Math 25 Syllabus and Homework Assignments
Fall 2012
Updated: November 3


There will often be last minute changes in the syllabus and homework, so check this page before doing any reading or homework.

  Jump to Week 1| Week 2|Week 3|Week 4|Week 5|Week 6|Week 7|Week 8|Week 9|Week 10|Week 11 |

Week 1

September 10
  • Introduction, divisors, Euclidean algorithm.
  • Read Section 1.1
  • Homework for Week 1 can be found at Homework Week 1.
September 11
  • X-hour, 12:00 - 12:50
  • Euclidean algorithm, Bezout's identity
  • Read Section 1.2
September 12
  • No class today.
September 14
  • Least common multiple, linear Diophantine equations
  • Read Sections 1.3 & 1.4
Week 2

September 17
  • Prime numbers, the fundamental theorem of arithmetic
  • Read: Section 2.1
  • Homework for Week 2 can be found at Homework Week 2.
September 19
  • Homework for Week 1 due today.
  • Distribution of primes, Fermat and Mersenne primes
  • Read: Sections 2.2 & 2.3
September 21
  • Primality testing and factorization.
  • Read: Section 2.4
Week 3

September 24
  • Modular arithmetic.
  • Read: Sections 3.1
  • Homework for Week 3 can be found at Homework Week 3.
September 26
  • Homework for Week 2 due today.
  • Linear congruences.
  • Read: Section 3.2
September 28
  • The Chinese remainder theorem.
  • Read: 3.3
Week 4

October 1
  • A little group theory
  • Read: Class notes
  • Homework for Week 4 can be found at Homework Week 4.
October 3
  • Homework for Week 3 due today.
  • Arithmetic of Z_p
  • Read: Section 4.1
October 5
  • Pseudoprimes and Carmichael numbers, congruences modulo a prime power
  • Read: Section 4.2, class notes
Week 5

October 8
  • Congruences modulo a prime power, the Fibonacci sequence
  • Read: Class notes
  • Homework for Week 5 can be found at Homework Week 5.
October 9
  • X-hour, 12:00 - 12:50
  • First midterm exam: in-class portion
October 10
  • Homework for Week 4 is due today.
  • Units in Z_n
  • Read: Sections 5.1
October 12
  • The Euler phi function
  • Read: Sections 5.2
Week 6

October 15
  • Introduction to cryptography
  • Read: Section 5.3
  • Homework for Week 6 can be found at Homework Week 6.
October 17
  • Homework for Week 5 is due today.
  • Quadratic residues
  • Read: Section 7.1 & 7.2
October 19
  • The Legendre symbol
  • Read: Section 7.3
Week 7

October 22
  • Quadratic reciprocity
  • Read: Section 7.4
  • Homework for Week 7 can be found at Homework Week 7.
October 24
  • Homework for Week 6 is due today.
  • Quadratic reciprocity, finding square roots, solving quadratic congruences.
  • Class notes
October 26
  • Solving quadratic congruences, odds and ends from Chapter 6, multiplicative functions
  • Read: Class notes & Section 8.1
Week 8

October 29
  • Multiplicative functions, perfect numbers
  • Read: Sections 8.1 & 8.2
  • Homework for Week 8 can be found at Homework Week 8.
October 30
  • X-hour, 12:00 - 12:50
  • Second midterm exam: in-class portion
October 31
  • The Moebius inversion formula
  • Read: Section 8.3
November 2
  • Homework for Week 7 is due today.
  • The Dirichlet product
  • Read: Section 8.6
Week 9

November 5
  • Gaussian integers & sum of two squares
  • Read: Sections 10.1, 10.2 & class notes
November 7
  • Pythagorean triples
  • Read: Sections 11.1, 11.2 & 11.3
November 9
  • Homework for Week 8 is due today.
  • Classification of Pythagorean triples
  • Read: Sections 11.4 & 11.5
Week 10

November 12
  • LAST CLASS
  • Questions, Comments, Discussion of Final Exam, etc.