Algebra and Number Theory

Course Information

This course is open to all students interested in Algebra and Number Theory. Some prior knowledge of Linear Algebra will be helpful but not necessary. The course will cover the basic notions of abstract algebra with a view toward applications in number theory. This course will be a preparation for Armenian students for the CIMPA summer school I am co-organizing in 2025. 

• Location: The auditorium of the Institute of Mathematics of the Academy of Sciences (24/5 Marshal Baghramyan Avenue, Yerevan).

• Duration: September 13 - December 13, 2024. 

• Schedule:  Tuesday and Friday every week, 17:00-19:00.

• Each lecture will be 90 minutes long, followed by a 30-minute recitation (practice session). 

• I will join and deliver the lectures over zoom. The recitations will be taught by the course TA (Ruben Hambardzumyan) in person.

• Prerequisites: Basic knowledge of English. I will lecture in Armenian but the slides will be in English. Some knowledge of Linear Algebra will be helpful but not necessary.

• Grades: The course will have weekly homework assignments, one midterm exam and a final exam.

Week 1 (Sep 9 - Sep 13 , 2024)

• Lecture 1 Notes

• Lecture 1 Recording

Week 2 (Sep 16 - Sep 20, 2024)

• Lecture 2 Notes

• Lecture 2 Recording

• Lecture 3 Notes

• Lecture 3 Recoding

• Homework 1 (due September 27)

Week 3 (Sep 23 - Sep 27, 2024)

• Lecture 4 Notes

• Lecture 4 Recording

• Lecture 5 Notes

• Lecture 5 Recording

• Homework 2 (due October 4)

Week 4 (Sep 30 - Oct 4, 2024)

• Lecture 6 Notes

• Lecture 6 Recording

• Lecture 7 Notes

• Lecture 7 Recording

• Homework 3 (due October 11)

Week 5 (Oct 7 - Oct 11, 2024)

• Lecture 8 Notes

• Lecture 8 Recording

Week 6 (Oct 14 - Oct 18, 2024)

• Lecture 9 Notes

• Lecture 9 Recording

• Lecture 10 Notes

• Lecture 10 Recording

Week 7 (Oct 21 - Oct 25, 2024)

• Midterm Solutions

• Lecture 12 Notes

• Lecture 12 Recording

Week 8 (Nov 4 - Nov 8, 2024)

• Homework 4 (due October 12)

• Project

• Lecture 13 Notes

• Lecture 13 Recording

• Lecture 14 Notes

• Lecture 14 Problems

• Lecture 14 Recording

Week 9 (Nov 11 - Nov 15, 2024)

• Lecture 15 Notes

• Lecture 15 Recording (part 1)

• Lecture 15 Recording (part 2)

• Lecture 16 Notes

• Lecture 16 Recording

Week 10 (Nov 18 - Nov 22, 2024)

• Lecture 17 Notes

• Lecture 17 Recording

Week 11 (Nov 25 - Nov 29, 2024)

• Lecture 19 Notes

• Lecture 19 Recording

• Homework 5 (due December 3)

Week 12 (Dec 2 - Dec 6, 2024)

• Lecture 20 Notes

• Lecture 20 Recording

• Lecture 21 Notes

• Lecture 21 Recording

Week 13 (Dec 9 - Dec 13, 2024)

• Lecture 22 Notes

• Lecture 22 Recording

• Lecture 23 Notes

• Lecture 23 Recording