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Six lectures and examples of an exhibit presented to the Fellows of
the Henry Koerner Center for Emeritus Faculty at Yale University by
Professor Frank Firk are reproduced here. The lectures were given
to colleagues who were experts in fields often far removed from
Physics and Mathematics; they are therefore suitable for
non-specialist, inquisitive readers. The following topics are
covered: 1. Understanding Einstein 2. Nuclear Power and Related
Issues 3. The Mysterious Primes 4. New Dimensions - a Tribute to
Benoit Mandelbrot 5. Perspective and Beyond 6. E = mc2: a
neo-Newtonian Approach 7. Some Examples of Drawings and Paintings
from an Exhibition.
Throughout the decade of the 1990's, Professor Firk taught a
one-year course of a specialized nature to students who entered
Yale College with excellent preparation in Mathematics and the
Physical Sciences, and who expressed an interest in Physics or a
closely related field. The students were required to take the
highest level of introductory Mathematics in parallel with the
course. The book covers topics taught in the first semester; they
include: 1. MATHEMATICAL PRELIMINARIES 2. KINEMATICS: THE GEOMETRY
OF MOTION 3. CLASSICAL AND SPECIAL RELATIVITY 4. NEWTONIAN DYNAMICS
5. INVARIANCE PRINCIPLES AND CONSERVATION LAWS 6. EINSTEINIAN
DYNAMICS
This book has its origin in a one-year course for non-science
majors that Professor Firk taught at Yale throughout the decade of
the 1970's. It is intended for the inquisitive reader who wishes to
gain an understanding of the immortal work of Einstein, the
greatest scientist since Newton. Special Relativity deals with
measurements of space, time and motion in inertial
(non-accelerating) frames of reference. A popular account of
Einstein's Theory of General Relativity, a theory of space, time,
and motion in the presence of gravity, is given. The contents
include: 1. Understanding the physical universe 2. Describing
everyday motion; relative motion, Newton's Principle of Relativity,
problems with light, 3. Einstein's Theory of Special Relativity
simultaneity and synchronizing clocks, length contraction and time
dilation, examples of Einstein's world, 4. Newtonian and
Einsteinian mass 5. Equivalence of energy and mass, E = mc2 6.
Principle of Equivalence 7. Einsteinian gravity; gravity and the
bending of light, gravity and the flow of time, and red shifts,
blue shifts, and black holes.
Group Theory, with its emphasis on Lie Groups and their application
to the study of symmetries of the fundamental constituents of
matter is introduced at a level suitable for Seniors and advanced
Juniors majoring in the Physical Sciences. The book has its origin
in a one-semester course that Professor Firk taught at Yale
University for more than ten years. It is not generally appreciated
by Physicists that continuous transformation groups (Lie Groups)
originated in the Theory of Differential Equations. The
infinitesimal generators of Lie Groups therefore have forms that
involve differential operators and their commutators, and these
operators and their algebraic properties have found, and continue
to find, a natural place in the development of Quantum Physics.
Topics covered include: Galois Groups Algebraic Invariants
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