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