MAS 3203 Introductory Number Theory

# MAS 3203 Introductory Number Theory (Spring 2018)

Instructor:  Dr. Shi Bai
Office:  Science Building (SE43), Room 230.
Email:  sbai@fau.edu
Lecture time and location:  W F 12:30PM-2:00PM in FL 404.
Office hours:  Wed, Fri 3 - 4 pm; and by appointment.
Outline: Textbook and Syllabus.
Quizzes: In case there are > 10 quizzes, only your best 10 quizzes will be taken into account towards your final grade; the others will be dropped.
Mid-Exam: 12:30pm-2:00pm, Feb 28 (Wed), 2018. Room: FL 404.
Final exam: Fri (Apr 27) 10:30am - 1:00pm. Room: FL 404.

## Schedule

Reading Topics Homework Annoucements
Week 1 Chap 1.1, 1.2. The set of all integers;
mathematical induction.
[p. 13] 2, 3, 4, 7.
Week 2 Chap 1.3, 1.4. Division algorithm and divisibility;
basis representation theorem;
greatest common divisor.
[p. 16] 4, 8, 9, 11.
[p. 23] 4, 5, 6, 7, 8.
Quiz 1
Week 3 Chap 1.6, 2.1-2.3. Bézout's lemma;
The Euclidean algorithm.
Homework 3 Quiz 2
Week 4 Chap 2.3, 2.4. Prime numbers;
Sieve of Eratosthenes;
Fundamental Theorem of Arithmetic.
Homework 4 Quiz 3
Week 5 Chap 2.5. Least common multiple; Solving linear Diophantine equations. Homework 5 Quiz 4
Week 6 Chap 3.1, 3.2, 3.3. Fundamental of congruences. Homework 6 Quiz 5
Week 7 Chap 3.5 Theorems of Fermat, Euler, and Wilson. Quiz 6
Week 8 Mid-Exam. Mid-exam
(Wed Feb 28th
12:30PM-2PM)
Week 9 Spring break Homework 7
Week 10 Chap 3.4. Chinese Remainder Theorem. Homework 8 Quiz 7
Week 11 Chap 4. Multiplicative arithmetic functions:
Euler's totient, number of divisors,
sum of divisors.
Homework 9 Quiz 8
Week 12 Chap 5. Order of integers modulo n. Homework 10 Meeting (Wed, SE271);
Quiz 9
Week 13 Chap 5. Primitive roots. Meeting (Wed, SE271);
Presentation (Fri, FL404);

Quiz 10
Week 14 Chap 5. Quadratic residues. Quiz 11
Week 15 Chap 6. Legendre and Jacobi symbols. Quiz 12 (Wed)
Exam week (April 26 – May 2) Final exam.