MASS 2003

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 TheoryAnalysis, 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:


  • 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
  • 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


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


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


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.


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