Math 4371
Modern Algebra
Instructor: Todd Frauenholtz
Office: 367 HS
Phone: 755-2817
Class meets: M, W, F in HS 233 from 2:00 - 2:50 pm.
Office hours: M, W, F from 3:00 pm – 4:00 pm or by other arrangement
Required Text: Contemporary Abstract Algebra, sixth ed. by Joseph A. Gallian
Description: A study of abstract algebraic systems with an emphasis on groups and an introduction to rings. Prerequisite: Math 3310.
Goals and objectives of the course:
Students will:
Homework: Homework assignments will be made in class. You should read and understand all sections of the chapters and assigned problems to prepare for quizzes and exams. Points will be given for homework.
Class participation and quizzes: Class participation is expected and in order to participate you need to be present. Quizzes will be unannounced and given frequently to help you prepare for the exams. Quizzes cannot be made up but your lowest quiz score will be dropped from the calculation of your grade. Cell phones must be turned off during class.
Exams: There are two exams planned including the final exam. See me in advance to schedule a time to take the exam if you will be missing class on an exam day. The mid-term will depend on course timing and the final exam is scheduled for Tuesday, December 20th from 1 – 3 pm.
Grades: Grades for this course will be based upon homework, quizzes, tests, and a comprehensive final exam; some of the quizzes may be unannounced. Items for both will come from the assigned homework. The following grading scale will be used to determine grades:
A | 90 – 100 % |
B | 80 – 89 % |
C | 70 – 79 % |
D | 60 – 69 % |
F | Below 60% |
Make-ups are not allowed for missed quizzes, instead I will
allow you to drop your lowest quiz score from the term.
All tests will count toward your final grade.
The instructor reserves the right to adjust the grading scale if
necessary.
Working through the assigned problems is essential to
learning mathematics. Showing your
work is the only way to receive partial credit and hence is very important.
Academic integrity:
Students are expected to practice the highest standards of ethics,
honesty, and integrity in all of their academic work.
Any form of academic dishonesty (e.g., plagiarism, cheating,
misrepresentation) may result in disciplinary action. Possible disciplinary actions may include failure for part or
all of a course, as well as suspension from the University.
Upon request, this document and others distributed in this course can be made available in alternate formats. Please contact the instructor, Todd Frauenholtz, at 755-2817 or Kathi Hagen in the Office for Students with Disabilities at 755-3883 for assistance.
Daily Course Outline
Day 1 |
Ch 0 – division algorithm (pictorial), GCD linear combination, Fund. Thm arithmetic, modular arithmetic, equivalence relations, functions. Ch 0: 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 15, 16, 17, 20, 25, 27, 29, 33, 34, 41, 42, 47, 48, 49, 53. |
Day 2 |
Continue Ch. 0. |
Day 3 |
Ch. 1 – Construct Cayley table for triangle (D3). Abelian (pg. 34) Ch 1: 1, 2, 3, 6, 7, 8, 9, 10, 16, 18, 19. |
Day 4 |
Continue Ch. 1. |
Day 5 |
Ch. 2 – Groups (is our class a “group?”), Identity, Inverses. Ch 2: 1, 2, 3, 4, 5, 8, 13, 14, 15, 16, 19, 24, 25, 26, 35. |
Day 6 |
Continue Ch. 2. Identity and inverse |
Day 7 |
Continue Ch. 2. |
Day 8 |
Ch. 3 - Subgroups Ch 3: 1, 2, 3, 4, 7, 8, 12, 13, 17, 21, 22, 28, 29, 34, 38, 43. |
Day 9 |
Continue Ch. 3. |
Day 10 |
Continue Ch. 3 |
Day 11 |
Continue Ch. 3 |
Day 12 |
Ch. 4 - Cyclic groups Ch. 4: 3, 4, 5, 6, 7, 9, 13, 14, 19, 21, 22, 30, 32, 37, 38, 49, 63. |
Day 13 |
Continue Ch. 4. |
Day 14 |
Continue Ch. 4. |
Day 15 |
Ch. 5 - Permutation Groups Ch. 5: 1-4, 9, 10, 11, 17, 18, 20, 23, 27, 28, 31, 38. |
Day 16 |
Continue Ch. 5 |
Day 17 |
Continue Ch. 5 |
Day 18 |
Finish Ch. 5 |
Day 19 |
Ch. 6 - Isomorphisms Ch. 6: 1, 2, 3, 4, 5, 6, 11, 12, 16, 17, 22, 24, 25, 29. |
Day 20 |
Oct. 14th - no classes |
Day 21 |
Review for exam |
Day 22 |
Mid-term Exam |
Day 23 |
Continue Ch. 6 - isomorphism in graph theory |
Day 24 |
Continue Ch. 6 |
Day 25 |
Ch. 7 - Cosets Ch. 7: 1, 2, 3, 7, 8, 9, 10, 13, 14, 17, 19, 21, 25, 26, 35. |
Day 26 |
Continue Ch. 7 |
Day 27 |
Review Ch. 6 - Isomorphisms |
Day 28 |
Continue Ch. 7 |
Day 29 |
Continue Ch. 7 |
Day 30 |
Ch. 8 - External Direct Products Ch. 8: 1, 4, 5, 6, 7, 8, 9, 12, 14, 15, 20, 35. |
Day 31 |
Continue Ch. 8 |
Day 32 |
No classes - Veteran's Day |
Day 33 |
Ch. 9 - Normal Subgroups and Factor Groups Ch. 9: 1, 3, 4, 6, 8, 15, 16, 21, 22, 23, 25. |
Day 34 |
Continue Ch. 9 |
Day 35 |
Continue Ch. 9 |
Day 36 |
THANKSGIVING BREAK |
Day 37 |
Ch. 10 - Group Homomorphisms Ch. 10: 1, 2, 5, 7, 9, 10, 14, 26, 27. |
Day 38 |
Continue Ch. 10 |
Day 39 |
Continue Ch. 10 |
Day 40 |
Ch. 12 - Introduction to Rings Ch. 12: 1, 2, 3, 4, 8, 13, 15, 17, 19, 20, 41. |
Day 41 |
Continue Ch. 12 |
Day 42 |
|
Day 43 |
Review for final |
Day 44 |
FINAL EXAM - December 20th from 1 pm to 3 pm. |
updated 11/28/2005
by Todd
Frauenholtz