# Math 3230 - Fall 2017 Abstract Algebra I

Email kconrad at math dot uconn dot edu. (When you send an email message, please identify yourself at the end.)
Office hours W 10-11 and 3:30-4:30, or by appointment in MONT  234.
Course info
 Lecture T/Th 12:30-1:45 in MONT 113. Midterms: Sept. 28 (Thursday) and Nov. 9 (Thursday). Midterm 1 average: 64.4. Midterm 2 average: 64.8. Final: Dec. 16th, 8:00-10:00 AM in Monteith 113.

Text Required: Abstract Algebra: Theory and Applications, 2017 edition by Thomas Judson available online here.

Abstract Algebra Sites

Development of group theory.

Isometries of the plane.

The MathDoctorBob online group theory lectures.

Biographies of Cauchy, Cayley, Galois, Jordan, Klein, Lagrange, and Sylow.

A song about a group of order two.

Puzzle Sites

A 15-puzzle applet. A biography of its inventor, Sam Loyd.

I learned how to solve Rubik's cube (typically in 3 to 4 minutes) using the second solution described by Mark Jeays here (this link is to the Wayback Machine since the original site is no longer working) together with some thinking about orientation. He posted some videos about this on You Tube here.

Speed cubing, by Lars Petrus. (His initial remark on the mental aspects of speed cubing might be worth taking into account before you start.)

Erno Rubik and the history of his cube.

Course handouts

Applications of the Sylow theorems.

Statement and proof of the Sylow theorems.

Proof of Cauchy's theorem. (The proof in this file does not use group actions; a proof by group actions is at the end of the group actions handout above.)

Relativistic velocity and group theory (optional): an isomorphism relevant to physics.

Conjugation in a group.

A proof comparison (optional).

Dihedral groups.

The 15 puzzle and Rubik's cube (optional).

Sign of a permutation.

Subgroups of a cyclic group.

Proofs by induction.

Some tips on writing mathematics.

Recent Announcements

12/3: Final exam review will be on 12/13 at 7 PM in Monteith 110.

11/7: From now on, submit all homework assignments by email.

9/22: Exam 1 review will be on 9/25 at 6 PM in Monteith 226. See review material in course handouts section above.

8/29: First class.

5/4: Course page created.

Syllabus: We plan to cover the theory of groups, using both the textbook and course handouts. Our focus will be on the following topics.

• Cyclic and dihedral groups
• Symmetric and alternating groups
• Matrix groups (GLn, SLn, Aff)
• Cosets and congruences in a group; Lagrange's theorem
• Conjugacy classes; the class equation
• Homomorphisms; Cayley's theorem
• Normal subgroups and quotient groups; Cauchy's theorem
• Direct products
• Group actions
• Sylow's theorems and some applications

Prerequisites: Math 2710. You are expected to know something about writing proofs, although the course itself will provide a lot of further practice. If you did not develop in Math 2710 some skill with expressing mathematical ideas well and writing proofs, then you need to focus some serious efforts in that direction early on.

Course grade:  This will be based on the following weighting:

• homework (20%), quizzes (10%), first and second midterms (15% each), final exam (40%). The lowest homework and quiz grade will be dropped. This includes a grade of 0 for a homework or quiz that is not submitted. Your lowest midterm exam score will be replaced with the average of the original score on that exam and your final exam score if it is higher (i.e., if it benefits you).
Homework: Homework assignments will be posted on the bottom of this web page, and are due at the time and place indicated on the assignment. As a general rule, no late homeworks will be accepted. Read the homework guidelines here and pay close attention to the rules about submissions.
• An integral part of each homework is the assigned reading from the text or handout and the re-reading of your lecture notes. Focus on both explanations and examples.
• Homework will be done in student groups. The procedure will be discussed during class in the first week.
• You are encouraged to discuss homework problems with the instructor during office hours.
• It is a mistake to skip homework, because no skills (in mathematics, foreign language, athletics, and so on) can be learned by passive involvement, but only by regular practice. Moreover, many skills are learned over time, so do not expect to understand everything perfectly right away. You should find your understanding of basic topics improving gradually from one week to the next.
• Proofs on homeworks should not be simply a string of logical and mathematical symbols, but include complete sentences in English. The role of English is to explain the strategy of your proof and the details as well. There will not be partial credit based on having misunderstood a question.
Quizzes:  In weeks when homework is not due, there will be a short quiz at the start of one class, usually on Thursdays. The purpose of quizzes is to provide you some feedback about how well you are following the basic ideas of the course.
• The quizzes will be short.
• You are not allowed to bring any aids with you to the quiz.
• There are no makeup quizzes. If you miss a quiz, your grade is 0.
Exams:  There will be two midterms and a final.
• There are no makeup exams. If you miss a midterm, that midterm grade is 0.
• If you need exam accommodations based on a documented disability, you need to speak with both the Center for Student Disabilities and the course instructor within the first two weeks of the semester.

Attendance: Since you will be working in groups, your workmates can get frustrated if you regularly skip class and then cannot meaningfully contribute to the homework. This course involves a point of view on mathematics unlike anything you have met before. The best way to adjust is to come to class without exception, see examples and techniques discussed in real time, and ask lots of questions. The way you should think about the material will develop from the way it is presented in class.

Course conduct: To respect everyone's right to a productive learning environment, please refrain from disruptive activities during class. On a positive note, do feel free to ask questions!

Academic integrity: Students are expected to avoid academic misconduct. Your integrity is not worth losing (and the course not worth failing) by falsely presenting yourself in any aspect of this course. For further information on academic integrity, see Appendix A of the Student Code.

 Due Week of Homework Assignment 1. Aug. 28 2. Sept. 4 Avg: 88.8/100 Set 1. 3. Sept. 11 4. Sept. 18 Avg: 78.3/100 Set 2. 5. Sept. 25 6. Oct. 2 Avg: 87.4/100 Set 3. 7. Oct. 9 8. Oct. 16 Avg: 77.5/100 Set 4. 9. Oct. 23 10. Oct. 30 Avg: 90.0/100 Set 5. 11. Nov. 6 12. Nov. 13 Avg: 82.0/100 Set 6. 13. Nov. 20 None (it's Thanksgiving). 14. Nov. 27 15. Dec. 4 Avg: 71.3/100 Set 7.