MATH 3GR3
Abstract Algebra
Fall 2021


Important Announcement:

Announcements:

Course Information:


Assignments, Tests, and Solutions:




Test Dates:

There will be two 50-minute tests held during the semester. These tests will be held in-person during the scheduled tutorial time (10:30am – 11:20am) on Friday, October 22 and on Friday, November 19.  Each test will be worth 25% of your final grade.

Final Exam Information:

A final exam for this courses will be scheduled by the registrar.  Details will be posted on the course website as they become available.


Lecture Schedule (tentative):

Lecture #Datetopics coveredreading/resources/comments
107/09/21Course introduction, equivalence relations
section 1.2 from textbook
209/09/21equivalence relations, partitions section 1.2
313/09/21partitions, division algorithm, Euclidean algorithm , gcd(a,b)sections 1.2, 2.2
414/09/21division algorithm, Euclidean algorithmsections 1.6, 3.1
516/09/21brief SageMath demonstration,symmetries of rectangle and triangle, Cayley table of symmetry groups of rectangle
 and triangle
section 3.1
620/09/21definition of a group, examples, basic properties
section 3.2
721/09/21 group of integers modulo n, group of units modulo n, the cancellation law for groupssection 3.2
823/09/21properties of the Cayley table, exponentiation laws, subgroups, examples, Proposition 3.30
sections 3.2, 3.3
927/09/21examples of subgroups, cyclic subgroups, and cyclic groupssections 3.3,  4.1
1028/09/21cyclic groups, order of groups, elements.  Cyclic groups are abelian, every subgroup of a cyclic group is cyclicsections 4.1
1130/09/21cyclic groups, orders of elements in a cyclic group, permutation groupssections 4.1, 5.1
1204/10/21permutation groups, examples, cyclessection 5.1
1305/10/21cycle decomposition of permutations, transpositions, examplessection 5.1
1407/10/21even and odd permutations, the alternating groups
section 5.1
1518/10/21Lemma 5.14, dihedral groups
section 5.2
1619/10/21dihedral groups, cosets
sections 5.2, 6.1
1721/10/21left and right cosets of a subgroup
section 6.1
1825/10/21cosets, Lagrange's Theorem
section 6.1, 6.2
1926/10/21

2028/10/21

2101/11/21

2202/11/21
2304/11/21

2408/11/21

2509/11/21

2611/11/21
2715/11/21
2816/11/21

2918/11/21

3022/11/21

3123/11/21

3225/11/21

3329/11/21

3430/11/21
3502/12/21
3606/12/21
3707/12/21

SageMath:

The following cell can be used to enter and then execute a sequence of SageMath commands.  This can be used to perform calculations for some of the homework questions or just to explore some of the concepts that are covered in this course.  To save the commands and results you can copy and paste them into the document that contains your homework solutions, or you could take a screenshot (or a picture) of the cell (after you have performed the calculation) and include the screenshot file  in your homework solutions document.  Alternatively you can copy and paste the link that is produced when the "share" button is pressed.  This button appears once the "Evaluate" button has been pressed.

For more details on SageMath, consult the online version of the course textbook, or the SageMath website, or the SageCell website. Here is a link to a SageMath tutorial:  https://doc.sagemath.org/html/en/tutorial/





Matt Valeriote