# 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.

### Course Evaluation:

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

30% **Midterm exam**: The midterm exam will be in-class. The tentative date for the midterm exam is: ** Wednesday November 1, 2017**. 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.

50% **Final Exam**: The final exam will be comprehensive. It will be scheduled by the registrar for the
December exam period. The last date to drop the course is **Friday, November 10, 2017**.