Instructor: Paul Baginski

Meeting Time: MWF 11:00am - 12:10pm

Meeting Room: Burton 307

Office Hours: Wed 2:30-3:30, Thu 4-6, and by appointment

Office: Burton 310

Email:

Welcome to the course. Please bookmark this webpage since many announcements will be placed here.

**Required Books:**

1. Rosen, Kenneth. *Elementary Number Theory and Its Applications, 4th Edition* **Please note the edition!!!! This is not the newest edition of the book (and it is not available in the bookstore)**

2. Andrews, George. *Number Theory* (available in the bookstore)

- 11/25: The final homework will be assigned Mon 11/26 with a due date of Wed 12/12, the final day of class.
~~I may add a few additional questions to the assignment on Fri 11/30.~~11/27: The current form is final. - 11/12: Presentations have been assigned to groups of two. Please email me to schedule a group meeting during the week after Thanksgiving. Presentations are to be given the week of December 3. Instructions can be found here.
- 10/28: No class on Monday 10/29 due to Hurricane Sandy. Homework 6 is now due Friday due to the disruption. I will be posting solutions on Friday so that you can consult them for the exam.
- 10/26: Your second exam is a take-home exam from Friday November 2 - class on Monday November 5. You are allowed to use your notes, the two books, calculators, and any material on the course website. You are not allowed to consult other books or the web. You must work ALONE. Do not discuss the exam with classmates or people other than myself. I will be available by email during the weekend during reasonable hours to answer questions. The topics covered on the exam include the previous exam's topics, as well as: Andrews 1.2, 2.3, 4.1, Rosen 2.3, 3.1, 3.3, 3.4, 3.6, 4.1, and the in-class material on asymptotic growth and algorithm runtimes.
- 10/26: Homework 6's due date has been extended to Wednesday October 31. No new problems have been added.
- 9/28: As announced in class today, your first exam is Friday October 5. It will be in class and you are allowed one 3x5 index card of notes (double-sided), which you will hand in with the exam. No calculators. The exam will feature at least one proof and you will be asked to prove something you have seen stated in class. The topics covered on the exam are: induction, recursion, ordering, and well-ordering, Andrews 1.1, 2.1, 2.2, 2.4 (and the corresponding material in Rosen 1.1, 1.2, 1.3, 1.4, 3.2, 3.3, 3.4).
- 9/26: Homework 3: typo in definition of lcm is fixed.
- 9/18: Office hours set for the semester, Homework 1 solutions up.
- The questions from Rosen on well-ordering have been moved from Homework 1 to Homework 2.
- Office hours during the week of 9/10: Tuesday 2:30-4, Wednesday 2:30-4.

- Mon 12/10: Möbius Inversion (A 6.4, R 7.4), Cryptography, RSA Encryption (R 8.4)
- Mon 12/10: Möbius Inversion (A 6.4, R 7.4)
- Fri 12/07: Presentations: Polynomials: A Beautiful High School Topic (Th+G); Prime Number Races (R+D)
- Wed 12/05: Presentations: Power Values of Divisor Sums (M+A); Wild and Wooley Numbers (K+E)
- Mon 12/03: Presentations: A Familiar Recurrence Occurs Again (I+S); Zero-sum Sets of Prescribed Size (J+Ti)
- Fri 11/30: The Sum and Number of Divisors (A 6.2, R 7.2), Multiplicative Functions (A 6.3), Möbius Inversion (A 6.4, R 7.4)
- Wed 11/28: Euler's Totient (A 6.1, R 7.1), The Sum and Number of Divisors (A 6.2, R 7.2)
- Mon 11/26: Polynomial Congruences (A 5.4, R 4.4)
- Mon 11/19: The Chinese Remainder Theorem (A 5.3, R 4.3), Polynomial Congruences (A 5.4)
- Fri 11/16: Wilson's Theorem (A 3.3, A 5.2, R 6.1), The Chinese Remainder Theorem (A 5.3, R 4.3)
- Wed 11/14: Fermat's Little Theorem (A 3.2, A 5.2, R 6.1), Euler's Theorem (A 5.2, R 6.3)
- Mon 11/12: Presentations assigned. Fermat's Little Theorem (A 3.2, A 5.2, R 6.1)
- Fri 11/9: Linear Congruences (A 5.1, R 4.2), Systems of Residues (A 4.1, 4.2, R 4.1)
- Wed 11/7: Linear Congruences (A 5.1, R 4.2), Arithmetic in Z_m
- Mon 11/5: Linear Congruences (A 5.1, R 4.2), Arithmetic in Z_m
- Fri 11/2: Congruences, Systems of Residues (A 4.1, 4.2, R 4.1), Divisibility tests (R 5.1)
- Wed 10/31: Congruences, Systems of Residues (A 4.1, 4.2, R 4.1)
- Mon 10/29: No class (Hurricane Sandy)
- Fri 10/26: Dirichlet's Theorem (R 3.1, R 3.4), Euler's totient function and congruences (A 4.1, R 4.1)
- Wed 10/24: Theorems and Conjectures about Primes (R 3.1)
- Mon 10/22: Basis representation (A 1.2, R 2.1), more on asymptotic growth (extra)
- Fri 10/19: Primality Testing and Factorization Algorithms, Basis representation (A 1.2, R 2.1), Prime Number Theorem (R 3.1)
- Wed 10/17: Complexity of Integer Operations (R 2.3), Big-Oh Notation (R 2.3)
- Mon 10/15: Complexity of Integer Operations (R 2.3)
- Fri 10/12: Euclidean Algorithm runtimes (R 3.3)
- Wed 10/10: Linear Diophantine equations (A 2.3, R 3.6)
- Fri 10/5: Exam 1
- Wed 10/3: Exam 1 review, Linear Diophantine equations (A 2.3, R 3.6)
- Mon 10/1: Division Lemma (A 2.1), Euclidean Algorithm (A 2.1, R 3.3)
- Fri 9/28: Greatest common divisors (A 2.2, R 3.2)
- Wed 9/26: The Fundamental Theorem of Arithmetic (A 2.4, R 3.4), greatest common divisors (A 2.2, R 3.2)
- Mon 9/24: The Fundamental Theorem of Arithmetic (A 2.4, R 3.4)
- Fri 9/21: Well-ordering, divisibility (A 2.2, R 1.4)
- Wed 9/19: Well-ordering for partial orderings
- Mon 9/17: Well-ordering for total orderings (R 1.1)
- Fri 9/14: Recursive definitions, Well-ordering (R 1.1, R 1.2)
- Wed 9/12: Proof by Contradiction, Proof by Induction (A 1.1, R 1.1, R 1.2)
- Mon 9/10: Notation, Proofs
- Fri 9/7: Introduction

- Homework 8, due Dec 12. Solutions.
- Homework 7, due Nov 19. Solutions.
- Homework 6, due
~~Oct 29~~~~31~~Nov 2. Solutions. - Homework 5, due Oct 22. Solutions.
- Homework 4, due Oct 15. Solutions.
- Homework 3, due Oct 1. Solutions.
- Homework 2, due Sep 24. Solutions.
- Homework 1, due Sep
~~14~~17. Solutions.