Math 4413-01W: Abstract Algebra I
Instructor: Dr. David G. Robinson, Boyd #326, 678-839-4137
Office Hours (Tentatively): MWF 8 – 9:50 a.m., 12 – 12:50 p.m.
Class Meetings: MWF 1 – 1:50 p.m., TLC #1106 (to be changed)
These will consist of a combination of lectures, question-and-answer sessions, problem presentations, and general discussions. All reading will be assigned in advance of the meeting thereon.
Text/Resources: Saracino, Dan, Abstract Algebra: A First Course, Waveland Press, Inc., Long Grove, IL, 1980, 1992
Prerequisites: Math 3413
Topics: Sets and Relations (Sections 0,1,7, 8 and9; » 2 weeks): sets, subsets, Boolean algebra, posets and lattices, well-ordering principle, mathematical induction, equivalence relations, partitions, functions, permutations, binary operations, associativity, commutativity, etc.
Groups (Sections 2 – 6, 8 - 14; » 7 weeks): group axioms, group tables, cancellation laws, abelian groups, cyclic groups, subgroups, direct products, symmetric groups, cycle structure of a permutation, dihedral groups, cosets, Lagrange’s Theorem, normal subgroups, quotient groups, group homomorphisms, isomorphism theorems, abelian group factorizations, etc.
Rings and Fields (Sections 16 -21; » 5 weeks): ring axioms, units, zero-divisors, nilpotency, integral domains, division rings, fields, subrings, ideals, quotient rings, principal ideals, prime ideals, maximal ideals, ring homomorphisms, isomorphism theorems, prime fields, polynomial rings, irreducible polynomials, simple field extensions, finite fields, principal ideal domains, unique factorization domains, Euclidean domains, sums of squares, Fermat’s theorems, etc.
Objectives: Besides developing your understanding of the topics mentioned above, there are some particular skills you should improve upon along the way in order to be able to apply what you learn in this course to future courses of study. These include:
· use of appropriate mathematical terminology and notation
· mathematical abstraction and conjecturing
· recognition of algebraic structures throughout math and science
· mathematical proof techniques
· writing skills – both formal and informal
This is a Writing Across the Curriculum (WAC) course, as indicated by the “W” after the section number of the course. Like all such courses, it emphasizes writing as a tool for both learning and communication. Therefore the writing assignments for this course are divided into two types according as the main objective is either “writing to learn” (WTL) or “writing to communicate” (WTC). The specific assignments are as follows:
· Problem solutions/proofs (approximately three or four per week)
· Short-answer test questions (two or three per test)
· Logbook of definitions, theorems and conjectures (to be submitted at the end of each test, though entries should be made daily)
· Formal Paper (five-pages, type-written) on some application of or some aspect of the historical development of abstract algebra. You will submit this in three stages: (1) Description of the topic and the references to be used (2) Rough draft (3) Final draft. (See the attached schedule for exact due dates.)
Procedures: Your understanding of the subject material and your progress toward the aforementioned objectives will be evaluated on the basis of your written solutions/proofs of selected homework problems*, your performances on three written tests, your Logbook, your applications/history paper , and your class participation (attendance, preparedness and contributions.)
[*Homework problems from the text or from class will be assigned regularly and discussed in class whenever possible. Be prepared to discuss them, along with the readings, as soon as possible after they are assigned!]
Criteria: Grades on all work will be based upon
· accuracy of information (including calculations and
use of mathematical symbols and terminology)
· depth and breadth of solutions
· logic and clarity of arguments
· neatness and clarity of presentation
· correctness of grammar and spelling
· thoroughness and timeliness of work
· intellectual honesty and creativity
· achievement of personal potential
· difficulty of the assignment/test
Grades: My scale for converting numerical grades (i.e., percentage points) to letter grades will be as follows:
89-100 A, 77-88 B, 65-76 C, 50-64 D, below 50 F
Your final grade will be based on your problem solutions/proofs (30%), test scores (40%), Logbook entries (10%), application/history paper (10%) and class participation (10%). Class participation includes attendance: Missing more than three class meetings for any reason will result in a deduction of 1 point per absence (beyond the third) from the 10 points available.
· Attendance is important! However, should you find for some reason that you must miss a class meeting, remember that you are still responsible for any and all material you may have missed during your absence.
· Problem set solutions/proofs must be turned in at the prescribed times (TBA) in order to be eligible for any credit. All work on these assignments must be your own, i.e., no help from anyone, without prior permission from the instructor. Failure to abide by this policy will lead to serious consequences: automatic zero on the assignment in question, possible expulsion from the class, etc.
· Tests must be taken at the prescribed times (see attached schedule), except by prior permission from the instructor, which will only be given under the direst of circumstances (serious illness, e.g.). In order for you to obtain such permission, I must be notified of your “dire circumstances”, by e-mail, phone, or otherwise, before the test is over. Otherwise you will almost certainly receive a score of zero for that test.
· If you find yourself falling behind in the course, do not delay in seeking out appropriate help and advice from someone who is competent in the subject area and who has your best interests at heart!
· I assume you will abide by the UWG Honor Code. So will I!