EXCO: CRUNCHING EPSILONS - WORKSHOP IN
MATHEMATICAL ANALYSIS (SPRING 2017)
Basic Information
: Class time: Wednesday, 3:30 - 5:20 PM in Peters 129
: Instructor: Chris Marx, he/his/him ([email protected]), King 220C
In general, I respond to emails regularly Mo - Fri between 8:00 am and 6:00 pm.
If you write to me at other times, it may take me longer to respond.
: Office hours:
• Monday, 11:00 - 11:50 AM (in my office, King 220C)
• Friday, 11:00 AM - 11:50 PM (in my office, King 220C)
If you’d like to see me at other times, please talk to me before or after class or
send me an email to make an appointment.
Office phone: (440) 775-5247
Course Description
Mathematical analysis is one of the main subfields of modern mathematics. Since
its origin in the 18th century as a generalization of calculus, analysis has probably also
been the sub-discipline of mathematics with closest ties to the sciences. From celestial
mechanics and chaos theory to quantum theory or the theory of stochastic processes,
the language and ideas of analysis form the foundations of much of applied mathematics
today. Consequently many graduate programs in pure and applied mathematics, the
sciences, and economics often take a good working knowledge of the concepts and
techniques of analysis for grantued.
Goal of this workshop is to engage students in a great variety of interesting problems
from analysis that demonstrate the area’s rich connections to other fields of mathematics
and the sciences. The workshop’s intention is to enhance the existing introductory
course to analysis (Foundations of Analysis, Math 301) by giving students a hands-on
working experience in analysis.
For each class unit, the topic will be introduced to the students in a 20 minutes
webinar-style talk given by faculty from one of six participating universities with research interests in analysis. Students will then spend the remaining time of the class
unit working in small groups on problems that follow up on the webinar talk.
General requirements. The only requirement is that students have previously taken
or are currently (i.e. in Spring 2016) enrolled in Foundations of Analysis (Math 301).
1
2 EXCO: CRUNCHING EPSILONS - WORKSHOP IN MATHEMATICAL ANALYSIS (SPRING 2017)
Outline & Topics. The following table lists dates and topics of each class unit. Note
the class starts in week 2.
class (week)
02/08 (week
02/15 (week
02/22 (week
03/01 (week
03/08 (week
03/15 (week
03/29 (week
04/05 (week
04/12 (week
04/19 (week
04/27 (week
05/03 (week
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
topic (speaker)
Introduction to LaTeX in math & the sciences (Chris Marx, Oberlin College)
Irrational rotations on the unit circle (Cesar Silva, Williams College)
Fractals - Sums and products of cantor sets (May Mei, Denison University)
Introduction to Hausdorff dimension (Mihai Stoiciu, Williams College)
Periodic dynamical systems (Jim Walsh, Oberlin College)
Fourier series meet linear algebra - 1 (Eyvi Palsson, Virginia Tech)
Fourier series meet linear algebra - 2 (Eyvi Palsson, Virginia Tech)
Ergodicity and irrational rotations - 1 (Chris Marx, Oberlin College)
Ergodicity and irrational rotations - 2 (Chris Marx, Oberlin College)
Functions of bounded variation - 1 (Pamela Pierce, The College of Wooster)
Functions of bounded variation - 2 (Pamela Pierce, The College of Wooster)
Algebra of Riemann-integrable functions (Steven Abbott, Middlebury College)
Learning goals.
• Students will develop the practical skills and the confidence to apply the tools
of analysis to a variety of questions in mathematics and the sciences.
• Students will get a solid training in performing estimates, using standard
techniques, like − δ-arguments, successive approximation, Cantor diagonalization, various standard inequalities, etc.
• Students will practice communicating mathematical ideas in both speaking
and writing; this includes an introduction to LaTeX, the standard typesetting system in the mathematical sciences.
Class material & ressources. All class related resources will be provided either in
class or posted on blackboard. Go to blackboard.oberlin.edu to access these materials.
Grading
The class is a one-credit practicum graded on a Pass/No Pass basis. To
receive a Pass grade, each of the following has to be satisfied:
: Attendance: at least 9 out of 12 class meetings
: Participation: at least 9 check grades in total (details under course policies)
: Portfolio: turn in written-up problems for 2 class units (excludes unit 1) (details
under course policies)
EXCO: CRUNCHING EPSILONS - WORKSHOP IN MATHEMATICAL ANALYSIS (SPRING 2017) 3
Course Policies & Due dates
Participation & Attendance.
• Participation and collaboration are key elements of the class. Engaging with the material during class time by asking questions, participating in
group work and discussions, and generally supporting a positive and respectful
environment is vital to the learning process.
• Students will be working in small groups and are expected to contribute
to their group in a way that is respectful to other students and generally fosters
a positive, inquisitive, and creative atmosphere.
• To ensure above mentioned standards are met, a participation grade (check
or minus) is given for each class unit. A total of 9 check grades has to be
achieved for an overall Pass grade in the class.
• Students have to attend at least 9 class units to receive an overall Pass grade
in the class.
Class portfolio.
• To practice their written communication skills for the mathematical sciences,
students are expected to turn in the problem sets for 2 class units of
their choice to the instructor. The total of these 2 sets of problems forms the
class portfolio.
• Each of the problem sets that the student turns in has to be typed using
LaTeX.
• To ensure continuity in the learning process, students have to turn in their
work by the following deadlines:
– by Friday 03/17 (end of week 7), 5:00 PM: problem set no. 1
– by Friday 05/05 (end of week 13), 5:00 PM: problem set no. 2