Introduction to Abstract Algebra, Math 417, Spring 2021, Sections BCEF

Basic information

  • Final Exam Update: The final exam will be take-home. It will be posted on Friday, May 7, and it will be due on Friday, May 14.
  • Section B/C
  • Section E/F
  • Main course website: http://jpascale.pages.math.illinois.edu/417sp21
  • Moodle site: This course has a Moodle site at learn.illinois.edu. You will use the Moodle site to submit your assignments and to view your grades.
  • Prerequisites: Either MATH 416 or one of ASRM 406, MATH 415 together with one of MATH 347, MATH 348, CS 374; or consent of instructor.
  • Textbook: Frederick M. Goodman, Algebra: Abstract and Concrete version 2.6. This e-book is available free of charge: website for the book.

  • If you are unsure which section you are in, please compare your registration with this table:

      Section CRN Instructor Time
    Section B B13 or B14 57716 or 57717 Dodd, C. MWF 9:00am
    Section C C13 or C14 37997 or 37999 Dodd, C. MWF 10:00am
    Section E E13 or E14 38000 or 38009 Pascaleff, J. MWF 1:00pm
    Section F F13 or F14 70906 or 70907 Pascaleff, J. MWF 2:00pm

Course outline

  • Lectures and lecture notes: Video lectures will be posted on Kaltura/Mediaspace, and written notes for the lectures will be posted on this website. Lectures notes may not correspond perfectly to the videos, but the content will be the same. For instance, one set of lecture notes may be broken up into several videos.
  • Synchronous meetings: During the scheduled class times, we will meet on Zoom to discuss the course material. This time may be used for reviewing lecture material, expanding on the lectures, discussing homework problems, or answering other questions.
  • Homework: There will be 11 9 homework assignments whose due dates (usually Fridays) are listed in the schedule. There is no homework due on weeks when there is an exam.
  • Update [2021-04-16 Fri]: Due to some changes in the schedule, there will now be only 9 homework assignments in total. The two lowest homework scores will still be dropped.
  • Exams: There will be three midterm exams, and a final exam. These exams will have a take-home format, and will need to be completed within a certain window of time. The midterm exams will be held on the following Fridays: February 26, March 26, April 23. The final exam will have a similar format, date to be determined.
  • Discussion forum: On the Moodle site, there is a discussion. Please post questions about lectures, homework, and other course concerns. When posting about homework, please refrain from posting complete solutions, since we want to give everyone a chance to develop their own understanding of the problems. It is OK to talk about strategies for solving particular problems, though.

Policies

  • Assessment: Grades will be based on homework (25%), three midterm exams (15% each), and the final exam (30%). The two lowest homework scores will be dropped. Grade cutoffs will never be stricter than 90% for an A- grade, 80% for a B-, and so on. Individual exams may have grade cutoffs set more generously depending on their difficulty.
  • Late homework will not be accepted, but the lowest two scores are dropped, so you may miss one or two assignments without penalty.
  • Missed exams: If you need to miss an exam (for reasons such as illness, accident, or family crisis), please let the instructor know as soon as possible. You will be excused from the exam so that it does not contribute to your final grade (there will not be a make-up exam).
  • Collaboration and Academic Integrity:
    • For homework assignments, collaboration on homework is permitted and expected, but you must write up your solutions individually and understand them completely.
    • For exams, you are permitted to use your textbook, notes, and any of the course materials. You are not permitted to use internet resources not connected to this course, and you are not permitted to collaborate with other students.
  • Disability accommodations: Students who require special accommodations should contact the instructor as soon as possible. Any accommodations on exams must be requested at least one week in advance and will require a letter from DRES.

Homework assignments

Please go to the Moodle site to upload your homework and to view solutions to past assignments.

Schedule

Week № Lectures for the week Dates Comments
Week 1 1. Symmetries. [§§ 1.1–1.4, 1.10] BC: video, notes. EF: video. [2021-01-25 Mon]  
  2. Permutations. [§ 1.5] BC: video 1, video 2. EF: video. [2021-01-27 Wed]  
    [2021-01-29 Fri]  
Week 2 3. Integer arithmetic. [§ 1.6] BC: video. EF: video. [2021-02-01 Mon]  
  4. Primes, modular arithmetic. [§§ 1.6–1.7] BC: video 1, video 2. EF: video. [2021-02-03 Wed]  
    [2021-02-05 Fri] Homework 1 due
Week 3 5. More modular arithmetic, basic group properties. [§§ 1.7, 2.1] BC: video. EF: video. [2021-02-08 Mon]  
  6. Subgroups, isomorphisms, Cayley’s theorem. [§ 2.2] BC: video. EF: video. [2021-02-10 Wed]  
    [2021-02-12 Fri] Homework 2 due
Week 4 7. Cyclic groups. [§ 2.2] BC: video 1, video 2. EF: video. [2021-02-15 Mon]  
    [2021-02-17 Wed] Break day
    [2021-02-19 Fri] Homework 3 due
Week 5 8. Subgroups of cyclic groups, dihedral groups. [§§ 2.2–2.3] BC: video 1, video 2. EF: video. [2021-02-22 Mon]  
  9. Homomorphisms and kernels. [§ 2.4] BC: video. EF: video. [2021-02-24 Wed]  
    [2021-02-26 Fri] Exam 1
Week 6 10. Cosets and Lagrange’s theorem. [§ 2.5] BC: video. EF: video. [2021-03-01 Mon]  
  11. Equivalence relations and partitions. [§ 2.6] BC: video. EF: video. [2021-03-03 Wed]  
    [2021-03-05 Fri] Homework 4 due
Week 7 12. More on equivalence relations. [§ 2.6] EF: video. [2021-03-08 Mon]  
  13. Quotient groups and homomorphisms. [§ 2.7] BC: video. EF: video. [2021-03-10 Wed]  
    [2021-03-12 Fri] Homework 5 due
Week 8 14. Isomorphism theorems. [§ 2.7] BC: video. EF: video. [2021-03-15 Mon]  
  15. Diamond isomorphism, direct products of groups. [§§ 2.7, 3.1] BC: video. EF: video. [2021-03-17 Wed]  
    [2021-03-19 Fri] Homework 6 due
Week 9 16. Semi-direct products. [§ 3.2] EF: video. [2021-03-22 Mon]  
    [2021-03-24 Wed] Break day
    [2021-03-26 Fri] Exam 2
Week 10 17. Examples of semi-direct products, group actions. [§§ 3.2, 5.1] EF: video. [2021-03-29 Mon]  
  18. Orbit-stabilizer theorem. [§ 5.1] EF: video. [2021-03-31 Wed]  
    [2021-04-02 Fri] No homework due
Week 11 19. Burnside/Cauchy-Frobenius lemma. [§ 5.2] EF: video. [2021-04-05 Mon]  
  20. Class equation and applications. [§ 5.4] EF: video. [2021-04-07 Wed]  
    [2021-04-09 Fri] Homework 7 due
Week 12 21. Sylow theorems and applications. [§ 5.4] EF: video. [2021-04-12 Mon]  
  22. Proofs of Sylow theorems. [§ 5.4] EF: video. [2021-04-14 Wed]  
    [2021-04-16 Fri] Homework 8 due
Week 13 23. Introduction to rings and fields. [§§ 1.11, 6.1] EF: video. [2021-04-19 Mon]  
  24. Polynomial rings over fields. [§ 1.8] EF: video. [2021-04-21 Wed]  
    [2021-04-23 Fri] Exam 3
Week 14 25. Ring homomorphisms and ideals. [§ 6.2] EF: video. [2021-04-26 Mon]  
  26. Quotient rings, homomorphism theorem for rings. [§ 6.3] EF: video. [2021-04-28 Wed]  
    [2021-04-30 Fri]  
Week 15 27. Maximal and prime ideals, integral domains. [§ 6.4] EF: video. [2021-05-03 Mon]  
    [2021-05-05 Wed] Homework 9 due