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
We will also do longer group projects  including presentations.

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

Examples of mathematical writing:


LaTex Installation: 
TexShop for Mac  •  MikTex for PC • latex source examplelatexed pdf of example source file • latex slides examplelatexed 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 1Explained 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 3More 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 4Watched 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 5More 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 6Presentation by Zachary Lizee from the Science and Engineering Library:
Week 7Organized groups and group projects. Watched Jeffrey Weeks' "Shape of Space" lecture.
Writing Assignment due  10/25/18:
Write a critical review of Jeff Weeks' presentation.

Week 8Listen 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 9University 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).