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 2002:

## Schedule

*Elements of Fractal Geometry and Dynamics*

Instructor: Yakov Pesin, Professor of Mathematics

Teaching Assistant: Danijela Damjanovic

103 MCALLISTER BUILDING*Number Theory with a Tilt at Elliptic Curves*

Instructor: Dale Brownawell, Professor of Mathematics

Teaching Assistant: Arsen Elkin

103 MCALLISTER BUILDING*Intuitive Topology*

Instructor: Sergei Tabachnikov, Professor of Mathematics

Teaching Assistant: Dan Genin

103 MCALLISTER BUILDING*MASS Seminar*

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

103 MCALLISTER BUILDING*MASS Colloquium*

Instructor: Multiple invited speakers

103 MCALLISTER BUILDING

## Course Outline

MATH 497A: Honors MASS Algebra

Number Theory with a Tilt at Elliptic Curves

INSTRUCTOR: Dale Brownawell

TIME: MWRF 10:10 a.m. - 11:00 a.m.

Course Objectives: Primarily to introduce students both to classical number theory and to one of the most modern branches, the arithmetic of elliptic curves. Students will also become comfortable with a standard mathematics package and with THE standard typesetting language for mathematics and other technical reports, (LA) Tex.

MATH 497B: Honors MASS Geometry

Elements of Fractal Geometry and Dynamics

INSTRUCTOR: Yakov Pesin

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

Course Objectives: This course is an invitation to Fractal Geometry and Dynamical Systems. These two areas have a long history of development and are associated with such great names as Poincare, Hausdorff, and Besicovich. Currently they are the subject of intensive mathematical study and have much to offer to gifted students to help them come closer to contemporary ideas in mathematical research. Therefore, the focus of the course is on ideas rather than complicated mathematcial techniques and the goal is to make these ideas accessible to students.

MATH 497C: Honors MASS Analysis

Intuitive Topology

INSTRUCTOR: Sergei Tabachnikov

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

Course objectives: This course is an invitation to Geometric Topology, an extremely important area of contemporary mathematics, which goes back to pioneering work of Euler, Gauss, Riemann, and Poincare. Topology can be considered a far-reaching extension of geometry; it also provides a language for various branches of mathematics and theoretical physics (as distant as functional analysis and quantum gravity). Usually topology is taught in graduate school, first a course of point-set topology, and then 1 - 2 semesters of algebraic topology. This course will focus on the most important geometrical intuition and pay much attention to examples. Special attention will be given to applications in physics, chemistry, microbiology and other fields.

MATH 497D: HONORS MASS SEMINAR

Interdisciplinary Seminar

INSTRUCTOR: Sergei Tabachnikov

TIME: T 10:10 a.m. - 12:05 p.m.

This seminar is designed to focus on selected interdisciplinary topics in algebra, geometry and analysis. These areas will be related to the other MASS courses. Seminar sessions may include presentations from student homework solutions.

## Calendar of Events

Arrival Day | 08/24 |

MASS Welcome Party & Orientation | 08/26 |

Classes Begin | 08/27 |

Labor Day Holiday | 09/02 |

Midterm Exams | 10/07-10/12 |

Fall Break | 10/14-10/15 |

Thanksgiving Holiday Classes end at 2:15 p.m. on Wednesday 11/27 |
11/28-11/29 |

Classes End | 12/06 |

Study Period | 12/09-12/12 |

Final Exams | 12/13, 16, 18 |

MASS Graduation Ceremony | 12/19 |