# Introduction to Number Theory: MATH3141

# Fall 2017

### General Information:

**Instructor**: Dr. Youness Lamzouri.

Office: N515 Ross Building.

Email: lamzouri@mathstat.yorku.ca.

Website: www.math.yorku.ca/~lamzouri.

**Time and location **: Monday, Wednesday and Friday 12:30-1:20 pm in DB 1005.

**Office hours**: Mondays, Wednesdays and Fridays 10:30-11:00 am.

**Textbook**: *"Elementary Number Theory"*
by James K. Strayer. Waveland Press.

### Course Description :

This course is an introduction to number theory, the branch of mathematics that deals with the properties of numbers in general and integers in particular. It is also one of the oldest branches of mathematics, and one of the largest. This course is a rigorous mathematical course, so there will be a certain amount of definitions, theorems, and proofs. However, there will also be a good deal of concrete, hands-on computations, and many interesting and fun applications.

** Syllabus**: We will cover the first four chapters of the Strayer textbook essentially in full: Divisibility, Congruences, Arithmetic functions and Quadratic residues.

### List of practice problems:

**Week 1 and 2 (Sept 8-15)**: Section 1.1 : 5, 7, 8, 9, 12, 14. Section 1.2 : 16, 17, 19, 23.

** Week 3 (Sep 18-22)**: Section 1.2 : 28, 29. Section 1.3 : 33, 36, 37, 38, 41, 45, 47. Section 1.4: 54, 56, 58.

** Week 4 (Sep 25-29)**: Section 1.5 : 61, 64, 68, 69, 71, 77, 80, 87.

** Week 5 (Oct 2- Oct 6)**: Section 2.1 : 3, 4, 8, 9, 11, 13, 14, 18, 23, 26. Section 2.2: 28.

** Week 6 (Oct 9- Oct 13)**: Section 2.2 : 29, 30, 31, 32.

** Week 7 (Oct 16- Oct 20)**: Section 2.3 : 33 b), c), d), e); 34, 35, 38. Section 2.4: 42, 44, 46, 48.

** Week 8 (Oct 23- Oct 27)**: Section 2.5 : 52, 54 a), 57, 59, 60, 62, 65 a), b), and e).

** Week 9 (Oct 30- Nov 3)**: Section 2.6 : 68, 69, 71, 73, 74, 75.

** Week 10 (Nov 6-10) **: Section 3.1 : 4, 5, 6, 7. Section 3.3 : 30, 31, 34, 38, 39.

** Week 11 (Nov 13-17) **: Section 3.4 : 42, 44, 45, 46, 49. Section 3.5 : 53, 55, 57. Section 3.2 : 10, 13, 15, 16, 17, 27.

** Week 12 (Nov 20-24) **: Section 3.6 : 64, 65, 66, 67, 69. Section 4.1 : 1, 2, 5, 7, 8.

** Week 13 (Nov 27- Dec 1) **: Section 4.2 : 14, 15, 18, 20. Section 4.3 : 28, 30, 31, 33, 35, 36, 37.

### Course Evaluation:

20% ** Assignments** : There will be two assignments counting for 10% each. Late assignments will not be accepted.

Assignment 1 (Due Wednesday November 1, 2017 at the beginning of class). Here is the solution of Assignment 1.

Assignment 2 (Due Monday December 4, 2017 at the beginning of class).

30% **Midterm exam**: The midterm exam will be in-class. It will be held on ** Wednesday November 1, 2017**. The material of the test includes Sections 1.1, 1.2, 1.3, 1.4, 1.5, 2.1, 2.2, 2.3, 2.4, and 2.5. Here is the midterm exam from the Fall 2016 term. Here is the solution of the midterm.
If you miss the midterm exam and have a valid excuse (with an acceptable documentation), the exam weight will be transferred to the final exam. The last date to drop the course is **Friday, November 10, 2017**.

50% **Final Exam**: The final exam will be comprehensive. It will be held on Wednesday December 20, 2017 from 9:00 am to 12 pm in ACW 005. Here is the final exam from the Fall 2016 term