Math 432 Abstract Algebra Spring 10 by FWvp68C


									                                                                           MATH 432—SPRING 2010

                               Mathematics 432: Abstract Algebra

Instructor:      Dr. Chris Thron
Office:          TAMUCT North Campus 16B
Contact:         512.293.0715 (cell); (email)
                 chris.thron (skype) (google chat)

Office Hours:
       Mon. 5 – 6
       Tues 9:00 – 1:30
       Wed. 5 – 6
       Thurs 9:00-11:30
       Sat (virtual) 8:30 – 9:30 pm (contact via phone, Google chat or Skype)
          You are welcome to schedule appointments outside of office hours at your convenience.

1.0    Course Overview:
The study of preliminary notions, group theory, the theory of rings and ideals, and polynomial
Extended description: Topics to be covered include set theory, including elementary concepts of
sets, set operations, indexed collections of sets, and products of sets; the theory of functions and
relations, including relations, equivalence relations, partitions, composition of functions, inverse
functions, and extension and restriction functions; group theory, including permutations, basic
definitions and properties of groups, subgroups, group structures, operation preserving maps
between groups, cyclic groups, and quotient groups; and ring theory if time permits, including
basic definitions and properties of rings, subrings, ring structures, integral domains, fields, ideals,
operation preserving maps between rings, quotient rings, and polynomial rings.
Prerequisite: MATH 332, Linear Algebra. Students will be asked to demonstrate competence in
prerequisite material that is essential for success in this course.

2.0   Competency Goal Statements:
Students will:
     comprehend definitions;
     state and write rigorous proofs of related mathematical theorems according to the
      standards of mathematics;
     perform the computations related to the material;
     demonstrate the use of the theoretical results and computational aspects on required
      applications; and
     connect the material to other courses.

3.0       Required Materials
         Abstract Algebra, Theory and Applications by Thomas Judson
          ( This is a free textbook that you can download
          and print for yourself.
         Facebook: Abstract Algebra: Theory and Applications
         Twitter: aata_sfa
                                                                         MATH 432—SPRING 2010

4.0       Course Requirements
         Reading questions (16%). You are expected to read the textbook outside of class and
          answer questions posed by the instructor. Your answers must be posted on Blackboard 8
          hours before the next class period.
             You should expect a reading assignment before every class. However, the weekday
          reading assignment will be much lighter than the weekend assignment. Expect to spend
          2-3 hours per week outside of class in reading the textbook. (28 assignments total – the
          lowest 4 will not be counted)
         Homework problems (16%). These will be due once a week, the same time every week (to
          be determined by the instructor). Expect to spend 3-4 hours per week outside of class in
          doing homework. (14 assignments total – the lowest 2 will not be counted)
         Exams (68%). There are 3 midterm exams and a final. Exams will be in class, and will
          closely follow the homework. Students will be allowed to use a “cheat sheet”, as per
          instructor guidelines.
          Note: The final has the same weight as two midterms. Thus there are essentially five
          midterm grades. Your score will be based on the best four of these five grades.
          Please note: It is mathematically impossible to pass the course without doing at
          least some of the reading and homework. I will not substitute an exam grade for the
          reading or homework grades.

5.0    Grading Criteria Rubric and Conversion
       Reading Questions                       (240 points) 16%          90-100%=A
       Homework                                (240 points) 16%          80- 89%= B
       Each exam (midterm or ½ final)          (255 points) 17%          70- 79%= C
       Each exam (midterm or ½ final)          (255 points) 17%          60- 69%= D
       Each exam (midterm or ½ final)          (255 points) 17%          Below 60 % F
       Each exam (midterm or ½ final)          (255 points) 17%
       TOTAL                                   (1500 points) 100%
Scoring for each of these categories is as follows:
 Each biweekly Reading assignment will be assigned up to 10 points. Grading is based on
   completion plus detailed grading of a random sampling of the questions. The lowest four
   reading assignment grades will not be counted.
 Each weekly Homework assignment will be assigned up to 20 points. Grading is based on
   completion plus detailed grading of a random sampling of the questions. The lowest two
   homework assignment grades will not be counted.
 Exams will be a combination of multiple-choice, diagram, and short-answer questions at the
   instructor’s discretion. The instructor reserves the right to determine the relative proportion of
   these questions, to provide best coverage of the material.
 In addition to the point values given above, up to 20 points extra credit (1%) may be given at
   instructor’s discretion for additional class or take-home activities.
                                                                         MATH 432—SPRING 2010

6.0     Course Calendar FALL 2009

      Class dates Chapter and Selected Topics

       1/19-21     Chapter 0, Preliminaries: Proofs, sets, equivalence relations

       1/25-28     Chapter 0 and Section 1.1: Induction

         2/1-4     Section 1.2 Division Algorithm: Section 2.1 Integers mod n and symmetries

        2/8-11     Section 2.2 Definitions and Examples

       2/15-18     Review and Exam 1 Covers up to page 43

                   Section 2.3 Subgroups Section 3.1 Cyclic Groups; Section 3.2 The group

         3/1-4     Complex numbers and Section 4.1 Permutations: definitions

        3/8-11     Complex roots and Section 4.2 Dihedral groups

       3/15-17                          S P R I N G B R E A K (yeah!)

       3/22-25     Review and Exam 2 Covers pages 44-64 and 67-88

                   Section 5.1 Cosets Section 5.2 Lagrange’s Theorem; Section 5.3 Fermat’s
      3/29 – 4/1
                   and Euler’s

         4/5-8     Section 8.1 Isomorphisms Section 8.2 Direct products

                   Section 9.1 Factor groups and normal subgroups; Section 9.2

       4/19-22     Section 10.1 Matrix groups; Section 10.2 Symmetry

       4/26-29     Review and Exam 3

         5/3-6     TBD

7.0 Drop Policy
If you discover that you need to drop this class, you must go to the Records Office and ask for the
necessary paperwork. Professors cannot drop students; this is always the responsibility of the
student. The Records Office will give a deadline by which the form must be returned, completed
and signed. Once you return the signed form to the records office and wait 24 hours, you must go
into Duck Trax and confirm that you are no longer enrolled. If you are still enrolled, FOLLOW-UP
with the records office immediately. You are to attend class until the procedure is complete to
avoid penalty for absence. Should you miss the deadline or fail to follow the procedure, you will
receive an F in the course.
The last date to drop with no record on the transcript is Feb 3.

8.0 Academic Honesty (Tarleton State University Catalog, p. 37)
                                                                         MATH 432—SPRING 2010

Texas A&M University-Central Texas expects all students to maintain high standards of personal
and scholarly conduct. Students guilty of academic dishonesty are subject to disciplinary action.
Academic dishonesty includes, but is not limited to, cheating on an examination or other
academic work, plagiarism, collusion, and the abuse of resource materials. The faculty member is
responsible for initiating action for each case of academic dishonesty.

9.0 . Disability Services
It is the policy of Texas A&M University-Central Texas to comply with the Americans with
Disabilities Act and other applicable laws. If you are a student with a disability seeking
accommodations for this course, please contact Sarina Swindell, Assistant to the President for
Diversity and External Education Initiatives, at 254.519.5711 or Student
Disability Services is located in TAMUCT Main Building, room 104C.

10. Library Services
INFORMATION LITERACY focuses on research skills which prepare individuals to live and work
in an information-centered society. Librarians will work with students in the development of critical
reasoning, ethical use of information, and the appropriate use of secondary research techniques.
Help may include, yet is not limited to: exploration of information resources such as library
collections and services, identification of subject databases and scholarly journals, and execution
of effective search strategies. Library resources are outlined and accessed at

11. Grading Policies
Regular attendance is extremely important to your success in this course. If you are absent, it is
your responsibility to find out what material was covered.

In general, makeup work is not accepted. I compensate for this by dropping the three lowest
reading grades and the two lowest homework assignments.

Exceptions to this policy may be made at the instructor's discretion in case of:
    Prolonged illness
      Death in the immediate family
      Legal proceedings
                                                                        MATH 432—SPRING 2010

                                  Appendix: Course Philosophy
A.      Instructor Goals
      Algebra is the foundation of all mathematics. Many mathematicians never use calculus, or
      geometry, but all use algebra, or at least some concepts from algebra.
      The key to abstract algebra is abstraction—that is, taking something concrete and
      generalizing it. We all know what + and  are – but algebra takes these well-known
      concepts, strips away the specifics, and generalizes them so that they can take on a whole
      new meaning.
      Probably the most important thing to be gained from this course is an understanding of the
      process of abstraction, which is the heart of theoretical mathematics.

B.    Course Methodology
      In most courses, there are these common components:
      A)       Reading the textbook
      B)       Lecture /classwork
      C)       Homework Problems
      D)       Projects and Lab exercises
      E)       Quizzes or Tests

      A. As higher-level mathematics students, it is important that you learn to read mathematics
      for yourself. For each class I will assign reading comprehension questions.
      B. Lectures will be overviews of what you have read for yourself in the textbook. To
      understand the lectures, you will need to read the textbook before class. I will also work a
      fair number of example problems.
      C. In this course, Homework is central. When you get right down to it, doing math means
      being able to do the problems. If you can't do the problems, then you can't do math.
      Homework will be graded partly for completion grade, partly for content. Homework will be
      due every week on the first class day.
      E. Tests will be roughly every 5 weeks. Each test will cover about 4 chapters. The final will
      count twice as much as a midterm. Of the five grades (3 midterm grades and 2 half-final
      grades), the highest 4 will be counted.
C. Instructor Responsibilities:
     Post necessary study materials on Blackboard
      Respond effectively to all email requests within 36 hours (Please use
      Solicit feedback and respond effectively to student concerns about class organization,
       presentation, and content.
      Return all papers no more than 1 week after they are handed in
      Make all grades available to students via Blackboard after each midterm test.

D. Student Responsibilities:
     Complete each assignment by the specified due date.
      Sign up for the Google Group for this class.
                                                                    MATH 432—SPRING 2010

 Obtain assignments and other information for classes from which they are absent.
 If necessary materials are missing from Blackboard, request the instructor to put
  them up.
 Make use of all available study-aid options to resolve any questions that they might have
  regarding course material. These include:
      Coming to office hours
      Contacting the instructor outside of office hours via phone, chat, or email
      Tutoring on campus
   Discussion with other students
 Give as much of an effort as it takes to pass this course. You should expect to spend two
  hours outside of class for every in-class hour. If your background is weak, you may have
  to spend more time than this.
 Save all graded work. If there is a dispute about grades, no recorded grade will be
  changed unless the paper in question is produced.

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