 Overview
Foremost, this is a 300-level mathematics course. Rather than
attempting to give a comprehensive survey of the history of
mathematics, we will focus on the development of three main topics:
Cantor's surprising results on infinite sets, the long journey towards
a proof of Fermat's Last Theorem, and the search for a general formula
to solve fifth degree polynomials (similar to the quadratic formula
for second degree polynomials). Our primary sources for each of these
topics are English translations of the original papers written on
these topics. I'm really looking forward to the semester.
Evaluation
Your final grade will be determined by
| Homework | 30% |
| Two Takehome Exams | 25% |
| Comprehensive Takehome Final Exam | 20% |
| Two Inclass Presentations | 20% |
| Reading Assignments | 5% |
|
Homework
A major emphasis in this course is that you learn how to
write rigorous and precise mathematical arguments. This can be a
challenging endeavor and may require several iterations, but the process will not only aid your
mathematical development but can also great improve your clarity of
thought in other disciplines and areas as well.
With this emphasis, your homework should be precise, comprehensible,
completely justified, and written in complete sentences.
Most of the homework problems will be worth 5 points, and the possible
grades will be 5, 4, or No Grade. A few of the problems may be worth 10 points,
and the possible grades will be 10, 9, 8, or No Grade.
After I have returned the homework, I will allow you one opportunity
to rewrite any problem that you have made a serious effort to
complete. However, you must turn in your rewrite, along with your original
paper, within one week of when I return the homework to the class.
An important aspect of your mathematical development is that you learn to discuss
mathematics with others and collaborate on problems.
The homework assignments will alternate between Individual
assignments and Group assignments.
On the group homework assignments, you will work in groups of two
and turn in one paper.
It is extremely important that both of you understand every solution
that your group produces. On each assignment, one student will
be designated as the
primary author who writes-up the solutions, and the role of primary
author must alternate between the members of the group.
You may discuss the Individual assignments with other
students, but each person must turn in a separate paper that
represents his/her own work.
Exams
You will have at least five days to complete each Takehome Exam and
at least one week to complete the Takehome Final. I would strongly
suggest that you begin early on these to leave time to ask me
questions about the exam.
Inclass Presentations
You will give two major group presentations during the semester,
each approximately 20 minutes long. The
first will be on one of the chapters from Journey Through
Genius, and the other will cover a topic referenced during the
semester that we have not covered in depth.
I have extremely high expectations for the quality of these
presentations.
Reading Assignments
I will put a copy of each reading assignment on the Math 104 homepage.
Each assignment will contain a specific reading assignment and will have
two or three questions that you should be able to answer after you have
read the section.
See the Guidelines for Submitting Reading Assignments and Suggestions for Reading a Math Book for more information.
A Few Notes on Your Homework and Exams
Here are a few guidelines for the presentation of your written work.
If you do not follow these, I reserve the right to return your homework ungraded!
- Your writing must be clear and legible.
- Your solutions should be well-written,
using complete sentences to justify your results where necessary. \newline
A list of answers without explanation is not acceptable.
- Here is a good rule of thumb to follow when writing up your
work:
Write your solutions so that you could hand them to another student in
the class and she could understand your
explanation.
- Do not turn in your first draft of the assignment. You should
expect to neatly recopy and organize your work.
- If you write in pen, there should be no scratch-outs.
- Do not turn in paper torn from a spiral notebook with ragged
edges.
- Clearly label each problem.
Be aware that
Late assignments are not accepted without a substantial penalty!!
Grading of Group Assignments
Each group assignment will receive a single grade, and the group will
determine how the points are allocated to each member.
For example, if a group of
three receives an 85 on a presentation, then the group will have
3x85=255 points to distribute among them.
I will be available to mediate this process, if necessary.
Few Other Suggestions
One idea that I believe will help you with the historical
perspective of the course is to keep your own timeline of
the mathematicians and their writings that we read.
I would also suggest that you keep your own glossary of
terms defined in the text and where they are defined.
Hudson River Undergraduate Mathematics Conference
The HRUMC will be held on April 28 at Skidmore College. I would strongly
encourage all of you to attend, and you should also consider giving a
talk. This is a really nice day to be involved with mathematics with
other undergraduates. A good time will be had by all.
If you do give a presentation, you
will receive an extra 5% on your final grade.
Each talk is attended by anywhere from 10 to 50 people, most of
whom are other mathematics students from around New England.
Before you submit an abstract to give a talk, we will need to discuss
your topic and make sure that it is at the appropriate level.
I have very high expectations for the quality of these talks so you
should expect to devote significant effort to your presentation.
I will, of course, work with each of you on your talk.
Class Attendance
Although class attendance is not a specified percentage of your grade,
I will keep a class roll to help me determine borderline grades at the
end of the semester. If you do miss class, you are responsible
for the material that was covered.
Getting Help
Please come see me during my office hours! If you have a conflict
and cannot make my office hours, please call or email me and we can set up
an appointment for another time.
Math 104 Home |
T. Ratliff's Home
|
