Math 101 Sets, groups, and topology (Fall 2018)

Instructor: Sebastien Vasey
Office: Science Center 321H
Email: sebv (at) math (dot) harvard (dot) edu
Office hours: W 5-6PM in SC 229, Th 4-5PM in SC 104, F 5-6PM in SC 232.
Lectures: MF 9AM-10h15AM, SC 310

Course assistants: Michele Tienni (micheletienni (at) college) and Grace Whitney (g_whitney (at) college)

• Michele's office hours: during math night, M 8PM-9PM, Leverett House Dining Hall.
• Grace's office hours: Th 3PM-4PM, SC 113.

Problem session: on Friday in SC 229: time alternates between 10h30AM and 3PM (see the announcements below).

Canvas page (for administrivia, hw solutions)

Do not forget to evaluate the class on the Q!

Latest news / Announcements

• August 13, 2018: This webpage is online, hurray! Please read the syllabus.
• September 6, 2018: This week, I will have office hours on Thursday 4-5PM in SC 321H.
• September 13, 2018: This Friday, Grace will run a problem session at 10h30am in room SC229.
• September 14, 2018: Michele is taking some unofficial notes during class.
• September 21, 2018: This week's problem session will be at 3PM in SC 229.
• September 25, 2018: This week's problem session will be at 10h30AM on Friday in SC 229.
• September 25, 2018: The pre-midterm exam will take place on October 5, 2018 in SC-B10, from 6PM to 8PM. More information.
• October 1, 2018: This week, my Friday office hours will be 4-5PM (instead of 5-6PM) in SC 321H.
• October 3, 2018: This week's problem session will be at 10h30AM again (to leave more time to rest before the pre-midterm) on Friday in SC 229.
• October 11, 2018: This week's problem session will be at 3PM in room SC 229.
• October 15, 2018: This Friday's problem session will be at 10h30AM in room SC 229.
• October 18, 2018: Information on the final project is now available.
• October 22, 2018: This Friday's problem session will take place at 3pm in room SC 229.
• October 24, 2018: The midterm exam will take place on November 2, 2018 in SC-B10, from 6PM to 8PM. More information.
• October 29, 2018: This week's problem session will take place at 10h30am on Friday in room SC 229. Because of the midterm, I will have office hours earlier than usual on Friday, from 3-4PM in SC 229.
• November 8, 2018: This week's problem session will take place at 3pm on Friday in room SC 229.
• November 12, 2018: This week's problem session will take place at 10h30am on Friday in room SC 229.
• November 14, 2018: The last exam will take place on December 3, 2018 in SC-B10, from 5PM to 7PM (note this is a different time than the other exams). More information.
• November 27, 2018: This week's problem session will take place at 3pm on Friday in room SC 229.
• December 3, 2018: The CAs and I will not be holding any regular office hours or problem sessions anymore, but feel free to email us to make an appointment. I will be holding last minute office hours 2-3h30pm today in SC321H.

Main course references

• Richard Hammack, Book of proof, 2nd ed., 2013.
• Tom Judson, Abstract algebra: theory and applications, 2017 ed., Orthogonal Publishing, 2017.
• Stephen Abbott, Understanding analysis, 2nd ed., Springer-Verlag, 2015.

Unofficial course notes

Michele Tienni is taking notes during class. These are not substitute for coming to class or doing the reading! Please read the disclaimer at the beginning of the document.

Exams

All the exams, including solutions, are now on Canvas.

Assignments

• Assignment 1 (due Monday, September 10). Latex source.
• Assignment 2 (due Friday, September 14). Latex source.
• Assignment 3 (due Monday, September 17). Latex source.
• Assignment 4 (due Friday, September 21). Latex source.
• Assignment 5 (due Monday, September 24). Latex source.
• Assignment 6 (due Friday, September 28). Latex source. Last updated on September 25, 2018 (clarifications added for problem 7).
• Assignment 7 (due Monday, October 1). Latex source.
• Assignment 8 (due Friday, October 12). Latex source.
• Assignment 9 (due Monday, October 15). Latex source. (Last updated on October 12, 2018 (fixed a mistake in 3b)) .
• Assignment 10 (due Friday, October 19). Latex source.
• Assignment 11 (due Monday, October 22). Latex source.
• Assignment 12 (due Friday, October 26). Latex source.
• Assignment 13 (due Monday, October 29). Latex source.
• Assignment 14 (due Friday, November 9). Latex source.
• Assignment 15 (due Friday, November 9). Latex source.
• Assignment 16 (due Monday, November 12). Latex source.
• Assignment 17 (due Friday, November 16). Latex source.
• Assignment 18 (due Friday, November 30). Latex source (Last updated on November 30, 2018 - more mistakes fixed in problem 2).

Assignment solutions are posted regularly on Canvas.

Reading assignments

See how to read a math book for reading advice.

• For Friday, Sep. 7: introduction, and sections 2.1, 4.1, 4.2 in Hammack.
• For the week of Sep. 10-Sep. 14: Chapters 4,5,6,7, 9 of Hammack.
• For the week of Sep. 17-Sep. 21: Chapters 10, 1, and 8 of Hammack.
• For the week of Sep. 24-Sep. 28: Section 1.2, Chapters 11, 12.1 of Hammack.
• For the week of Oct. 1-Oct. 5: Monday: sections 12.2, 12.4, 12.5 in Hammack. Friday: sections 13.1, and 13.2 of Hammack.
• For Friday, Oct. 12: Sections 3.1 and 3.2 in Judson.
• For the week of Oct. 15-19: Monday: Sections 3.3, 5.1, and 5.2 in Judson. Friday: sections 9.1, 11.1 in Judson.
• For the week of Oct. 22-26: Monday: Section 4.1 in Judson. Friday: Sections 6.1,6.2 in Judson
• For the week of Oct. 29-Nov. 2: Monday: Section 10.1 in Judson. Friday: Section 11.2 in Judson
• For the week of Nov. 5-Nov. 9: Monday: Sections 1.1, 1.2 in Abbott. Friday: Sections 1.3, 1.4 in Abbott. Check out also the reference sheet.
• For the week of Nov. 12-Nov. 16: Monday: Sections 2.2, 2.3 in Abbott. Friday: 2.3, 2.4.2, 2.5 in Abbott.
• For Monday, Nov. 19: The proof of 2.5.5 and the statement of exercise 2.5.8 in Abbott.
• For the week of Nov. 26-Nov. 30: Monday: the supplementary notes on the real line. Friday: nothing to read, come as you are!
• For Monday, Dec. 3: prepare questions for the review session.

Other course documents

• Supplementary notes on the real line.
• Quick reference sheet on the axioms, facts and theorems of the real line (Updated Nov. 13, 2018).
• The solution to the problem on the sum of interior angles of polygons discussed in class.
• The wrong proof that pi is four discussed during the first lecture.
• Information on the final project.
• Course syllabus (last updated September 4, 2018) .
• Tentative schedule (last updated August 13, 2018, now outdated).

Other resources

• For the project:
  Sample student papers from a class at MIT. The two projects there are longer and more advanced than what is expected of your own project, but the format could give you an idea of what a math project might look like.
• For foundational material:
  • Concepts of mathematics lecture notes (taken from a class I taught in 2014 at Carnegie Mellon University).
  • An introduction to proofs and the mathematical vernacular: Notes from a similar course taught by Martin V. Day.
  • John P. D'Angelo and Douglas B. West, Mathematical thinking: problem-solving and proofs. 2nd ed., Prentice Hall, 2000.
  • Karel Hrbacek and Thomas Jech, Introduction to set theory. 3rd ed., Marcel Dekker, 1999.
• For group theory:
  • John B. Fraleigh, A first course in abstract algebra, 7th ed., Pearsons, 2002.
  • David S. Dummit and Richard M. Foote, Abstract algebra, 3rd ed., Willey, 2003.
• For analysis and topology:
  • John Stillwell, The real numbers, Springer-Verlag, 2013.
  • Michael Spivak, Calculus, 4th ed., Publish or Perish, 2008.
  • James R. Munkres, Topology, 2nd ed., Pearsons, 2000.
• For LaTeX (completely optional) :
  • Overleaf is a free online LaTeX editor.
  • Interactive online introduction to LaTeX.
  • Detexify or the comprehensive LaTeX symbol list can help you find the symbol you want.
• Just for fun:
  • Would you like to learn about cool math from passionate people? Here are two regular events you may be interested in: Math table and the Open neighborhood seminar.
  • Numberphile's short videos on:
    • the square root of two.
    • The sizes of infinity.