Lecture Abstract Algebra

 

 

Course TaskThe first objective is to learn about algebraic structures, to get a profound knowledge about groups, rings and modules and basics in Galois theory. It will be connected with number theoretical and geometric applications. Secondly we strengthen the ability to workout and write abstract proofs in a more academic way.

 

Course ContentsThe algebraic behavior of real vector spaces carries over to a much wider class. Replacing the field of real numbers by a (more general) ring provides a theory with a much more diverse picture. Modules, the analogue for vector spaces, do not need to carry a basis anymore. Rings carry a beautiful set of ideals, which one could think about as a generalization of divisors of integers. Analyzing the behavior of ideals is very successful for proving difficult number theoretical problems. The theory of abstract algebra occurs in almost all mathematical directions. In this course we will learn about:

 

groups, rings, ideals, modules , number theoretical applications, Galois theory, localization, local-global principle

 

Here is the modified syllabus.

 

Literature:

  1. Lang, Serge Algebra, Springer, 2002, ISBN 978-7506271844
  2. Artin, Michael, Algebra, 2nd edition. Pearson, 2011, ISBN 978-0132413770
  3. Dummit, David S. and Foote, Richard M, Abstract Algebra, 3rd edition, John Wiley & Sons, 2003, ISBN 978-1119222910
  4. Frederick M. GoodmanPrentice Hall, Algebra Abstract and concrete; 1st edition (March 1, 1998), ISBN 978-0132839884

 

 

 

 

Problem sheets: Sheet 1, Sheet 2, Sheet 3, Sheet 4, Sheet 5,   Sheet 6  Sheet 7

Sheet 8  Sheet 9 Sheet 10 Sheet 11

   Hint for the solution of Problem 11.1  

Sheet 12 Sheet 13 Sheet 14  Sheet 15*

 

 

 

Final:  The final takes place in the teaching building room 404 on Thursday the 24th of June 2021 from 8:30 to 11:30 am.

 

Lecture notes: pages 1-160  161-178   179-223   224-264

 

 

Shanghaitech University

Teaching building 404

 

Tuesdays and Thursdays 8:15-9:55

Start 23rd of February 2021

 

Office hours: Tuesdays 10-11 IMS413

 

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© Daniel Skodlerack