ESP Biography

MENDEL KELLER, Lifelong student and lover of mathematics

Major: math

College/Employer: MIT

Year of Graduation: 2020

Brief Biographical Sketch:

Ever since I could walk and talk, I've been doing mathematics. When I was younger I used to multiply numbers in my head, and now I occupy myself with groups, rings, and the like.

A large part of my mathematical passion is in teaching. I feel that math is awesome, and so it must be shared to the furthest extent possible.

My mathematical interests are primarily in algebra and logic, as I identify most with their rigid structure and clear cut methodology.

Past Classes

(Clicking a class title will bring you to the course's section of the corresponding course catalog)

S13308: Evolution Revolution: Why Darwin Was Wrong in Splash 2019 (Nov. 23 - 24, 2019)
You might have heard in school about a fellow named Darwin, something about a boat and birds and then a book with words. What they might have left out was all the ways in which Darwin was dead wrong. In fact, as written, Darwinism is total bogus! I will be discussing how life really came to be. I will use proper evidence to draw the story of the tree of life, with an emphasis on how very wrong Darwin was.

P13309: A Sampling of Memes in Splash 2019 (Nov. 23 - 24, 2019)
Why are memes so popular? How did memes begin? How have memes evolved over time? What's all this fuss about "expanding brain" and "epic handshake?" In this class we will take a look at the history of memes, from the proto-memes of the early internet to the image macros and copypastas of the modern day.

X13313: Yuppies, Hippies, Tech Bros and Hipsters: Counter-Cultures on the Coasts in Splash 2019 (Nov. 23 - 24, 2019)
You might be one. You might try to not be one. Who are these people, and how did they come into existence? Alternative identities have an interesting history of rebellion and reinvention. For groups that lack organization, they manage to converge on identifiable aesthetics, values, and communities. In this class, we will identify what it means to fit-in while going against the grain.

X13321: How Does Music Technology Work? in Splash 2019 (Nov. 23 - 24, 2019)
How do you strum a saxophone? Current music technology lets performers have more control of their sound than ever before. From sensors and interfaces, to synthesizers and interpolation, we will cover how modern music technology works and connects together, focusing on the perspective of the synthesizer.

X13013: How to beat your dad at chess, MIT style. in Spark 2019 (Mar. 16 - 17, 2019)
Learn what's important in chess. How to take advantage of your opponents mistakes and weaknesses, how to defend, and how to get a queen. This is a beginner level class, designed for those with a basic knowledge of chess. We will go over a handful of important things to look out for, and some tricks that will help you beat your opponents.

X13014: A peek into the Talmud in Spark 2019 (Mar. 16 - 17, 2019)
A composite of law, logical reasoning, stories and even ancient medical remedies, the Talmud is the mainstay of the Jewish oral tradition. Known for it's vastness and complexity, it is the focal point of study and learning for some of the greatest Jewish minds in history Generally inaccessible for the uninitiated, this class will attempt to provide a brief glimpse at the inner workings of this great body of intellectual exercise.

P13021: A Sampling of Memes in Spark 2019 (Mar. 16 - 17, 2019)
Why are memes so popular? How did memes begin? How have memes evolved over time? What's all this fuss about "expanding brain" and "epic handshake?" In this class we will take a look at the history of memes, from the proto-memes of the early internet to the image macros and copypastas of the modern day.

M13022: Language and logic in Spark 2019 (Mar. 16 - 17, 2019)
Logic is a set of rules, which help us say true things. It is also a field of mathematics, where one can prove what restrictions a system of ideas is inherently subject to. In the 1930s, Kurt Godel made David Hilbert quite upset by proving that some true mathematical statements can't be proven. It turns out that this is probably better understood as showing that any set of descriptions isn't exhaustive. We will discuss what can be said about what can be said, and what the implications of these restrictions are. A mixture of philosophy and mathematics, we will together discover the limitations of language.

L13023: Evolution Revolution: Why Darwin Was Wrong in Spark 2019 (Mar. 16 - 17, 2019)
You might have heard in school about a fellow named Darwin, something about a boat and birds and then a book with words. What they might have left out was all the ways in which Darwin was dead wrong. In fact, as written, Darwinism is total bogus! I will be discussing how life really came to be. I will use proper evidence to draw the story of the tree of life, with an emphasis on how very wrong Darwin was.

S12574: Evolution Revolution: Why Darwin Was Wrong in Splash 2018 (Nov. 17 - 18, 2018)
You might have heard in school about a fellow named Darwin, something about a boat and birds and then a book with words. What they might have left out was all the ways in which Darwin was dead wrong. In fact, as written, Darwinism is total bogus! I will be discussing how life really came to be. I will use proper evidence to draw the story of the tree of life, with an emphasis on how very wrong Darwin was.

M12575: Infinite dimensional topology in Splash 2018 (Nov. 17 - 18, 2018)
Topology is the abstract study of shape. We will be covering some point-set topology. In particular, we will start by looking at the real line, generalize to higher dimensional real space, and then consider the infinite case. In doing so, we introduce topologies, as simple structures that can be given to sets. We study some basic operations that can be done on topologies, and focus on metric topologies, or rather metric spaces. Wherin we use a notion of distance to give a type of shape. We will then consider how to close a set. Which essentially looks like adding the things on its boundary. And using closures we will consider which topology on infinite dimensional space is most satisfying.

X12576: The gods of Gielinor in Splash 2018 (Nov. 17 - 18, 2018)
Come learn about the gods of Runescape, the myths, the history, and the ongoing struggle for control of the races of Gielinor. Learn about Zamorak's betrayal of Zaros, and about Guthix's banishment. Study the dragonkin, and their relationship with the stone of Jas. The divided dragon riders, and the diary of the last of a kind. Follow the staff of Armadyl through five ages. And hear all about Seren's introduction of the ritual to the Mahjarrat, culminating in the murder of Mah. We will be going over the gods arriving on Gielinor, and the relationships between them. This course will provide an overview of the developing story of the gods of Runescape, and the relationships between them. This will include cutscenes of the more major events, and depictions of many of the more minor ones. We will meet all of the 20+ gods Runescape has to offer, and trace back their often complex history. We will also take a look at how this lore developed in real time, as the developers tweaked their notion of the various gods they had already introduced, in order to fit the evolving narrative being offered.

M12578: A bit of Galois in Splash 2018 (Nov. 17 - 18, 2018)
Hold on to your hats, because this is a roller coaster of algebra. I will be rapidly presenting a bunch of complex algebraic concepts, for any students who want a taste of the tougher stuff. We're going to put the idea of the complex numbers in its appropriate wider context, that of field extensions. I will explain the fundamental algebraic reason why complex solutions to polynomials always come in conjugate pairs, and show you how to permute superfields which fix underlying subfields, using the polynomial ring over a field. I will introduce groups, fields, rings and vector spaces, and then put them all together using Galois theory. This class will move pretty fast, and it will be a whole lot of information to take in.

M12579: Ordinal Numbers in Splash 2018 (Nov. 17 - 18, 2018)
Come learn about the all the infinite infinities that come after the counting numbers! We will be discussing well-ordered sets, which are a particularly well behaved class of objects. Starting with the definition of a well ordered set, and continuing on to examples. We will then demonstrate the general process for constructing more and more well ordered sets, and write down a bunch of different sets. It's going to be a lot of fun, you should totally come!

X12061: The gods of Gielinor in HSSP Spring 2018 (Feb. 24, 2018)
Come learn about the gods of Runescape, the myths, the history, and the ongoing struggle for control of the races of Gielinor. Learn about Zamorak's betrayal of Zaros, and about Guthix's banishment. Study the dragonkin, and their relationship with the stone of Jas. The divided dragon riders, and the diary of the last of a kind. Follow the staff of Armadyl through five ages. And hear all about Seren's introduction of the ritual to the Mahjarrat, culminating in the murder of Mah. We will be going over the gods arriving on Gielinor, and the relationships between them. This course will provide an overview of the developing story of the gods of Runescape, and the relationships between them. This will include cutscenes of the more major events, and depictions of many of the more minor ones. We will meet all of the 20+ gods Runescape has to offer, and trace back their often complex history. We will also take a look at how this lore developed in real time, as the developers tweaked their notion of the various gods they had already introduced, in order to fit the evolving narrative being offered.

X12157: How to beat your dad at chess, MIT style. in Spark 2018 (Mar. 17 - 18, 2018)
Learn what's important in chess. How to take advantage of your opponents mistakes and weaknesses, how to defend, and how to get a queen. This is a beginner level class, designed for those with a basic knowledge of chess. We will go over a handful of important things to look out for, and some tricks that will help you beat your opponents.

X12193: The gods of Gielinor in Spark 2018 (Mar. 17 - 18, 2018)
Come learn about the gods of Runescape, the myths, the history, and the ongoing struggle for control of the races of Gielinor. Learn about Zamorak's betrayal of Zaros, and about Guthix's banishment. Study the dragonkin, and their relationship with the stone of Jas. The divided dragon riders, and the diary of the last of a kind. Follow the staff of Armadyl through five ages. And hear all about Seren's introduction of the ritual to the Mahjarrat, culminating in the murder of Mah. We will be going over the gods arriving on Gielinor, and the relationships between them. This course will provide an overview of the developing story of the gods of Runescape, and the relationships between them. This will include cutscenes of the more major events, and depictions of many of the more minor ones. We will meet all of the 20+ gods Runescape has to offer, and trace back their often complex history. We will also take a look at how this lore developed in real time, as the developers tweaked their notion of the various gods they had already introduced, in order to fit the evolving narrative being offered.

X12195: Chess to puzzle over in Spark 2018 (Mar. 17 - 18, 2018)
We will be presenting a bunch of chess puzzles, across a wide range of difficulties, for you to solve. There will be boards set up with puzzles on them.

L12196: Evolution revolution: why Darwin was wrong. in Spark 2018 (Mar. 17 - 18, 2018)
You might have heard in school about a fellow named Darwin, something about a boat and birds and then a book with words. What they might have left out was all the ways in which Darwin was dead wrong. In fact, as written, Darwinism is total bogus! I will be discussing how life really came to be. I will use proper evidence to draw the story of the tree of life, with an emphasis on how very wrong Darwin was.

M11546: Studying finite groups in Splash 2017 (Nov. 18 - 19, 2017)
I will be presenting the Sylow theorems, three powerful theorems which allow us to determine certain facts about the subgroups of a group, using only the order of the group. We will be playing around with groups a bit, and then launching directly into theorems. After presenting and proving the theorems, we will take a look at how they hold in a few examples. If you have already seen groups and liked them, this is probably the course for you.

M11601: Infinite dimensional topology in Splash 2017 (Nov. 18 - 19, 2017)
Topology is the abstract study of shape. We will be covering some point-set topology. In particular, we will start by looking at the real line, generalize to higher dimensional real space, and then consider the infinite case. In doing so, we introduce topologies, as simple structures that can be given to sets. We study some basic operations that can be done on topologies, and focus on metric topologies, or rather metric spaces. Wherin we use a notion of distance to give a type of shape. We will then consider how to close a set. Which essentially looks like adding the things on its boundary. And using closures we will consider which topology on infinite dimensional space is most satisfying.

M11602: Ordinal Numbers in Splash 2017 (Nov. 18 - 19, 2017)
Come learn about the all the infinite infinities that come after the counting numbers! We will be discussing well-ordered sets, which are a particularly well behaved class of objects. Starting with the definition of a well ordered set, and continuing on to examples. We will then demonstrate the general process for constructing more and more well ordered sets, and write down a bunch of different sets. It's going to be a lot of fun, you should totally come!

M11603: Fun with groups in Splash 2017 (Nov. 18 - 19, 2017)
We will be investigating some examples of groups and playing around with them. Some of the things we will investigate are the symmetries of squares, pyramids and other shapes. We will look at permutation groups, and fiddle a bit with matrix groups and isometries. If you like algebra, you'll love groups. It's a more visual type of mathematics that focuses on balance and symmetry. We will be looking at groups inside groups and groups that are similar and different to each other. If you're somehow not yet sold, I'd remind you that the Rubik's cube is a group, and that groups can be applied to a wide variety of problems, for example to examine the deeper properties of polynomials.

M11822: Higher algebra in Splash 2017 (Nov. 18 - 19, 2017)
Hold on to your hats, because this is a roller coaster of algebra. I will be rapidly presenting a bunch of complex algebraic concepts, for any students who want a taste of the tougher stuff. I will be presenting concepts such as local rings, tensor products and the Nullstellensatz. This class is more a hophodge collection of topics in ring theory than a coherent train of thought, I will be introducing a concept, motivating it, provide an example or two, and then moving on to the next topic. If you've been exposed to a bunch of abstract algebra (e.g. Artin, Dummit & Foote, Herstein) and would like to see what comes next, this is the class for you. I will be providing a glimpse of number theory and algebraic geometry, and the methods they employ.

M11823: Playing with shapes in Splash 2017 (Nov. 18 - 19, 2017)
What is a circle squared? (By squared I mean times itself, not turned into a square.) Well, it depends. We can write a circle squared as $$S^1\times S^1$$, $$S^1*S^1$$ or $$S^1\wedge S^1$$ and these are all different objects. Come learn how to build the cylinder and torus, and a few different sphere. I will be (mathematically) gluing a few different shapes together, to see what we can create. Playing with shapes in this way is one of the tools used in topology, and I will be giving you a feel for how topologists think about shapes, especially circles.

M11287: Taking apart spheres: an introduction to topology in Spark 2017 (Mar. 11 - 12, 2017)
Did you know that a sphere is two disks glued together? Have you ever wondered what a four dimensional sphere might look like? What mathematical use is there for a mobius band? (What is a mobius band?) These are some topics that will be addressed in this lecture. After sitting through this short class, you will never look at a circle the same way again. We will be investigating spheres, and showing how several different shapes are actually spheres in disguise. Topology is the field of math which studies shapes abstractly. Unlike geometry, topology ignores size, and even some elements of shape. We will be transforming one shape into another mathematically, in order to give you a taste of the awesome world of topology.