Honors 391D (and 391A)

Advanced Honors Seminar: Epistolary Vignettes in Mathematics

Spring Semester 2011

** Catalog Description:**
Advanced Honors Seminar is the second and final course in the two-part
Honors Seminar Series, formerly the Dean's Book Course. If you have
completed HONORS 291D, 291G, or 291R with a B or better, upon
successful completion, this course will satisfy the Honors Seminar
Series requirement of Commonwealth College. HONORS 391D carries a Gen
Ed I. In 391D, students participate in a topical seminar-style course
designed by its instructor. While the subject matter of each section
is different, the requirements for each section are the same. Every
section is open to students of any major, and advanced knowledge of
the topic is not necessary.
Section 1: Epistlary Vignettes in Mathematics Course Description
This Seminar will be a somewhat non-traditional but enriching math course on some patterns of mathematical thought in historical context. It is designed for a broad audience, not only those planning to major in mathematics or a related field. We will examine some vignettes of "mathematics in the rough" as it was being created, in most instances by reading famous letters between mathematicians. Some examples include: Cantor and Dedekind on the nature of infinity; Legendre and Jacobi on their mutual jealousy of, as well as respect for, the genius of Abel; Euler on his invention of what came to be known as the Riemann Zeta Function; Fermat taunting Wallis and other British mathematicians with Pell's equation.

**Class meetings:** Monday 10:10 - 11:00 Dickinson Room 209.

**Prerequisites:** There are no formal prerequisites, but
permission of Instructor is required. Please contact:

** Instructor:** Farshid Hajir

Lederle Graduate Research Tower 1118. Phone:
545-6015.

e-mail: * hajir atsymbol math.umass.edu*

** Course Web Address:** http://www.math.umass.edu/391D

** Text:** There is no required textbook for
the course, but notes will be handed out as needed.

**Assignments and Grading:** Details on the projects/papers and oral presentations will be distributed in class.
50% of your grade for Honors 391D will be determined by:
A research-based and documented paper, or project as defined by the instructor.
25% of your grade will be based on
An oral presentation, demonstration or performance of the creative project, or some other artifact as defined by the instructor.
25% of your grade will be determined by your preparedness and participation in course discussions and activities including
speaking up in full-group discussions;

taking the lead in small-group activities;

providing helpful follow-up questions to presenters;

eliciting comments from other classmates; and

contributing to the learning of your fellow students.

**
ATTENDANCE POLICY**
Absentee Policy and Extenuating circumstances (illness, death in the family, etc.) for which students must miss a class meeting
While attendance is crucial to participation in the Honors Seminar Series and therefore a significant factor in calculating your final grade in this course, extenuating circumstances may require you to miss a class meeting. Whether an absence is “excused” or counted in calculating participation grades is largely at the discretion of the instructor. Any student absent—whether the absence is “excused” or not—should contact the instructor as soon as possible to discuss assignments missed, class discussion, etc.
Student athletes, members of the band, and on occasion, students who are members of other groups will be allowed to miss class for games and other special events and make up work will be assigned.
(See http://www.umass.edu/umhome/events/religious.php for University attendance policies and religious holidays.)

**EXAM CONFLICTS**
University policy on exams scheduled at the same time a student’s Honors Seminar class meets
According to Faculty Senate Document 06-042, certain one-day-a-week courses, including Honors 391D, have priority over evening exams on Monday and Tuesday evenings. Evening exams (7-9 p.m.) have priority over all courses on Wednesday, Thursday, and Friday evenings.
Exams scheduled for 6 p.m. or earlier do not have priority over Honors 391D. If you have an exam scheduled during this class, you must be given the chance to make it up by the professor of the other course. If you miss a class because of an exam that has priority over this class (extremely rare), you will be given the chance to make up any work you have missed.

**PLAGIARISM POLICY**
Documenting the Writing, Speaking, and Thinking of Others
In all your writing, and in oral presentations too, it is essential that you acknowledge the ideas of others upon whom your own thinking depends, including ideas obtained from such non-written sources as lectures, interviews, class discussions, and even casual conversations with colleagues and friends. Give credit for ideas that are not your own as well as for passages of text that you summarize, paraphrase, or quote.
If material possessions are the property of our community at large, thoughts and ideas—expressed in speech or writing—constitute the “intellectual property” of our academic community. To take another’s words or ideas and present them as your own is to commit plagiarism, an act of academic theft, and the punishments can be severe (cf. University of Massachusetts Amherst Academic Regulations, “Academic Honesty”).

**UMass Amherst Academic Honesty Policy**
Since the integrity of the academic enterprise of any institution of higher education requires honesty in scholarship and research, academic honesty is required of all students at the University of Massachusetts Amherst. Academic dishonesty is prohibited in all programs of the University. Academic dishonesty includes but is not limited to: cheating, fabrication, plagiarism, and facilitating dishonesty. Appropriate sanctions may be imposed on any student who has committed an act of academic dishonesty.

**Topics**
Each week we will explore the mathematics as well as the social context of one or more pieces of mathematics which can be explained, at least in rough form, to an audience without specialized mathematical knowledge. The discussion will usually be sparked by one or more letters between mathematicians. We may spend more than one week on some of these topics. Examples:

Legendre and Jacobi on Elliptic Functions

Stieltjes and Hermite on Numerical Computations

Cantor and Dedekind on the nature of Infnity

Fermat and Pascal on Games of Chance Involving Dice (The Birth of Probability Theory)

Ramanujan and Hardy on Ramanujan's highly original amateur discoveries

Fermat taunting the British Mathematicians of his day

Grothendieck and Serre, two giants of 20th century mathematics help each other (and sometimes clash)

Newton and Leibniz trade ideas and accusations through intermediaries over their discovery of calculus

Euler discovers a method for computing the infinite sum 1+2+3+... (hint: the answer is not infinity).