
HigherDimensional Categories: an illustrated guide book
Category :Category Theory
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 This informal guide grew out of notes that we made when I was teaching Aaron about ncategories recently, in preparation for the IMA workshop on ncategories in June 2004. We made this available in a . . . . . 

Introduction to Chaos
Category :Chaos Theory
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Contents: 1. Lorenz Model: an introduction to chaos; 2. The Pendulum: the language of dynamical systems; 3. Nonlinear Oscillators: quasiperiodicity and frequency locking; 4. One Dimensional Maps; 5. T . . . . . 
Predicative Arithmetic
Category :Arithmetic
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13
Predicative Arithmetic. 
Reversible Markov Chains and Random Walks on Graphs
Category :Graph Theory
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Contents: Introduction; General Markov Chains; Reversible Markov Chains; Hitting and Convergence Time, and Flow Rate, Parameters for Reversible Markov Chains; coupling theory and examples; Special Gra . . . . . 
Dynamical Systems
Category :Dynamical Systems
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 Contents: Physical aspects of dynamical systems; Variational principles and applications; Formal aspects of dynamics; Stability of periodic motions; Existence of periodic motions; Application of P . . . . . 

COURSE OF ANALYTICAL GEOMETRY
Category :Geometry
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The elementary geometry, which is learned in school, deals
with basic concepts such as a point, a straight line, a segment.
They are used to compose more complicated concepts: a polygo
nal line, a . . . . . 
Lectures on Differential Geometry
Category :Differential Geometry
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 Contents:Chapter 1. Manifolds
1.1 Review of calculus
1.2 Manifolds:definitions and examples
1.3 Vectors and differentials
1.4 Submanifolds
1.5 Riemann metrics
Chapter 2. Tensor Calcu . . . . . 

Games, Fixed Points and Mathematical Economics
Category :Game Theory
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Contents: Games; Brouwer’s Fixed Point Theorem and Nash’s Equilibrium Theorem; More general Equilibrium Theorems; Cooperative Games; Differential Games. 
Ordinary Differential Equations and Dynamical Systems
Category :Differential Equations
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This manuscript provides an introduction to ordinary differential equations and dynamical systems. We start with some simple examples of explicitly solvable equations. Then we prove the fundamental re . . . . . 
An Introduction to Quantum Game Theory
Category :Game Theory
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This essay gives a selfcontained introduction to quantum game theory, and is primarily oriented to economists with little or no acquaintance with quantum mechanics. It assumes little more than a basi . . . . . 
Dynamical systems
Category :Dynamical Systems
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Contents: Iterations and ﬁxed points; Bifurcations; Conjugacy; Space and time averages; The contraction ﬁxed point theorem; Hutchinson’s theorem and fractal images; Hyperbolicity; Sy . . . . . 
Homeomorphisms in Analysis
Category :Analysis
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 Contents: The One Dimensional Case; Subsets of R; Baire Class 1; Differentiability Classes; The Derivative Function; Mappings and Measures on R^n; BiLipschitzian Homeomorphisms; Approximation by Ho . . . . . 

Electronic Statistics Textbook
Category :Probability and Statistics
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This Electronic Statistics Textbook offers training in the understanding and application of statistics. The material was developed at the StatSoft R&D department based on many years of teaching underg . . . . . 
Gödel's Theorem and Theories of Arithmetic
Category :Arithmetic
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I am working on what I hope will become another (big) book for C.U.P., on arithmetic and Gödel's incompleteness theorems. The early parts of the book will be a relaxed exposition of Gödel's theorems; . . . . . 
Elementary Number Theory
Category :Number Theory
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 This is a textbook about prime numbers, congruences, basic publickey cryptography, quadratic reciprocity, continued fractions, elliptic curves, and number theory algorithms. We assume the reader has . . . . . 
