Computation of grade: The grade is computed from your scores in homework (25%) two midterms (25% each) and the final part A and part B (25% for each part). The avid reader will have noticed that this adds up to 125%: We will choose the three best scores from your midterms and finals part A and B.

We will drop your two worst homework score for the homework component.

Exams: The exams will also be given on gradescope. There will be no make-up exams. The midterms will be given in class. For precise times and dates see the syllabus below.

Tentative Syllabus We will primarily study groups, roughly covering chapters 0 until 10 or 11, and perhaps a chapter or two of part 3 (special topics). The following is a tentative syllabus, which probably will be modified a few times during the course.

Lecture 1 Notes

Lecture 2 Euclid's lemma, modular arithmetic

Lecture 3 Def. of a group, examples

Lecture 4 Ch2 properties of groups, Ch1 symmetries of a square

Lecture 5 More examples, order of group, order of element (For the proof of last lemma see the recording - the ipad pen ran out of battery+)

Lecture 6 Subgroups

Lecture 7 subgroups, cyclic groups

Lecture 8 order of elements in cyclic groups, subgroups

Lecture 9 number of elements of a given order, permutations

Lecture 10 Review, groups generated by two elements

Lecture 11 Permutations

Lecture 12 odd and even permutations, A_n, remarks about midterm

Lecture 13 Isomorphisms

Lecture 14 Isomorphisms, automorphisms

Lecture 15 Automorphisms of cyclic groups

Lecture 16 Legendre's Theorem

Lecture 17 Legendre's theorem applications, normal subgroups

Lecture 18 normal subgroups, factor groups

Lecture 19 Factor groups, external direct products pages misaligned: please jump to the last page after the second page.

Lecture 20 Review

Lecture 21 External direct products

Lecture 22 Structure of U(n), homomorphisms

Lecture 23 First Isomorphism Theorem

Lecture 24 Fundamental Theorem of Finite Abelian Groups

Lecture 25 Review homomorphisms, finite abelian groups

Lecture 26 Review

Homework assignments Homework is to be turned in via gradescope Grade Scope for HW this quarter. You should have received an email prompt by now notifying you of your gradescope enrollment and providing a link to set up your personal account. Although homework counts comparatively little for the overall grade, it is extremely important that you do, or, at least, seriously try to do them. Most of the exam problems will be similar to homework or practice exam problems.

You can watch this video which explains how to scan and submit HW online.

For Jan 9: Chapter 0: 4, 8, 12, 16, 18, 28, 38

for Jan 16: Chapter 2: p. 54: 4bd, 5ab, 9, 10, 12, 23(try induction), 27, Chapter 3: p. 69: 2, 4, 18

for Jan 23: Chapter 3: 6, 23, 50, Chapter 4: 1, 2, 4, 12, 13

relevant for midterm (need not be turned in): Chapter 3: 30, 42 Chapter 4: 8, 16, 22, 60, Chapter 5: 2(a)

for Feb 6:: Chapter 5: 1, 5de, 6, 8cd, 10, 28, 32, 36, 38

for Feb 13:: Chapter 6: 4, 5, 12, 16, 26, 28, 30, 56

for Feb 20: Chapter 7: 1, 3, 7, 8, 9, 13, 20, 29,

for March 6: : Chapter 8: 8, 10, 12, Chapter 9: 6, 8, 10(a), 14, 18, 22, 27,

for March 12 (need not be turned in, but relevant for final): : Chapter 10: 9, 15, 25, 26, 27, Chapter 11: 5, 7, 15, 19, see practice final below practice midterms

practice for first midterm

practice for second midterm

practice final

Information about first midterm

CONTENT: The midterm will be a 50-minute exam, similar in nature to the practice exam, see above. You will have an additional 10 minutes to scan and upload the exam (see details below). It is your responsibility to upload your exam on time (10 minutes is a lot of time!). If you do not get it done in time, you wil end up with a serious penalty even if you email it to us soon after the time..

RULES: It will be an open book exam: you will be allowed to consult the textbook, your own notes or previous homework, and the notes posted on Canvas or my webpage by me or by the TAs, but no other resources may be used. In particular, you may not use any online resources, any other printed material (such as solution manuals), or any form of calculator (all arithmetic on the exam will be easy!) and you must not communicate in any way with anyone else during the exam. You will be required to write, sign and submit with your work a statement certifying that you have followed the regulations. Breaches of the rules will be reported to the Academic Integrity office.

TECHNICAL INFORMATION: The exam will be presented through Gradescope in a form similar to a homework assignment, except that it will be timed. When you log in to Gradescope you will be able to see (and/or download) a pdf copy of the exam paper. You should write your answers on your own paper, scan and upload them to Gradescope within 60 minutes - that's 50 minutes official exam time, plus 10 minutes allowance for upload time. (Please assign the pages corresponding to the questions, just as you do for homework.)

DATE AND TIME: The exam will take place during normal class time: 11-11.50am Friday, January 29 PT. Students who currently live in different time zones for whom the time would be very inconvenient should contact me about the possibility of taking the exam at another time by Thursday, January 28, noon (California time). If you do so, please state where you currently live! Only students who have been approved before the exam can take it at a different time.

Material: Chapters 1-4. Chapter 5: only definition of permutation group, cycle notation

for Jan 16:

for Jan 23: Chapter 2: p. 54: 4, 5, 9, 10, 13, 21, 23(try induction), 27, 29, Chapter 3: p. 69: 2, 4,

for Jan 30: Chapter 4: p. 85-87: 1, 2, 4, 12, 13, 22, 32, 34, click on additional problem

for Feb 6: (need not be turned in, but could be relevant for midterm) Chapter 4: p. 89-90: 67, 69, 70, Chapter 5: p. 112: 1, 2, 4, 5ab, Review: What are the elements of U(11)? Is it cyclic?

Midterm 1: The first midterm will take place this Wednesday in class. The material will go until what is covered in the last assignment. You are allowed to use one hand-written cheat sheet, but no calculators, books or other notes. You will not need a bluebook, but bring scratch paper.

Extra office hour: Tu: 3:30-4:30

for Feb 13: Chapter 5, p. 113-115: 6, 8cde, 10, 11, 28, 29, 32, 37, 39, 40

Solutions Midterm1

relevant for midterm (need not be turned in): Chapter 7, pages 150-152: 1, 3, 6, 7, 8, 9, 13, 20, 29, 30

Midterm 2: The second midterm will take place this Wednesday in class. The material will primarily go over what we covered from Chapters 5, 6 and 7. So you should make sure you understand all the definitions and assigned problems from these chapters. The same rules hold as for the first midterm: You are allowed to use one hand-written cheat sheet, but no calculators, books or other notes. You will not need a bluebook, but bring scratch paper.

for March 6: Chapter 9, p. 188-189: 6, 7, 8, 9, 10(a), 14, 17, 18

for March 13: Chapter 9, p. 189: 19, 22, 27, Chapter 10, p. 207: 25, 26, 27, 39, Chapter 8: 8, 10, 12 (3 groups, not four), not to be turned in but relevant for final: 18, 22, 29, 30

Review exercises from Chapter 6: 1, 4, 5, 16, 26

Solutions Midterm2

Practice Final