Math 115, Summer 2016

Syllabus and Course Policies

Homework

• June 23: 1.2 1ab, 3ab, 7, 23, 46 1.3 9, 11
• June 30: 1.3 17, 31, 41 1.4 5, 17 2.1 11, 27 2.3 2, 32
  Bonus: Write an identity (other than the ones in the textbook) that can be proven by counting a set in two ways, and demonstrate how to count them.
• July 7: 2.6 1, 10 2.4 20 2.5 3, 4 2.7 2, 6, 7 Bonus: 2.6.11
• July 14: 4.1 1, 9 4.2 4, 13 4.4 2, 7, 9
• July 21: 7.1 1, 5 7.3 3, 5 7.4 5 7.5 2
• July 28: 7.8 2 3.1 3, 9, 13 3.2 3, 6, 13
• Aug. 4: 3.4 2, 4, 6 3.5 1, 4, 9 3.6 4
• Aug. 9: 5.3 2, 3, 11, 17 5.4 1, 10, 12

Schedule of Quizzes

• Quiz 1: June 23rd
• Quiz 2: June 30th
• Quiz 3: July 7th
• Midterm: July 14th
• Quiz 4: July 21st
• Quiz 5: July 28th
• Quiz 6: August 4th
• Final: August 11th
The final may include any or all topics covered in lecture, with particular emphasis on those also discussed in the textbook. Two pages of double-sided, max 8.5x11in cheat sheets will be permitted for the final.

Outline of Topics Covered

• June 20th: Introduction
• June 21st: Divisibility, Primes (1.2, 1.3)
• June 22nd: Binomial Theorem (1.4)
• June 23rd: More on Polynomials; Interpolation
• June 27th: Congruences (2,1. 2.2)
• June 28th: Chinese Remainder Theorem (2.3)
• June 29th: More on Chinese Remainder Theorem
• June 30th: Prime Power Moduli (2.6)
• July 5th: Cryptography (2.5)
• July 6th: Prime Moduli (2.7)
• July 7th: Primitive Roots (2.8)
• July 11th: Arithmetic Functions (4.1, 4.2)
• July 12th: Recurrence Relations (4.4)
• July 13th: Review
• July 14th: Midterm
• July 18th: Continued Fractions (7.1-7.3)
• July 19th: Approximations of Irrationals (7.4-7.6)
• July 20th: Quadratic Irrationals (7.7)
• July 21st: Pell's Equation (7.8)
• July 25th: Quadratic Residues (3.1)
• July 26th: Quadratic Reciprocity (3.2)
• July 27th: Jacobi Symbols (3.3)
• July 28th: Quadratic Forms (3.4)
• Aug 1st: More Quadratic Forms (3.4)
• Aug 2nd: Reduction of Quadratic Forms (3.5)
• Aug 3rd: Pythagorean Triples (5.3)
• Aug 4th: Infinite Descent (5.4)
• Aug 8th: Rational Points on Curves (5.6)
• Aug 9th: Elliptic Curves (5.7)
• Aug 10th: Review
• Aug 11th: Final