Math 42: Introduction to Number Theory (Spring 2015)
This course introduces the basic ideas of number theory. It is aimed at non-majors and has no prerequisites.
Number theory is one of the most beautiful and ancient parts of mathematics, and is still a vibrant area of modern research. It is concerned with properties of whole numbers, especially how numbers break down into primes and which equations admit whole-number solutions. One of the most striking applications of number theory from the past century is its use in cryptography; a signicant part of the course will develop the material needed to discuss a famous cryptosystem called RSA. The course will end with a selection of topics, possibly including sums of squares, Diophantine equations, continued fractions, and the use of imaginary and complex numbers in number theory.
Announcements
- The last required day of class will be Wednesday, April 22. There will be an optional meeting on Friday, April 24 (in the usual classroom), but the material discussed will not appear on any assignments or the final exam.
- My office hours have changed. They will now be Wednesday from 3:00 to 4:20 and Thursday from 1:45 to 3:15. My dog Charley will be with me at my Thursday office hours unless requested otherwise.
Textbook and readings
- A Friendly Introduction to Number Theory by Joseph Silverman. You can read the first six chapters online for free at the link. The book should be available in the Brown bookstore.
Notes
- RSA crash course (2/2)
Problem sets and solutions
Solutions will be posted after class on the due date of each assignment.
- Problem Set 1. Reading: Silverman chapter 2. (Solutions)
- Problem Set 2. Reading: Silverman chapters 3,5. (Solutions)<li>Problem Set 3. Reading: Silverman chapters 6,7,8. (Solutions)
- Problem Set 4. (No new reading) (Solutions)
- Problem Set 5. Reading: Silverman chapter 9. (Solutions)
- Problem Set 6. Reading: Silverman chapters 10,11. (Solutions)
- Problem Set 7. Reading: Silverman chapters 16,17,18. (Solutions)
- Problem Set 8. Reading: Silverman chapters 14,15,19. (Solutions)
- Problem Set 9. Reading: Silverman chapter 20. (Solutions)
- Problem Set 10. Reading: Silverman chapters 21,22. (Solutions)
- Problem Set 11. Reading: Silverman chapter 28. (Solutions)
- Problem Set 12. Reading: Silverman chapters 24,25. (Solutions)
Exams and solutions
Bonus assignments
There are two optional bonus assignments: a programming assignment and an essay assignment. Only one will affect your grade, but if you wish to complete both of them I will use the higher of the two scores.
Programming assignment description.
| Programming task | Submission Deadline |
|---|---|
| Phi | SAMPLE (not for credit) |
| Dirichlet | Friday 10 April, 2pm |
| LeastNR | Friday 17 April, 2pm |
| Remainders | Friday 24 April, 2pm |
| Cracking | Friday 1 May, 2pm |