Analysis in Splash Fall 2018 (Oct. 27, 2018)
How is music put together? What structures does it obey? Why does it make us feel the way it does? We will not come even close to answering any of these questions (sorry), but we'll listen to some music with an ear to understanding it at a practical level.

How to Win (easy) Games! in Sprout Fall 18 (Sep. 29 - Oct. 13, 2018)
Ever wanted to become a grandmaster of tic tac toe? Do you often find yourself betting large sums of money on games involving some sort of taking of stones from piles? Then look no further! We shall develop tools to analyze (i.e. figure out how to win or know when to resign) various classes of games.

Conway's Soldiers in Sprout Fall 18 (Sep. 29 - Oct. 13, 2018)
Conway's soldiers is a simple game for one player, with rules somewhat like checkers. We will learn to play it and consider an interesting puzzle arising in its play.

Triangles inside triangles, oh my! in Splash Spring 18 (Apr. 07, 2018)
We will make big shapes out of smaller shapes and talk about making big shapes out of smaller shapes.

Triangles inside triangles, oh my! in Sprout Spring 18 (Feb. 17 - Mar. 03, 2018)
Math isn't all about numbers! Sometimes it's about pictures. Sometimes mathematicians just doodle all day and call it work! In this class, we will discuss a question about drawing triangles inside of triangles and then use it to guide a pictorial exploration.

Conway's Soldiers in Sprout Spring 18 (Feb. 17 - Mar. 03, 2018)
Conway's soldiers is a simple game for one player, with rules somewhat like checkers. We will learn to play it and consider an interesting puzzle arising in its play.

Proofs in Math in Sprout Fall 17 (Sep. 30 - Oct. 14, 2017)
In this course, we (i.e. you) will solve interesting questions involving math. Alongside solving problems, we will work on developing a language of proof that expresses both formal and intuitive notions of mathematics.

Harmony in Classical Music in Sprout Fall 17 (Sep. 30 - Oct. 14, 2017)
We will examine the harmonic language in music from the classical and romantic periods through listening and writing harmony exercises.

"Easy" Unsolved Problems In Mathematics in Splash Spring 17 (Apr. 08, 2017)
In this class, we will look at a number of unresolved questions in mathematics which are easy to state, but (apparently) hard to answer.

King Chickens and Proof in Splash Spring 17 (Apr. 08, 2017)
Wondered what it is mathematicians do all day? Heard of proof, but only the boring types, like "induction" and "contradiction"? We will explore the varied land of proof through difficult problems, talking about neat methods of proof in the context of chicken coup politics.

Bad Algebra Done Right in Splash Spring 17 (Apr. 08, 2017)
In this class, we will play with infinite sums and products in a way that your teachers probably told you was illegal, but which were used historically to achieve deep results.

The Art of Mathematics in Sprout Spring 17 (Feb. 11 - 25, 2017)
Ever wondered what keeps a mathematician up at night? The answer may surprise you! (Hint: It's not calculators) In this course, we will explore the wild and varied land of mathematical proof, aiming to appreciate and participate in the beauty of mathematics.

Why Play Nice?: Cooperation in Evolution in Splash Fall 16 (Nov. 05, 2016)
"Survival of the fittest" suggests that evolution is a fight, each organism vying for its own survival. Yet, in nature, we observe organisms cooperating and even making sacrifices for one another. Learn how evolution encourages cooperative behavior by playing simple games and using the lens of games to shed light on this peculiar aspect of evolution.

King Chickens and Proof in Splash Fall 16 (Nov. 05, 2016)
Wondered what it is mathematicians do all day? Heard of proof, but only the boring types, like "induction" and "contradiction"? We will explore the varied land of proof through difficult problems, talking about neat methods of proof in the context of chicken coup politics.

Make a Motor in Splash Fall 16 (Nov. 05, 2016)
We will learn how electric motors work, as well as create our own simple models of a motor.

Platonic and Archimedean Solids in Splash Fall 16 (Nov. 05, 2016)
Tired of boring, flat geometry? Sick of looking at rectangular prisms all day? In this class, we will take a break from such boring concepts to construct models of various more interesting shapes and talk about the mathematics underpinning them.

Make a Motor in Sprout Fall 16 (Oct. 01 - 15, 2016)
We will learn how electric motors work, as well as create our own simple models of a motor.

Nimbers (Not Numbers) in Sprout Fall 16 (Oct. 01 - 15, 2016)
Nimbers are a powerful tool which can reduce some simple games of strategy to mere calculating with a funny system of "numbers" called nimbers. We will talk about the winning strategy for the game of picking stones (Nim) and other simple games.

Diatonic Harmony in Sprout Fall 16 (Oct. 01 - 15, 2016)
We will discuss the concepts underpinning diatonic music, including the construction of basic chord progressions and voice leading.

Tilings in Sprout Fall 16 (Oct. 01 - 15, 2016)
Tilings appear often in art and naturally in many contexts where repeating designs are desired. We will investigate the mathematical basis for tilings, touching upon both old and new results in mathematics, learning fancy terms that will make your friends think you're really smart, Plus, we will get to look at neat pictures of the objects of study.

Integer Partitions in Sprout Fall 16 (Oct. 01 - 15, 2016)
We will talk about the mathematics of writing a number as a sum of other numbers, tying together some curious techniques of proof and combinatorics.

Mathematical Art in Sprout Fall 16 (Oct. 01 - 15, 2016)
We will look at mathematical art, looking at the mathematical principles underpinning works by artists like Escher and the artistic manifestations of mathematical concepts.

Nimbers (Not Numbers) in Splash Spring 16 (Apr. 02, 2016)
Nimbers are a powerful tool which can reduce some simple games of strategy to mere calculating with a funny system of "numbers" called nimbers. We will talk about the winning strategy for the game of picking stones (Nim) and other simple games.

Why Play Nice?: Cooperation in Evolution in Splash Spring 16 (Apr. 02, 2016)
"Survival of the fittest" suggests that evolution is a fight, each organism vying for its own survival. Yet, in nature, we observe organisms cooperating and even making sacrifices for one another. Learn how evolution encourages cooperative behavior by playing simple games and using the lens of games to shed light on this peculiar aspect of evolution.

"Easy" Unsolved Problems In Mathematics in Splash Spring 16 (Apr. 02, 2016)
In this class, we will look at a number of famous unsolved problems in mathematics which are easy to state but (apparently) hard to prove. The problems will come from a variety of fields of mathematics including number theory, geometry, and combinatorics.

Make a Motor in Splash Spring 16 (Apr. 02, 2016)
We will learn how electric motors work, as well as create our own simple models of a motor.

How Does a Pipe Organ Work? in Splash Spring 16 (Apr. 02, 2016)
Many of us have heard the sound of these huge instruments, but how do they work? They turn out to be quite simple. Using a small model of an organ, we will go over how this magnificent instrument functions and, in brief, every element of its construction.

The Wallpaper Groups in Splash Spring 16 (Apr. 02, 2016)
Wallpapers are full of symmetries - ranging from simple tiled patterns to highly symmetrical designs. We will explore the interesting mathematics arising from the symmetries and play around with designing our own symmetrical patterns.

Why Play Nice?: Cooperation in Evolution in Sprout Spring 16 (Feb. 13 - 27, 2016)
"Survival of the fittest" suggests that evolution is a fight, each organism vying for its own survival. Yet, in nature, we observe organisms cooperating and even making sacrifices for one another. Learn how evolution encourages cooperative behavior by playing simple games and using the lens of games to shed light on this peculiar aspect of evolution.

The Fibonacci Sequence and Other Recurrences in Sprout Spring 16 (Feb. 13 - 27, 2016)
Ever wondered where the seemingly magical formulae for Fibonacci numbers and other recursive sequences come from? Wish you could derive impressive results with just a little algebra? In this class, we will explore the concept of a generating function, which lets us apply algebraic techniques to determine closed forms for a large variety of recursive sequences. We will go into depth to show a variety of insights lent by this point of view.

Random Walks and the Central Limit Theorem in Sprout Spring 16 (Feb. 13 - 27, 2016)
In this class, we will discuss the concept of a random walk, exploring the deep behavior that arises from the process of randomly moving left and right on a line, and its connections to statistics and combinatorics.

Nimbers (Not Numbers) in Sprout Spring 16 (Feb. 13 - 27, 2016)
Nimbers are a powerful tool which can reduce some simple games of strategy to mere calculating with a funny system of "numbers" called nimbers. We will talk about the winning strategy for the game of picking stones (Nim) and other simple games.

The Fibonacci Sequence & More in Splash Fall 15 (Nov. 14, 2015)
Ever wondered where the seemingly magical formulae for Fibonacci numbers and other recursive sequences come from? Wish you could derive impressive results with just a little algebra? In this class, we will explore the concept of a generating function, which lets us apply deceptively simple algebraic techniques to determine closed forms for a large variety of recursive sequences.

Why Play Nice?: Cooperation in Evolution in Splash Fall 15 (Nov. 14, 2015)
"Survival of the fittest" suggests that evolution is a fight, each organism vying for its own survival. Yet, in nature, we observe organisms cooperating and even making sacrifices for one another. Learn how evolution encourages cooperative behavior by playing simple games and using the lens of games to shed light on this peculiar aspect of evolution.