TEXAS A&M UNIVERSITY-Corpus Christi
Division of Computing and Mathematical Sciences

MATH 4306.001
Modern Algebra
Spring 2002

I. COURSE INFORMATION

  1. Meeting Time & Place: Tuesday, Thursday, 7 to 8:15 PM. CCH 104, though Tuesday meetings will be held in a computer lab, CCH 206.
  2. Professor: Dr. George Tintera
  3. Office Phone: (361) 825-6028
  4. Office Address: CI 303
  5. E-MAIL Address: tintera@falcon.tamucc.edu
  6. Web Page Address: http://www.tamucc.edu/~tintera/sp02/4306
  7. Calendar Page: http://www.tamucc.edu/~tintera/sp02/4306/4306cal.html
  8. Wiki Page: http://www.sci.tamucc.edu/wiki/Math4306/HomePage
  9. Office Hours: M/W from 1 to 2:30 PM; T/Th from 5:30 to 7 PM. Others by appointment

II. COURSE DESCRIPTION

Fundamentals of set operations, maps and relations, groups, rings and field theory, Topics include groups, cosets, homomorphisms, isomorphisms, direct products of groups, and rings, integral domains, field of quotients, fundamental properties of integers, the ring of integers modulo n and rings of polynomials. Applications.

III. PREREQUISITES for the COURSE

MATH 3311 and MATH 3313 with a grade of A or B

IV. TEXT and OTHER SUPPLIES REQUIRED

Learning Abstract Algebra, by Dubinsky and Leron, Springer Verlag, 1994.

V. COURSE OBJECTIVES

This course is designed to enable students to:

  1. Understand the importance of sets and mappings in algebra and other areas of mathematics.
  2. Understand the properties of the most important algebraic structures, and to recognize the relationship between them.
  3. Use phyical and programming models to discover properties and relationships
  4. Read and reproduce proofs for relevant theorems, and apply these techniques to construct arguments and proofs for textbook and other problems.
  5. Perform guided self-teaching to support the development of independent thinking, and participate in classroom discussions and presentations to develop communication skills.
  6. Establish coneections between Modern Algebra and other topics in mathematics.

VI. INSTRUCTIONAL METHODS AND ACTIVITIES

The heart of the instructional method for this course is the use of the programming language ISETL by students to 'sense' and develop models of mathematical objects. Students will complete activities using ISETL, participate in class discussion to formalize mathematical concepts, and then, complete exercises to demonstrate complete understanding. Participation in group and class activities will be key to the success of most students in the class.

VII. EVALUATION AND GRADE ASSIGNMENT

Course grades will be based on ISETL activities (25%), homework (25%), group work (0%), class discussion (0%), midterm (25%), final exam (25%).

  • ISETL Activities will be done at the start of each week. They are due by the start of the second class meeting of each week. Time allotted in class for ISETL activities may not be used for doing homework. You must choose as to whether you want to do the activities in a group or by yourself.
  • Homework will be assigned each Thursday meeting and due the following Thursday. It may be discussed with classmates, but the solutions turned in should be done individually
  • Groupwork will not be graded but is strongly encouraged.
  • Class Discussion will not be graded but is strongly encouraged.
  • Midterm will take place during the 7th week of class. It will include only mathematical topics, not programming in ISETL.
  • The Final Exam will be held 7 to 9:30, Wednesday, May 8. It will be comprehensive and
  • multiple choice.

Grading Scale:

Grade
A
B
C
D
F
Score
90% - 100%
80% - 89%
70% - 79%
60% - 69%
0% - 59%

VIII. TENTATIVE COURSE SCHEDULE

Attached.

IX. CLASS POLICIES

  • This class is run for the mathematical development of all participants. All students must accept responsibility for participating and consequences of not participating.
  • You are the only person responsible for your registration. No one will drop you for not attending class. Please make sure that you drop the class yourself if you are not able to continue coming to class. Please note that the last day to drop the class with a grade of "W" is March 29.
  • Please turn off phones and beepers before coming to class.
  • Attendance is expected. It is the only way to do in-class work.
  • All absences from the midterm and final exam will be considered unexcused unless they are documented in advance as excusable with the instructor or as soon as possible in the case of emergencies. No credit will be awarded for unexcused absences from the final exam or midterm.