Math 348 SPRING 2019, 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 1: Numbers in other bases. Sections 13-14. Here is homework!

Wednesday, April 3: Fractions in the decimal base. Section 15.

Friday, April 5: Periods of fractions. Section 15.

Monday, April 8: More on fractions. Section 15. We will have QUIZ on Friday!!!

Wednesday, April 10: Pythagorean triangles. Section 16. New homework!

Friday, April 12: Pythagorean triangles and the Unit circle. Section 16. Here are solutions to the quiz.

Monday, April 15: Quadratic Equations and Infinite descent. Sections 16-17. We will have QUIZ on Friday!!! Handout on the Unit Circle.

Wednesday, April 17: Legendre's theorem. Handout (by Pete Clark) on Legendre's Theorem (only Section 2 is important for us). New homework!

Friday, April 19: Great Fermat Theorem for n=4. Section 17. Here are solutions to the quiz.

Monday, April 22: Sums of two squares. Section 18.

Wednesday, April 24: Primes which are sums of two squares. Section 18. New homework!

Friday, April 26: Sums of two squares: proof. Section 18.

Monday, April 29: Sums of four squares. Section 19. We will have QUIZ on Friday!!!

Wednesday, May 1: Square-triangular numbers. Section 20 and handout. New homework!

Friday, May 3: Pell's equation for square-triangular numbers. Section 20. Here are solutions to the quiz.

Monday, May 6: General Pell's equation. Section 20.

Wednesday, May 8: Generalized Pell's equation. Section 20. New homework!

Friday, May 10: Diophantine Approximation. Section 20. Please find here practice problems for midterm.

Monday, May 13: Pell's equation always has a nontrivial solution! Section 20 and handout. We will have MIDTERM on Friday!!!

Wednesday, May 15: First look at continued fractions. Section 20. Here are solutions to the practice midterm.

Friday, May 17: Midterm. Here are solutions.

Monday, May 20: Periodic continued fractions. Section 20 and handout.

Wednesday, May 22: Continued fractions and Pell's equation. Section 20. New homework!

Friday, May 24: Distribution of prime numbers. Section 21.

Monday, May 27: Memorial Day, no classes.

Wednesday, May 29: Middle binomial coefficient and primes. Section 21. We will have QUIZ on Friday!!! Last homework!

Friday, May 31: Bounds for prime counting function. Sections 21. Here are solutions to the quiz.

Monday, June 3: Bertrand postulate. Sections 21-22. Please find here practice problems for the final.

Wednesday, June 5: Gauss circle problem. Handout.

Friday, June 7: Review. Here are solutions to the practice final.

END