MASS Selecta: Teaching and Learning Advanced Undergraduate MathematicsShare this page
Edited by Svetlana Katok; Alexei Sossinsky; Serge Tabachnikov
Mathematics Advanced Study Semesters
This book results from a unique and innovative program at Pennsylvania State University. Under the program, the “best of the best” students nationwide are chosen to study challenging mathematical areas under the guidance of experienced mathematicians. This program, Mathematics Advanced Study Semesters (MASS), offers an unparalleled opportunity for talented undergraduate students who are serious in the pursuit of mathematical knowledge.
This volume represents various aspects of the MASS program over its six-year existence, including core courses, summer courses, students' research, and colloquium talks. The book is most appropriate for college professors of mathematics who work with bright and eager undergraduate and beginning graduate students, for such students who want to expand their mathematical horizons, and for everyone who loves mathematics and wants to learn more interesting and unusual material.
The first half of the book contains lecture notes of nonstandard courses. A text for a semester-long course on \(p\)-adic analysis is centered around contrasts and similarities with its real counterpart. A shorter text focuses on a classical area of interplay between geometry, algebra and number theory (continued fractions, hyperbolic geometry and quadratic forms). Also provided are detailed descriptions of two innovative courses, one on geometry and the other on classical mechanics. These notes constitute what one may call the skeleton of a course, leaving the instructor ample room for innovation and improvisation.
The second half of the book contains a large collection of essays on a broad spectrum of exciting topics from Hilbert's Fourth Problem to geometric inequalities and minimal surfaces, from mathematical billiards to fractals and tilings, from unprovable theorems to the classification of finite simple groups and lexicographic codes.
Table of Contents
Table of Contents
MASS Selecta: Teaching and Learning Advanced Undergraduate Mathematics
- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents v6 free
- A brief description of MASS Program 18 free
- Teaching in the MASS Program 714
- Part I. Lecture Notes 916
- Part II. MASS Colloquium 161168
- MASS Colloquium 163170
- Hilbert's fourth problem in two dimensions 165172
- Integral lexicographic codes 185192
- The classification of finite simple groups 191198
- Billiard balls count π 197204
- Rep-tiles revisited 205212
- Fractals and dynamics 219226
- Unprovable theorems and fast-growing functions 235242
- Minimal surfaces and random walks 246253
- The tale of a geometric inequality 257264
- Part III. Student Research Papers 263270
- Appendices 301308
- Back Cover Back Cover1321
Professors of mathematics; general mathematical audience.