**Lectures:
**Tuesdays 11-12 and Thursdays 10-12 at NE142.

**Instructor: **Professor Ilia Binder (ilia@math.toronto.edu), South Building 4038, Phone: (905) 569-4381.

**Office Hours:** Tuesdays and Thursdays, 1-2; and by appointment.

**TA:** Payman Eskandari (payman@math.utoronto.ca).**
TA's Extra office hours:** Friday April 1st: 12-1pm and Wednesday April 6th: 10am-12pm in the Math Aid room 3039H South Building.

**Tutorial:** Fridays, 9-10 at NE140 (no tutorial on Friday, January 7).

**Required Text: **G.A. Jones and J.M. Jones,* Elementary Number Theory, *Springer Undergraduate Mathematics Series, Springer-Verlag 1998.

**Course website: ** http://www.math.toronto.edu/ilia/Teaching/MAT315.2011/index.html

**Prerequisites: **MAT102H5, 134Y5/135Y5/137Y5/(MAT133Y5, 233H5), 223H5, 224H5, 301H5

**Topics. **This course will be a detailed introduction to the basic concepts and results of number theory: divisibility, prime numbers and factorization, Diophantine equations, congruencies and the arithmetic of residue classes, quadratic reciprocity, and sums of squares. We will also discuss Fermat’s Last Theorem. The plan is to cover chapters 1-7 and 10-11 of the textbook.

**Covered topics. **

January 4: Section 1.1

January 6: Sections 1.2-1.4

January 11: Section 2.1

January 13: Sections 2.2, 2.3

January 18: Sections 2.4, 3.1

January 20: Sections 3.1, 3.2, 3.3

January 25: Section 3.4

January 27: Sections 3.5, 4.1

February 1: Section 4.1

February 3: Sections 4.2, 4.3, Appendix B

February 8: Appendix B

February 10: Appendix B, Sections 5.1, 5.2

February 15: Section 5.3

March 1: Sections 5.3, 6.1, 6.2

March 3: Sections 6.3, 6.4

March 8: Sections
6.5, 6.6, 6.7

March 10: Sections 6.7, 6.8

March 15: Sections 7.1, 7.2

March 17: Sections 7.2, 7.3

March 22: Section 7.3, 7.4

March 24:
Sections 7.4, 7.5

March 29:
Sections 7.5, 7.6

March 31:
Sections 11.1 - 11.7

**Homework. **Weekly homework assignments will be due on Thursdays at the beginning of the class, starting January 13. The assignments will be posted the preceding Thursdays on the course website.

*Assignment #1, due January 13.*

*Assignment #2, due January 20.*

*Assignment #3, due January 28.*

*Assignment #4, due February 4.*

*Assignment #5, due February 11.*

**Midterm Test. **There will be an in-class midterm test on Thursday, February 17. You are allowed to use one double-sided page of notes. Textbooks or calculators are not allowed for this test. The test will consist of five problems covering Chapters 1-- 4 and Appendix B.
Solutions to problems 1 and 3.

**Suggested practice problems for the test (do not hand in): ** 1.4, 1.10, 1.22, 2.3, 2.7, 2.20, 3.4, 3.7, 3.10, 3.13, 3.14, 3.20, 4.2, 4.5, 4.16, 4.19.

**Final exam. ** You will be allowed to use one one-sided letter-sized page of notes. Textbooks or calculators are not allowed for this exam.

**Suggested practice problems for the final exam (do not hand in): ** 1.4, 1.10, 1.22, 2.3, 2.7, 2.20, 3.4, 3.7, 3.10, 3.13, 3.14, 3.20, 4.2, 4.5, 4.16, 4.19, 5.7, 5.8, 5.14, 5.20, 5.21, 6.3, 6.5, 6.10, 6.13, 6.16, 6.18, 6.26, 7.2, 7.5, 7.8, 7.9, 7.15, 7.24.

**Grading. **Grades will be based on regular weekly homework (20%), midterm tests (30%) and the final exam (50%). The two lowest homework grades will be dropped. I will also occasionally assign bonus problems.

**Late work.** Late assignments will normally not be accepted, except if substantial and verifiable reasons are provided (e.g. illness for a longer period of time with medical certificate). In no case marks can be given after the solutions have been discussed in the tutorial.

**Missed term test.** Students who miss the term test for reasons entirely beyond their control may, within one week of the missed test, submit the instructor a written request for special consideration explaining the reason for missing the test, and attaching appropriate certification, such as medical certificate or a College Registrar’s note. A student whose explanation is accepted will have their final exam weighted by 60% and the assignments by 40%.

**Plagiarism and Academic Honesty.** Students are expected to adhere to the academic regulations of the University as outlined in the “Code of Behaviour on Academic Matters” which can be found in the UTM Calendar or on the web at http://www.utm.utoronto.ca/regcal/WEBGEN124.html.

The work you submit must be your own and cannot contain anyone else’s work or ideas without proper attribution. Plagiarism is a form of academic fraud and is treated very seriously. Please have a look at http://www.utoronto.ca/writing/plagsep.html.