MAS-3203 Introductory Number Theory

# MAS-3203 Introductory Number Theory (Spring 2019)

Instructor:  Dr. Shi Bai
Office:  Science Building (SE43), Room 230.
Email:  sbai@fau.edu
Lecture time and location:  M W F 11:00 am - 11:50 am in SE-271.
Office hours:  Wed, Fri 2 - 3 pm; and by appointment.
Outline: Textbook and Syllabus.

***Project presentation: Apr 22 (Mon), 10-12pm.
***Final exam: May 1 (Wed), 10-12pm.

## Schedule

Week 1 Chap 1.1, 1.2. The set of all integers;
mathematical induction.
Homework 1
Week 2 Chap 1.3, 1.4. Division algorithm and divisibility;
basis representation theorem;
greatest common divisor.
Homework 2 Quiz 1
Week 3 Chap 1.6, 2.1-2.3. Bézout's lemma;
The Euclidean algorithm.
Homework 3 Quiz 2
Week 4 & 5 Chap 2.3, 2.4. Prime numbers;
Fundamental Theorem of Arithmetic.
Homework 4 Quiz 3
Week 6 Chap 2.5. Least common multiple; Solving linear Diophantine equations. Homework 5 Quiz 4, Quiz 5
Week 7 Chap 3.1, 3.2, 3.3. Fundamental of congruences; Linear congruence;
Reduced residue set;
Homework 6 Quiz 6
Week 8 Chap 3 Mid-Exam;
modulo inverses;
Mid-exam (Monday)
Week 9 Spring break
Week 10 Chap 4 Theorems of Fermat, Euler, and Wilson. Homework 7 Quiz 7
Week 11 Chap 4. Chinese Remainder Theorem. Homework 8 Quiz 8
Week 12 Chap 4. Multiplicative arithmetic functions:
Euler's totient, number of divisors,
sum of divisors.
Homework 9 Quiz 9
Week 13 Chap 5. Order of integers modulo n. Homework 10
Quiz 10
Week 14 Chap 5. Primitive roots. Homework 11
Quiz 11
Week 15 Chap 5. Quadratic residues. Legendre and Jacobi symbols. Quiz 12
April 22 (Mon) Project presentation.
May 1 (Wed) Final exam: May 1, Wed, 10:00 - 12:00.