AMAT 680/681/682, Section 1: Master's Seminar

Spring 2020, (Class #s 1843, 1844, 4280)

MW 2:45-4:05, ES 146

Instructor: Michael Lesnick
mlesnick [at] albany [dot] [the usual thing]
Office: Earth Sciences 120D
Office Hours: Monday, Wednesday 4:10-5:10, and by appointment

Send Anonymous Feedback

Lecture Notes

About this Course:
The main goal of this course is to provide students with experience doing independent research and presenting mathematics to a live audience.

Each student will give two 30-40 minute expository presentations during the semester. These can be done either be blackboard talks or computer talks. Computer talks are encouraged.

Each presentation will be on a topic outside of the standard undergraduate/masters level curriculum for mathematics majors. (Suggestions are below.) The level of the talk should be appropriate for beginning graduate students and challenging for a typical senior pursuing a degree in mathematics.

The suggested (broad) theme for the seminar talks is computational mathematics. Ideally, every talk should mention least one theorem and one algorithm.

For each presentation, the student will spend substantial time researching the topic and preparing notes/slides. Topics of presentations will be chosen by the student with the input of the instructor. We will coordinate to ensure that no topic is covered by more than one student.

There may also be shorter, less formal assignments intended to help students prepare for the main presentations. Software for making mathematics presentations on a computer (in particular, the typesetting language LaTex) will be introduced as needed.

Most presentations will be on Mondays. Most (but not all) Wednesday class periods will be devoted to individual meetings with students about their presentations.

Presentation Schedule:

Feb 10: John, fast Fourier transform
Feb 17: Shu, the classifiction problem in machine learning
Feb 24: Sih, matching problems in graph theory
March 2: Lu, public key crypotgraphy
March 9: Julia, PageRank
March 16: SPRING BREAK
March 23: John, Markov Chains
March 30: Shu, deep learning
April 6: Sih
April 13: Lu, spectral clustering
April 20: Julia

Suggested Topics for Presentations:

Persistent Homology
Mapper (topological data analysis tool)
The bootstrap method for computing confidence intervals
Basic theory of Markov Chains
PageRank (Google's original websearch algorithm)
Network flow problems
Matching problems in graph theory
The P=NP problem
Linear programming
Spectral clustering
The singular value decomposition
Numerical stability of linear system solving.
Fast Fourier transform
Groebner bases
Hilbert-Nullstellensatz---basics of algebraic geometry
Cryptography
Rubik's groups
Addition on a cubic curve
Colouring and graph theory

Prequisites:
The prerequisite for this class is good standing in the graduate program.

Grading:
The class will use the university's S/U grading scheme. For a satisfactory grade, the student will have to: sucessfully give both of the presentations, putting in a substantial effort to prepare for each; participate actively in after-talk discussions; and complete any other assigned work. Attendance is required, and is very important in a class of this size; students who miss more than two classes without advance permission from the instructor are at risk for a grade of U.

Resources:

Some advice on giving mathematics talks. See also the links at the bottom of the linked page for additional resources on this.
An introduction to LaTeX, the standard language for typesetting mathematics.
An introduction to Beamer, a LaTeX package for creating mathematics presentations.
Overleaf, a convenient online tool for preparing LaTeX documents.

Academic Regulations:
Naturally, the University's Standards of Academic Integrity apply to this course, and students are expected to be familiar with these.

There will be no leeway on missed exams or last-minute exam rescheduling, except as noted in the regulations. If you anticipate an issue with the timing of an exam, please let me know as soon as possible.