Abstract Algebra 5210 and 4210 - (Fall 2017)


Instructor: Ralf Schiffler
Office: MONT 336
Phone: (860) 486-8381
E-mail: schiffler at math dot uconn dot edu
Schedule:
TT 2:00-3:15 in MONT 111
Office Hours:
Tu 3:15-4:15, Wed 3-4 or by appointment


Exams:
Midterm Exam: Tue Oct 24, 6:00 PM - 8:00 PM in MONT 226

Final Exam:
Sat Dec 16, 10:30-12:30 in MONT 111     
The final exam is cumulative.

Description: 
Group theory: quotient groups, direct product, group actions, Sylow theorems, semidirect product,
universal mapping properties
Ring theory: ideals, quotient rings, rings of fractions, Euclidean domains, principal ideal domains, polynomial rings,
Module theory:
free modules, direct sums, homomorphisms, submodules, quotient module, vector spaces, basis, dimension.

Prerequisites: You are supposed to be already familiar with the following topics:
Groups, homomorphisms,
subgroups, cyclic groups, cosets, normal subgroups, Theorems of Lagrange and Cauchy, Integers modulo n, Chinese remainder theorem, rings and fields.

Textbook:  
Dummit and Foote, Abstract Algebra, third edition, Wiley and Sons.
QA162.D85 2004.


This is the book I will use most of the time. It will also be the textbook for the second part of the course Abstract Algebra II in the spring.
image


Other textbooks: 
... because sometimes it is nice to see things from a different point of view ...

- Lang, Algebra, QA154.3.L3 2002
- Godement, Algebra, QA155G5913
- Rotman, Theory of groups, QA171R67 1973
- Artin, Algebra, QA154.2.A77 1991

These books are available in the Library.  

Course Grade: 3 homework assignments, 1 midterm, 1 final exam (cumulative)

Homework
30 %

Midterm 1

30 %

Final Exam

40 %



Following up on discussions or questions in class:
- For a classification of groups with planar subgrouplattices see page 3 of this paper. Thanks to Jack for finding this.

Practice Exercises: Here is a list of practice exercises from which you can choose. These will not be handed in.

Section
Exercise

Section Exercise
1.2
1-8

7.1 1-10,13,14,18,21,23-26
1.3
1-7

7.2
1-5
1.4
1-11

7.3
1-8, 10,19,22,26,28-32,34
1.5
1-3

7.4
4,5,7-11,13,15,19,26,27,30-32
1.6
1, 7-9, 11, 13-18, 20
7.5
4
2.1
1,3,4,6-12,16,17

8.1
7, 8a,9-11
2.2
1-4,7,10,12-14

8.2
1-3,5
2.3
1-3,6-8,11,12,15

8.3
1,2,5,6
2.4
1,2,5-12

9.1
1-7,15,16
2.5
2,3,4,8,9,11,12,15

9.2
1-5,8
3.1
1,4,5,10,11,17,21,24,35,36-41

9.3
3
3.3
1,4

9.4
1,2,5-8
3.5
2-4,6,9,13

10.1
1,3-12,17-20,
4.1
1,2,9

10.2
1-6,9
4.2
1-3,5a,7

10.3
1,3-7,9-15,23,27
4.3
2-8,10,12,22,25,31,32



4.4
1,3,10,17



4.5
1-7,13,17,22,24,26



5.1
1,5,7



5.2
1,4,9



5.4
1-5,10,13



5.5
1-3,6,7





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