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Road to Reality A Complete Guide to the Laws of the Universe

ISBN-10: 0679776311

ISBN-13: 9780679776314

Edition: N/A

Authors: Roger Penrose, Roger Penrose

List price: $29.00
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Description:

Roger Penrose, one of the most accomplished scientists of our time, presents the only comprehensive and comprehensible account of the physics of the universe. From the very first attempts by the Greeks to grapple with the complexities of our known world to the latest application of infinity in physics,The Road to Realitycarefully explores the movement of the smallest atomic particles and reaches into the vastness of intergalactic space. Here, Penrose examines the mathematical foundations of the physical universe, exposing the underlying beauty of physics and giving us one the most important works in modern science writing.
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Book details

List price: $29.00
Publisher: Knopf Doubleday Publishing Group
Publication date: 1/9/2007
Binding: Paperback
Pages: 1136
Size: 6.20" wide x 9.20" long x 1.90" tall
Weight: 2.706
Language: English

Albert Einstein was born on March 14, 1879 in Ulm. He spent his childhood in Munich where his family owned a small machine shop. By the age of twelve, Einstein had taught himself Euclidean Geometry. His family moved to Milan, where he stayed for a year, and he used it as an excuse to drop out of school, which bored him. He finished secondary school in Aarau, Switzerland and entered the Swiss Federal Institute of Technology in Zurich. Einstein graduated in 1900, by studying the notes of a classmate since he did not attend his classes out of boredom, again. His teachers did not like him and would not recomend him for a position in the University. For two years, Einstein worked as a substitute…    

Preface
Acknowledgements
Notation
Prologue
The roots of science
The quest for the forces that shape the world
Mathematical truth
Is Plato’s mathematical world ‘real’?
Three worlds and three deep mysteries
The Good, the True, and the Beautiful
An ancient theorem and a modern question
The Pythagorean theorem
Euclid’s postulates
Similar-areas proof of the Pythagorean theorem
Hyperbolic geometry: conformal picture
Other representations of hyperbolic geometry
Historical aspects of hyperbolic geometry
Relation to physical space
Kinds of number in the physical world
A Pythagorean catastrophe?
The real-number system
Real numbers in the physical world
Do natural numbers need the physical world?
Discrete numbers in the physical world
Magical complex numbers
The magic number ‘i’
Solving equations with complex numbers
Convergence of power series
Caspar Wessel’s complex plane
How to construct the Mandelbrot set
Geometry of logarithms, powers, and roots
Geometry of complex algebra
The idea of the complex logarithm
Multiple valuedness, natural logarithms
Complex powers
Some relations to modern particle physics
Real-number calculus
What makes an honest function?
Slopes of functions
Higher derivatives; C1-smooth functions
The ‘Eulerian’ notion of a function?
The rules of differentiation
Integration
Complex-number calculus
Complex smoothness; holomorphic functions
Contour integration
Power series from complex smoothness
Analytic continuation
Riemann surfaces and complex mappings
The idea of a Riemann surface
Conformal mappings
The Riemann sphere
The genus of a compact Riemann surface
The Riemann mapping theorem
Fourier decomposition and hyperfunctions
Fourier series
Functions on a circle
Frequency splitting on the Riemann sphere
The Fourier transform
Frequency splitting from the Fourier transform
What kind of function is appropriate?
Hyperfunctions
Surfaces
Complex dimensions and real dimensions
Smoothness, partial derivatives
Vector Fields and 1-forms
Components, scalar products
The Cauchy–Riemann equations
Hypercomplex numbers
The algebra of quaternions
The physical role of quaternions?
Geometry of quaternions
How to compose rotations
Clifford algebras
Grassmann algebras
Manifolds of n dimensions
Why study higher-dimensional manifolds?
Manifolds and coordinate patches
Scalars, vectors, and covectors
Grassmann products
Integrals of forms
Exterior derivative
Volume element; summation convention
Tensors; abstract-index and diagrammatic notation
Complex manifolds
Symmetry groups
Groups of transformations
Subgroups and simple groups
Linear transformations and matrices
Determinants and traces
Eigenvalues and eigenvectors
Representation theory and Lie algebras
Tensor representation spaces; reducibility
Orthogonal groups
Unitary groups
Symplectic groups
Calculus on manifolds
Differentiation on a manifold?
Parallel transport
Covariant derivative
Curvature and torsion
Geodesics, parallelograms, and curvature
Lie derivative
What a metric can do for you
Symplectic manifolds <br