MATH 434, Abstract Algebra
Spring 2014
January 19, 2014
Bryan Smith
Contents
1 Introduction
2 Course Information
2.1 Textbook
2.2 Basic Information
2.3 Office Hours
2.4 Day to Day Structure
3 Examinations
4 Homework
4.1 Writing Projects
5 Talk/Paper
6 Course Information Updates
7 Total Points
8 Additional Information
8.1 "Writing" Problem Guidelines
1 Introduction
Abstract Algebra 434 is a
senior level course and is essential either for graduate
school or a career in secondary
education. In this course, you will investigate a bit more of group theory and
learn the basics of a the algebraic structures called rings
and fields (and perhaps modules). I recommend
that you take the time to find and use additional references
besides our textbook. In
particular, there are an abundance of useful books in the library
and mathematics reading room.
For an official description of this course, see
http://www.math.ups.edu/~matthews/Syllabi/MATH433_434_May2006.pdf
[].
By the time we finish this course, you should have refined
the skills outlined in the information sheet for first semester
abstract algebra as well as enhancing your abilities to research,
understand, summarize, and verbally present an application of the
concepts you have learned in this course.
2 Course Information
2.1 Textbook
The textbook is Abstract Algebra, Theory and Applications,
2013 Edition, Thomas Judson, ©1997, GNU Free Documentation License
We will address the information in Chapters 16-23 but will not
necessarily follow the textbook.
2.2 Basic Information
You can find information pertinent to all of my classes at the
link below and, once there, information specific to this class by
clicking on the Math 434 link.
http://math.ups.edu/~bryans/ []
Location Th 383, 9:00-9:50am M,F, 8:30-8:20am T,Th
2.3 Office Hours
| Professor Bryan Smith | 879-3562 | bryans[at]pugetsound.edu | Thompson Hall 390D |
|
| Office Hours | | Tue, Thu | 8:00-8:25 am |
| \ | | | 12:00-12:25 pm |
| \ | | | 1:30-1:55 pm |
| | | Wed | 2:00-3:20 pm |
| | | Other | By Appointment |
|
2.4 Day to Day Structure
The class weeks will be structured in essentially the same way
as last semester. One difference is that an appropriate number
of days at the end of the semester will be reserved for each of you to
present your research project to the rest of the class.
3 Examinations
There will be no examinations during the semester but there might be
a final consisting of problems from the student presentations.
Final Examination Time: Monday May 12 at 8:00 A.M.
4 Homework
4.1 Writing Projects
Many homework problems will be assigned throughout the semester.
They represent a selection of the available problems that highlight
important concepts, techniques, or computational skills. Most of
these problems will not be collected so you are expected to work as
many of them as you feel necessary to master the material.
However, 23 problems will be collected and marked. Of these, 20
will be marked for mathematical accuracy and graded as pass/fail.
When you present
these, you are to provide a clear, easy to read argument with the
students in the analogous course at PLU as your audience. In particular,
provide justifications for every step in your argument that is not
clear to this audience. Credit is earned when
you turn in a complete and accurate solution. If you turn in an
incomplete or inaccurate solution, I will make a few comments and
return it. You may then re-submit the problem. This process may be
repeated. To provide some reinforcement for being timely and thoughtful,
you may
submit no more than 4 problems per week.
In addition, over the course of the semester, you are to
designate 3 of the 23 problems as "writing" problems which I
will mark for both mathematical accuracy and clarity of
exposition (see below and my web page for some basic guidelines
for writing mathematics). Do not turn in more than one of these
writing problems in any week since their purpose is to provide
feedback as you develop your mathematical writing style. I expect
at least 2 of these problems to be turned in by midterm.
Writing problems may only be resubmitted one time.
Feel free to use (or not) any technology that you like (e.g.,
Sage, Scientific Notebook,
calculators, Mathematica, MATLAB, etc.) but do not use
the internet to look up solutions. You may also
work with others in solving these problems but there is to be no
collaboration (other than consulting with me) in the writing of
the solutions.
Moreover, you must cite each resource
you use. Do this in a reference paragraph at the beginning of
your paper affirming you have not used the internet to solve the
problems and either affirming the work is completely yours or
citing each resource you use: names of participants in
discussions (other than the in-class discussions), technological
tools, reference texts employed, and anything else other than
your own thoughts. Failure to include references is intellectual
theft! Please see the "Academic Honesty" section of the
Logger to see how serious this issue is to the university
community.
The "writing" problems are actually the mathematical equivalent
of assigned papers in humanities courses. In particular, be sure
to invest adequate time in analysis and research before you
completely explain that analysis of the problem. You are also
expected to follow standard mathematical style in your
presentation. The easiest way to see examples of this standard
style is to peruse any copy of
Mathematics Magazine or the American Mathematical
Association Monthly. You can find copies of these journals
in the Mathematics Reading Room, my office or the library.
Remember, your "writing" papers will be graded both for
mathematical content and for written presentation using the
grading rubric on the last page of this
document.
The "writing" problems are to be written using LATEX as will
the written portion of your research project.
5 Talk/Paper
Due Dates:
- March 7: Last day to have your topic accepted. This will
require that you convince me you have a reasonable topic.
- March 31: Last day to schedule a time for your oral presentation.
Times are available first come, first served to those who have
accepted topics. You will have 25 minutes
to present your results and will be expected to use LATEX and Beamer to
generate your slides.
- April 18: submit your completed paper to me as a PDF.
Include two "exercises" appropriate as problems on an in-class examination.
I will make copies of your paper available to the other students so they can
look it over before your talk.
The last 6 days of class will be devoted to talks given by the
class members. You may investigate any topic that involves higher
algebra. Those of you with interests in physics or chemistry will
have no trouble finding many possibilities. I will supply a list
of possible options when I pass out the Research Project assignment
sheet but you are not limited to those possibilities. Here are a
few that come to mind while I am typing: more depth on the Sylow theorems,
the classification of finite simple groups, combinatorial group
theory, knot groups, knot polynomials, quadratic forms, algebraic
graph theory, more depth on boolean algebras, 2 and 3 dimensional
symmetry groups, non-associative algebras,
lattice theory, and quantum computing.
You will receive grades on your proposal, the oral presentation
of your investigations and the paper that you will write using
LATEX and submit to me electronically.
6 Course Information Updates
If you wish, I will post (and update) a grade report on your
current standing in the class on my university web page.
7 Total Points
| Homework + Final | 60% +10% |
| Homework: Writing | 10% |
| Talk/Paper: Proposal | 4% |
| Talk/Paper: Oral | 6% |
| Talk/Paper: Written | 10% |
8 Additional Information
Please review university
emergency preparedness and response procedures posted at
http://www.pugetsound.edu/emergency/. There is a link on the
university home page. Familiarize yourself with hall exit doors and
the designated gathering area for your class and laboratory
buildings.
If building evacuation becomes necessary (e.g. earthquake), meet
your instructor at the designated gathering area so she/he can
account for your presence. Then wait for further instructions. Do
not return to the building or classroom until advised by a
university emergency response representative.
If confronted by an act of violence, be prepared to make quick
decisions to protect your safety. Flee the area by running away
from the source of danger if you can safely do so. If this is not
possible, shelter in place by securing classroom or lab doors and
windows, closing blinds, and turning off room lights. Stay low,
away from doors and windows, and as close to the interior hallway
walls as possible. Wait for further instructions.
If you have a physical, psychological, medical or learning disability that may
impact your course work, please contact Peggy Perno, Director of the Office of
Accessibility and Accommodations, 105 Howarth, 253.879.3395. She will determine
with you what accommodations are necessary and appropriate. All information and
documentation is confidential.
References
- []
- Bryan Smith's Homepage
http://math.ups.edu/~bryans/
- []
- Math 434A Course Webpage
http://math.ups.edu/~bryans/Current/Spring_2011/434Index_Spring2011.html
- []
- Department Calculator Policy
http://www.math.ups.edu/info/calcpolicy.pdf
- []
- Department Syllabus for MATH 434
http://www.math.ups.edu/~matthews/Syllabi/MA434Syllabus.pdf
- []
- Location of MikTeX package for using LATEX
miktex.org
- []
- Development tools for composing LATEX documents
miktex.org/Links.aspx
- []
- William Rapaport's "How to Study"
http://www.cse.buffalo.edu/~rapaport/howtostudy.html
- []
- TI-86 Manual
http://education.ti.com/us/product/tech/86/guide/86guideus.html
8.1 "Writing" Problem Guidelines
It is best to think of these writing projects as officially
assigned papers in which you completely explain and justify your
analyses of the problems. You may work with others in solving
these problems but there is to be no collaboration on the
written exposition of the solutions. In addition I expect your
papers to be
- Fully documented - specifically:
- You must include a reference paragraph at
the beginning of your paper either affirming the work is
completely yours or listing each resource you use:
names of participants in discussions (other than the
in-class discussions), technological tools, reference
texts employed, and anything else other than your own
thoughts.
- Any idea obtained during brainstorm sessions or in discussions is
cited in-line.
- All textbook results (theorems, propositions, and lemmas) are cited in-line
and include the name of the result.
- Any use of technology is cited in-line.
- Written up using using complete, accurately punctuated sentences and
in LATEX.
- Presented in active voice, the first person plural and with
a clear, easy-to-follow expository style.
- Targeted at an audience consisting of students in the equivalent course
at PLU.
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