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 2003:

## Schedule

*Number Theory with Applications to Communication Networks*

Instructor: Winnie Li, Professor of Mathematics

Teaching Assistant: Kimberly Schneider

103 MCALLISTER BUILDING, MWRF 11:15-12:05- Topological Dynamics

Instructor: Bryna Kra, Assistant Professor of Mathematics

Teaching Assistant: Ilie Ugarcovici

103 MCALLISTER BUILDING, MWRF 10:10-11:00 *Geometry and Relativity: An Introduction*

Instructor: John Roe, Professor of Mathematics

Teaching Assistant: Bob Yuncken

103 MCALLISTER BUILDING, MWRF 1:25-2:15*MASS Seminar*

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

103 MCALLISTER BUILDING, Tuesday 10:10-11:00*MASS Colloquium*

Instructor: Multiple invited speakers

103 MCALLISTER BUILDING, Thursday 3:35-4:25

## Course Outline

MATH 497A: Honors MASS Algebra

Number Theory with Applications to Communication Networks

INSTRUCTOR: Winnie Li

TIME: MWRF 11:15 a.m. - 12:05 p.m.

Various number-theoretic techniques are used to construc efficient communication networks which are being used in the real world. In this course we shall learn the relevant number background leading to the eventual explicit constructions of good networks.

MATH 497B Honors MASS Geometry

Topological Dynamics

INSTRUCTOR: Bryna Kra

TIME: MWRF 10:10 am - 11:00 am

This course studies the phenomenon of recurrence in dynamical systems, where the underlying space is assumed to be a topological space. Recurrence is a fundamental property for understanding the stitistics of many systems, such as planetary motion or motion of a gas. We start with the basics of metric space theory and topology needed for background and then study concepts such as minimality, equicontinuity and distality. We apply this theory to obtain results in combinatorics and number theory and conversely see how how these fields influence topological dynamics.

MATH 497C: Honors MASS Analysis

Geometry and Relativity: An Introduction

INSTRUCTOR: John Roe

TIME: MWRF 1:25 p.m. - 2:15 p.m.

This course will be two thirds an introduction to differential geometry and one third an introduction to general relativity. The differential geometric component of the course will present the extrinsic and intrinsic theory of curved surfaces in Euclidean space, followed by an introduction to abstract Riemannian manifolds. The relativistic component will begin with a mathematical account of special relativity. The treatment of general relativity will reach as far as the Schwarzschild solution to Einstein's equations.

MATH 497D HONORS MASS SEMINAR

Interdisciplinary Seminar

INSTRUCTOR: Sergei Tabachnikov

TIME: T 9:05 am - 11:00 am

The objective is to introduce students to the topics that are not likely to be part of the standard curriculum but constitute a part of good mathematical education. To bring about elements of unity of modern mathematics and to coordinate the three core MASS courses, and to prepare students for the upcoming MASS colloquium talks are the goals of this seminar.

## Calendar of Events

Arrival Day | August 28 |

MASS Welcome Party & Orientation | September 2 |

Classes Begin | September 2 |

Midterm Exams | October 13-17 |

Thanksgiving Holiday Classes end at 2:15 p.m. on Wednesday |
November 26-28 |

Classes End | December 5 |

Study Period | December 8-11 |

Final Exams | December 12, 15, 17 |

MASS Graduation Ceremony | December 18 |