NEW: Grades may be filed a few days later than the deadline of Monday, January 2. My apologies for the inconvenience.
A review session has been scheduled for Sunday, December 18 from 4:10 to 5:30 pm in 312 Math. Please bring your questions, as there are no other agenda.
The final examination will take place as planned on Tuesday, December 20 from 4:10 to 7 pm in 312 Math. Best of luck!
Practice Midterm #1 and
Answers
Midterm Examination #1 and
Answers
Practice Midterm #2 and
Answers
Midterm Examination #2 and
Answers
Practice Final Exam and
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Final Examination and
Answers
Modern Algebra II is being rescheduled and will be offered in Spring 2017 at the same time as this course, Tuesdays and Thursdays 4:10-5:25 pm. Sorry for the inconvenience.
Assignment #1, due Monday,
September 12 at 5 pm.
Assignment #2, due Monday,
September 19 at 5 pm.
Assignment #3, due Monday,
September 26 at 5 pm.
Assignment #4, due Monday,
October 3 at 5 pm.
Assignment #5, due Monday,
October 10 at 5 pm.
Assignment #6, due Monday,
October 17 at 5 pm.
Assignment #7, due Monday,
October 24 at 5 pm.
Assignment #8, due Monday,
October 31 at 5 pm.
Assignment #9, due Wednesday,
November 9 at 5 pm.
Assignment #10, due Wednesday,
November 16 at 5 pm.
Assignment #11, due Wednesday,
November 23 at 5 pm.
Assignment #12, due Wednesday,
November 30 at 5 pm.
Assignment #13, due Wednesday,
December 7 at 5 pm.
Assignment #14, due Wednesday,
December 14 at 5 pm.
Since Election Day we have switched to Wednesday due dates for the assignments.
Hand in your assignments to the collection box marked "Intro to
Modern Algebra" outside 417 Mathematics.
Remember that the use of a staple or paper clip is absolutely
compulsory.
Also, the entire assignment must be handed in at once. Addenda
to your assignment will not be graded.
Unfortunately, electronic submission of assignments (by fax or
e-mail) cannot be accepted. Only a physical copy in the
collection box will do. If you must be out of town, please ask
a fellow student to print out and submit your assignment.
Tentative list of topics
A table is given below of topics to be covered in the course from
October onwards, together with relevant sections of both recommended
texts. Several disclaimers apply.
(1) The presentation in lecture will not closely follow either
text and may include facts presented in other sections, or not at all, in one text or the other.
(2) The last few topics may or may not be covered, depending on timing.
(3) The lecturer reserves the right to permute or alter the topics at any time!
| Topic | Fraleigh | Dummit & Foote |
|---|---|---|
| Groups and examples | 1.3 | 1.1 |
| Subgroups | 1.4 | 2.1 |
| Cosets & Lagrange's theorem | 2.3 | 3.2 |
| Order of an element | 1.4 | 1.1 |
| Subgroups generated by subsets | 1.5 | 2.4 |
| Dihedral group, quaternion group | 2.1 | 1.2, 1.5 |
| Homomorphisms | 3.1 | 3.1 |
| Kernel & image | 3.1 | 3.1 |
| Normal subgroups | 3.1 | 3.1 |
| The isomorphism theorems | 4.1 | 3.3 |
| Cycles in the symmetric group | 2.2 | 1.3 |
| Sign & the alternating group | 2.2 | 3.5 |
| Simplicity of the alternating group | 3.3 | 4.6 |
| Simple groups | 3.3 | 3.4 |
| The Jordan-Hölder theorem | 4.1 | 3.4 |
| Group actions | 3.5 | 4.1 |
| Cayley's theorem | 2.1 | 4.2 |
| Orbits & stabilizers | 3.5 | 4.1 |
| Burnside's lemma | 3.6 | |
| Orbit counting & conjugation | 4.3 | 4.3 |
| The Sylow theorems | 4.2 | 4.5 |
| Groups of order 12 | 4.5 | |
| Semidirect products | 5.5 | |
| Abelian groups | 2.4 | 5.1 |
| The Chinese remainder theorem | 2.4 | 5.1 |
| Classification of finite ab gps | 2.4 | 5.2 |
| Classification of finitely gen ab gps | 2.4 | 5.2 |
| Free groups | 4.5 | 6.3 |
| Generators & relations | 4.6 | 1.2 |