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Math 312GT: Group Theory
MWF 11:30-12:45, Clapp 420
Jessica Sidman, jsidman at mtholyoke dot edu
Syllabus
Course notes
Symmetry is a vast subject, significant in art and nature. Mathematics lies at its root, and it would be hard to find a better one on which to demonstrate the working of the mathematical intellect. Hermann Weyl, Symmetry

In our own time in the period 1960-1980, we have seen particle physics emerge as the playground of group theory. Freeman Dyson

The notion of a "group," viewed only 30 years ago as the epitome of sophistication, is today one of the mathematical concepts most widely used in physics, chemistry, biochemistry, and mathematics itself. Alexy Sosinsky, 1991

Week Monday Wednesday Friday
1/23 Read: 1.1 and Syllabus Read: 1.2
Online assignment due.		 Read: 1.3
Mini-HW1 due. PDF LaTex
If you have not seen a proof of the division algorithm you may also want to watch the video (Proof of the division algorithm) on this playlist.
1/30 Read: 1.4
Online assignment: See Gradescope for pre-class questions.
Self-check definition quiz: 1-1 (injective), onto (surjective), center, centralizer.		 Read: 2.1
Quiz:Be prepared to do (parts of) problems from HW1.
 Read: 2.2
HW2 due. PDF LaTex
2/6 Read: 2.3
Online assignment: See Gradescope for pre-class questions.
Self-check definition quiz: S_n, Division Algorithm, GL(n,F).		 Read: 2.4
Quiz: Be prepared to do (parts of) problems from HW2.
 Read: 2.5
HW3 due. The PDF and LaTex file are in this folder.
2/13 Read: 2.6
Online assignment: See Gradescope for pre-class questions.
Self-check definition quiz: isomorphism, direct product.		 Work day/review
Quiz: Be prepared to do (parts of) problems from HW3.
 Read: 3.1
HW4 due. The PDF and LaTex file are in this folder.
2/20 Read: 3.2
Portfolio check due.
Self-check definition quiz: m-cycle, disjoint cycles, transposition.		 Exam 1
Read: 4.1
Take-home problem due.
2/27 Read: 4.3
Online assignment: See Gradescope for pre-class questions.
Self-check definition quiz: group action, conjugation action.		 Read: 4.4 We'll do a proof workshop in class, problems TBA.
 We'll wrap up Chapter 4 today.
HW5 due. The PDF and LaTex file are in this folder.
3/6 Read: 5.1
Online assignment: See Gradescope for pre-class questions.
Self-check definition quiz: orbit, stabilizer, normalizer.		 Read: 5.2
Quiz: Be prepared to do (parts of) problems from HW 5. 		Read: 5.3
HW6 due. The PDF and LaTex file are in this folder.
3/20 Read: 6.1
Online assignment: See Gradescope for pre-class questions.
Self-check definition quiz: right coset, |G:H|		 Read: 6.2
Quiz: Be prepared to do (parts of) problems from HW 6. 		Read: 6.3
HW7 due. The PDF and LaTex file are in this folder.
3/27 Review:
Online assignment: See Gradescope for pre-class questions.
Read: 10.1 through Remark 10.8.
 Exam 2
Portfolio check 2 due. The PDF and LaTex file are in this folder.
4/3 Read: 10.2
Take-home exam problem due.
Online assignment: See Gradescope for pre-class questions.
Read: 10.3
 Read: 11.1
HW8 due. The PDF and LaTex file are in this folder.
4/10 Read: 11.2
Online assignment: See Gradescope for pre-class questions.
Self-check definition quiz: group homomorphism, image, pre-image		 Read: 11.3
Quiz: Be prepared to do (parts of) problems from HW 8. 		Read: 11.4
HW9 due. The PDF and LaTex file are in this folder.
4/17 Read: 11.5
Online assignment: See Gradescope for pre-class questions.
Self-check definition quiz: TBA		 Read: TBA
Quiz: Be prepared to do (parts of) problems from HW 9. 		Read: TBA
HW10 due. The PDF and LaTex file are in this folder.
4/24 Read: TBA
Online assignment: See Gradescope for pre-class questions.
Self-check definition quiz:TBA		 Read: TBA
Quiz: Be prepared to do (parts of) problems from HW 10. 		Read: TBA
Portfolio Check #3 due. The PDF and LaTex file are in this folder.