MA743 Algebraic Number Theory I
				 Fall 2002
 
Professor: 		Dan Abramovich
Office: 		MCS 232
Phone: 			353-9547
E-mail: 		abrmovic@bu.edu
Course meets: 		Mon,Wed,Fri 10:00-11:00am at MCS B29
Office hour: 		(TBA) Mon 2-3, W,F 11-12

Text: Number Fields, by Daniel A. Marcus

Prerequisites: 
  MA741-742 or equivalent understanding of graduate level algebra. 
  Basic complex analysis.

Material covered: Chapters 1-7

Number fields and Rings of integers; Prime decomposition, ramification and
splitting; Algebraic invariants: discriminant, ideal class group, unit group;
The Zeta function; The Class Number Formula.

Homework will be assigned but not graded. A biweekly portion of class or
additional time will be devoted to problems.

Grades based on two take-home exams, which will in turn be based on
homework-type problems. 

The book has the advantage that we can quickly get to significant material
without an enormous amount of preliminary topics. It has the disadvantage that
it ignores, or sometimes delegates to the exercises, material which a serious
number theorist must know, like localization in number rings, differents,
fractional ideals, and more.

An alternative to one take-home exam will be to study and write a summary of
one of these omitted topics.