Activities, homework problems, and the syllabus can be found here. The tasks listed for each day are to be completed before the following day's class.
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.