Theory of Numbers [Math 356], Fall 2013 (Rutgers U. (NB))

• TextBook

  There is NO required textbook

  We will not follow any book closely, that's why it is very important to take good notes in class. Rather, we will use wikepedia and other links (and my own posted notes). The following are recommended for supplementary reading.

  • A Friendly Introduction to Number Theory by Joseph H. Silverman (free download!).

  • Elementary Number Theory by Edwin Clark (free download!).

  • Elementary Number Theory: Primes, Congruences, and Secrets by William Stein (free download!).

• Instructor: Dr. Doron ZEILBERGER ("Dr. Z") .

• Dr.Z's Email: zeilberg at math dot rutgers dot edu (MUST have PrimesRock in the subject!)

• Place and Times of Lectures:
  • Mondays and Thursdays, 2nd period, 10:20-11:40am, SEC-218 (Busch Campus)

• Free Tutoring: MTh 7:40-8:30, PH-115

• Additional Office Hours: Mondays and Thursdays, 12:00-1:00pm, Hill 704.

• Dr. Z.'s Class Policy

• Thu. Sept. 5: Lecture 1: Natural Numbers     HW (due Sept. 12)
  wiki1   wiki2   mathworld   wiki3   B. Russell's essay
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Mon. Sept. 9: Lecture 2: Proof by Induction     HW (due Sept. 19)
  wiki
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Thu. Sept. 12: Lecture 3: Fibonacci numbers     HW (due Sept. 19)
  wiki
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Mon. Sept. 16: Lecture 4: Representation of integers; Addition and Multiplication     HW (due Sept. 26)
  wiki1   wiki2  wiki3
  Guest Lecturer: Mr. Matthew Russell
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Thu. Sept. 19: Lecture 5: Prime numbers and the sieve of Eratosthenes     HW (due Sept. 26)
  wiki1 wiki2
  Guest Lecturer: Mr. Matthew Russell
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Mon. Sept. 23: Lecture 6: The Fundamental Theorem of Arithmetic     HW (due Oct. 3)
  wiki
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Thu. Sept. 26 Lecture 7: Greatest Common divisor     HW (due Oct. 3)
  wiki
  [quiz 1 (on lectures 1-5)]
  Here is quiz 1, and here are the solutions to quiz 1.
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Mon. Sept. 30: Lecture 8: The Euclidean Algorithm     HW (due Oct. 10)
  wiki Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Thu. Oct. 3: Lecture 9: Modular arithmetic     HW (due Oct. 10)
  wiki
  [quiz 2 (on lectures 6 and 7)]
  Here is quiz 2, and here are the solutions to quiz 2.
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Mon. Oct. 7: Lecture 10: Linear Congruences     HW (due Oct. 17)
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Thu. Oct. 10: Lecture 11: The Chinese Remainder Theorem     HW (due Oct. 17)
  wiki
  [quiz 3 (on lectures 8 and 9)]
  Here is quiz 3, and here are the solutions to quiz 3.
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Mon. Oct. 14: Exam 1 (On lectures 1-10)
  Here is Exam I, and here are the solutions to Exam I.

• Thu. Oct. 17: Lecture 12: Divisibility Rules and Perpetual Calendar     HW (due Oct. 24)
  wiki1 wiki2
  [quiz 4 (on lectures 10 and 11)]
  Here is quiz 4, and here are the solutions to quiz 4.
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Mon. Oct. 21: Lecture 13: Wilson's Theorem and Fermat's Little Theorem     HW (due Oct. 31)
  wiki1 wiki2. See also pp. 10-11 of Dr. Z.'s essay .
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Thu. Oct. 24: Lecture 14: Pseudoprimes and probabilistic primality tests     HW (due Oct. 31)
  wiki1   wiki2   wiki3   wiki4   wiki5
  [quiz 5 (on lectures 12)]
  Here is quiz 5, and here are the solutions to quiz 5.
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Mon. Oct. 28: Lecture 15: Lecture 15: Euler's Totient (Phi) function     HW (due Nov. 7)
  wiki
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Thu. Oct. 31: Lecture 16: Euler's Theorem and the RSA encrypton algorithm     HW (due Nov. 7)
  wiki1 wiki2
  [quiz 6 (on lectures 13 and 14)]
  Here is quiz 6, and here are the solutions to quiz 6.
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Mon. Nov. 4: Lecture 17: The sum and number of divisors     HW (due Nov. 14)
  wiki     mathworld
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Thu. Nov. 7: Lecture 18: Perfect Numbers and Mersenne Primes     HW (due Nov. 14)
  wiki1 wiki2
  [quiz 7 (on lectures 15 and 16)]
  Here is quiz 7, and here are the solutions to quiz 7.
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Mon. Nov. 11: Lecture 19: The Möbius function and The Möbius inversion formula     HW (due Nov. 21)
  wiki1     wiki2
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Thu. Nov. 14: Lecture 20: Quadratic residues and the law of Quadratic Reciprocity     HW (due Nov. 21)
  wiki     mathworld
  [quiz 8 (on lectures 17 and 18)]
  Here is quiz 8, and here are the solutions to quiz 8.
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Mon. Nov. 18: Lecture 21: Integer Partitions I     HW (due Nov. 26)
  wiki
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Thu. Nov. 21: Lecture 22: Integer Partitions II     HW (due Nov. 26)
  wiki
  [quiz 9 (on lectures 19 and 20)]
  Here is quiz 9, and here are the solutions to quiz 9.
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Mon. Nov. 25: Review

• Tue. Nov. 26: Exam 2 (On lecures 1-22, with an emphasis on lectures 11-22)

• Mon. Dec. 2: Lecture 23: Integer Partitions III: The Pentagonal Number Theorem, Recurrence for p(n)     HW (due Dec. 9)
  wiki         Bressoud-Zeilberger gem
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Thu. Dec. 5: Lecture 24: Continued Fractions     HW (due Dec. 9)
  wiki   Benjamin-Zeilberger gem (optional reading)
  [quiz 10 (on lectures 21 and 22)]
  Here is quiz 10, and here are the solutions to quiz 10.
  Here is the attendance quiz, and here are the solutions to the attendance quiz.

• Mon. Dec. 9: REVIEW

Optional Review

• Thurs. Dec. 12, 3:05-5:00pm, our usual classroom (SEC-218) (note new time!)

Final Exam

• Dec. 23, 2013, 8:00-11:00am (in our classroom [SEC-218])

• Kelsey Horan: 195
• Abbie Shieh: 195
• Josefina Mansour: 194
• Scott Farro: 194

Added Jan. 6, 2014: Here are the students' evaluations.