• Text: Ireland and Rosen, A Classical Introduction to Modern Number Theory,(2nd edition), Springer, Graduate Text in Math, vol.84, 1990
  • additional recommended reading: Niven and Zuckerman, Borevich and Shafarevich, Serre (course in arithmetic), Janusz.
  • Suggested problems from Ireland and Rosen
  • P.14. 6,7,10,11,14,23,25-28,34
  • P.18. Exercise
  • P.26. 4,5,7-11,13-15
  • P.36. 4,5,10,11,14,15
  • P.48. 1,2,18
  • P.63. 1,2,4,5.
  • P.77. 9-12, 18, 21
  • Question on Z_p: let Y=(y_1,y_2,...) not belong to Z_p. Say y_n does not reduce to y_(n-1). Let A_i = Z/p^i. Consider the set in Product (A_i) consisting of {y_1}X...{y_n}XA_(n+1)XA_{n+2}X..... This set clearly contains Y, does NOT meet Z_p, and is a sub-basic open set in the product since A_i is given the discrete topology. So Z_p is closed in the product.
  • P.86. 4,6-8,10,11,14,16-21.
  • P.105. 1-6.

    FINAL

    Information on Final

  • Time: Friday, May 11, 8-10 AM.
  • Place: Vincent Hall 301
  • Office Hours 11-12, Thursday May 10.
  • Please note: exam is comprehensive covering the semester's work. You are allowed to bring a page 8.5 by 11 with notes.
  • Some suggested practice problems:
  • Herstein Page 227. 7,13,14
  • Page 232. 9
  • Page 236. 12,13.
  • Page 249. 16.
  • Page 256. 1,3
  • Page 177. 14
  • Page 183. 7,8,9,10,16
  • Page 199. 10,12
  • Page 205.10, 12
  • Page 215. 5,6,15
  • Page 219. 2
  • I hope to add more practice problems from Herstein Chapter 6.
  • Page 312. 5,6