Math 480(O), Senior Seminar
Instructor: Pavel Guerzhoy
The class meets Tuesdays, 3 - 5pm at Keller Hall 402
Office: 501, Keller Hall (5-th floor)
e-mail: pavel(at)math(dot)hawaii(dot)edu (usually, I respond to e-mail messages within a day)
Office hours: Tuesdays 11:30-1pm and Thursdays 3-5pm
General Expectations
The Department of Mathematics has a general expectations statement, which we are assumed to follow in this class.
Course Objective
This is a class directed to Math majors who are close to their graduation.
The primary goal of the class is to develop mathematics presentation skills of the students.
This includes oral presentation skills in the first place, while using technology such as
LaTeX beamer class and/or powerpoint and/or keynote is highly encouraged.
For instructions on LaTeX beamer class, see, for instance,
one,
two,
three,
and, possibly, tons of other web-sites.
I know little about Microsoft Powerpoint and other proprietary presentation making software,
while those who use that may achieve quite impressive outcome.
For the Mac users, keynote is an extremely powerful and convenient tool, probably my personal tool of choice for doing math presentations during the recent years.
This is a mathematics class which is designated to have an oral focus.
As a consequence, various types of oral mathematical presentations is a subject of emphasis.
Grading Policy
Math 480 is offered only as a CR/NC class. Students cannot pass the class without completing the following to the satisfaction of the instructor:
- attending regularly and participating in class discussions,
- presenting solutions to homework assignments during the semester (oral presentations),
- taking the mathematics department assessment exam at the end of the semester.
Textbook
In this class, we use the book
Thirty-three Miniatures Mathematical and Algorithmic Applications of Linear Algebra
by Jiří Matoušek
Student Mathematical Library, Volume 53, published by American Mathematical Society.
Much of the book assumes and freely uses linear algebra which is beyond the scope of MATH411.
For those students who did not take MATH411 or just do not want to struggle with linear algebra, an alternative will be offered.
Contents
In this class, we focus on mathematical presentations .
- To start with, during the first several classes, every student gives a short (10-15 minutes) general presentation
Why have I chosen Mathematical major, and what is it good for?
The questions to be addressed may be:
- Original motivation/story which led to this choice of major
- Were the initial expectations met?
- How the math major aligns with the further career goals/expectations?
- Meanwhile, miniatures from the textbook will be distributed.
Alternatively, instead of a miniature from the textbook, a student may take as an assignment a general mathematical presentation. That would be a talk on an area or a notion of contemporary mathematics on his/her choice.
Examples include but are not limited by
- Differential geometry
- Algebraic geometry
- Algebraic topology
- Group theory
- Analytic number theory
- Algebraic number theory
- Cohomology theories
- Motives
- Elliptic curves
In such a presentation, while one certainly should not go deep (Wikipedia may be a sufficient source), one must deliver a general idea on what mathematicians are doing in the chosen area of research, and, more importantly, what motivates their enthusiasm to devote their lives to the research in the specific area.
Yet another alternative is to pick a great theorem and present it in a way such that the listeners can appreciate the importance of the theorem and/or the elegance of its proof.
Examples:
and tons of other beautiful, surprising, and important theorems.
Every presentation takes 30 minutes and yields a 30 minutes discussion.
The student must have in mind the goal of a mathematical presentation: the majority of listeners can clearly articulate their take-aways following the presentation.
- Besides the above, there will probably be external presentations both mathematical and profession-related given by invited professionals.
- A take home assessment exam (3 parts) will be given during the semester as a part of the classwork.