ALGEBRA I

Last Update : May 26, 1998

Teaching Staff in AY1997 : Hiroshi SUZUKI
- Office : NS-S309, Tel.:3292, E-mail:hsuzuki@icu.ac.jp
Term and Schedule : Spring Term, Mon + Thurs 4
Class Room : NS-S312
Class Schedule
Refernces
List of Exercises
- Ex.1, Ex.2, Ex.3, Ex.4, Ex.5,
  Ex.6, Ex.7, Ex.8, Ex.9, Ex.10
AY1998 Take-Home Midterm Test
- Solutions
AY1996 Midterm Test
AY1996 Final Test
Classes in AY1998
Index

Month/Day	Title	Subjects
April 13	Definition and Examples of Groups	Semigroup, Monoid, Group, Basic Properties
16	Subgroups	Cyclic Subgroups, Permutation Groups
20	Recitation
23	Recitation
27	Cosets	Equivalence Relations, Classes, Lagrange's Theorem
30	Cyclic Groups	Subgroups of Cyclic Groups, Finite and Infinite Cyclic Groups
May 7	Recitation
11	Recitation
14	Normal Subgroups	Normal Subgroups and Factor Groups,Normalizer and Centralizer
*18	Isomorphism and Homomorphism	Kernels and Images of Homomorphisms
*21	Recitation
25	Recitation
28	Isomorphism Theorems	Isomorphisms and their Applications
June 1	Group Actions	Orbits, Stabilizers, Transitivity
4	Fundamental Theorem of Abelian Groups	Direct Product of Cyclic Groups and System of Invariants
8	Recitation	Sylow's Theorem
11	Recitation
15	Recitation and Review

Take-Home Midterm is scheduled in mid May.
Final will be given during the final week.
Recitation problems are not assigned. Please solve them and present them on the board voluntarily.

Hiroshi Nagao, "Daisugaku", Asakura Publisher (in Japanese)

Very well written and widely used but a bit difficult for individual study. This text book will be used in Algebra II and III.

(References for Algebra including groups, rings, fields and modules

Serge Lang "Undergraduate Algebra" second edition, Springer-Verlag
Widely used text book. Lang writes a lot of popular text books.
Serge Lang "Algebra" third edition, Addison-Wesley Graduate student's level text book. The material is widely covered but it is possible to read. I, Suzuki, read this as students seminar with friends from sophomore to senior when I was a student.
van der Waerden "Modern Algebra", Springer
Classical text book.
(Text book of group theory.)
Michio Suzuki, Group Theory I, II, Springer.
The best text book of group theory in the world. (Translation of Japanese version.) There will be International Symposium in honor of Professor Suzuki's 70 birthday at ICU. For further information see its Home Page