Math 346 SPRING 2017, List of lectures

On this page I will post content of all lectures with reference to the book. All handouts also will be posted here.

Monday, April 3: Overview. Chapter 0.

Wednesday, April 5: The Greatest Common Divisor and Least Common Multiple. Section 1.1. Here is homework!

Friday, April 7: The Division Algorithm. The Euclidean Algorithm. Sections 1.2-1.3.

Monday, April 10: Linear combinations. Section 1.4. We will have QUIZ on Friday!!!

Wednesday, April 12: More on linear combinations. Section 1.4. New homework!

Friday, April 14: Congruences. Section 1.5. Here are solutions to the quiz.

Monday, April 17: Mathematical Induction. Section 1.6. We will have QUIZ on Friday!!!

Wednesday, April 19: Strong Principle of Induction. Primes and composite numbers. Why uniqueness of prime decomposition is not obvious. Sections 2.1-2.2. New homework!

Friday, April 21: The Fundamental Theorem of Arithmetic. Sections 2.2-2.4. Here are solutions to the quiz.

Monday, April 24: Any composite number has a divisor less than its square root. Sections 2.4-2.5. We will have QUIZ on Friday!!!

Wednesday, April 26: The set of primes is infinite. The digit theorem. A formula for the number of divisors. The sum of divisors. Sections 2.6-3.1, 3.3. New homework!

Friday, April 28: Perfect numbers. Mersenne primes. Sections 3.3-3.4. Here are solutions to the quiz.

Monday, May 1: Fermat primes. Euler phi function. Sections 3.4-3.5. We will have QUIZ on Friday!!!

Wednesday, May 3: Solving congruences. Linear congruences. Section 4.1. New homework!

Friday, May 5: More on linear congruences. Section 4.1. Here are solutions to the quiz.

Monday, May 8: The Chinese Remainders Theorem. Section 4.2. We will have MIDTERM on Friday!!! Please find here practice problems for midterm.

Wednesday, May 10: Euler and Fermat theorem. Section 4.3. Here are the solutions to practice midterm. New homework!

Friday, May 12: MIDTERM. Here are solutions.

Monday, May 15: Order of a modulo b. Section 4.3. We will have QUIZ on Friday!!!

Wednesday, May 17: Primality testing. Section 4.4. New homework!

Friday, May 19: RSA. Section 4.5. Here are (now corrected!) solutions to the quiz.

Monday, May 22: Higher degree congruences. Section 5.1. We will have QUIZ on Friday!!!

Wednesday, May 24: Congruences with Prime Power Moduli. Section 5.2. New homework!

Friday, May 26: Quadratic Residues. Section 5.3. Here are solutions to the quiz.

Monday, May 29: no classes, Memorial Day.

Wednesday, May 31: Euler criterion for quadratic residues. Legendre symbol. Section 5.3. We will have QUIZ (covering Sections 5.1-5.4) on Monday!!!

Friday, June 2: Gauss Lemma. Computation of the Legendre symbol (2/p). Section 5.4. Last homework (due next Friday)!

Monday, June 5: The Legendre symbol (3/p). The Pepin test. Sections 5.4 and 4.4. Please find here practice problems for the final. Here are solutions to the quiz.

Wednesday, June 7: The quadratic reciprocity. Sections 5.4-5.5.

Friday, June 9: Jacobi symbol. Flipping a coin over the phone. Section 5.5. Please find here solutions for the practice problems.

END