Professor Gordana G. Todorov
MTH 3175 · Group Theory
Fall 2013

* Course Information and Class schedule

Course MTH 3175 · Group Theory
Instructor Gordana Todorov       Email g.todorov@neu.edu
Time Place MWTh 9:15-10:20 in 229 Richards Hall
Office 531 Lake Hall            Office Hours: MWTh 12:00-1:00pm
TA Floran Kacaku, Office: 534 NI            Recitation Session: W 2:00-4:00pm, Place: TBA
Textbook Contemporary Abstract Algebra Joseph A. Gallian
Grade 60% in-class exams, 40% final exam

* Course Description

    The course presents basic concepts and techniques of the group theory: symmetry groups, axiomatic definition of groups, important classes of groups (abelian, cyclic, additive and multiplicative groups of residues, permutation groups), Cayley table, subgroups, group homomorphisms, cosets, the Lagrange theorem, normal subgroups, quotient groups, direct products. Studies structural properties of groups. Possible applications include geometry, number theory, crystallography, physics, and combinatorics.

* Grading Policies

    There will be 5 quizzes. You will be allowed to drop your lowest quiz grade. If you miss a quizz for justifyable reason (illness or any other serious problem), you may drop one more quiz grade. There will be no make up quizzes.
    Quizzes count 60% and Final exam is 40%
    Course letter grades require the following minimum percent grades:
    A (95%), A-(90%), B+(86.7%), B(83.4%), B-(80%), C+(76.7%), C(73.4%), C-(70%), D+(66.7%), D(63.4%), D-(60%)

* Course Policies

    1. Students are responsible for ALL information and announcements given when they are absent.
    2. If you must leave class early, please, see me before class. No other early departures or walking during the class will be tolerated, with the exception of severe medical problems.
    3. All cell-phones must be turned off! If you are expecting important phone call, please, see me before class. Points will be deducted each time you use your phone in class!
    4. It is University policy that no grade, including an incomplete, can be changed after one year. Exceptions must be authorized by the Academic Standing Committee.
    5. All students without legitimate conflicts (approved by the instructor) will take the final exam at the scheduled time. Do not make travel plans that conflict with the final exam.

* About the course and you!

    This is a very beautiful course, with a lot of theory together with, both examples and strict proofs.
    You will be expected to write proper mathematical proofs!
    You are expected to do a lot of work in this course!
    You are expected to do HW without my collecting it and checking up on you. Discussion of the HW will form the first part of the next class.
    PLEASE REMEMBER, YOUR SUCCESS DEPENDS ON YOUR WORK!!!
 
W, Sep 4 Ch.0 - Preliminaries - HW p21: 1,2,4,7,8,9,11,14,20,21,22,53,54
Th, Sep 5 Ch.0 - Preliminaries
M, Sep 9 Ch.1 - Examples of symmetry groups - HW p35: 5,13,17,19,20,22
W, Sep 11 Ch.2 - Definition and Examples of Groups - HW p52: 1, 2, 3, 4, 5, 6, 7, 8
Th, Sep 12 Ch.2 - Elementary properties of groups - HW p52: 9, 14, 15, 16, 20, 23, 25, 32, 34
M, Sep 16 Ch.3 - Finite Groups; Subgroups - HW p64: 1, 2, 3, 10, 12, 18, 19, 20, 23, 26, 30
W, Sep 18 Ch.3 - Finite Groups; Subgroups - HW p67: 36, 37, 38, 39, 46, 47, 48, 51, 59, 60
Th, Sep 19 Quiz 1   &   Solving some additional problems from Ch.3
M, Sep 23 Ch.4 - Properties of Cyclic Groups - HW p81: 1-10, 14, 21, 26, 28
W, Sep 25 Ch.4 - Classification of Sugroups of Cyclic Groups - HW p83: 36,37,38,39,46,47,48,49, 50,51,59,60, 65, 66, 67
Th, Sep 26 Ch.4 - Cyclic Groups & Supplementary Exercises p91: 1-10, 17, 18, 22, 23,24,26, 27, 34, 35, 36
M, Sep 30 Ch.5 Permutations - HW p113: 1, 2, 3, 4, 5, 6, 7, 8, 9, 17, 18, 23, 24, 25, 26,
W, Oct 2 Ch.5 Permutations - HW p113: 27, 28, 31, 33, 43, 55, 58, 59
Th, Oct 3 Quiz 2   &   additional problems from Ch.5
M, Oct 7 Ch.6 - Isomorphisms - HW p133: 1-10, 14, 24, 25, 27, 29, 31, 32, 35, 37, 39
W, Oct 9 Ch.6 - Isomorphisms - HW p133: 35, 37, 39, 40, 47
Th, Oct 10 Ch.6 - Cosets and Lagrange's Theorem - HW p149: 1-9, 13, 14, 15, 16, 18, 25, 26
M, Oct 14 Ch.7 - ............................. Columbus Day - No NU classes ..........................
W, Oct 16 Ch.7 - Cosets and Lagrange's Theorem - HW p150: 34, 35, 38, 39, 45, 46, 47, 48, 50
Th, Oct 17 Quiz 3     &   Ch.8 - External Direct Product - HW p174: 1-20, 22, 24, 26, 27
M, Oct 21 Ch.8 - External Direct Product - HW p169: 44, 45,46,49, 53, 59, 62, 63, 74, 75
W, Oct 23 Ch.8   &   Supplementary Exercises p174: 5, 6, 7, 10, 13, 14, 25, 26,35, 50
Th, Oct 24 Ch.9 - Normal Subgroups - HW 193: 1,2,3,4,5,7,13,15,16,17,19,21
M, Oct 28 Ch.9 - Normal Subgroups
W, Oct 30 Ch.9 - Factor Groups - p193: 10,14,15,16,17,18
Th, Oct 31 Quiz 4   &   Ch.9 - Factor Groups - p193: 27,28,29,30,32,33,34,37,38,40,45,46,49,50,51,53,54,65,66,68
M, Nov 4 Ch.10 - Group homomorphisms, The First Isomorphism Theorem - p211: 5-27,48,53,54,55,56,62
W, Nov 6 Ch.11 - Fundamental Theorem of Finite Abelian Groups - p230: 1,3,4,5,7,13,15,16,17,19,21
Th, Nov 7 Ch.11 - Isomorphism Classes of Abelian Groups
M, Nov 11..................................... Veteran's day - no classes .....................
W, Nov 20 Group Actions    
Th, Nov 21 Quiz 5   &   Group Actions
M, Nov 25 Ch. 24 - Syllow Theorems - p.414: 5-8, 10-14, 16-22
W, Nov 27 ................................... Thanksgiving recess .....................................
Th, Nov 28 ................................... Thanksgiving day .........................................
M, Dec 2 Ch.24 - Syllow Theorems - p. 414: 24-28,30,31,39,40, 46,47 & Applications of Syllow Theorems
W, Dec 4 Review - Last day of NU classes
Th, Dec 5................................... Reading Day ................. No NU classes ..........
Department of Mathematics  Office:  531 Lake Hall  Messages:  (617) 373-2450 
Northeastern University Phone:  (617) 373-2450  Fax: (617) 373-5658
Boston, MA, 02115  Email:  g.todorov@neu.edu Directions

Home Started:  September 11, 2009
Last modified:  September 3, 2013