|TIME OF MEETING:||Mon, Wed, & Fri 10:10 - 11:05|
|PLACE:||Earth Science 144|
This course is an introduction to the most basic concepts of abstract algebra: groups, rings, and fields. The previous course “Classical Algebra” presented the study of groups, rings and fields through a careful analysis of many concrete classical examples.
This course aims toward understanding what is true in the same vein about large precisely defined classes of groups, rings, and fields. For example, every principal ideal domain is necessarily a unique factorization domain but not conversely.
The process of constructing a new ring from a given ring by passing to “congruence classes” emerges as the general quotient construction.
|Final examination||100||Fri., May 9, 10:30 - 12:30|
|Midterm test||50||Mon., Mar. 17, in class|
|Written assignments (5 @ 10 each)||50||as announced|
|Occasional quizzes (5 @ 5 each)||25||with little or no notice|
|Writing Intensive Requirments||--||Admission by permission|
Attendance at class meetings is a requirement for passing the course unless the student has been granted a special exception. Unexcused absence may result in failure or grade reduction. There will be no excused absences from tests except for compelling emergencies and religious holidays.
G. Chrystal, Algebra: An Elementary Textbook (2 vols.), Chelsea.
K. Ireland & M. Rosen, A Classical Introduction to Modern Number Theory, Springer.
M. Artin, Algebra, Prentice Hall.
N. McCoy & G. Janusz, Introduction to Modern Algebra, Allyn & Bacon.
A. Weil, Number Theory: An Approach through History, Birkhauser.
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