Math 346 SPRING 2010, 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, March 29: Overview. Chapter 0.

Wednesday, March 31: The Greatest Common Divisor and Least Common Multiple. Section 1.1. Here is homework!

Friday, April 2: The Division Algorithm. The Euclidean Algorithm. Sections 1.2-1.3.

Monday, April 5: Linear combinations. Section 1.4. We will have QUIZ on Friday!!!

Wednesday, April 7: More on linear combinations. Section 1.4. Here is homework!

Friday, April 9: Congruences. Section 1.5.

Monday, April 12: Mathematical Induction. Section 1.6.

Wednesday, April 14: 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 16: The Fundamental Theorem of Arithmetic. Sections 2.2-2.4.

Monday, April 19: The digit theorem. Any composite number has a divisor less than its square root. The set of primes is infinite. Sections 2.4-2.5. We will have QUIZ on Friday!!!

Wednesday, April 21: A formula for the number of divisors. The sum of divisors. Perfect numbers. Sections 2.6-3.1, 3.3. New homework!

Friday, April 23: Mersenne primes and Fermat primes. Section 3.4.

Monday, April 26: Multiplicative functions. Euler phi function. Sections 3.2, 3.5.

Wednesday, April 28: Solving congruences. Linear congruences. Section 4.1. New homework!

Friday, April 30: More on linear congruences. Section 4.1.

Monday, May 3: The Chinese Remainders Theorem. Section 4.2. We will have MIDTERM on Friday!!!

Wednesday, May 5: Euler and Fermat theorem. Section 4.3. Please find here practice problems for midterm. Here are the answers. New homework!

Friday, May 7: MIDTERM.

Monday, May 10: Orders of a modulo b. Wilson Theorem. Section 4.3.

Wednesday, May 12: Primality testing. Section 4.4. New homework!

Friday, May 14: RSA. Section 4.5.

Monday, May 17: Higher degree congruences. Section 5.1. We will have QUIZ (covering Chapter 4) on Wednesday!!!

Wednesday, May 19: Congruences with Prime Power Moduli. Section 5.2. New homework!

Friday, May 21: Quadratic Residues. Section 5.3.

Monday, May 24: Euler criterion for quadratic residues. Legendre symbol. Gauss Lemma. Sections 5.3-5.4. We will have QUIZ (covering Sections 5.1-5.3) on Wednesday!!!

Wednesday, May 26: Computation of the Legendre symbol (2/p). Section 5.4. Last homework (due next Friday)!

Friday, May 28: The Legendre symbol (3/p). The Pepin test. Sections 5.4 and 4.4.

Wednesday, June 2: The quadratic reciprocity. Sections 5.4-5.5. Please find here practice problems for the final. We will have QUIZ on Friday!!!

Friday, June 4: Sums of squares. Sections 7.2-7.3. Please find here the answers for the practice problems.

END