Course No.：S070101ZY001
Course Category：Professional Course
Period/Credits：40/2
Prerequisites：Abstract algebra; commutative algebra; homological algebra; algebraic topology
Aims & Requirements：
The course is the professional course for all students for the master and PhD degree in the department of mathematics, also can be the elective course for other departments, the students who choose the course need the basic knowledge about abstract algebra, commutative algebra and homological algebra; algebraic topology and some other relative knowledge.
The course uses Rosenberg’s “Algebraic K-Theory and Its Applications” as the text book to teach the fundamental theorem in algebraic K-theory and its relative applications. We encourage students to finish the exercises in the textbook which can help them to understand its language, method, ideas and basic results of modern algebraic K-theory which initiated by Grothendieck in 1959 and developed by many great mathematicians.
Primary Coverage：
Chapter 1
definition of -group of a ring, -group of specific rings, relative -group, excision of -group and applications of -groups.
Chapter 2
definition of -group of a ring, -group of specific rings, relative -group and applications of -groups.
Chapter 3
-group of an exact category, -group of an exact category, negative K-theory, the fundamental theorem of the algebraic K-theory.
Chapter 4
homology of a group, definition of -group of a ring and applications of -groups.
Chapter 5
definition of higher K-group, basic properties and its applications of higher K-groups.
Teaching Material
Jonathen Rosenberg, Algebraic K-Theory and Its Applications, Springer, GTM147, 1994
References：
[1] Jonathen Rosenberg, Algebraic K-Theory and Its Applications, Springer, GTM147, 1994
[2] Milnor, Introduction to Algebraic K-Theory, Annals of mathematics Studies, Vol 72, Princeton University Press, 1971
Author：Guoping Tang（Academy of Mathematics and Systems Science）
Date：June, 2009
