M 373K Algebraic Structures I: Fall 2024

Day/Time: TTH 9:30 - 11am; Location: PMA 5.120; Unique: 54090

Instructor
Mirela Ciperiani (mirela at math dot utexas dot edu); Office: PMA 12.164

Office Hours
TBA in PMA 12.164 or Zoom.

Text
Algebra (2nd edition) by Michael Artin, Prentice Hall. We will cover material from chapters 2, 6, 7, 11, 12. The book should be available at the University Co-op.

Prerequisites
Either consent of Mathematics Advisor, or two of M341, 328K, 325K (Philosophy 313K may be substituted for M325K), with a grade of at least C.

Exams
Midterm Exam I: Thursday, September 26, 9:30 -11am in PMA 5.120
Midterm Exam II: Thursday, November 14, 9:30 - 11am in PMA 5.120
Final Exam: Monday, December TBA, tba in PMA 5.120
  • Notes, books, computers, phones, and calculators cannot be used or even be visible during exams.
  • Your final exam grade will replace the lower of your two midterm exam grades, if the final exam score is higher than either of them.
  • Students will be excused from the exams only because of a serious illness or another emergency of similar gravity. In such a case you must contact me via email before the exam (if physically possible) and have documentation indicating your inability to take the exam at the scheduled time. In such a case the grade weight of a midterm will be shifted to the following exams in the most advantageous way for the student and a make-up final will be given.

Use of Class Time
Tuesdays: Standard lecture style with about 15 mins probably at the end available for questions (about homework or general material covered).
Thursdays: For the first 20 mins the class will break into small groups and work on a homework problem, then we come together and discuss. When we are done, we will proceed with new material in a lecture format.

Homework
  • The homework assignments will be posted on Gradescope by Friday morning each week and will be due the following Wednesday at 11pm.
  • No late work will be accepted. We will drop the two lowest assignment scores to allow for legitimate reasons for not turning in or underperforming in an assignment.

Grading
Homework 20%
Midterms 20% (each)
Final exam 30%
Participation in the problem solving portion of class 10%
  • The grade of the final exam will replace the lowest of the two midterm grades if it is better than either of them.
  • Plus/minus grades will be assigned for the final grade in this course.
  • All your grades will be posted on Gradescope. It is your responsibility to insure that your grades are recorded correctly on Gradescope. If an error occurs you must alert the instructor within two weeks from the date when the correct grade should have appeared.
  • On all work, your grade will be computed as a percentage: the number of points you earned divided by the number of points possible. The percentages of each type of work that will be used to compute your final grade are given above. Your letter grade will be given based on your numerical average earned in the class, on a scale not stricter than the following: you are guaranteed a D for 40 or above, C- for 50 or above, C for 55 or above, C+ for 65 or above, B- for 70 or above, B for 75 or above, B+ for 85 or above, A- for 90 or above, and an A for 93 or above.

Conflicts
Students with special concerns, be they athletes who might miss class meetings, students with religious observances that interfere with class meetings, or students with disabilities who need special accommodation, are all supposed to notify the instructor about these special needs.

Disabilities
Students with disabilities may request appropriate academic accommodations from the Division of Diversity and Community Engagement, Services for Students with Disabilities, 512-471-6259.

Student Conduct
  • Attendance: This course is structured with the expectation that you will attend every class. Please join the class on time; joining late will affect your ability to benefit from the class and may disturb others.
  • Participation: I appreciate your questions. Having a discussion about one person's confusion (whatever the cause) helps others in various ways. So, please don't hesitate to interrupt me.
  • Academic Honesty: Copying your written work from somebody else or from any other source is considered cheating and will be dealt with severely. Cheating will be penalized as harshly as possible under the rules of UT.



Schedule of lectures

This schedule is tentative and may be modified as necessary.

Date
Reading
  Aug. 27, 29   2.1: Sets, Functions, Groups
  Sept. 3, 5   2.2- 2.5: Subgroups, Examples, Homomorphisms
  Sept. 10, 12   2.6- 2.7, 2.10: Isomorphisms, The correspondence theorem, Equivalence relations and partitions
  Sept. 17, 19   2.8- 2.9, 2.11- 2.12: Cosets, Modular arithmetic, Quotient groups, Products of groups
  Sept. 24
Review
  Sept. 26
First Midterm

On the material covered Aug. 27 - Sept. 12.
  Oct. 1, 3   Classifying groups of order 1 - 6
  Oct. 8, 10   6.7 - 6:9: Group operations, The operation on cosets, The counting formula
  Oct. 15, 17   7.1, 7.2: Cayley'sTheorem, The Class Equation, Cauchy's Theorem
  Oct. 22, 24   7.3, 7.7: p-Groups, Sylow theorems
  Oct. 29, 31   7.8: Classifying groups of order 7-12
  Nov. 5, 7   11.1- 11.3: Definition of a ring, Polynomial rings, Homomorphisms and ideals
  Nov. 12
Review
  Nov. 14
Second Midterm

Focussed on the material covered Sept. 17 - Oct. 31.
  Nov. 19, 21  11.3.- 11.8: Quotient rings, Maximal ideals,
  Dec. 3, 5  11.6.- 11.7: Product rings, Fractions.