BASIC INFO:

Course Title: Mathematical Gems

Course Section: 30

Class meeting days and times: W 4:00-4:50

Class Location: ELM 214

Instructor Name: Jenia Tevelev

Office: LGRT 1236

Office Hours: Tu 3-4, Th 3-5

Email: tevelev(at)math(dot)umass(dot)edu

Phone: 5452856

Instructor’s Course Web Address:http://www.math.umass.edu/~tevelev/391A_2015/

Honors Seminar Web Address: https://www.honors.umass.edu/academics/courses/honors391a

COURSE SCHEDULE

This course schedule is tentative: in reality we will certainly cover fewer topics as some of the discussions will take longer than one lecture.

Class Meeting | Topic | Assigned reading | Remarks |

Jan 21 | History and Mathematics | ||

Jan 28 | Measuring the Gardens of Eden Slides |
Words and Pictures: New Light on Plimpton 322 by Eleanor Robson | |

Feb 4 | Power of the Elements Slides | Familiarize yourself with
the structure
of the Elements and work through
Euclid's construction of the regular pentagon.
I am also going to briefly discuss Euclid's proof of
infinitude of primes.
| |

Feb 11 | The Great Feud - I | Read this excerpt
from Great Feuds in Mathematics by Hal Hellman
| |

Feb 18 | The Great Feud - II Slides | ||

Feb 25 | Fluxions and Fluents - I Slides Sir Isaac Newton on Star Trek TNG | Read this excerpt from Book I and
this excerpt from Book III of Newton's Principia and this excerpt
from his Fluxions and Infinite Series
| Prospectus due |

Mar 4 | Fluxions and Fluents - II | ||

Mar 11 | Student presentations | ||

Mar 25 | Student presentations | ||

Apr 1 | Student presentation. Romantic Genius - I | ||

Apr 8 | Romantic Genius - II Slides Topics of papers | Read this excerpt from Measuring the World by Daniel Kehlmann | |

Apr 15 | Unsolvable Equation Slides | Read Galois's last letter | |

Apr 29 | Modern Sages. We discussed research of Maryam Mirzakhani
using as a starting point this short documentary.
Paper due by 11:59PM, Babylonian time |

GENERAL COURSE DESCRIPTION:

In 391A Honors Seminar 2: Topics, students participate in a topical seminar-style course designed by the instructor. Every section is open to students of any major. Advanced knowledge of the topic is not necessary.

INSTRUCTOR'S COURSE DESCRIPTION:

We will explore the history of mathematics from ancient civilizations to present day. How did mathematical concepts evolve? How and why do mathematical theories emerge? Is mathematics an art or a science? What do we really learn when we learn mathematics? To help us answer these questions, each week we are going to focus on a different mathematical discovery and discuss its historical context. We will try to understand the ways of thinking of mathematicians of different eras, and their major breakthroughs and failures. On this breath-taking journey we will reverse-engineer riddles of Babylonian scribes, trace the evolution of the concept of infinity, listen to mathematical debates on the piazzas of Renaissance Italy, walk the bridges of Konigsberg with Leonard Euler, and stay up all night before the duel with 19-year-old Evariste Galois pondering equations. Will we agree with Hermann Weyl, who said of the Galois' last testament that "this letter, if judged by the novelty and profundity of ideas it contains, is perhaps the most substantial piece of writing in the whole literature of mankind"?

INSTRUCTOR'S COURSE REQUIREMENTS AND GRADING:

Required readings will be distributed in class or linked from the course webpage. Some of the papers can get quite technical - don't let that discourage you. It's OK to just skim through parts you don't understand.

30% of your grade will be based on a 20-minute oral presentation prepared in collaboration (teams of 2-3 students). Topics for presentations will be distributed on January 28. They will complement material covered in class. The presentations will be given at a specially scheduled "mini-conference" (date and time TBA) during the last week before the spring break. February 25 is the deadline for submitting a prospectus for the presentation (a one-page informal summary).

30% of your grade will be determined by a five-page long paper about some of the themes and threads discussed in class. Papers must be prepared individually. Topics for papers will be announced during the spring break. The deadline for submitting a paper is April 29.

40% of your grade will be determined by your preparedness and participation in course discussions and activities.

TOPICS OF PRESENTATIONS

Classical construction problems and modern proofs of impossibility -

Zeno of Elea and the evolution of the concept of infinity -

Fermat’s principle of infinite descent and other forms of mathematical induction -

Projective geometry of perspective drawing -

Bernoulli’s discovery of the Law of Large Numbers -

SAMPLE PAPERS

Women’s Difficulties in Science and Mathematics Throughout the Ages by

Fermat’s Last Theorem by

Gauss and Ceres by

History of Logarithms by

Mathematics Behind the Construction of Islamic Geometric Patterns by

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 2: Topics 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/gateway/religious-observance 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 391A, 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 391A. 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’S 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.