Hardcover ISBN:  9780821833636 
Product Code:  MASS 
List Price:  $74.00 
MAA Member Price:  $66.60 
AMS Member Price:  $59.20 
Electronic ISBN:  9781470424916 
Product Code:  MASS.E 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 

Book Details2003; 313 ppMSC: Primary 00;
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 sixyear 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 semesterlong 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.ReadershipProfessors of mathematics; general mathematical audience.

Table of Contents

Cover

Title

Copyright

Contents

A brief description of MASS Program

Teaching in the MASS Program

Part I. Lecture Notes

padic analysis in comparison with real

Geometrical methods of mechanics

Geometric structures, symmetry and elements of Lie groups

Continued fractions, hyperbolic geometry and quadratic forms

Part II. MASS Colloquium

MASS Colloquium

Hilbert's fourth problem in two dimensions

Integral lexicographic codes

The classification of finite simple groups

Billiard balls count π

Reptiles revisited

Fractals and dynamics

Unprovable theorems and fastgrowing functions

Minimal surfaces and random walks

The tale of a geometric inequality

Part III. Student Research Papers

Summer REU Program at Penn State

Partitions of n and connected triangles

Triangles gone wild

Determinacy of games

On the nonexistence of odd perfect numbers

Appendices

Appendix 1. MASS and REU courses and instructors

Appendix 2. MASS colloquia

Appendix 3. MASS and REU participants

Back Cover


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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 sixyear 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 semesterlong 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.
Professors of mathematics; general mathematical audience.

Cover

Title

Copyright

Contents

A brief description of MASS Program

Teaching in the MASS Program

Part I. Lecture Notes

padic analysis in comparison with real

Geometrical methods of mechanics

Geometric structures, symmetry and elements of Lie groups

Continued fractions, hyperbolic geometry and quadratic forms

Part II. MASS Colloquium

MASS Colloquium

Hilbert's fourth problem in two dimensions

Integral lexicographic codes

The classification of finite simple groups

Billiard balls count π

Reptiles revisited

Fractals and dynamics

Unprovable theorems and fastgrowing functions

Minimal surfaces and random walks

The tale of a geometric inequality

Part III. Student Research Papers

Summer REU Program at Penn State

Partitions of n and connected triangles

Triangles gone wild

Determinacy of games

On the nonexistence of odd perfect numbers

Appendices

Appendix 1. MASS and REU courses and instructors

Appendix 2. MASS colloquia

Appendix 3. MASS and REU participants

Back Cover