Math 3330: Abstract Algebra, Spring 2018
Basic Info
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.
- Growth Mindset is the belief that your ability to learn is not fixed, that
you become better at any subject with effort and practice, and that failure is not
permanent.
- Grit is the ability to stick with and pursue a goal over a long period of
time. This includes the ability to stay determined and motivated
despite experiences with failure or adversity.