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:

  1. develop a deeper understanding of mathematical topics covered.
  2. explore modular arithmetic as an example of a cyclic group.
  3. know the definition of a group and be able to determine if something is an example, or a non-example, of a group.
  4. learn about subgroups, including definition and examples.
  5. further develop their mathematical vocabulary with terms such as isomorphism.
  6. seek relevance to related professions, for example the secondary mathematics curriculum.

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.  

Current Grade Sheet

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.

 


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updated 11/28/2005
by Todd Frauenholtz