## MATH-UA.248.001 THEORY OF NUMBERS

Fall 2017, Mon, Wed 3:30pm-4:45pm, WWH 201

Office hours : Mod, Wed 2:30pm-3:30pm, WWH 611

Optional references:
Joseph H. Silverman, A friendly introduction to Number Theory.
David Burton, Elementary Number Theory, available here or here.

Topics include: divisibility theory, Euclidean algorithm, congruences, prime numbers, Fermat's theorem, applications to cryptography, quadratic reciprocity, classical number-theoretic functions, primitive roots and sums of squares, prime number theorem, Diophantine equations, continued fractions, diophantine approximation, transcendence of e and pi, analytic theory.

QUIZ I: October, 11, 2017.
Midterm: October, 25, 2017.
QUIZ II: December, 1, 2017.
Last lecture December, 15, 2017. Final: December, 20, 4pm-5.50pm.

December schedule: lectures on Dec, 1, 11, 13, 15; recitations on Dec 4,6,8.

Grades: 0.4 Final+0.3 Midterm+0.3 Homework

### Lectures

- Lecture 1: Chapters 1,3 here.
- Lecture 2: Chapter 2.1 in Burton's book (see the links above to download).
- Lecture 3: Chapters 5, 6 here or Chapters 2.2, 2.3 and 2.4 in Burton's book.
- Lecture 4: Chapters 1.1 and 3.1 in Burton's book.
- Lecture 5: Chapter 4.2, 4.4 (Thm. 4.7 only), 5.3 in Burton's book.
- Lecture 6: Chapter 2 here and RSA (optional).
- Lecture 7: Chapters 5.4, 7.2, 7.3 (statements) in Burton's book.
- Lecture 8: Chapters 7.2, 7.3 (proofs) in Burton's book.
- Lecture 9: Chapters 4.4, 8.2 (Theorem 8.5) in Burton's book.
- Lecture 10: QUIZ, Chapters 8.2, p. 162-164 in Burton's book.
- Lecture 11: Chapter 6.1 in Burton's book.
- Lecture 12: Chapters 6.2, 7.4 in Burton's book.
- Lecture 13: Chapter 8.2 in Burton's book.
- Lecture 14: Chapter 6.3 in Burton's book.
- Lecture 15: Chapters 9.1, 9.2 in Burton's book.
- Lecture 16: Chapters 9.2, 9.3 in Burton's book.
- Lecture 17: Chapter 9.4 in Burton's book.
- Lecture 18: Chapter 12.2 in Burton's book.
- Lecture 19: Chapter 13.3 in Burton's book.
- Lecture 20: Chapter 13.4 in Burton's book.
- Lecture 21: Chapter 13.5 in Burton's book.
- Lecture 22: Review.
- Lecture 23: Review. QUIZ.

### Homework