Math 3330: Abstract Algebra, Spring 2018

Basic Info

Instructor: Dr. Mark Tomforde
Office: 601 PGH
Office Hours: TuTh 3:00--3:50PM in 601PGH.
Lecture: TuTh 4:00--5:20PM in Room 104 of Agnes Arnold Hall (AH)
Syllabus: Download the Syllabus
Tutoring Session:
 		 10AM-11AM on Tuesdays in MUSL (Fleming Basement, Room 11), run by Shahzad.
2PM-3PM on Wednesdays in MUSL (Fleming Basement, Room 11), run by Shahzad.
  Schedule for all tutoring in MUSL (Any tutor should be able to help you with Math 3330 material.)



Assignments

Homework #11, Due Thursday, April 26
Chapter 10, p.219, Problems 10, 11, 12, 48; Chapter 11, p.234, Problems 4, 6, 9, 10, 12, 22


Reading Assignment #10, to be done prior to class on Thursday, April 26
Chapter 11, The Fundamental Theorem
Chapter 11, The Isomorphism Classes of Abelian Groups
Chapter 11, Proof of the Fundamental Theorem


Homework #10, Due Thursday, April 19
Chapter 9, p.200, Problems 6, 7, 12, 13, 14, 31, 32, 37, 38, 40


Reading Assignment #9, to be done prior to class on Thursday, April 19
Chapter 8, Definition and Examples
Chapter 8, Properties of External Direct Products
Chapter 8, The Group of Units Modulo n as an External Direct Product
Chapter 9, Internal Direct Products
Chapter 10, Definition and Examples
Chapter 10, Properties of Homomorphisms
Chapter 10, The First Isomorphism Theorem


Homework #9, Due Thursday, April 5
Chapter 7, p.156, Problems 17, 18, 20, 21, 23, 24, 30, 33, 42, 44


Reading Assignment #8, to be done prior to class on Thursday, April 5
Chapter 9, Normal Subgroups
Chapter 9, Factor Groups
Chapter 9, Applications of Factor Groups


Homework #8, Due Thursday, March 29
Chapter 7, p.156, Problems 1, 2, 5, 7, 8, 11, 12, 15, 16, 19


Reading Assignment #7, to be done prior to class on Thursday, March 29
Chapter 7, Section "Properties of Cosets"
Chapter 7, Section "Lagrange's Theorem and Consequences"


Homework #7, Due Thursday, March 22
Please turn in these problems.


Reading Assignment #6, to be done prior to class on Thursday, March 22
Chapter 6, Section "Cayley’s Theorem"
Chapter 6, Section "Properties of Isomorphisms" (reread)
Chapter 6, Section "Automorphisms"


Homework #6, Due Thursday, March 8
Chapter 5, p.118, Problems 2(a)(b), 6, 7, 8, 11(a)(b)(c)(d)(e), 15, 23; (Scoring: #2 is 3 points total, #11 is 2.5 points total, #15 is 0.5 points, and the rest are 1 point each)


Reading Assignment #5, to be done prior to class on Thursday, March 8
Chapter 5, Section "Definition and Notation"
Chapter 5, Section "Cycle Notation"
Chapter 5, Section "Properties of Permutations"


Homework #5, Due Thursday, March 1
Please turn in these problems.


Reading Assignment #4, to be done prior to class on Thursday, March 1
Chapter 6, Section "Definition and Examples"
Chapter 6, Section "Properties of Isomorphisms"
Also read p.208-210, including Theorem 10.1 parts (1)-(4) and their proofs. Ignore parts (5) and (6) of Theorem 10.1


Homework #4, Due Thursday, February 15
Please turn in these problems.


Reading Assignment #3, to be done prior to class on Thursday, February 15
Chapter 5, Section "Definition and Notation"
Chapter 5, Section "Cycle Notation"
Chapter 5, Section "Properties of Permutations"


Homework #3, Due Thursday, February 8
Please turn in these problems.


Reading Assignment #2, to be done prior to class on Thursday, February 8
Chapter 3, Section "Terminology and Notation"
Chapter 3, Section "Subgroup Tests"
Chapter 3, Section "Examples of Subgroups"
Chapter 4, Section "Properties of Cyclic Groups"
Chapter 4, Section "Classification of Subgroups of Cyclic Groups"
For Fun: More info on Latin Squares


Homework #2, Due Thursday, February 1
Please turn in these problems. Be sure to follow the Homework Rules in the Syllabus, since you will lose points for each infraction. Also keep in mind that homework is late once I start lecturing on February 1, and late homework will not be accepted.


Reading Assignment #1, to be done prior to class on Thursday, February 1
Chapter 1, Section "Symmetries of a Square"
Chapter 1, Section "The Dihedral Groups"
Chapter 2, Section "Definition and Examples of Groups"
Chapter 2, Section "Elementary Properties of Groups"
Chapter 2, Section "Historical Note"

Also, the material in Chapter 0: Preliminaries should be familiar to you from your Transitions to Advanced Mathematics course. You should skim p.3-40 of the book, and read in detail any sections dealing with topics you don't feel comfortable with or believe you would benefit from review on.


Homework #1, Due Tuesday, January 23
Please complete and turn in this information sheet.


Dates of Exams

Exam 1: Tuesday, February 20 in class.
Exam 2: Tuesday, March 27 in class.
Final: Thursday, May 10, 5PM--8PM in our usual classroom.


Some Additional Resources

If this is one of your first proofs courses, you might find the following two guides useful:

Advanced mathematics courses are difficult, and you will be challenged in many ways throughout this course. Research has shown that the students that are the most successful are the ones who have two qualities: Growth Mindset and Grit. View, read, and watch the following resources on Growth Mindset and Grit. Throughout the course, do your best to keep these ideas in mind as you encounter difficult portions of the material.