MATH 417: Group Theory
MWF 1130 – 1220 PM
Spring 2015
Section 001
Prof. Tim Susse
e-mail: [email protected]
Office: AH308
Office Hours: By Appointment
websites: www.math.unl.edu/~tsusse2
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Topics:
• Set Theory and other background
• Equivalence Relations
• Binary Operations, Definition of a Group
• Products & Quotients
• Symmetry Groups & Other Examples
• Sylow’s Theorems
• Infinite Groups, Free Groups, Presentations
• Homomorphisms
ACE Outcome 10: This course satisfies ACE Outcome 10: “Generate a creative or scholarly
product that requires broad knowledge, appropriate technical proficiency, information collection,
synthesis, interpretation, presentation, and reflection.” The course will focus on technical proficiency
and presentation of information through proof writing, as well as synthesis and interpretation of
abstract Mathematical ideas.
Required Textbook: Saracino, Dan Abstract Algebra: A First Course, Second Edition. Pearson/Addison Wesley, 2008. ISBN-13: 978-1577665366.
Attendance: Due to the sequential nature of this course, attendance is vital for achieving the
outcomes listed above. So, you are expected to attend every class. You are responsible for
any announcements made in class, for the material discussed in class, and for reading the textbook.
Please be advised that more than two unexcused absences and/or recurrent tardiness will
most likely result in your final grade being lowered. Leaving class early is considered the
same as arriving late.
Grades: Your performance in this course will be evaluated using weekly homework, two in-class
midterms and a final exam. Approximate dates for these can be found in the course outline. Your
grade will then be computed as follows:
Tests (20% each)
Homework
Final Exam
Total
40%
30%
30%
100%
ADA Notice: Students with disabilities are encouraged to contact the instructor for a confidential
discussion of their individual needs for academic accommodation. It is the policy of the University
of Nebraska-Lincoln to provide flexible and individualized accommodation to students with documented disabilities that may affect their ability to fully participate in course activities or to meet
course requirements. To receive accommodation services, students must be registered with the
Services for Students with Disabilities (SSD) office [http://www.unl.edu/ssd/home], 132 Canfield
Administration, 472-3787 voice or TTY.
Course Evaluation: The Department of Mathematics Course Evaluation Form will be available through your Blackboard account during the last two weeks of class. You’ll get an email when
the form becomes available. Evaluations are anonymous and instructors do not see any of the responses until after final grades have been submitted. Evaluations are important—the department
uses evaluations to improve instruction. Please complete the evaluation and take the time to do so
thoughtfully.
Departmental Grading Appeals Policy: Students who believe their academic evaluation has
been prejudiced or capricious have recourse for appeals to (in order) the instructor, the departmental chair, the departmental appeals committee, and the college appeals committee.
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Course Outline
The following table shows the material expected to be covered and the corresponding tentative
problem assignments for each week of the semester. Note that what is shown here is approximate;
please be alert for changes throughout the semester.
Week of
January 12
January 19
January 26
February 2
February 9
February 16
February 23
March 2
March 9
Sections
Syllabus
Section 0: Set Theory & Notation
Section 1: Binary Operations
January 19 is MLK day
Section 2: Definition of a Group
Examples of Groups
Friday, January 23 is the last day to file a drop to remove course from student’s record
Section 3: Basic Properties of Groups
Section 4: Cyclic Groups
Section 5: Subgroups
Section 7: Groups of Functions
Section 8: Symmetric Groups & Cayley’s Theorem
Section 6: Direct Products
Section 9: Cosets & Equivalence Relations
Section 10: Lagrange’s Theorem
Review/Catch-up
Midterm 1 on Wednesday, February 25
Section 11: Normal Subgroups
Section 12: Homomorphisms
Section 13: Isomorphism Theorems
Friday, March 6 is the last day to change to P/NP
Section 14: Classification of Finite Abelian Groups
Group Actions on Sets
March 16
March 23
March 30
April 6
April 13
April 20
April 27
More Group Actions – the Orbit-Stabilizer Theorem
Section 15: Sylow’s Theorems
Counting Groups
No Classes: Spring Break
Other Types of Groups
Catch-up Week
More Catch-up & Review
Midterm Exam 2 is Wednesday, April 8
Automorphism Groups
Friday, April 10 is the last day to withdraw from one or more courses
Semi-direct Products
Free Groups
Properties of Free Groups
Group Presentations
Cayley Graphs
Geometry for Infinite Groups
Algorithmic Problems in Group Theory
Catch-up & Review
The Final Exam is 3:30 pm – 5:30 pm, Wednesday, May 6