Hello friends. Here is another reading list. This is
a personal list of recommended books of a nonreligious nature. They
are books that I have read lately, or was greatly influenced by at
some point in my life. I hope you find something here that you find
enjoyable or worthwhile. If you purchase any books through the links
on this site, the parish gets a small percentage. In fact, if you
purchase any book at all by entering Amazon from a link here, the
parish gets a small percentage. The percentage is larger for books
which are specifically recommended here.
Physics
Just lately I have discovered the Feynman lectures in
physics. Of course many others have already discovered them, that's
why they're found on so many bookshelves, but they were new to me.
I ran across the first volume of the audio tape version at Powell's
in Portland. Since it was used, it was in a price range I could afford.
The first audio volume is quantum mechanics, and it is fascinating
to hear Feynman's point of view. He won the Nobel Prize for his work
on quantum electrodynamics, and he knows what he is talking about.
He always has a unique point of view, and one firmly based on reality.
After listening to the tapes, I ordered the books from Amazon, and
I can't remember a recent purchase that has brought me so much pleasure.
If you decide to buy the books, the hardbooks cost little more than
the paperback, so you might as well get the hardback. The audio tapes
run into quite a bit of money, but at least Amazon sells them for
below list price. Both are worthwhile because the printed edition
has been "improved" but lacks the comments and asides of the audio
version.
Lectures
on Physics in three volumes by Richard Feynmann.
Audio
tapes volume 1: Quantume Mechanics
Audio
tapes volume 2: Advanced Quantum Mechanics
Audio
tapes volume 3: From Crystal Structure to Magnetism
Audio
tapes volume 4: Electrical & Magnetic Behavior
Audio
tapes volume 5: Fundamentals: Energy & Motion
Audio
tapes volume 6: Fundamentals: Kinetics & Heat
There seem to be a volume 7 and a volume 8 now available,
but I can't find out what is on them.
If you would like something easier to read, also by
the great physicist Richard Feynman, check out his book QED,
The Strange Theory of Light and Matter Jn this little gem, Feynman
sets out to explain some of the most advanced topics in physics to
the average person in a series of public lectures at UCLA. The book
is short, and you can decide for yourself whether he succeeds. Even
for someone who plans to learn the full theory, having Feynman explain
the basic ideas in simple language will give you a leg up.
And my newest interest is in quantum computing. In the
early 80's, Richard Feynman gave some lectures on the theory of computing.
Among other topics he described how to make computers that utilized
quantum states of atoms or particles to store information, and also
described some of the advantages. One of the advantages was not understood
until the work of Bell on quantum entanglement. With Peter Shorr's
announcement of his algorithm to factor large numbers in polynomial
time, the quantum computer became a realistic threat to much of modern
computer cryptography (providing we can build one of course). The
standard book on quantum computing is Quantum
Computing by Jozef Gruska who is on the faculty of Masaryk University
in the Czech republic. It helps to know a little abstract algebra
and functional analysis to read this book, also to know the basics
of Feynman's approach to quantum mechanics. A very inexpensive book
without mathematics is The
Feynman Processor by Gerard Milburn who is at the University of
Queensland and is one of those practical physicists who is actually
working on building quantum computers. Finally, why not read the master
himself? Feynman's Lectures
on Computation are still in print. I thought they were available
on audio tape too, but I can't locate those.
Mathematics
Well, no list of books compiled by me could ever be
complete without some math books.
One of the most influential books in my life is Calculus
by Michael Spivak. (It's rather expensive new, so you might want to
check out a used book store. Powell's here in Portland always has
several copies.) It is a calculus book by one of the great math teachers
of the twentieth century. It is really a first calculus book for people
who have already studied calculus before. It explains all the theory
of why calculus is true in clear terms. Naturally this exposition
leads into many of the most interesting areas of advanced mathematics,
and Spivak introduces a relative beginner to enough advanced topics
to fuel a lifetime of fascination. If you decide to buy this book,
be sure to buy the supplement as well with answers to the exercises.
Spivak wrote another book on calculus, this time for
multivariable calculus. It is a deceptively small paperback called
Calculus
on Manifolds. It is not a good place to learn multivariable calculus
the first time, but is an elegant presetation of the theory to anyone
already fluent in the theorems and calculations of vector calculus.
Spivak's magnum opus is a five volume (five large volumes)
presentation of Differential Geometry. Unfortunately, the first two
volumes seem to be out of print, but the last three are available:
Volume
3, Volume
4, Volume
5. This subject is the science of curved objects in higher dimensions.
The science began with Gauss at the beginning of the nineteenth century
when Gauss analyzed curved surfaces. A surface is "intrinsically"
curved if it is impossible to make a flat map with no distortions.
We all know that a distortion free map of the earth is impossible,
and Gauss correctly analyzed when this is possible for any surface
at all. It's interesting to think about how a two dimensional creature
might know that his universe is intrinsically curved. One way to tell
is to measure the angles in a triangle. As you can easily see, there
are many triangles on the surface of a sphere that do not have 180
degrees in their three angles. In fact, on the surface of a sphere,
you can make a triangle with three right angles. Another test for
intrinsic curvature is to measure the circumference of a circle. As
you can see, on a sphere, the circumference will be less than one
expects, that is less than 2 x pi x radius. Interestingly enough,
Gauss asked the question of whether or not we live in a curved space
almost one hundred years before Einstein, and tried to investigate
the question by measuring some counties in Germany. (In case you're
interested, Gauss found that our space is flat within experimental
error.) Towards the end of his career, Gauss brought a young genius
to his university by the name of Riemann. Riemann has been called
a "supernova" in the history of mathematics. It is difficult to find
a parallel in other fields of knowledge of a man who was so important,
with such a short career. When Riemann was required to give a lecture
as part of his promotion, a lecture called a "habilitation lecture",
Riemann proposed three topics, assuming the committee would choose
the first or second. He proposed as his third topic, the foundations
of geometry, and was surprised when Gauss chose that third topic.
In only six weeks, he put together a short lecture in which he explained
how to generalize all of Gauss' ideas on curvature to any number of
dimensions. Like so many of Riemann's ideas, it took decades of work
by the best minds to fill in all the details. When Einstein formulated
his theory that gravitation is just inertia in a curved space, also
know as general relativity, in 1915, it was these tools forged by
Riemann that made the calculations possible. One of the wonderful
things about Spivak's books is that they begin the subject of differential
geometry by guiding you through the seminal papers of Gauss and then
Riemann before moving on to the many modern formulations. Also, Spivak
lucidly explains the many modern formulations of the subject without
bias, preparing the reader for any modern research in mathematics
or physics involving this vast subject.
Number Theory
If you are interested in mathematics, but never quite
made it past algebra, you might enjoy some books on number theory.
Number theory is all about the properties of whole numbers like 7,
11, 2, and 33, for example. The most ancient book on number theory
is by an ancient Greek named Diophantus.
Here is a simple problem which has been around since
the ancient Greeks, and is still unsolved. A number is called perfect
if it is equal to the sum of its divisors. For example, 6 = 1 + 2
+ 3, and 28 = 1 + 2 + 4 + 7 + 14. All the even perfect numbers were
in a sense classified as long ago as Euclid. Is there an odd perfect
number? Nobody knows. Maybe a clever young person reading this web
site will answer the question.
Did you ever wonder what whole numbers could be the
sides of right triangles? 3, 4, and 5 can because 3x3+4x4=5x5. There
are an infinite number of such triples which form an interesting pattern,
also classified in Euclid.
If questions like these seem interesting to you, I highly
recommend the book Recreations
in the Theory of Numbers by Ball. I used to use this book for
my bedtime reading for many years. The book is never abstract, and
always uses concrete examples in a very very entertaining style.
If you have can do simple algebra, you might enjoy a
more advanced book (but not too advanced) called Solved
and Unsolved Problems in Number Theory by Daniel Shanks. You might
find a problem in this book that you will solve and make you world
famous.
In modern number theory, the most advanced tools are
used from all branches of mathematics, and number theory is used in
the cutting edge theories of encoding on the internet. Number theory
has been used for several decades now to encrypt and verify electronic
financial transfers. The most ancient branch of mathematics is now
the most modern, and still one of the most difficult.
Amazingly enough, there was no great book written on
number theory for almost two thousand years after Diophantus. Then
Gauss launched the modern era with his Disquistiones
Arithmeticae which he finished at the amazing age of 19. This
book is very expensive, and probably not worth buying unless you are
making a career of it.
One gateway into modern number theory as it is used
in encryption is through a readable jewel called Rational
Points on Elliptic Curves by Tate and Silverman. This book grew
out of some popular lectures by a great modern number theorist. The
book will introduce you to many of the most advanced ideas in mathematics.
A little gem of a book that I just discovered and am
reading is Representation
Theory of Finite Groups by Martin Burrow. It is an elementary
introduction to a cutting edge branch of mathematics with applications
in quantum physics, particle physics, and many branches of mathematics
including number theory. You'll be glad to know that this book is
an inexpensive Dover paperback. God bless Dover Publications!!! And
God bless Chelsea too!
