ESP Biography
JOSHUA FRISCH, ESP Teacher
Major: Course 18 College/Employer: MIT Year of Graduation: 2016 

Brief Biographical Sketch:
Not Available. Past Classes(Look at the class archive for more.)All About That Beef in Splash 2015 (Nov. 21  22, 2015)
Steer yourself on over! We'll give you a tour of the cow from head to tail and show you how to cook (and eat) it all. We'll moove from the science of preparing meat to useful tools and techniques for preparing beef. Welldone classes are rare, so it would be a missteak to miss this one.
Lots of delicious beef will be served.
Modular Arithmetic and Different Bases in Splash 2015 (Nov. 21  22, 2015)
What is the last digit of $$17^{2013}$$? what about $$7^{7^{2013}}$$? why is $$2010!+1$$ a multiples of 2011 and $$2016!+1$ a multiple of 2017 but $2014!+1$ not a multiple of 2015 and what do these facts have to do with each other? Finally, what does all of this have to do with cryptography, the internet, and how computers work on a basic level?
We will answer as many of these questions as we can in the space of two hours using the powerful tool of modular arithmetic.
Autism, Aspergers and the Spectrum in Splash 2015 (Nov. 21  22, 2015)
Autism, Asperger's syndrome, and related conditions, are some of the fastest growing mental health challenges in the country. In this class I will give firsthand knowledge about living with Autism, its effects on socialization and intelligence, and the importance and success that early occupational and social therapy can have to alleviate social and communicative difficulties.
1 square 2 square 3 square 4 square in Splash 2015 (Nov. 21  22, 2015)
What numbers can be written as the sum of 2,3, or 4 square numbers? (1 is left as an exercise to the student). In this class we'll fully answer the question including showing the incredibly cool result that ALL natural numbers are the sum of four squares. En route we'll cover connections to geometry, modular arithmetic, complex numbers, and a weird 4 dimensional version of the complex numbers called quaternions and how this all depends on the fact that $\pi^2>8$
Sex Laws in the United States in Splash 2015 (Nov. 21  22, 2015)
In this class we will study laws regarding where you can put what it whom, what things you may put where, and which pictures, movies and books, you may take of whom in various states throughout the history of the United States, and the relationship that these laws have to religion, cultural mores, and international diplomacy.
Math, Games, and Puzzles in Splash 2015 (Nov. 21  22, 2015)
Games are fun. Puzzles are tricky. Math is mysterious. This class will discuss the interrelationship between all three. In this game and puzzle centered course various games and puzzles with deep and nonobvious mathematical structure will be played. We will play with, discuss, and discover a variety of games and puzzles including impossible puzzles, seemingly impossible puzzles, games where we know who should win but not how they should win, games which are used to model nuclear warfare, and games which can be used to represent every other game, if time permits we will also discuss computers, games, and a million dollar math problem.
how to be PUNny in Splash 2015 (Nov. 21  22, 2015)
Cow you beeflieve it, a splash class strictly dedicated to food puns, sure some may say it's corny but if you don't pepper you speech with wordplays how will you ever elicit the proper groans. Alright this class isn't strictly about food puns, we'll create puns of all sorts. Together we'll see just how many puns are possible to fit in an hour. Learn important punning principles like "quantity over quality," "say them all really quickly so they don't notice until a few seconds later," and "fancy puns" and then put that knowledge to use to end a highspeed pun frenzy.
Autism, Aspergers and the spectrum in Splash 2014 (Nov. 22  23, 2014)
Autism, Asperger's syndrome, and related conditions, are some of the fastest growing mental health challenges in the country. In this class I will give firsthand knowledge about living with Autism, its effects on socialization and intelligence, and the importance and success that early occupational and social therapy can have to alleviate social and communicative difficulties.
Math, Games, and Puzzles in Splash 2014 (Nov. 22  23, 2014)
Games are fun. Puzzles are tricky. Math is mysterious. This class will discuss the interrelationship between all three. In this game and puzzle centered course various games and puzzles with deep and nonobvious mathematical structure will be played. We will play with, discuss, and discover a variety of games and puzzles including impossible puzzles, seemingly impossible puzzles, games where we know who should win but not how they should win, games which are used to model nuclearwarfare, and games which can be used to represent every other game, if time permits we will also discuss computers, games, and a million dollar math problem.
Information. Computation, and provability in Splash 2014 (Nov. 22  23, 2014)
In early 1930s Godel proved two shocking theorems, firstly that there are true mathematical statements which can not be proven and secondly, that you can never prove your axiom system consistent. 30 years later Kolmogorov introduced a notion of how "complex" a number which allows 1000000000000000000000000000000000000 to be seen as less complex then 239340934238409238490237432480 despite being longer. We will use this idea in order to prove the first two incompleteness theorems and, on the way give some shockingly unprovable problems, in particular we will describe a property satisfied by over 99.9999% of numbers which it's impossible to prove any particular number satisfies.
History of Homosexuality in Splash 2014 (Nov. 22  23, 2014)
Gays, Lesbians, and alternate sexualities have existed for thousands of years and controversies and opinions about them for nearly as long. We will discuss same gender relationships, different societies reactions and tolerance to them, and the affect that individuals had in a variety of places and times, modern and ancient, foreign and familiar. We will discuss issues ranging from the silly to the striking with, hopefully, a healthy dose of humor.
The almost prime number theorem in Splash 2014 (Nov. 22  23, 2014)
The prime number theorem says that the chance of a number $$N$$ being prime is roughly $$1/(ln(N))$$. The prime number theorem is really hard to prove. The almost prime number theorem says that the chance of a number $$N$$ being prime is between $$.5/(ln(N))$$ and $$2/ln(N)$$, the almost prime number theorem is much easier to do, in this class we will prove it.
The Bigger Number Game in Spark 2014 (Mar. 15  16, 2014)
100, 99999, 10^1000, what is the biggest number you can name? What does this have to do with logic, computers, and the nature of computation itself. This class will be a combination of competing and lecture.
Bases and Mods in Spark 2014 (Mar. 15  16, 2014)
How do you calculate the last digit of 7^(7^2014)? What is binary and how do you multiply in it? We will talk about how to do math in different number bases, what modular arithmetic is, and what they have to do with each other.
How to add infinitely many things in Spark 2014 (Mar. 15  16, 2014)
What is $1+1/2+1/3+1/4...$? $1+1/2+1/4+1/8...
What about $11/2+1/31/4...$
We will talk about what happens when you sum infinitely many things and what can go wrong.
Math, Games, and Puzzles in Spark 2014 (Mar. 15  16, 2014)
Games are fun. Puzzles are tricky. Math is mysterious. This class will discuss the interrelationship between all three. In this game and puzzle centered course various games and puzzles with deep and nonobvious mathematical structure will be played. We will play with, discuss, and discover a variety of games and puzzles including impossible puzzles, seemingly impossible puzzles, games where we know who should win but not how they should win, games which are used to model nuclearwarfare, and games which can be used to represent every other game, if time permits we will also discuss computers, games, and a million dollar math problem.
Steak: Theory and Practice in Splash! 2013 (Nov. 23  24, 2013)
Steer yourself on over! By the end of this class, you'll have herd how to cook a delicious prime steak. We'll moove from the science of cooking meat to useful tools and techniques for preparing beef. Classes this well done are rare, so it would be a missteak to miss this.
Information. Computation, and provability in Splash! 2013 (Nov. 23  24, 2013)
In early 1930s Godel proved two shocking theorems, firstly that there are true mathematical statements which can not be proven and secondly, that you can never prove your axiom system consistent. 30 years later Kolmogorov introduced a notion of how "complex" a number which allows 1000000000000000000000000000000000000 to be seen as less complex then 239340934238409238490237432480 despite being longer. We will use this idea in order to prove the first two incompleteness theorems and, on the way give shocking some shockingly unprovable problems, in particular we will describe a property satisfied by over 99.9999% which it's impossible to prove any particular number satisfies.
The games people play in Splash! 2013 (Nov. 23  24, 2013)
Presidential elections, the price of tea in china, and poker, despite their initial dissimilarities are all intimately related. The common bond, the extremely important mathematical field known as game theory. In this class we will discuss what game theory is, how it relates to our world, and give lots of examples of games which show up in the real world on an astoundingly regular basis. If you want to know why nuclear disarmament, pollution, and buying overpriced entrees at dinner are all basically the same problem, this class is for you.
Modular Arithmetic and different bases in Splash! 2013 (Nov. 23  24, 2013)
What is the last digit of $$17^{2013}$$? what about $$7^{7^{2013}}$$? why are $$1000^{2011}1000$$ and $$2010!+1$$ multiples of 2011 and what do these facts have to do with each other? Finally, what does all of this have to do with cryptography, the internet, and how computers work on a basic level?
We will answer as many of these questions as we can in the space of two hours using the powerful tool of modular arithmetic.
The computability hierarchy in Splash! 2013 (Nov. 23  24, 2013)
Imagine you had a computer with unlimited time and unlimited memory, a genius capable of writing brilliant programs. While you would be able to solve all sorts of problems with this machine, perhaps surprisingly, there would be some simple problems that, no matter how smart you are, you wouldn't be able to solve. Even if you could solve those problems there are yet more difficult problems you couldn't solve. In this class we will discuss computability theory, the field which studies these questions and has links with fields as diverse as math, computer science and linguistics.
Sex laws in the united states in Splash! 2013 (Nov. 23  24, 2013)
In this class we will study laws regarding where you can put what it whom, what things you may put where, and which pictures, movies and books, you may take of whom in various states throughout the history of the united states, and the relationship that these laws have to religion, cultural mores, and international diplomacy.
Symmetry, Structure, and Size, Combinatorics in HSSP Spring 2013 (Mar. 02, 2013)
In math we tend to deal with objects with that either have a lot of structure, have a small of size, or have a some sort of symmetry. In combinatorics we often try and figure out how to deal with things with a large size. In particular, if we need to figure out how many ways we can do something, we can often just list them (for example, figuring out how many whole numbers are solutions to the equation $$x^24$$
In combinatorics though, you don't just count solutions, you determine possibilities. So if you figure out that there are 2,598,960 different hands of 5 cards, it would be really, really, nice to use a better method then just listing them all out.
In this class we will discuss how combinatoricss interacts with probability, number theory, graph theory and geometry. As well as developing enough combinatorics on our own to solve a tremendous number of problems (If you haven't heard of some of these words, that's fine.)
Bases and Mods in Spark! 2013 (Mar. 16, 2013)
We will use the magic of modular arithmetic and different bases to figure out how to solve problems like what is the last digit of $7^{7^2013}$ and figure out why 10!+1 is a multiple of 11.
Space filling curves in Spark! 2013 (Mar. 16, 2013)
When you think of a curve you might think of many things, you might think of a circle, a line, a squiggle, a helix, or a figure eight. If you are really knowledgeable you might even think of a fractal like the Koch Snowflake. But curves get much weirder than that, there are curves that get near all points in space, and weirder still, there are curves which cover every point in a square, there are curves that cover the entire space, There are Space Filling curves!
Take this class to learn the relevant knowledge to construct and understand these objects, we will discuss in depth what curves are, how they work with limits, and how the concept of a metric space can help illuminate these concepts.
The irrationality of rationality in Spark! 2013 (Mar. 16, 2013)
Rational behavior can lead to self destruction, self harm, and generally awful results for the person acting rationality. In this class we will discuss how acting "irrationally" can often cause you to behave in ways which yield you better results, how having less options can cause you to perform better (even if you have infinite computation) and how "rational" people will turn down millions of dollars for one.
Unique Factorization! in Splash! 2012 (Nov. 17  18, 2012)
Over 400 years ago Fermat claimed that a prime number can be written as the sum of two squares if and only if it is of the form $$4n+1$$ where n is a whole number. over 2000 years ago Euclid described an algorithm for finding the greatest common factor of two numbers. 164 years ago Gabriel Lame thought he had found a proof of Fermat’s last theorem which was later shown to be fatally flawed. All three of these concepts (as well as many, many, many more) and intimately related with the concept of unique factorization. Contrary to what you might think not every type of number has unique factorization, when unique factorization does occur however, we can use it as a very powerful tool to prove very cool results. In this class we will cover Various “Euclidean algorithms” (including ones discovered thousands of years after Euclid himself was dead, as well as the original) how these algorithms allow you to prove unique factorization. Examples of when unique factorization fails. And how this all relates, and allows you to prove Fermat’s 400 year old claim. If time permits we will also discuss primes of the form $$x^2+2y^2$$, and unique factorization for polynomials.
Math, Games, and Puzzles in Splash! 2012 (Nov. 17  18, 2012)
Games are fun. Puzzles are tricky. Math is mysterious. This class will discuss the interrelationship between all three. In this game and puzzle centered course various games and puzzles with deep and nonobvious mathematical structure will be played. We will play with, discuss, and discover a variety of games and puzzles including impossible puzzles, seemingly impossible puzzles, games where we know who should win but not how they should win, games which are used to model nuclearwarfare, and games which can be used to represent every other game, if time permits we will also discuss computers, games, and a million dollar math problem.
Math, Games, and the Irrationality of rational deductions in Splash! 2012 (Nov. 17  18, 2012)
In this class we will discuss, from a mathematical perspective various ways in which acting in your own self interest can hurt or help yourself. Particular topics of discussion will include whether you can make valid threats, whether it is worthwhile to renege on alliances, and why bidding what you think something is worth at auctions can hurt you. Rather than being just theoretical the topics covered are regularly used when considering war, elections, and in explaining incentives in psychology
Infinity+1 in Splash! 2012 (Nov. 17  18, 2012)
Since you were young you probably heard that you couldn't add infinity to regular numbers. That expressions like $$\infty +1$$ make no sense. They told you that you couldn't do arithmetic with infinity, that it "made no sense". Well, they were wrong, in this class we will discuss the various ways to add using infinity including adding infinite amounts of things, adding infinities, and, as time permits, sizes of infinities.
Expect your intuition to be broken $$a+b\neq b+a$$ will occur
Philosophy of Game Design in Splash! 2012 (Nov. 17  18, 2012)
Balancing a game is far more complicated than it may at first seem. A game which consist of nothing more than flipping a coin is (almost) perfectly fair but incredibly boring. Chess on the other hand has a well known bias for white yet is incredibly fun to play. In this class we will discuss the various factors such as fairness, a variety of strategies, and psychology that go into designing "balanced" games.
Autism in Splash! 2012 (Nov. 17  18, 2012)
Autism and other related diagnoses have dramatically increased in recent years. In this class we will discuss what Autism and the spectrum are, how autistic people think and how we vary from and are similar to nonautistic persons. The class will include a large Question/Answer session.
Awesome Abstract Algebra in HSSP Spring 2012 (Feb. 18, 2012)
Algebra in high school is, to be honest, not particularly interesting. Algebra (as done in college) is novel, exciting, and interesting . Based on less than a half dozen rules you can describe a HUGE variety of interrelated structures which are intimately related with such seemingly disparate things as the structure the universe, how credit card data is encrypted on the web, and how google functions. Although we will not cover these specific applications we will discuss symmetry and (rather miraculously) a way to describe all of them, unique factorization (i.e. what makes primes work) and situations where it fails. And, as time permits, the connections between two thousand year old greek geometry problems, complex conjugation, and the insolvability of the quintic.
Unique Factorization and the Sum of Squares in Spark! 2012 (Mar. 10, 2012)
Over 400 years ago Fermat claimed that a prime number can be written as the sum of two squares if and only if it is of the form 4n+1 where n is a whole number. over 2000 years ago Euclid described an algorithm for finding the greatest common factor of two numbers. 164 years ago Gabriel Lame thought he had found a proof of Fermat's last theorem which was later shown to be fatally flawed. All three of these concepts (as well as many, many, many more) and intimately related with the concept of unique factorization. Contrary to what you might think not every type of number has unique factorization, when unique factorization does occur however, we can use it as a very powerful tool to prove very cool results. In this class we will cover Various "Euclidean algorithms" (including ones discovered thousands of years after Euclid himself was dead, as well as the original) how these algorithms allow you to prove unique factorization. Examples of when unique factorization fails. And how this all relates, and allows you to prove Fermat's 400 year old claim. If time permits we will also discuss primes of the form x^2+2y^2, and unique factorization for polynomials.
Autism, Aspergers and the spectrum in Spark! 2012 (Mar. 10, 2012)
Autism, Asperger's syndrome, and related conditions, are some of the fastest growing mental health challenges in the country. In this class I will give firsthand knowledge about living with Autism, its effects on socialization and intelligence, and the importance and success that early occupational and social therapy can have to alleviate social and communicative difficulties.
Math, games and puzzles in Spark! 2012 (Mar. 10, 2012)
Games are fun. Puzzles are tricky. Math is mysterious. This class will discuss the interrelationship between all three. In this game and puzzle centered course various games and puzzles with deep and nonobvious mathematical structure will be played. We will play with, discuss, and discover a variety of games and puzzles including impossible puzzles, seemingly impossible puzzles, games where we know who should win but not how they should win, games which are used to model nuclearwarfare, and games which can be used to represent every other game, if time permits we will also discuss computers, games, and a million dollar math problem.
History of Homosexuality in Splash! 2011 (Nov. 19  20, 2011)
Gays, Lesbians, and alternate sexualities have existed for thousands of years and controversies and opinions about them for nearly as long. We will discuss same gender relationships, different societies reactions and tolerance to them, and the affect that individuals had in a variety of places and times, modern and ancient, foreign and familiar. We will discuss issues ranging from the silly to the striking with, hopefully, a healthy dose of humor.
Dominion in Splash! 2011 (Nov. 19  20, 2011)
Dominion is an amazing deck building game by Donald X. Vaccarino which is easily capable of eating obscene amounts of your time, want to learn how to play and, possibly, get addicted! Come to this walk in seminar for a few fast and friendly games.
The Mathematics of Games in Splash! 2011 (Nov. 19  20, 2011)
Games, though they may seem frivolous they have applications to multitrillion dollar, and multimillion live decisions in everything from Finance to War to Love. In this class we will learn The theory of Games, its applications to politics, and life in general, as well as well as various mathematical topics related to games.
Why Math is cool! in Splash! 2011 (Nov. 19  20, 2011)
For some reason, in the majority of public highschools mathematics mathematicians take is rarely, if ever, taught. This should not be taken as evidence that there is no such thing as cool math. In this class we will discuss several cool concepts in math, including modular arithmetic, the irrationality of the squareroot of 2, and the infinitude of primes and, if time permits A proof of Fermat's little theorem
The mathematics of games in SPICY Delve 2011 (Oct. 23, 2011)
Games, though they may seem frivolous they have applications to multitrillion dollar, and multimillion live decisions in everything from Finance to War to Love. In this class we will learn The theory of Games, its applications to politics, and life in general, as well as well as various mathematical topics related to games.
