MATH-UA.248.001 THEORY OF NUMBERS
Fall 2020, Mon, Wed 3:30pm-4:45pm, online
Office hours : by appointment
Final exam:
session 1 on December 16, 4-5.50pm NY time
session 2 on December 17, 8-9.50am Shanghai time
Openbook, camera on required
Submit a photo or a scan of your solutions no later than 5mi after the end of exam
Some problems from previous years are here
Midterm:
session 1 on October 21, 3.30-4.45pm NY time
session 2 on October 21 8-9.15pm NY time (8-9.15am on October 22 Shanghai time)
Openbook, camera on required
Submit a photo or a scan of your solutions no later than 5mi after the end of exam
Some problems from previous years are here
More exercises are here
Optional references:
Joseph H. Silverman, A friendly introduction to Number Theory.
David Burton, Elementary Number Theory.
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.
Homework
Program
- Lecture 1: Chapters 1,3 in Silverman's book.
- Lecture 2: Chapters 2.1, 2.2 in Burton's book.
- Lecture 3: Chapters 2.3, 2.4 in Burton's book.
- Lecture 4: Chapters 3.1 in Burton's book.
- Lecture 5: Chapters 4.2,4.3 in Burton's book.
- Lecture 6: Chapter 5.3 in Burton's book.
- Lecture 7: Chapter 4.4 in Burton's book.
- Lecture 8: Chapters 4.4, 7.2, 7.3 (statements) in Burton's book. Chapter 2 in Silverman's book.
- Lecture 9: Chapters 7.2, 7.3, 5.4 in Burton's book.
- Lecture 10: Chapters 5.4, 6.1, 6.2 in Burton's book.
- Lecture 11: Chapter 8.1 in Burton's book.
- Lecture 12: Chapter 8.2 in Burton's book.
- Lecture 13: Review, Chapter 8.2 in Burton's book.
- Lecture 14: Chapters 8.3, 9.1 in Burton's book.
- Lecture 15: Chapters 21, 22 in Silverman's book.
- Lecture 16: Chapter 23 in Silverman's book.
- Lecture 17: Chapters 12.2, 12.3 in Burton's book.
- Lecture 18: Chapters 10.3, 12.3 in Burton's book, Chapter 30 in Silverman's book.
- Lecture 19: Chapter 13.3 in Burton's book, Chapter 30 in Silverman\
's book.
- Lecture 20: Chapters 13.3, 13.4 in Burton's book.
- Lecture 21: Chapter 13.4 in Burton's book.
- Lecture 22: Chapter 13.5 in Burton's book.
- Lecture 23: Chapter 6.2 in Burton's book.