Friday, June 1, 2007

Free math books

Here is a list of free math books.Yes free free math books.........
Professor Jim Herod's Multivariable Calculus
Calculus,by Gilbert Strang is made available through MIT's OpenCourseWare electronic publishing initiative.
Linear Methods of Applied Mathematics, by Evans Harrell and James Herod.
Yet another one produced at Georgia Tech is
Linear Algebra, Infinite Dimensions, and Maple, by James Herod.
One more recent one by
Professor Herod is Partial Differential Equations.
Complex Analysis, Complex Variables , by Robert Ash and W. P. Novinger. This is a substantial revision of the first edition of Professor Ash's complex variables text originally published in 1971.
E.H. Connell of the University of Miami has made available on the web his book Elements of Abstract and Linear Algebra. An introductory algebraic topology book, Algebraic Topology I, by Professor Allen Hatcher, of Cornell University, is available, and Professor Hatcher promises the second volume, Algebraic Topology II, will be ready soon.
The Geometry and Topology of Three-Manifolds, by William Thurston. This is an electronic edition of the 1980 lecture notes distributed by Princeton University.
Professor Jim Hefferon of Saint Michaels's College has made available his undergraduate textbook Linear Algebra.
Another elementary linear algebra textbook is
Elementary Linear Algebra, by Keith Matthews.
Introduction to Probability, by Charles Grinstead & J. Laurie Snell.
An Introduction to Probability and Random Processes, by Gian-Carlo Rota and Kenneth Baclawski. This is the 1979 manuscript of the work Professor Rota had been working on for some time. It is made available through the efforts of David Ellerman.
Professor Herbert Wilf (and the publisher, A. K. Peters) has made available his book generatingfunctionology.
Perhaps the greatest textbook of them all is
Euclid's Elements.
Originally published by
Springer-Verlag, the book A Course in Universal Algebra, by Stanley Burris, and H. P. Sankappanavar, is available online.
Professor Robert Ash has written and made available Abstract Algebra:The Basic Graduate Year.
Another one by
Professor Ash is A Course In Algebraic Number Theory.
Professor Ash has also completed and made available A Course in Commutative Algebra.
The Calculus Bible is an elementary calculus textbook from Professor G. S. Gill of the Brigham Young University Mathematics Department.
Calculus Without Limits, by John C. Sparks.
Originally published by Prindle, Weber & Schmidt but currently out of print,
Elementary Calculus: An Approach Using Infinitesimals, by Professor H. Jerome Keisler, is now freely available online.
Handbook of Applied Cryptography, by Alfred J. Menezes , Paul C. van Oorschot, and Scott A. Vanstone, is freely available thanks to the publisher, CRC Press.
Graph Theory, by Reinhard Diestel.
Available for self-study from
The Trillia Group is Basic Concepts of Mathematics, by Elias Zakon.
Another one from
The Trillia Group is An Introduction to the Theory of Numbers by Leo Moser.
Yet another from
The Trillia Group is Mathematical Analysis I, by Elias Zakon.
Thanks to Malaspina Great Books,
Mechanism of the Heavens (1831), by Mary Somerville, is available online. This second edition was prepared by Russell McNeil.
Lecture Notes on Optimization, by Pravin Varaiya. This is a re-issue of a book out of print since 1975. It is an introduction to mathematical programming, optimal control, and dynamic programming.
A Manual of Mathematical Ilustration, by Bill Casselman, shows, at several levels of sophistication, how to use PostScript for producing mathematical graphics.
Chebyshev and Fourier Spectral Methods (2nd. Edition), by John P. Boyd. This is the free online version of the Dover 2001 edition.
A Problem Course in Mathematical Logic, by Stefan Bilaniuk .
Concepts and Applications of Inferential Statistics, by Richard Lowry.
To be published soon by Cambridge University Press,
A Computational Introduction to Number Theory and Algebra, by Victor Shoup will nevertheless remain freely available on-line.
Out of print for sometime, but freely available is
Graph Theory with Applications, by J. A. Bondy and U. S. R. Murty.
Yet another one out of print, but now freely available is
Convergence of Stochastic Processes, by David Pollard.
Designed for undergraduate physics students is
Mathematical Tools for Physics, by James Nearing.
Elementary Number Theory, by William Stein.
A Modern Course on Curves and Surfaces, by Richard Palais.
A First Course in Linear Algebra, by Rob Beezer.
Group Theory, by Pedrag Civitanovic.
Shlomo Sternberg has written Theory of Functions of a Real Variable.
Lie Algebras Semi-Riemann Geometry and General Relativity
Advanced Calculus, by Lynn Loomis and Schlomo Sternberg
Originally published by Springer-Verlag and now out of print,
Non-Uniform Randon Variate Generation, by Luc Devroye is now, thanks to the author, freely available.
Difference Equations to Differential Equations, by Dan Sloughter.
The Calculus of Functions of Several Variables is another one by Professor Sloughter.
Notes on Differential Equation, by Bob Terrell.
Sets, Relations, Functions, by Ivo Düntsch and Günther Gediga.
Another one by
Düntsch and Gediga is Rough Set Data Analysis.
Predicative Arithmetic, by Edward Nelson.
Toposes, Triples and Theories, by Michaele Barr and Charles Wells.
Information Theory, Inference, and Learning Algorithms, by David J. C. MacKay is published by Cambridge University Press, but is, nevertheless, freely available online.
Linear Partial Differential Equations and Fourier Theory , by Marcus Pivato.
Another one by
Professor Pivato is Voting, Arbitration, and Fair Division: The Mathematics of Social Choice.
Introduction to Vectors and Tensors, Volume 1, Linear and Multilinear Algebra, and Introduction to Vectors and Tensors, Volume 2, Vector and Tensor Analysis by Ray M. Bowen and C.-C.Wang, are revised versions of books originally published by Plenum Press in 1976.
Another one by
Professor Bowen and originally published by Plenum Press is Introduction to Continuum Mechanics for Engineers.
Numerical Methods and Analysis for Engineers, by Douglas Wilhelm Harder.
Analysis of Functions of a Single Variable, by Lawerence Baggett, was originally written to be used for a one semester senior course, but the author suggests that it is more appropriate for first year graduate students.
Convex Optimization, by Stephen Boyd, and Lieven Vandenberghe is freely available thanks to Cambridge University Press.
Mathematics Under the Microscope, by Alexandre Borovik, is, according to the author, an attempt "to start a dialogue between mathematicians and cognitive scientists."
Introduction to Statistical Signal Processing, by R. M. Gray and L. D. Davisson is, according to Professor Gray, a "...much revised version of the earlier text Random Processes: An Introduction for Engineers, Prentice-Hall, 1986, which is long out of print." The current book is published by Cambridge University Press.
Not simply an online textbook, but certainly in the same spirit is the
Topology Webcourse project undertaken by Topology Atlas.
This is, I suppose, not a textbook, but nevertheless an interesting reference:
The Matrix Cookbook, by Kaare Brandt Petersen, and Michael Syskind Pedersen.
Not really a textbook either,
Constants, by Steven Finch, is, nevertheless, a nice collection of essays. The title pretty much describes the subject.
So you got your math books........


Tuesday, May 1, 2007

Monday, April 9, 2007

A new way to test time travel

When i was searching for time travel at google i got an article at newscientist titeled
At last, a way to test time travel
But now that is not available.I suddenly found it at
Here is the article:

THE title of Heinrich Päs's latest paper might not
mean much to you. To
those who know their theoretical physics, however,
"Closed timelike
curves in asymmetrically warped brane universes"
contains a revelation.
It suggests that time machines might be far more
common than we ever
thought possible.

Forget trawling the universe in search of rotating
black holes or exotic
wormhole tunnels that could supposedly let us hop
from one instant to
another. According to Päs, a physicist at the
University of Hawaii at
Manoa, and his colleagues, the door to a time
machine could be anywhere
and everywhere in our universe. And unlike most
other scenarios for time
travel, we can test this one here on Earth. "I
think the ideas presented
are wonderful and exciting," says Bill Louis,
a physicist at Los Alamos
National Laboratory in New Mexico and co-spokesperson
for the MiniBoone
neutrino experiment at Fermilab, near Chicago. "The
question is are they
true or not."

Louis is right to be cautious. Although nothing in
the laws of nature
appears to rule out time travel, physicists have
always been uneasy
about it because it makes a mockery of causality,
the idea that cause
always precedes effect. Violating causality would
play havoc with the
universe, for instance, allowing you to travel back
in time and prevent
your own birth.

Such paradoxes are what led Stephen Hawking to
propose his "chronology
protection conjecture". This basically says that
some principle of
physics, perhaps as yet undiscovered, will always
come to the rescue and
prevent time travel from happening. Yet no one
had been able to flesh
out the details until three years ago when several
groups of researchers
claimed that string theory, physicists' best stab
at a prospective
"theory of everything", was beginning to close the
door on time machines
(New Scientist, 20 September 2003, p 28).

All very well, except theoretical physicists are
notorious for never
taking no for an answer. Päs and his colleagues
Sandip Pakvasa of the
University of Hawaii and Thomas Weiler of Vanderbilt
University in
Nashville, Tennessee, have been re-examining
string theory. It views the
fundamental building blocks of the universe not
as point-like particles
but vibrating strings of energy; the faster the
vibration the greater
the mass of the particle.

Such vibrating strings can account for the myriad
interactions of all
the known subatomic particles, such as quarks and
electrons. But there
is a catch - it only works if the strings vibrate
in a space-time with
10 dimensions rather than the four with which we
are familiar.
Proponents of the idea maintain that the extra
dimensions are either so
fantastically small that we have not noticed them,
or so large and
warped in such a way that, again, they have remained
hidden from view.

This has led to the suggestion that our universe
may be like a
four-dimensional membrane or "brane" adrift in
a higher-dimensional
space-time. All of the particles and forces in
our universe would be
trapped in our brane like flies on fly-paper,
so we would have no
knowledge of any dimensions other than the four
we experience, even
though our brane might be floating in a 10-dimensional

space-time, or
"bulk". "If it is, then there is the possibility of
short cuts through
higher-dimensional space," says Päs. "It's such short
cuts that make
time travel possible."

?Time machines might be far more common than we
ever thought possible?

It is not too difficult to visualise such a short
cut. Suppose our
brane-universe is bent back on itself within a
large extra dimension,
making it the four-dimensional equivalent of a
pancake folded in two.
Then you could imagine leaving the brane at one
point, travelling a
short distance through the bulk and re-entering

the brane at a point far
away from your starting point.

There is a problem with this picture, however.
Although we can visualise
a universe where such a short cut is possible,
it cannot be our
universe. That is because the space-time of such
a severely folded brane
is not compatible with Einstein's special theory
of relativity, which
posits a "Euclidean geometry" where space is
perfectly flat. Since
numerous tests of special relativity have shown
that its predictions in
our locality are accurate to better than 1 part
in a million, it is very
unlikely that our universe is shaped like a folded pancake.

Instead Päs, Pakvasa and Weiler consider a space-time
where our universe
is a flat brane that is immersed in a bulk whose own
dimensions are
seriously warped. Because the brane is flat, special
relativity still
applies there. Yet in the bulk, Päs, Pakvasa and
Weiler have found that
the large dimensions can be distorted in such a
way that special
relativity does not apply within them. This means
that anything moving
through the fifth dimension can break one of the
founding principles of
special relativity: it can travel faster than the
speed of light as we
know it.

This has dramatic consequences for inhabitants stuck
on the brane. To
them, any entity that takes a short cut through the
bulk appears to
vanish and then pops up again at some point on the
brane far sooner than
it could have had it kept to the brane. For some
inhabitants of the
brane world, the entity appears to have travelled
faster than the speed
of light. Weirder still, to others it has also
travelled backwards in
time. That's because special relativity says that
from certain frames of
reference, faster-than-light travel is equivalent
to travelling
backwards in time. "Such off-brane short cuts can
appear as 'closed
timelike curves'," says Päs - again, that's code
for time machines.

Escape from the brane

The trouble with this idea is that it assumes there
is some way to
escape the confines of the brane and travel out into
the bulk. How could
we do this? Fortunately string theory provides a way
out. In the theory
almost all of the building blocks of matter are
represented by strings
whose ends are forever anchored to the brane.
This means they can never
escape into the fifth dimension and take a short
cut through space-time.
But there are two crucial exceptions: the hypothetical
carrier of the
gravitational force, called the graviton, and a fourth
type of neutrino
called a sterile neutrino (after the three ordinary
kinds of neutrino).
In string theory these are represented by closed loops
of string. Since
they have no ends attached to the brane, they are free
to leave and
travel into the bulk.

String theorists have pointed to this property of
gravitons to explain
why gravity is tremendously weaker than nature's
other fundamental
forces, such as electromagnetism. The idea is that
gravity is so weak
because a large proportion of gravitons leak away
into the extra
dimensions of the bulk. More intriguingly, however,
their ability to
take short cuts through the bulk also means gravitons
and sterile
neutrinos are potential time travellers. "If we can
manipulate them, we
can study time travel experimentally," says Päs.

None of this will be easy. No one has ever spotted a
graviton or a
sterile neutrino, and the odds of detecting them are
slim, to say the
least (New Scientist, 18 March, p 32). Trillions of o
rdinary neutrinos
pass through our bodies every second, yet we feel
nothing because they
so rarely interact with electrons and atoms.
Sterile neutrinos are even
less communicative because they are thought to
interact only via the
feeble gravitational force and the exchange of
the elusive Higgs boson -
an as yet undetected particle believed to endow
all particles with mass.

Päs and his colleagues point out that a quirk
of quantum mechanics could
save the day. According to the laws of quantum
physics, neutrinos can
flip from one kind to another. Experiments in
Japan and the US designed
to detect neutrinos on the rare occasions they
do interact with matter
have confirmed that neutrinos spewed out by the
sun and those from space
do indeed change type. This phenomenon should
affect sterile neutrinos
too, changing them into ordinary, detectable
neutrinos and back again.
What's more, the odds of this happening increase
whenever the density of
the material the neutrinos are travelling through
changes abruptly.

?A quirk of quantum mechanics could allow us to test
time travel right
here on Earth?

This has inspired Päs and his colleagues to propose
an experiment that
could test their ideas. They suggest sending a
beam of ordinary
neutrinos through the Earth, from a research station
at the South Pole
towards a detector located at the equator. When they
enter the ground,
some of the neutrinos will flip into sterile neutrinos.
Capable of
taking a short cut though the extra dimensions of the
bulk, these
sterile neutrinos will reach the other side of the
Earth first,
apparently having travelled faster than light. As
they pass out of the
ground into the air again, they will flip back into
ordinary neutrinos,
which can be detected. Because the Earth is rotating,
faster-than-light neutrinos can appear to have arrived
before they set off.

Such an experiment is beyond our current technological
capabilities but,
remarkably, Päs says it is a realistic proposition within
the next 50
years. Of course, it requires two things. The first is the
existence of
sterile neutrinos. While many physicists are keen on the
idea of sterile
neutrinos, they are barely beyond theoretical flights of
fancy. The
other is that we live in an asymmetrically warped space-time,
as Päs
prescribes. How plausible is this?

When Einstein's came up with his general theory of
relativity, he showed
us how space-time can be warped or flat, but his
equations tell us
nothing about the actual shape of our universe -
merely that different
shapes are possible. For instance, cosmologists have
no way of knowing
if space stretches out to infinity or curves back on
itself. This opens
the door to many different types of time machines,
some more plausible
than others.

One famous solution to Einstein's equations, formulated
by mathematician
Kurt Gödel, describes a universe that rotates rapidly.
Instead of
travelling in straight lines, light will appear to
travel in a spiral.
Gödel realised that this allows a traveller to outrun
light and return
to their starting point before they left. In other
words, Gödel's
rotating universe is a time machine. "But we know we
don't live in such
a universe," says Päs.

Another time machine exists inside rotating
black holes, where
space-time becomes so warped that space and time
change places. The
trouble is, as Päs points out, rotating black holes
are inaccessible to
us. Then there is the space-time surrounding an
infinitely long, rapidly
rotating cylinder, as proposed by physicist Frank
Tipler. Päs is quick
to dismiss it too. "It requires huge masses rotating
unphysically fast,"
he says.

Among the other leading contenders are wormholes,
microscopic tubes of
space-time that act as tunnels from one point to
another. But before you
climb into one, there is a problem: wormholes snap
shut in an instant
unless propped open by a supply of something called
exotic matter.
Unlike the familiar stuff found on Earth, which always
feels the pull of
gravity, this exotic matter has repulsive gravity,
halting the
wormhole's collapse. "We don't know whether such matter
exists and if it
is stable," says Päs.

Päs confesses that the scenario his team has examined
also requires
exotic matter to warp the fifth dimension, but he
still maintains that
it is more plausible than the other scenarios.
What sets their
space-time apart from wormholes is that the hypothetical
exotic matter
is hidden away in the higher-dimensional bulk instead
of roaming around
the brane. If it exists, this might explain why we have
never seen it.

Understandably, the idea is not without its critics.
Sydney Deser of
Brandeis University in Waltham, Massachusetts, is
convinced, as was
Einstein, that time machines are not possible and
does not like
"unphysical" exotic matter. He believes that concealing
it in the bulk,
as Päs's team suggests, is little better than a scenario
in which it is
out in the open. "It's only a matter of degree," he says.

Päs, however, points out that the kind of space-times
he and his
colleagues have considered can do away with a number
of problems that
have plagued general relativity. For instance,
connections between far-flung parts of the cosmos
would have allowed
heat to flow back and forth across the early universe.
This would have
evened out any temperature variations, explaining the
uniformity that
cosmologists observe. This could provide an alternative
to the theory of
inflation, in which cosmologists believe space-time was
unimaginably fast after the big bang, and which would
also account for
the evenness in temperature. While the majority of
cosmologists believe
in inflation, no one has explained the detailed
physics behind it.

Others do not find asymmetrically warped space-times
so plausible. "I
certainly think the idea is interesting, but I have
some worries," says
Tony Padilla of the University of Barcelona in Spain.
"For a start, I
think it is premature to claim that these space-times
are 'natural'. One
needs to examine their stability first, and in this
case I would expect
the solution to be unstable, although I could be wrong."

Padilla concedes that it is possible that we may one
day find a stable
brane universe with the properties described by
Päs's team. "I'm just
not convinced we are there yet," he says.

John Cramer of the University of Washington in
Seattle agrees that the
work outlines some interesting ideas. "The scheme,
however, requires
asymmetrically warped brane universes - and our
universe may not be one
of these," he cautions. "Nevertheless, it's a
fascinating proposal."

Of course, if time travel is possible in the way
Päs envisages, it may
be accessible only to special particles like sterile
neutrinos and
gravitons, and therefore won't cause much havoc in
the everyday
universe. Päs takes a pragmatic view of all this.
As long as the
possibility of time machines remains, he believes it
is worth exploring
experimentally. "Even if time travel is not possible,
by manipulating
particles like sterile neutrinos we can explore the
physics that
intervenes to prevent it," he says.

?Anything travelling through the fifth dimension
can move faster than
the speed of light as we know it?

The first answers might come soon courtesy of the
MiniBoone neutrino
experiment at Fermilab. It could confirm the existence
of sterile
neutrinos and short cuts in extra dimensions as early as
this year. Then
again, if time travel really is true, maybe the answer
has already been

From issue 2552 of New Scientist magazine, 22 May 2006,
page 34