MATH 3031 Abstract Algebra I

Fall 2017, Dalhousie University

Professor: Sara Faridi
Time and location: Monday & Wednesday & Friday 9:35 -- 10:25 in DUNN 302.


Office hours: Tuesdays 10--11 am & Wednesdays 1:30--2:30 pm in Chase 314.


Course Syllabus: can be found here.


Homework:

Homework Problems Due Date
HW#1 (Solutions) Chapter 1: 5.1, 5.3; Chapter 2: 2.4, 2.6, 3.2, 4.3 Wednesday Sept 20
HW#2 (Solutions) Chapter 2: Write a full proof for Prop. 2.3.8; Exercises: 4.6, 4.7, 4.9, 5.1 Wednesday Sept 27
HW#3 (Solutions) Chapter 2: Exercises: 5.2, 6.2, 6.7, 6.10 Wednesday Oct 4
HW#4 (Solutions: 1, 2) Chapter 2: Exercises: 12.1, 12.5, 10.5, 10.2, 9.4 Wednesday Oct 18
HW#5 Chapter 6: Exercises: 7.1, 7.3, 7.10, 8.2; Chapter 7: Exercises: 1.1, 2.2, 2.8, 2.13, 3.3 Wednesday Nov 15
HW#6 Chapter 7: Exercises: 6.4, 7.3, 7.4, 7.5(a) Wednesday Nov 22
HW#7 Chapter 7: Exercises: 7.9(a), 7.10 Wednesday Nov 29


Calendar:

Prove the fixed point theorem
Date Sections Covered Practice Problems/ Further reading
W Sep 6 2.1 Read Chapter 1 and do exercises outlined in class
F Sep 8 2.1, 2.2 started definition and examples of groups assigned in class (do them, and watch for where you need associativity!)
M Sep 11 2.2, permutation groups, and started 2.3 Read 1.5 and do exercises from class
W Sep 13 2.4, order of an element and cyclic groups Chapter 2: 2.1, 2.3
F Sep 15 2.4, 2.5: cyclic groups, generators of groups, started homomorphisms
M Sep 18 2.5: some examples of homomorphisms
W Sep 20 2.5: kernels and normal subgroups read about generators of S_3 on p42 to be comfortable with symmetric group operations
F Sep 22 2.5: discussion on the symmetric group
M Sep 25 2.6: isomorphism theorems, Cayely's theorem Read 2.6; Chapter 2, problems: 6.5, 6.6
W Sep 27 2.7: partitions and equivalence relations Read section 2.7
F Sep 29 2.8: cosets and Lagrange's theorem Do problem from class and read 2.8
M Oct 2 2.8: applications of cosets Read in Section 2.8 about using right cosets
W Oct 42.8, 2.12: normal subgroups and beginning of quotient groups
F Oct 62.12: the quotient group please do problems mentioned in class
M Oct 9 THANKSGIVING-- NO CLASS
W Oct 11 2.12: First Isomorphism Theorem; 2.9
F Oct 13 2.9: Modular arithmetic; 2.10
M Oct 16 2.10: The correspondence Theorem
W Oct 18 2.11: Products of Groups
F Oct 20 2.11: Products of Groups work out the proof of Prop. 2.11.4 and Prop. 2.11.5
M Oct 23 MIDTERM
W Oct 25 The Dihedral Group
F Oct 27 6.7: operations of groups on sets, orbits, stabilizers
M Oct 30 6.7, 6.8: more on orbits and stabilizers; operations on cosets
T Oct 31[LAST DAY TO DROP WITH W] NO CLASS
W Nov 1 7.1: The class equation Read and do details of the class equation for SL_2(F_3) in Section 7.2
F Nov 3 7.3: p-groups
M Nov 6 STUDY BREAK -- NO CLASS
W Nov 8 STUDY BREAK -- NO CLASS
F Nov 10 STUDY BREAK -- NO CLASS
M Nov 13 REMEMBRANCE DAY -- NO CLASS
W Nov 15 7.6, 7.7: The normalizer of a subgroup, beginning of Sylow theorems
F Nov 17 7.7: Classifying groups of order 6 and 15 Read and try find isomorphism classes of groups of order 21
M Nov 20 Permutation representations and proof of First Sylow Theorem
W Nov 22 Proof of Second and part of Third Sylow Theorem try exercises in book to classify groups using Sylow theorems, not just homework problems!
F Nov 24
M Nov 27
W Nov 29
F Dec 1
M Dec 4
T Dec 5 LAST DAY -- MONDAY SCHEDULE