Math 145a Set theory I (Fall 2019)
Instructor: Sebastien Vasey
Office: Science Center 321H
Email: sebv (at) math (dot) harvard (dot) edu
Office hours: Monday, 4-5pm (SC 321H)
Lectures: Tuesday and Thursday, 12-1h15PM, SC 310
Canvas page (for administrivia)
Do not forget to evaluate the class on the Q!
Latest news / Announcements
- There will be no more office hours, but feel free to write if you want to meet. Best of luck for the exam, and enjoy the break!
- The last exam will be a 48 hours take home from Dec. 3 to Dec. 5. More information about the last exam.
Course notes
Can be downloaded here: Lecture Notes (Last updated Nov. 18, 2019).
Note that these notes are a work in progress and will be updated often throughout the term. Please only print the sections currently being covered in class: the later sections will probably be changed extensively.
Please send me any mistakes or typos you find, or any other comments you may have.
Reading assignments
Unless noted otherwise, the section numbers refer to the course notes.
- For the week of Sep. 2-Sep. 6: Section 1 (introduction), and Section 2 (for Thursday).
- For the week of Sep. 9-Sep. 13: Sections 2.3, 2.4 and 3 (for Tuesday) and sections 4, 5 (for Thursday).
- For the week of Sep. 16-Sep. 20: Sections 5 (for Tuesday) and section 6 (for Thursday).
- For the week of Sep. 23-Sep. 27: sections 6, 7 (for Tuesday), section 8 (for Thursday).
- For the week of Sep. 31-Oct. 4: sections 8, 9 (for Tuesday), section 10 (for Thursday).
- For the week of Oct. 7-Oct. 11: section 11 (for Tuesday), section 12.1 (for Thursday).
- For the week of Oct. 14-Oct. 18: read the rest of section 12 for Tuesday. Review for the midterm on Thursday.
- For the week of Oct. 21-Oct. 25: read the proof of 12.21 and sections 12.4-12.5 for Tuesday. Read section 13 for Thursday.
- For the week of Oct. 28-Nov. 1: Read section 14 for Tuesday. Read sections 15.1 and 15.2 for Thursday.
- For the week of Nov. 4-Nov. 8: Rest on Tuesday, read sections 15.3-15.4 for Thursday.
- For the week of Nov. 11-Nov. 15: Section 16.
- For the week of Nov. 18-Nov. 22: Section 17 (for Tuesday) and section 18.1 (for Thursday).
- For Nov. 26: The rest of section 18.
- For Dec. 3: No reading. Let me know if you would like to give a short presentation of your project (for extra credit).
Assignments
- Assignment 1 (due Tuesday, September 10). Latex source. Questionnaire. Solution.
- Assignment 2 (Updated 9/12: fixed a typo. Due Tuesday, September 17). Latex source. Solution.
- Assignment 3 (Updated 9/19: a part of problem 4 was removed due to a mistake.) Latex source Solution.
- Assignment 4 (due Tuesday, October 1). Latex source Solution.
- Assignment 5 (due Tuesday, October 8). Latex source Solution.
- Assignment 6 (due Tuesday, October 15, 11h59pm). Latex source Solution.
- Assignment 7 (due Thursday, October 24). Latex source Solution.
- Assignment 8 (due Tuesday, October 29). Latex source Solution.
- Assignment 9 (Updated 10/30; due Wednesday, November 6, 11h59pm). Latex source Solution.
- Assignment 10 (due Wednesday, November 13, 11h59pm). Latex source Solution.
- Assignment 11 (due Tuesday, November 19). Latex source Solution.
- Assignment 12 (due Tuesday, November 26, 11h59pm). Latex source Solution.
Exams
Other course documents
Other resources
- Some textbooks on set theory (the first two are at the level of the class, the next two are graduate references) :
- Karel Hrbacek and Thomas Jech, Introduction to set theory. 3rd ed., Marcel Dekker, 1999.
- Ernest Schimmerling, A course on set theory, Cambridge University Press, 2011.
- Kenneth Kunen, Set theory, College Publications, 2011.
- Thomas Jech, Set theory, the third millenium edition, Springer 2011.
- For logic generally:
- Herbert B. Enderton, A mathematical introduction to logic, 2nd ed., Academic Press, 2001.
- Kenneth Kunen, The foundations of mathematics, College publications, 2009.
- If you are struggling with proofs, I recommend Hammack's Book of Proof. Another reference, specifically on the real numbers, is Abbott, Understanding analysis (accessible to Harvard students for free) .
- For LaTeX (completely optional) :
- Just for fun:
- Would you like to learn about cool math from passionate people? Check out Math table/the open neighborhood seminar.
- Cantor's attic is a repository of all mathematical notions of infinity, including large cardinals.
- The metamath project is a library of formalized proofs of basic mathematical facts, from the axioms of set theory.
- A paper version of the metamath project is Edmund Landau's book Foundations of analysis (AMS Chelsea Publishing, 2001 – first published in German in 1930), which builds the complex numbers from the Peano axioms.