Winter Quarter 2005, Math 115A, Homework Assignments (And Miscellanea)


Miscellanea:

In this space, I shall post various articles, papers, etc. that may perhaps be of interest to some students taking the course:

(1) Here is an English translation of Euler's paper in which he showed that not all Fermat numbers are prime (cf. Problem 1 on Problem Sheet I): Euler

(2) Here is a recent paper of K. G. Hare that shows that any odd perfect number must have at least 69 (not necessarily distinct) prime factors: Hare

(3) Here is a recent paper of Green and Tao in which they prove that there are arbitrarily long arithmetic progressions of primes: Green-Tao

(4) Here is a recent paper of Andrew Granville on primality testing (in particular he discusses the recent work of Agrawal, Kayal and Saxena on a polynomial time primality test). Highly recommended!: Granville

(5) Here is a paper of Ram Murty on Artin's conjecture for primitive roots. (The journal reference for this atricle is: M. Ram Murty, `Artin's conjecture for primitive roots', Mathematical Intelligencer, vol. 10, no. 4 (Fall 1988), 59--62.): Murty

(6) Here is a link to a webpage (maintained by Franz Lemmermeyer) which lists a very large number of proofs of the law of quadratic reciprocity: Lemmermeyer

Homework 1 ( Assigned 1/6, due 1/13):
Do the problems on the following problem sheet:
  • Problem Sheet
  • Solutions


    Homework 2 ( Assigned 1/13, due 1/20):
    Do the problems on the following problem sheet:
  • Problem Sheet
  • Solutions


    Homework 3 ( Assigned 1/20, due 1/27):
    Do the problems on the following problem sheet:
  • Problem Sheet
  • Solutions


    Homework 4 ( Assigned 1/26, due 2/10):
    Do the problems on the following problem sheet:
  • Problem Sheet
  • Solutions


    Homework 5 ( Assigned 2/10, due 2/17):
    Do the problems on the following problem sheet:
  • Problem Sheet
  • Solutions


    Homework 6 ( Assigned 2/17, due 2/24):
    Do the problems on the following problem sheet:
  • Problem Sheet
  • Solutions


    Homework 7 ( Assigned 2/24, due 3/3):
    Do the problems on the following problem sheet:
  • Problem Sheet
  • Solutions


    Homework 8 ( Assigned 3/3, due 3/10):
    Do the problems on the following problem sheet:
  • Problem Sheet
  • Solutions