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SyllabusThe topic of this course is Abstract Algebra. The basic approach is to isolate or 'abstract out' the important properties of the fundamental number systems (the complex numbers C, the reals R, the rationals Q, and the integers Z) which we utilized when learning algebra in high school. Then, utilizing these select assumptions or axioms, we see what results follow; there are many important and deep and even beautiful consequences of our relatively few assumptions.We will begin with the notion of a 'group.' A 'group' is a collection of objects (say R) with a distingushed binary operation (say +) satisfying particular properties including associativity, the existence of an identity, and the existence of inverses. We will spend approximately twothirds of the course in Chapters 1 to 10 becoming thoroughly acquainted with groups by studying specific examples of groups, distinguished groups with further 'nice' properties, subgroups, mappings between groups, and special subsets of groups including cosets and normal subgroups.
The remaining third of the course will be spent in
Chapters 12 to 18 with the notion of a 'ring.'
A 'ring' is a collection of objects (say R) with
two distingushed binary operations (say + and x) satisfying particular properties
including being a commutative (or Abelian) group under the first operation and
having certain 'distributive' relations hold between the operations.
The study of rings will roughly parallel that of groups;
we will study specific examples of rings, distinguished rings including
integral domains and fields, special subsets of rings including subrings and ideals,
and mappings among rings.
LecturesProfessorMy name is Alex McAllister and I will be teaching Math 31 for Winter 1999. My office is 411 Bradley Hall and my telephone number is 6462960. If you need to speak with me, you may come to my office hours, or contact me via email at Alex.M.McAllister@dartmouth.edu. You might also be interested in visiting my home page at http://www.math.dartmouth.edu/~amcallis/.TextbookThe textbook for this course is:
GradesYour grade for the course will be determined by the following:ExamsAs mentioned above, there will be a Midterm Exam and a Final Exam. The Midterm Exam has already been scheduled; the Final Exam will occur between March 12th and March 16th at the time and place regularly scheduled by the registrar.Unless reported to me before January 11th, a scheduling conflict is not a sufficient excuse to take the Midterm Exam at any time other than the official time listed below. The Final Exam will occur between March 12th and March 16th. If you must make travel plans before the schedule for final exams appears, Do Not make plans to leave Hanover on or before March 16th. The Final Exam Will Not be given early to accommodate travel plans. The exams will take place at the following times and places:
Class ParticipationClass participation is an essential part of the course; mathematics is not a spectator sport. For this course, class participation consists of class attendance, reading assignments, quizzes, and homework problems.You are expected to attend every class. You have invested a large sum of money for the opportunity to come to class and I will invest a large amount of time in preparing for class; I do not want any of us wasting the investments we have made. Reading assignments will be given daily and should be read before coming to class. For some of my thoughts on reading mathematics texts, click here. Quizzes will be administered at the end of class on Monday covering material presented in class the previous week. They will consist of a couple of questions and should only take 10  15 minutes to complete. If you do the homework for the lectures given the previous week (including Friday's homework), then you should do fine on the quizzes.
Homework problems will be assigned daily and collected the following class period.
Homework will be turned in and picked up from the boxes outside of 103 Bradley Hall.
Late homework will not be accepted and a grade of 0 will be assigned
(of course, exceptions can be made for emergencies such as illness, death, natural disasters...).
The solutions you present must be coherent and written in complete sentences whenever possible.
Simply stating answers or turning in garbled, unclear solutions will result in a grade of 0.
For further details consult the
Homework Schedule.
Honor PrincipleWork on all quizzes and exams should be strictly your own.
Collaboration on homework is encouraged (and expected);
although, you should first spend some time in individual concentration to gain
the full benefit of the homework. On the other hand, copying is discouraged.
You should not be leaving a study group with your homework ready
to be turned in; write up your solution sets by yourself.
DisabilitiesI encourage students with disabilities, including but not limited to disabilities like chronic diseases, learning disabilities, and psychiatric disabilities, and students dealing with other exceptional circumstances to come see me after class or during office hours so that we can make appropriate accommodations. Also, you should stop by the Academic Skills Center in Collis Center to register for support services.QuestionsIf you have any questions about this syllabus or about the material presented in this course, come talk to me. Although, I do enjoy mathematics, I am not here just to have fun. My primary goal is to help you learn and understand abstract algebra. Your questions are an important part of your learning process, and I can help you find answers.Some Final ThoughtsThe bulk of the course will be studying formal concepts and proving formal theorems. Do not get behind; it will be very difficult, if not impossible, to catch up. Study all the material as it is covered and make sure that you understand it. Simply remembering it, although necessary, will not be adequate.Also, take care in crafting your own proofs. You should be creating clear, coherent arguments. Use complete English sentences and pay careful attention to the use of logical connectives.
Mathematics ... may claim to be the most original creation of the human spirit.
