MATH 432—SPRING 2010 Mathematics 432: Abstract Algebra Instructor: Dr. Chris Thron Office: TAMUCT North Campus 16B Contact: 512.293.0715 (cell); email@example.com (email) chris.thron (skype) firstname.lastname@example.org (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 rings. 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 (http://abstract.ups.edu/download.html). 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 2/22-25 C* 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 4/12-15 Homomorphisms 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 Note: 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 email@example.com. 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 http://www.tarleton.edu/centraltexas/departments/library/ 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 firstname.lastname@example.org) 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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