This handout for a workshop on writing a math paper presents three versions of the same paragraph. The writing samples are designed to illustrate how ordering information within sentences can strengthen connectivity between sentences, thus creating flow and making the logic easier to follow. From Pedro Reis’ Undergraduate Seminar in Applied Physical Mathematics at MIT.
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Guidance from Steven Kleiman for how to write a math paper, written for a now defunct writing requirement but with much good general guidance. Because the guidance is written in the form of a journal article, the text file can act as a template for students to use to create their own papers. This zip file includes supporting style files (from M.I.T.’s Undergraduate Journal of Mathematics, no longer in publication). Before use, the extensions for math2e and thmp2e must be changed from .txt to .sty
Read more →This semester schedule is from Andrew Snowden’s Undergraduate Seminar in Topology at MIT. February W Feb 2 Andrew Organizational meeting F Feb 4 Andrew Introduction to the fundamental group M Feb 7 Scott Paths and homotopies Umut The fundamental group W Feb 9 Kyle The fundamental group of the circle JJ Applications of previous lecture F Feb 11 Marcel Contractible and simply connected spaces Danny The fundamental group of a product M Feb 14 John Functoriality of the fundamental group Noah Homotopy equivalences W Feb 16 Rafael The fundamental group of S1 ∨ S1 Gabriel Amalgamated free products F Feb
Read more →This syllabus is for Andrew Snowden’s Undergraduate Seminar in Topology at MIT. Description This course is a seminar in topology. The main mathematical goal is to learn about the fundamental group, homology and cohomology. The main non-mathematical goal is to obtain experience giving math talks. Lectures will be delivered by the students, with two students speaking at each class. There are no exams. There will be some homework assignments and a final paper. Seminar leader Andrew Snowden e-mail: asnowden at math dot mit dot edu Office: 2-175 Office hours by appointment Time and location The seminar typically meets Monday, Wednesday
Read more →Before the (spring 2010) term started, I talked with some alumni about their experiences in the undergraduate seminar classes at M.I.T., and they suggested that I add more structure to my class (Seminar in Number Theory) than just student talks. In particular, some of the alumni felt that they only managed to establish a solid grasp of the subjects of their own talks, and that some kind of exercises after each talk might help solidify things. I think the format I chose has some room for improvement, but the students did seem to be on top of all of the
Read more →In spring 2011, I ran the 18.904 seminar (Seminar in Topology). Below are some comments about how I ran the seminar and recommendations for people who will run it in the future. See also the course webpage. Organization. The class met for one hour three times a week. Each time, two students spoke for about 25 minutes each. This worked very well. I think it’s preferable to having one student speak for the entire time for a few reasons: for instance, it gives the students less to prepare for their lecture and if someone is not doing so well
Read more →The purpose of this undergraduate seminar at M.I.T. is to give students experience reading, writing and presenting results in mathematics. There is no fixed set of topics to be covered, instead students may choose from a broad selection of topics within discrete mathematics. Course Structure Give at least 3 presentations on some topic(s) in discrete mathematics. At least one of your talks should be based on a research paper published in a reputable mathematics journal. Submit an abstract and before each of your presentations, and provide possible quiz questions after your presentation. Write 3 quizzes based on the content of
Read more →[The following schedule is for Steven Kleiman’s 2010 Undergraduate Seminar in Computational Commutative Algebra and Algebraic Geometry, in which the students give the lectures. The main page for this course is here.] Homework: Problems with numbers between braces ({}) are to be written up formally in TeX and passed in by Thursday of the week after they are assigned; they may be emailed either in TeX form or dvi form directly to the TA. Assignments Date First lecture Second Lecture 1. T. 2/2 Steve Kleiman Sec. 1-1 p.5: 2, {6b} Steve Kleiman Sec. 1-2 p.12: {6}, 8, 10 2.
Read more →[The following notes are from Steven Kleiman’s 2010 Undergraduate Seminar in Computational Commutative Algebra and Algebraic Geometry at MIT. Many of the files below can be downloaded in one zip folder.] Here are some files to help you write mathematics in a way that is more professional in style and format. The following files are the two source files and two compiled versions of the guide, “Writing a Math Phase Two Paper:” piiUJM2.tex || figure.ps || piiUJM2.dvi || piiUJM2.pdf This guide gives a lot of tips on writing a short math paper, and also serves as a model of one.
Read more →[The following notes are about Steven Kleiman’s 2010 Undergraduate Seminar in Computational Commutative Algebra and Algebraic Geometry, in which the students give the lectures and write a term paper. The main page for this course is here.] The term paper is to be a ten-page essay on a topic related to the course. The goal is for you to learn something new, and to explain it clearly to others in the class, or better, to other upper-class math majors. The paper must be written in a professional style, and formatted in AMS-LaTeX, like the papers in MIT’s Undergraduate Journal of
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