Activities, homework problems, and the syllabus can be found here. The tasks listed for each day are to be completed before the following class.
Wednesday, July 2
Review today's activity and complete the A-side and B-side (if you didn't finish them in class).
Read through all of the homework problems, then choose 3-4 problems to solve and submit your typed or neatly handwritten solutions on Gradescope.
Review the feedback you received on any recent homework problems or assessments.
Tuesday, July 1
Review today's activity and complete the A-side and B-side (if you didn't finish them in class).
Read through all of the homework problems, then choose 3-4 problems to solve and submit your typed or neatly handwritten solutions on Gradescope. This is due at 9:00am on Thursday and will be the last homework assignment of the course.
Review the feedback you received on any recent homework problems or assessments.
Submit this form to request a reassessment at the end of class on Thursday. (Submit the form once for each day.) Please submit the form by 9:00am the day before you would like the reassessment.
Monday, June 30
Review today's activity and complete the A-side and B-side (if you didn't finish them in class).
Read about the following topics and complete this questionnaire.
Irreducible polynomials (definition and examples)
Polynomial irreducibility tests
Degree 2 and 3 polynomials
Reducibility over Q implies reducibility over Z
Mod p irreducibility test
Eisenstein's criterion
The fact that F[x]/<f(x)> is a field if f is irreducible
Read through all of the homework problems, then choose 3-4 problems to solve and submit your typed or neatly handwritten solutions on Gradescope.
Review the feedback you received on any recent homework problems or assessments.
Submit this form to request a reassessment at the end of class on Wednesday or Thursday. (Submit the form once for each day.) Please submit the form by 9:00am the day before you would like the reassessment.
Friday, June 27
Review today's activity and complete the A-side and B-side (if you didn't finish them in class).
Read about the following topics and complete this questionnaire.
The polynomial ring R[x] over a commutative ring R (definition, terminology like degree, monic, leading coefficient)
The division algorithm for F[x], where F is a field
The fact that f(a) is the remainder when f(x) is divided by x - a
The fact that over a field, a is a zero of f if and only if x - a divides f
Principal ideal domains, and the fact that F[x] is a PID if F is a field
Read through all of the homework problems, then choose 3-4 problems to solve and submit your typed or neatly handwritten solutions on Gradescope.
Review the feedback you received on any recent homework problems or assessments.
Submit this form to request a reassessment at the end of class on Monday or Tuesday. (Submit the form once for each day.) Please submit the form by 9:00am the day before you would like the reassessment.
If you are doing a project, I would like a rough draft from you by Sunday at 5pm. It's okay if it's not complete, but aim to have around 70% or more done.
Complete the Week 4 Check-In and Project Proposal form.
Thursday, June 26
Review today's activity and complete the A-side and B-side (if you didn't finish them in class).
Read about the following topics and complete this questionnaire.
Ideals (definition and examples)
Quotient/factor rings (definition and examples)
Ring homomorphisms (definition, properties, examples)
The fact that kernels of ring homomorphisms are ideals, and vice versa
Read through all of the homework problems, then choose 3-4 problems to solve and submit your typed or neatly handwritten solutions on Gradescope.
Review the feedback you received on any recent homework problems or assessments.
Submit this form to request a reassessment at the end of class on Monday or Tuesday. (Submit the form once for each day.) Please submit the form by 9:00am the day before you would like the reassessment.
If you are doing a project, I would like a rough draft from you by the end of the day tomorrow. It's okay if it's not complete, but aim to have around 70% or more done.
Wednesday, June 25
Review today's activity and complete the A-side and B-side (if you didn't finish them in class).
Read about the following topics and complete this questionnaire.
Rings (definition, basic properties, examples)
Subrings
Integral domains and fields (definition and examples)
The characteristic of an integral domain
There is no homework today. Use the time to review today's activity instead, and try some problems related to the fundamental theorem of finite abelian groups in preparation for tomorrow's assessment.
Review the feedback you received on any recent homework problems or assessments.
Submit this form to request a reassessment at the end of class on Friday or Monday. (Submit the form once for each day.) Please submit the form by 9:00am the day before you would like the reassessment.
If you are doing a project, I would like a rough draft from you by the end of the day Friday. It's okay if it's not complete, but aim to have around 70% or more done.
Tuesday, June 24
Review today's activity and complete the A-side and B-side (if you didn't finish them in class).
Read about the following topics and complete this questionnaire.
Fundamental theorem of finite abelian groups (statement and examples only--don't bother with the proof)
There is no homework today. Use the time to review today's activity instead, and try a problem or two using Burnside's lemma.
Review the feedback you received on any recent homework problems or assessments.
Submit this form to request a reassessment at the end of class on Thursday or Friday. (Submit the form once for each day.) Please submit the form by 9:00am the day before you would like the reassessment.
If you are doing a project, I would like a rough draft from you by the end of the day Friday. It's okay if it's not complete, but aim to have around 70% or more done.
Monday, June 23
We did not do an activity in class today; instead we discussed simple groups and tests for non-simplicity based on the order of the group. If you weren't in class, review those topics.
Read about the following topics and complete this questionnaire.
The statement and examples of Burnside's lemma
Read through all of the homework problems, then choose 3-4 problems to solve and submit your typed or neatly handwritten solutions on Gradescope.
Review the feedback you received on any recent homework problems or assessments.
Submit this form to request a reassessment at the end of class on Wednesday or Thursday. (Submit the form once for each day.) Please submit the form by 9:00am the day before you would like the reassessment.
Friday, June 20
Review today's activity and complete the A-side and B-side (if you didn't finish them in class).
Read about the following topics and complete this questionnaire.
Simple groups
Tests for nonsimplicity (e.g. two times odd, Generalized Cayley theorem)
Simplicity of A_5
Read through all of the homework problems, then choose 3-4 problems to solve and submit your typed or neatly handwritten solutions on Gradescope.
Review the feedback you received on any recent homework problems or assessments.
Submit this form to request a reassessment at the end of class on Monday or Tuesday. (Submit the form once for each day.) Please submit the form by 9:00am the day before you would like the reassessment.
If you have not done so yet, please complete the Week 3 Check-In and Project Proposal form.
Wednesday, June 18
There is no class tomorrow, so today's assignments are due before class on Friday.
Review today's activity and complete the A-side and B-side (if you didn't finish them in class).
Read about the following topics and complete this questionnaire.
The Sylow theorems
The application of the Sylow theorems to groups of order pq
Read through all of the homework problems, then choose 3-4 problems to solve and submit your typed or neatly handwritten solutions on Gradescope.
Review the feedback you received on any recent homework problems or assessments.
Submit this form to request a reassessment at the end of class on Friday. (Submit the form once for each day.) Please submit the form by 9:00am the day before you would like the reassessment.
Tuesday, June 17
Review today's activity and complete the A-side and B-side (if you didn't finish them in class).
Read about the following topics and complete this questionnaire.
The action of a group on itself by multiplication
The action of a group on itself by conjugation
The class equation
The conjugacy class of a group element
Conjugacy classes in the symmetric group
There is no homework today. Use the time to review today's activity instead. Tomorrow there will be a homework assignment about group actions.
Review the feedback you received on any recent homework problems or assessments.
Submit this form to request a reassessment at the end of class on Friday. (Submit the form once for each day.) Please submit the form by 9:00am the day before you would like the reassessment.
Monday, June 16
Review today's activity and complete the A-side and B-side (if you didn't finish them in class).
Read about the following topics and complete this questionnaire.
The definition and examples of (left and right) group actions
Orbits, stabilizers, and transitive actions
Read through all of the homework problems, then choose 3-4 problems to solve and submit your typed or neatly handwritten solutions on Gradescope.
Review the feedback you received on any recent homework problems or assessments.
Submit this form to request a reassessment at the end of class on Tuesday, Wednesday, or Friday. (Submit the form once for each day.) Please submit the form by 9:00am the day before you would like the reassessment.
Friday, June 13
Review today's activity and complete the A-side and B-side (if you didn't finish them in class).
Read about the following topics and complete this questionnaire.
The definition of permutation groups and symmetric groups
Cycle notation for elements of symmetric groups
The fact that every permutation can be written as a product of one or more disjoint cycles
The fact that disjoint cycles commute
The order of a permutation
The fact that every permutation can be written as product of (not necessarily disjoint) 2-cycles
The definition of an even permutation and an odd permutation
The definition of the alternating groups
Read through all of the homework problems, then choose 3-4 problems to solve and submit your typed or neatly handwritten solutions on Gradescope.
Review the feedback you received on any recent homework problems or assessments.
Submit this form to request a reassessment at the end of class on Monday, Tuesday or Wednesday. (Submit the form once for each day.) Please submit the form by 9:00am the day before you would like the reassessment.
Thursday, June 12
Review today's activity and complete the A-side and B-side (if you didn't finish them in class).
Read about the following topics and complete this questionnaire.
The first isomorphism theorem
The fact that normal subgroups are kernels of homomorphisms
The G/Z theorem (if G/Z(G) is cyclic, then G is abelian)
The isomorphism between G/Z(G) and Inn(G)
Read through all of the homework problems, then choose 3-4 problems to solve and submit your typed or neatly handwritten solutions on Gradescope.
Review the feedback you received on any recent homework problems or assessments.
Submit this form to request a reassessment at the end of class on Monday or Tuesday. (Submit the form once for each day.) Please submit the form by 9:00am the day before you would like the reassessment.
Wednesday, June 11
We did not do an activity in class today; instead we discussed cosets and Lagrange's theorem. If you weren't in class, review those topics.
Read about the following topics and complete this questionnaire.
The definition and examples of a normal subgroup
The definition and examples of a quotient group (or factor group)
Read through all of the homework problems, then choose 3-4 problems to solve and submit your typed or neatly handwritten solutions on Gradescope.
Review the feedback you received on any recent homework problems or assessments.
Submit this form to request a reassessment at the end of class on Friday or Monday. (Submit the form once for each day.) Please submit the form by 9:00am the day before you would like the reassessment.
Submit this form indicating how the course is going for you so far.
Tuesday, June 10
Review today's activity and complete the A-side and B-side (if you didn't finish them in class).
Read about the following topics and complete this questionnaire.
The (external) direct product of groups
Orders of elements in direct products
The criterion for when Z/(mn)Z is isomorphic to the product of Z/mZ and Z/nZ
Read through all of the homework problems, then choose 3-5 problems to solve and submit your typed or neatly handwritten solutions on Gradescope.
Revise 1-3 problems from previous homework or assessments, and submit your revisions on Gradescope. Clearly indicate which problems you’re revising, and for each problem write a sentence or two explaining what was unsatisfactory about your original attempt and how you improved it.
Review the feedback you received on any recent homework problems or assessments.
Submit this form to request a reassessment at the end of class on Thursday or Friday. (Submit the form once for each day.) Please submit the form by 9:00am the day before you would like the reassessment.
Monday, June 9
Review today's activity and complete the A-side and B-side (if you didn't finish them in class).
Read about the following topics and complete this questionnaire.
The definition, examples, and properties of cosets
Lagrange's theorem and its corollaries:
The order of a group element divides the order of the group
Groups of prime order are cyclic
Fermat's little theorem
The classification of groups of order 2p, where p is an odd prime
Read through all of the homework problems, then choose 3-5 problems to solve and submit your typed or neatly handwritten solutions on Gradescope.
Revise 1-3 problems from previous homework or assessments, and submit your revisions on Gradescope. Clearly indicate which problems you’re revising, and for each problem write a sentence or two explaining what was unsatisfactory about your original attempt and how you improved it.
Review the feedback you received on any recent homework problems or assessments.
Submit this form to request a reassessment at the end of class on Wednesday, Thursday, or Friday. (Submit the form once for each day.) Please submit the form by 9:00am the day before you would like the reassessment.
Friday, June 6
Review today's activity and complete the A-side and B-side (if you didn't finish them in class).
Read about the following topics and complete this questionnaire.
The definition and examples of a group homomorphism
The kernel and image of a homomorphism, and the inverse image of an element or a subset
Read through all of the homework problems, then choose 3-5 problems to solve and submit your typed or neatly handwritten solutions on Gradescope.
Revise 1-3 problems from previous homework or assessments, and submit your revisions on Gradescope. Clearly indicate which problems you’re revising, and for each problem write a sentence or two explaining what was unsatisfactory about your original attempt and how you improved it.
Review the feedback you received on any recent homework problems or assessments.
Submit this form to request a reassessment at the end of class on Monday and Tuesday. (Submit the form once for each day.) Please submit the form by 9:00am the day before you would like the reassessment.
Thursday, June 5
Review today's activity and complete the A-side and B-side (if you didn't finish them in class).
Read about the following topics and complete this questionnaire.
The definition and examples of a group isomorphism
Properties of group isomorphisms
The definition and examples of an automorphism
The automorphism group of the group of integers under addition mod n
Read through all of the homework problems, then choose 3-5 problems to solve and submit your typed or neatly handwritten solutions on Gradescope.
Revise 1-3 problems from previous homework or assessments, and submit your revisions on Gradescope. Clearly indicate which problems you’re revising, and for each problem write a sentence or two explaining what was unsatisfactory about your original attempt and how you improved it.
Wednesday, June 4
Read the syllabus.
Review today's activity and complete the A-side and B-side (if you didn't finish them in class).
Read about the following topics and complete this questionnaire.
The definition of a cyclic group
The fact that every finite cyclic group of order n is isomorphic to Z/nZ, and every infinite cyclic group is isomorphic to Z
The subgroups of a cyclic group
The criterion for two powers of an element to be equal
The fact that the order of an element equals the order of the subgroup generated by that element
The order of a power of a generator of a cyclic group
The number of elements of each order in a cyclic group
Read through all of the homework problems, then choose 3-5 problems to solve and submit your typed or neatly handwritten solutions on Gradescope.
Tuesday, June 3
Review today's activity and complete the A-side and B-side (if you didn't finish them in class).
Read about the following topics and complete this questionnaire.
The definition of a subgroup, and examples of subgroups
The order of a group, and the order of a group element
The cyclic subgroup generated by a group element
The center of a group
The centralizer of a group element
Read through all of the homework problems, then choose 3-5 problems to solve and submit your typed or neatly handwritten solutions on Gradescope.
Monday, June 2
Review today's activity and complete the A-side and B-side (if you didn't finish them in class).
Watch the video "Group theory, abstraction, and the 196,883-dimensional monster".
Read about the following topics and complete this questionnaire.
The definition of a group, and an abelian group
Basic properties of groups, such as uniqueness of the identity, uniqueness of inverses, cancellation, socks-shoes property
Additive and multiplicative notation for the group operation
Examples of groups, including the integers, rationals, reals, and complex numbers under addition, the nonzero rationals, reals, and complex numbers under multiplication, the integers mod n, the multiplicative group of integers mod n, the general linear groups, the special linear groups, and the dihedral groups
Read through all of the homework problems, then choose 3-5 problems to solve and submit your typed or neatly handwritten solutions on Gradescope.