Assignments

The first part of this assignment consists of a preliminary report on the assigned paper. The report must be written in \( \LaTeX{} \), and must have the following sections.

1. A brief (roughly one-to-two page) summary of the result presented in the paper.
2. A list of important terms presented in the paper.
3. A brief (at most one page, probably only one-or-two paragraph) discussion of the historical context of the result.
4. An outline of the talk as you envision it. Plan for the talk to last about 15 minutes.
5. A (running) list of supplemental references.

You will turn in the preliminary report in-person outside of the lecture, and must submit your \( \LaTeX{} \) source code electronically for this portion of the assignment. When you hand me the report, we will have a short (20 minutes) discussion concerning the report and your plan for the presentation.

The second part of this assignment is giving the presentation. This will happen during lecture, and should be roughly 15 minutes long.

While slides are not required, you will receive a "credit bump" for this part of the assignment if you…

1. give the talk using \( \LaTeX{} \) and beamer,
2. create all important figures in their slides with TikZ, and
3. give me a copy of the \( \LaTeX{} \) source code.

The third part of this assignment is a short (one-page) follow-up reflection essay written in \( \LaTeX{} \). This reflection should address the following questions.

1. How do you feel that the presentation went?
2. What do you think you did well? What do you think you could improve?
3. If you had to give this presentation again, what would you change?

The reflection must be submitted physically, and the \( \LaTeX{} \) source code must be submitted electronically.

Note: Even though these questions are numbered, your reflection essay should not number the questions!

This section will contain a list of the papers for presentation in the near future.

You will first propose a subject for the term paper (deadline). To do so, you need only choose a mathematician (actually, for practical reasons you should pick three you'd like to learn more about). As you are selecting your subject, keep in mind that you will need to write about both (1) this person's life and times, and (2) their mathematics. For this reason, I suggest you choose a mathematician in an area of mathematics that interests you.

The following are some suggestions, with their Wikipedia pages linked so you can do some preliminary reading about them.

Ada Lovelace

computer science

Albert Turner Bharucha-Reid

probability, statistics

Alonzo Church

logic, computer science, philosophy

Andrey Kolmogorov

topology, probability, computer science

Andrey Markov Jr.

topology, logic, foundations of mathematics

Andrey Markov

dynamics, combinatorics

Andrey Tychonoff

topology, analysis, mathematical physics

Arthur Cayley

algebra

Ashutosh Mukherjee

euclidean geometry, differential geometry

Charlotte Scott

algebraic geometry, mathematics education

Chen Jingrun

number theory

Claude Shannon

cryptography, computer science

David Blackwell

game theory, probability, information theory

Elbert Frank Cox

combinatorial algebra

Emmy Noether

algebra, physics

Eric Temple Bell

number theory

Evgraf Fedorov

combinatorial geometry

Gaṅgeśa

logic, philosophy

Georg Cantor

number theory, set theory

Georgia Caldwell Smith

group theory

Georgy Voronoy

convex geometry, lie groups

Gottlob Frege

logic, axiomatic geometry, philosophy of mathematics

Haskell Curry

logic, computer science

Heinz Hopf

topology, geometry

Hua Luogeng

number theory

Hypatia

euclidean geometry, number theory, philosophy

Israel Gelfand

group theory, analysis

John Napier

arithmetic, spherical trigonometry

John von Neumann

algebra, logic, computer science

Julia Robinson

number theory, computer science

K. S. S. Nambooripad

semigroups

Marjorie Lee Browne

algebra, mathematics education

Mary Cartwright

dynamics, differential equations

Mary Ellen Rudin

topology, combinatorial topology

Maryam Mirzakhani

topology, differential geometry, dynamics

Moses Schönfinkel

logic, foundations of mathematics

Nicolai A. Vasiliev

logic, philosophy

Nikolai Lobachevsky

hyperbolic geometry

Nilakantha Somayaji

infinite series, spherical geometry

Nobuo Yoneda

category theory, logic, computer science

P. K. Srinivasan

mathematics education

Pao-Lu Hsu

probability, statistics

Pavel Alexandrov

set theory, topology

Pavel Urysohn

topology

Raj Chandra Bose

combinatorics, finite geometry

Saunders Mac Lane

category theory

Sharadchandra Shankar Shrikhande

combinatorics

Shiing-Shen Chern

differential geometry, algebraic topology

Sofya Kovalevskaya

analysis, differential equations

Sophie Germain

number theory, philosophy

Su Buqing

differential geometry

Wei-Liang Chow

algebraic geometry

Someone Else

mathematics at large

Full disclosure: this list contains some mathematicians I would like to know more about, and whom I think might make good subjects for a paper like this.

Next you will compose a list of references, both mathematical and biographical (deadline).

This should be an annotated list, meaning that you will give a brief (one-or-two paragraph) explanation of what each source on your list covers. Expect to have at least two mathematical sources, and at least five biographical sources.

All sources must be respectable, as defined by me. Shady websites are not respectable. Wikipaedia is not respectable. If you have any doubts about a source, ask me in advance.

Next you will submit a preliminary report on the mathematics you plan to discuss in the paper (deadline).

This should detail your understanding of some aspect of the mathematics that your subject did. Ideally, you will expand this for the mathematics portion of later drafts. Shoot for three pages detailing the following.

1. Describe the mathematics in layman's terms. This should include a description of the problem solved or the theorem proved for a non-technical audience.
2. Give a brief discussion of the methods they used.
3. Compile a list of important definitions and theorems. It may be a good idea to summarize proof/solution ideas here as well.
4. Anything else about the mathematics you deem important.

Next you will submit a preliminary report on the life and times of your subject (deadline).

This should give an overview of your subject's life. This portion of the paper is a good place to let your personal writing style and interests flow! Here are some things you might want to think about.

1. Summarize the subject's personal life. Where did they grow up? What kind of person were they? Who/what influenced them? What challenges did they face? What advantages did they have?
2. Summarize the subject's academic life. What got them interested in mathematics? Who/what influenced them? Did they go to school for mathematics? What challenges did they face? Were they just a mathematician, or did they do other things as well?
3. Summarize the subject's cultural and academic environment.
4. What do you find inspiring about the subject? What's maybe not so inspiring about the subject?

Next, you will synthesize a first draft of the paper (deadline).

Ideally, this is a synthesis of the mathematical and biographical reports. Try to capture what you find exciting about the subject and their mathematics! You should expand your previous work as necessary, and round out the rough edges. Make sure it flows.

Next you will make revisions based on my feedback (deadline).

Address any comments I make, and expand/contract as necessary. Start to polish your work, and make sure that it is written in a clear and informative way.

Finally, you will submit the completed version of the paper (deadline).