Math 411 Introduction to Abstract Algebra I


Instructor: Ralf Schiffler
Office: LGRT 1342
Phone: (413) 545-2871
E-mail: schiffler at math dot umass dot edu
Office Hours: Mon, Wed 2-3 PM or by appointment        		Schedule: MF 10:10 - 11:00  in  LGRT 121
Text: Algebra: Pure and Applied, Aigli Papantonopoulou, Prentice-Hall, Inc. 2002.
Syllabus (in PDF)
Make-up policy for exams

Exams

 
Grading:  Course Grade = Homework (30%) + Midterm 1 (20%) + Midterm 2 (20%) + Final (30%)

Final Exam:        Solutions

Wed May 23
8-10 am
LGRT 321
No notes allowed


An old exam ...                            ... and its solution

Homework

Homework #1: (due Mon, Feb 12)
Section 1.1: # 4, 9, 11, 18
Section 0.3: # 24
read sections 0.3 and 1.2
Homework #2: (due Wed, Feb 21)
Section 1.1: # 14, 19, 28, 29  [Hint for # 29: Use # 28 and the equation a²-1=(a-1)(a+1).]
read section 1.3
Homework #3: (due Mon, Feb 26)
Section 1.2: # 7, 14, 20, 26, 28, 30

Homework #4: (due Mon, Mar 5)
Section 1.2: # 32, 34
Section 1.3: # 1, 4, 14, 16
Bonus : Show that (R,+), the group of real numbers under addition, is not cyclic.
read section 1.4

Homework #5: (due Mon, Mar 12)
Section 1.4: # 10, 12, 16, 26, 35

Homework #6: (due Wed, Mar 28)
Section 2.1: # 8, 17, 21, 28, 38

Homework #7: (due Mon, Apr 2)
Section 2.2: # 4, 8, 18, 19, 40, 48
Read Section 2.3

Homework #8: (due Mon, Apr 9)
Section 2.3: # 5, 7, 9, 13, 23
Read Sections 2.5 & 3.1

Homework #9: (due Tue, Apr 17)
Section 2.4: # 5,16, 19
Section 2.5: # 4, 7
Bonus:  Section 2.5: # 22
Try also (but do not hand in) Section 2.4:  1-3, 7-9
Read Sections  3.2 and 3.3

Homework #10: (due Mon. Apr 23)
Read Sections 4.1 and 4.2

Homework #11: (due Mon. Apr 30)
Section 3.4: # 11
Section 4.1: # 3, 4, 5,
Section 4.2: # 1, 5    
(Note that G acts faithfully on X iff the only element of G that fixes every element of X is the identity e in G)
Read Sections 4.4 and 4.5

Homework #12: (due Wed. May 9)
Section 4.2: # 10
Section 4.3: #  4, 7
Section 4.4: #  15, 18
Bonus:: Section 4.4: # 26 (Hint: Use the class equation)