The course is entirely on-line, but some office hours are in presence.

SCHEDULE: WEDNESDAY-FRIDAY 16:15-17:30

OFFICE HOURS: Monday 13:30 - 14:30 (LB 927)

OUTLINE: This is a first course in the study of algebraic number fields. In the first part of the course, we will concentrate on proving the two main basic results in the subject: the ideal class group is finite and the unit group is finitely generated. Other topics will include: the distribution of ideals, the Dedekind zeta function and the class number formula, and the Artin map.

TEXT: Number Fields (Marcus), Algebraic Number Theory (Janusz) or your favorite text on the subject.

EVALUATION: Assignments and course presentations.

ASSIGNMENTS:

Assignement 1. Due Friday September 24.

Assignement 2. Due Friday October 8.

The course is entirely on-line, including the exams.

OUTLINE: This is a standard first course in group theory, assuming no background in the subject, but some mathematical maturity, as the ability to work formally and prove results. We will cover (in parts) Chapter 1,2,3,4 in Dummit and Foote.

Course Outline

SCHEDULE: W-F 11h45-13h00

OFFICE HOURS: W-F 13h15-14h15

TEXT: Abstract Algebra, by David S. Dummit and Richard M. Foote.

GRADING: The grading will be the higher of:

(a) Assignments 20%, Midterm 30%, Final 50%

(b) Assignments 20%, Final 80%

MIDTERM: Friday October 30

For the assignments, I am counting the best 8 ones out of 10.

The assignments have to be sent by email AS A PDF FILE to the marker at the due date BEFORE 14h00. Late assignments will NOT be accepted.

The assignments and their solutions will be available on this WEB page.

ASSIGNMENTS:

Assignement 1. Due Friday September 25. Solutions 1.

Assignement 2. Due Friday October 2. Solutions 2.

Assignement 3. Due Friday October 9. Solutions 3.

Assignement 4. Due Friday October 16. Solutions 4.

Assignement 5. Due Friday October 23. Solutions 5.

Assignement 6. Due Friday November 6. Solutions 6.

Assignement 7. Due Friday November 13. Solutions 7.

Assignement 8. Due Friday November 20. Solutions 8.

Assignement 9. Due Friday November 27. Solutions 9.

Assignement 10. Due Friday December 4. Solutions 10.

The final exam will cover all the material that we saw in class during the term. The material that is in the textbook but that we did not covered in class is not included.

SCHEDULE: W-F 11h45-13h00

OFFICE HOURS: W-F 14h00-15h00, LB 927.09

TEXT: Abstract Algebra, by David S. Dummit and Richard M. Foote.

GRADING: The grading will be the higher of:

(a) Assignments 20%, Midterm 30%, Final 50%

(b) Assignments 20%, Final 80%

For the assignments, I am counting the best 7 ones out of 9.

The assignments and their solutions will be available on this WEB page.

OUTLINE: This is a standard first course in group theory, assuming no background in the subject, but some mathematical maturity, as the ability to work formally and prove results. We will cover (in parts) Chapter 1,2,3,4 in Dummit and Foote.

Solutions to Midterm

Practice Final Exam

Solutions to Practice Final Exam

Assignement 1. Due Friday September 20. Solutions 1.

Assignement 2. Due Friday September 27. Solutions 2.

Assignement 3. Due Friday October 4. Solutions 3.

Assignement 4. Due Friday October 11. Solutions 4.

Assignement 5. Due Friday October 18. Solutions 5.

Assignement 6. Due Friday November 8. Solutions 6.

Assignement 7. Due Friday November 15. Solutions 7.

Assignement 8. Due Friday November 22. Solutions 8.

Assignement 9. Due Monday December 2. Solutions 9.

The final exam will cover all the material that we saw in class during the term. The material that is in the textbook but that we did not covered in class is not included. Here are the sections of the textbook that we covered (some of them only partially).

Section 0.3

Chapter 1, all sections.

Chapter 2, all sections except 2.4.

Chapter 3, all sections except 3.4.

Chapter 4, 1.2, 4.2, 4.2 and part of 4.5.

(a) Assignments 20%, Midterm 30%, Final 50%

(b) Assignments 20%, Final 80%

Practice Midterm

Practice Midterm Solutions

Solutions to Midterm

Assignment 1 Due Friday January 24. Solutions to Assignement 1.

Assignment 2 Due Friday February 7. Solutions to Assignement 2.

Assignment 3 Due Friday February 21. Solutions to Assignement 3.

Assignment 4 Due Wednesday April 8. Solutions to Assignment 4.

Assignment 1 Due Friday January 31. Solutions 1

Assignment 2 Due Friday February 21.

Assignment 3 Due Wednesday April 1.

Wednesday April 1 16h15-17h00: David Ayotte "Modular symbols"

Wednesday April 1 17h00-17h45: Sivasankar Nair "Distribution of discriminants of Abelian number fields"

Friday April 3 16h15-17h00: Habid Alizadeh "Vinogradov's Theorem on sums of three primes"

Friday April 3 17h00-17h45: Arghya Datta "Some Tauberian Theorems related to coin tossing"

Wednesday April 8 16h15-17h00: Danny Shu, "Dirichlet's Class Number Formula"

Wednesday April 8 17h00-17h45: Andy Ramirez-Cote "Effective bounds for class numbers"

Wednesday April 15 16h15-17h00: Arihant Jain "Artin's Conjecture on primitive roots"

Wednesday April 15 17h00-17h45: Neha Nanda "Equidistribution"

Friday April 17 16h15-17h00: Subham Roy "Zeroes of L-functions and random matrix theory"

Friday April 17 17h00-17h45:

ASSIGMENT 1:

Due Wednesday September 19.

Exercises (1.1 or 1.2), 1.3, 1.6, 1.7, 1.8, 1.10, 1.11, 1.12 in Silverman.

Exercise on infinite Galois groups, Section 14.9, no 19, Dummit and Foote

B.SC. students: Do 2 of them.

M.SC. students: Do 3 of them.

Ph. D. students: Do 4 of them.

Partial solutions to Assignement 1.

ASSIGMENT 2:

Due Wednesday October 3.

Assignement 2.

Partial solutions to Assignement 2.

ASSIGMENT 3:

Due Wednesday October 24.

Assignement 3.

Partial solutions to Assignement 3.

ASSIGMENT 4:

Due Wednesday November 14.

Assignement 4.

ASSIGMENT 5:

Due Wednesday November 28.

Exercises 8.1, 8.2, 8.4, 8.12 (do 6 of them), 8.15, 8.19, 10.1 10.13, 10.14 in Silverman.

B.SC. students: Do 2 of them.

M.SC. students: Do 3 of them.

Ph. D. students: Do 4 of them.

Sunday March 10h00 AM

Section G (A to K) Room H-521

Section G (L to Z) Room H-561

Sample for Midterm Exam

Solutions for Midterm Exam

WEDNESDAY APRIL 24, 14h00-16h00

FRIDAY APRIL 26, 14h00-16h00

Fall 2018

Partial Solutions to Fall 2018 midterm

Winter 2018

Assignment 1

Solutions to assignment 1

Assignment 2

Solutions to assignment 2

Assignment 3

Solutions to assignment 3

Assignment 4

Solutions to assignment 4

Assignment 5

Solutions to assignment 5

Start date: Sunday April 21, 9h00 (AM)

End date: Tuesday April 23, 9h00 (AM)

Previous Years