Department of Mathematics of the Pennsylvania State University runs a yearly semester-long intensive program for undergraduate students seriously interested in pursuing a career in mathematical sciences. The *Mathematics Advanced Study Semesters* (MASS) program started in the Fall of 1996 and is held during the Fall semester of each year.

The principal part of the program consists of *three core courses* chosen from major areas in *Algebra/Number Theory*, *Analysis*, and *Geometry/Topology* respectively, specially designed and offered exclusively to MASS participants, and a weekly *MASS seminar*.

Additional features include *colloquium-type lectures* by visiting and resident mathematicians and mathematical research projects.

The following courses will be offered in the Fall of 2011:

## Schedule

*Introduction to Ramsey Theory*

Instructor: Jan Reimann, Assistant Professor of Mathematics

Teaching Assistant: Matt Katz

113 McAllister Building, MWRF 10:10-11:00*Spaces: from geometry to analysis and back*

Instructor: Anatole Katok, Raymond. N. Shibley Professor of Mathematics

Teaching Assistant: Paul Siegel

113 McAllister Building, MWRF 11:15-12:05pm*From Euclid to Alexandrov: a guided tour*

Instructor: Anton Petrunin, Professor of Mathematics

Teaching Assistant: Allan Yashinski

113 McAllister Building, MWRF 1:25-2:15*MASS Seminar*

Instructor: Sergei Tabachnikov, Professor of Mathematics, Director of MASS Program

113 McAllister Building, Tuesday 10:10-12:05*MASS Colloquium*

Instructor: Multiple invited speakers

113 McAllister Building, Thursday 2:30-3:30

## Course Outline

Math 497A - Honors MASS Algebra

Introduction to Ramsey Theory

Instructor: Jan Reimann, Assistant Professor of Mathematics

TA: Matt Katz

MWRF 10:10 - 11:00

**Description**: The course gives a basic introduction to Ramsey Theory and its applications in number theory, logic, and combinatorics

**Readings**: No textbook will be used only lecture notes.

Math 497B - Honors MASS Analysis

Spaces: from geometry to analysis and back

Instructor: Anatole Katok, Raymond Shibley Professor of Mathematics

TA: Paul Siegel

MWRF 11:15 - 12:05

**Description**: We will show how to translate problems of analysis, i.e. properties of functions such as differentiation, integration, expansion into series of various kinds and suchlike, into geometric problems in certain infinite-dimensional spaces. Geometry of those spaces will be studied using both analogies and insights coming from the familiar finite-dimensional situations (such as convexity) and new features associated with infinite dimension, e.g. reflexivity or its absence.

**Readings**: N/A

Math 497C - Honors MASS Geometry

From Euclid to Alexandrov; a guided tour

Instructor: Anton Petrunin, Associate Professor of Mathematics

TA: Allan Yashinski

MWRF 1:25 - 2:15

**Description**: Flexible and rigid polyhedral; piecewise linear isometries; Nash—Kuiper type theorems; intrinsic metric of convex surface; beginning of Alexandrov geometry.

**Readings**:

- A. Alexandrov. Convex polyhedra.
- D. Burago, Yu. Burago, S. Ivanov. A course in metric geometry.

## Calendar of Events

Arrival Day | August 21 |

MASS Welcome Party & Orientation | August 23 |

Classes Begin | August 22 |

Labor Day — No Classes | September 5 |

Midterm Exams | October 10-12 |

Thanksgiving Holiday — No Classes | November 21-27 |

Classes End | November 30 |

Final Exams | December 8,10,12 |

MASS Graduation Ceremony | December 13 |

## Enrollment

Participants are selected from applicants who will be juniors or seniors in the following academic year (sophomores may be admitted in some cases). All participants are expected to have demonstrated a sustained interest in mathematics and a high level of mathematical ability and to have mastered basic techniques of mathematical proof. The expected background includes a full calculus sequence, basic linear algebra, a transition course with proofs (such as discrete mathematics) and advanced calculus or basic real analysis. The search for participants is nationwide. International applications are invited as well. Each participant is selected based on academic record, two recommendation letters from faculty, and an essay (international applicants should demonstrate their mastery of English).

Candidates should submit:

- Application Form
- Transcript
- Record of Mathematics Courses
- A short essay describing their interest in mathematics
- Two letters of recommendation
- Financial disclosure form
- Transfer Protocol form

Application materials may be retrieved off the web, or requested by mail, fax, or e-mail.

Applications should be submitted through MathPrograms.org, ID: PSUMASS or sent by mail, fax, or e-mail to

107 McAllister Building

Department of Mathematics

Penn State University

University Park, PA 16802

(814) 863-8730 / Fax:(814) 865-3735

E-mail: mass@math.psu.edu

## Financial Arrangements

Successful applicants currently enrolled in U.S. colleges and universities will be awarded the Penn State MASS Fellowship which reduces the tuition to the in-state level. Best efforts will be made not to increase their out of pocked expenses. See the Financial Information for more details.

## Housing

All participants not enrolled at Penn State will be provided an opportunity to live in one of the residence halls on campus.

## Credits

The program elements total 16 credits, all of which are recognized by Penn State as honors credits and are transferable to participants' home universities. Students will also receive a certificate from the MASS Program at Penn State. Additional recognition may be provided through prizes for outstanding performance and for best projects.

## Administration

The overall supervision of the MASS program is provided by the Scientific Advisory Board which includes senior members of Penn State's mathematics faculty, and several outstanding mathematicians from other institutions.

The program is managed by the Director Sergei Tabachnikov.

Stephanie Zerby is the Administrative Assistant for the MASS program.

Participants are chosen by the *Selection Committee* headed by a member of the Scientific Advisory Board.