The main objective of this class is to practice writing about mathematics. We will also write a cover letter and vita for possible job/internship/grad school applications. All writing should be done in the word processing system LaTex. The mathematical writing will be based on

- Chapters from the book "The Poincare Conjecture" by Donal O'shea.
- Videos of general audience lectures given by mathematicians on related topics.

- Additional reading.

- Discussions in class.

Group projects

Nov 13: Project 1: Two dimensional manifolds: Gangi, Bugan, Regan, Baumbach, Magan

Nov 15: Project 2: Fundamental group and homology group: MacKenzie, Adinolfi, Rhodes, Sutton

Nov 27: Project 3: The hyperbolic plane and the parallel axiom: Marulis, Harte, Huang, Liu

Nov 29: Project 4: Tilings: spherical, planar, hyperbolic: Stangler, Higgins, Lerman, Monchamp, O'Neil

Dec 4: Project 5: Three dimensional manifolds: examples, constructions, how one distinguishes them: Truong E., Truong T., Hom, Xu

Dec 6: Project 6: Tilings of space by polyhedra: Hwang, Cheung, Li

Dec 11: Project 7: Curvature in dimensions 1,2 and 3: Kambli, Futa, Harper, Thunberg

Important dates

- October 11, 2018: class visit by librarian Zachary Lizee, who wil introduce us to the libraries at UMass, online search options, etc.This information will be useful whatever you will do after graduation, grad school, internships etc.
- October 30, 2018: University Museum of Contemporary Art, UMass Fine Arts Center, The Concinnitas Portfolio

and Pau Atela’s (Re)Creations and MathStudio. - November 8, 2018: Nessim Watson, Assistant Director for CNS Career Center, presentation on application writing: cover letter, resume.

Examples of mathematical writing:

- Steven Strogatz ''Elements of Mathematics'' and some of his writings you find in the NYtimes.
- Eugene Wigner ''The unreasonable effectiveness of mathematics in the natural sciences''
- Paul Lockhart ''A Mathematician's Lament" (specially recommended for anyone who wants to teach mathematics)
- Robert Kanigel "The Man Who Knew Infinity: A Life of the Genius Ramanujan"
- G. H. Hardy "A Mathematician's Apology"
- Simon Singh "Fermat's Last Theorem"
- Timothy Gowers "Mathematics. A Very Short Introduction"

- Edward Frenkel "Love and Math"
- Roger Penrose "The Road to Reality" (Introdurction & Prologue)

Resources

LaTex Installation: TexShop for Mac • MikTex for PC • latex source example • latexed pdf of example source file • latex slides example • latexed pdf of slide example

Umass Library

UMass Writing Center: tutoring and advise on your writing.

UMass Career Center: advise on job applications, internships, grad school applications, cover letters, vitae.

Course Log and assignments:

Week 1: Explained the first concepts of shapes; discussed some of the first chapters of the book

Reading Assignment : "The Poincare Conjecture" up to and including Chapter 5.

Writing Assignment due 9/11/18:

Circumference of the earth measurement by Eratosthenes. About 2 pages long, aim for structure (introduction, main parts, conclusion),

use LaTex environment.

Week 2: Watched John Morgan's lecture on the Poincare Conjecture, ICM Madrid. Started to explain what manifold, boundary, and compact means.

Reading Assignment : "The Poincare Conjecture" up to and including Chapter 8.

Writing Assignment due 9/20/18:

Write about the various ideas people had, and their believes/justifications/evidence for their ideas, on the shape of the earth through history up to the present. Our book gives some information about this and you may also follow up on some of the additional references the book provides. I usually expect at least around 2 pagers single spaced text in a regular 12pt or 14pt font. You should also incorporate the article in the NewYorker about flat earth. Try to read material consciously not just for content, but also for style, sectioning, sentence structures, overall story line etc.

Week 3: More on manifolds in dimension 3 and higher. Atiyah's lecture about geometry in various dimensions (which we haven't seen so far...), but here an overview of his Einstein Lecture ``The Nature of Space'' at the Univeristy of Nebraska.

Reading Assignment : Serge Lang's ``Beauty of Doing Mathematics'' part 3: Great Problems of Geometry and Space

Writing Assignment due 9/27/18:

Write about your present understanding of the various possible shapes in dimensions 1, 2 and 3. Use assigned reading, video lectures, the book, and discussion in class as reference materials.

Week 4: Watched Atiyah's ``Elementary Proof of the Riemann Hypothesis" lecture at the Heidelberg Laureat Forum, and discussed its pro/cons and ramifications.

Reading Assignment : Re-read Roger Penrose's "The Road to Reality" introduction and prologue, and chapters 5 and 6 of our book

about Euclid's work.

Writing Assignment due 10/4/18:

Write about what you think of mathematics: where does it originate (if anywhere), what are its connections (if any) to the ``physical world",

how real are the objects of mathematics, e.g. the elements of Euclid' geometry, points, lines; or the numbers 1,2,3....What is the Platonic world

Penrose and others refer to as a place where mathematical concepts etc. reside?

Week 5: More on 3-manifolds and how to construct some more interesting ones. Riemannian's habilitation lecture and the notion of curvature. How to deform a manifold so that curvature is evenly distributed.

Reading Assignment : Re-read chapter 8, read chapters 9 and 10. Watch the youtube video, also for inspiration of what we could do for final projects, by Andrea Valle on the Poincare Conjecture. Also, as a prelude to the more mathematically detailed lecture we watched in class by Curtis McMullan, look at his more low key, but for us very telling, lecture on the geometry of 3-manifolds.

Week 6: Presentation by Zachary Lizee from the Science and Engineering Library:

- Library 101 – covering library resources and services available (e.g. databases, Interlibrary Loan, how to access different materials, etc.)
- ArXiv; Math SciNet; VNR encyclopedia; and a more general database like EBSCO Academic Search Premier.
- Conducting effective literature searches/reviews – using databases, journals, Google/Google Scholar, other online resources proficiently.
- Why citations are necessary, how to cite, how to use citation manager (e.g. Zotero) – also addressing plagiarism.
- Research-Publishing cycle --Why publish? -- How to stay current in your field of research?
- Why everything is not found on the internet.
- Unique types of information (e.g. technical reports,
conference proceedings, standards, patents, etc.) on resources,
citation searches.

Writing Assignment due 10/25/18:

Write a critical review of Jeff Weeks' presentation.

Week 8: Listen to Roger Penrose talk about effectiveness of mathematics, the platonic reality, and emergence of consciousness.

Discussed curvature and the three constant curvature geometries.

Writing Assignment due 11/1/18: Write about your views/thoughts concerning the Penrose interview. What is your position on

the topics discussed?

Week 9: University Museum of Contemporary Art, UMass Fine Arts Center, The Concinnitas Portfolio

and Pau Atela’s (Re)Creations and MathStudio. Conversation over Math, Beauty, Art. Finsihing up constant curvature geometries and tilings.

Watch the "Not Knot" video.

Writing Assignment due 11/8/18: Write about your thoughts of the exhibtion in general; choose your favorite Concinnitas print, explain why it appeals to you, and write about what it depicts (or what you understand about it).