# Flooved

Flooved is an online education platform founded in 2011, that seeks to provide free education to a global audience by providing lecture notes, handouts, and study guides online, beginning with undergraduate mathematics and physics content.

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Nov 14, 2013 Daniel Kleitman;Peter Shor
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We suppose we want to be able to send messages that can be conveniently decoded even in the presence of errors.
Topics: Maths, Mathematics
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Nov 14, 2013 Arthur Mattuck;Haynes Miller;Jeremy Orloff;John Lewis
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The fundamental matrix _(t) also provides a very compact and ef�cient integral formula for a particular solution to the inhomogeneous equation x' = A(t)x + F(t). (presupposing of course that one can solve the homogeneous equation x' = A(t)x �rst to get _.) In this short note we give the formula (with proof!) and one example.
Topics: Maths, Differential Equations (ODEs & PDEs), Ordinary Differential Equations (ODEs), Linear...
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Nov 14, 2013 Oleg Goldberg
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Topics: Maths, Differential Equations (ODEs & PDEs), Mathematics
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Nov 14, 2013 Daniel Kleitman;Peter Shor
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We will discuss one of the classes of problems that have been suggested and deployed for communications of this public key type. It was actually developed here at M.I.T., a number of years ago. The hard problem that is more or less equivalent to breaking this code is that of factoring a rather large number. (There are variants of the coding scheme in which the inversion problem is exactly equivalent to factoring such a number.)
Topics: Maths, Mathematics
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Nov 14, 2013 James S. Milne
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These notes give a concise exposition of the theory of �elds, including the Galois theory of �nite and in�nite extensions and the theory of transcendental extensions. The �rst six sections form a standard course. Chapters 7 and 8 are more advanced, and are required for algebraic number theory and algebraic geometry repspectively.
Topic: Maths
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Nov 14, 2013 Albert R. Meyer
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The theorem below relates the greatest common divisor to linear combinations. This theorem is very useful; take the time to understand it and then remember it!
Topics: Maths, Mathematics
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Nov 14, 2013 Tomasz S. Mrowka
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Topics: Maths, Linear Algebra and Geometry, Geometry of Manifolds, Mathematics
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Nov 14, 2013 Trench, William F., 1931-
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Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. In writing this book I have been guided by the these principles: 1. An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student�s place, and have chosen to err on the side of too much detail rather than not enough. 2. An...
Topics: Maths, Differential Equations (ODEs & PDEs)|, Ordinary Differential Equations (ODEs), Linear...
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Nov 14, 2013 Igor Vilfan
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In this Chapter we will discuss models that can be described by classical statistical mechanics. We will concentrate on the classical spin models which are used notonly to study magnetism but are valid also for other systems like binary alloys or lattice gases.
Topic: Maths
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Nov 14, 2013 Richard Melrose
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Topics: Maths, Differential Equations (ODEs & PDEs), Methods, Fourier Analysis, Mathematics
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Nov 14, 2013 Rory Adams;Heather Williams;Wendy Williams
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In Grade 11 you were introduced to linear programming and solved problems by looking at points on the edges of the feasible region. In Grade 12 you will look at how to solve linear programming problems in a more general manner.
Topics: Maths, Mathematics
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Nov 14, 2013 Emma Carberry
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Topics: Maths, Linear Algebra and Geometry, Analysis and Calculus, Geometry, Differential Geometry,...
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Nov 14, 2013 Vera Mikyoung Hur
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The simpler the input signal is, the clearer we should expect the signature of the system pa_rameters to be, and the easier we predict how the system will respond to other more complicated signals. The simplest is the null signal, which corresponds to the homogeneous equation. We study two other standard and very simple signals: the unit step function and the unit impulse. Here, we study step signals. Impulsive signals will be discussed in later lectures.
Topics: Maths, Differential Equations (ODEs & PDEs), Mathematics
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Nov 14, 2013 Ben Simons
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The aim of this section is to introduce the language and machinery of classical and quantum �eld theory through its application to the problem of lattice vibrations in a solid. In doing so, we will become acquainted with the notion of symmetry breaking, universality, elementary excitations and collective modes � concepts which will pervade much of thecourse.
Topics: Physics, Condensed Matter, Particle Physics and Fields, Quantum Physics, General Theory of Fields...
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Nov 14, 2013 Vera Mikyoung Hur
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Topics: Maths, Differential Equations (ODEs & PDEs), Methods, Mathematics
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Nov 14, 2013 Michel X. Goemans
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In this lecture, we will introduce three related topics: graph orientations, directed cuts, and submodular �ows. In fact, we will use submodular �ows to prove results from the other topics.
Topics: Maths, Optimization and Control, Optimization, Mathematics
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Nov 14, 2013 James Nearing
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You could say that some of the equations that you encounter in describing physical systems can�t be solved in terms of familiar functions and that they require numerical calculations to solve. It would be misleading to say this however, because the reality is quite the opposite. Most of the equations that describe the real world are su_ciently complex that your only hope of solving them is to use numericalmethods. The simple equations that you �nd in introductory texts are there because...
Topics: Maths, Numerical Analysis, Mathematics
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Nov 14, 2013 Denis Auroux
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0.1. Lagrangian Floer Homology (contd). Let (M, _) be a symplectic man_ifold, L0, L1 compact Lagrangian submanifolds intersecting transversely.
Topics: Maths, Linear Algebra and Geometry, Geometry, Mathematics
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Nov 14, 2013 Richard Melrose
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Fourier series. Let us now try applying our knowledge of Hilbert space to a concrete Hilbert space such as L^2(a, b) for a �nite interval (a, b) _ R. You showed that this is indeed a Hilbert space. One of the reasons for developing Hilbert space techniques originally was precisely the following result.
Topics: Maths, Differential Equations (ODEs & PDEs), Partial Differential Equations (PDEs), Functional...
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Nov 14, 2013 Jeff Viaclovsky
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Topics: Maths, Analysis and Calculus, Differential Equations (ODEs & PDEs), Mathematics
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Nov 14, 2013 R. Victor Jones
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As we have seen, the Fock or number states....are complete set eigenstates of an important group of commuting observables...
Topics: Physics, Acoustics, Optics and Waves, Quantum Physics, Optics�, Quantum Optics�, Physics
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Nov 14, 2013 Jonathan Kelner
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In today�s lecture we are going to: � Discuss nonblocking routing networks � Start the description of a method for local and almost linear-time clustering and partitioning based on the Lovasz-Simonovits Theorem.
Topics: Maths, Mathematics
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Nov 14, 2013 Katrin Wehrheim
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Topics: Maths, Logic, Numbers and Set Theory, Analysis and Calculus, Countability and Uncountability,...
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Nov 14, 2013 Tomasz S. Mrowka
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Inverse, and implicit function theorems. Among the basic tools of the trade are the inverse and implicit function theorems. We will �rst state them in a coordinate dependent fashion. When we develop some of the basic terminology we will have available a coordinate free version.
Topics: Maths, Linear Algebra and Geometry, Geometry of Manifolds, Mathematics
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Nov 14, 2013 Denis Auroux
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1. Hodge Theory - Theorem 1 (Hodge)....
Topics: Maths, Linear Algebra and Geometry, Analysis and Calculus, Differential Equations (ODEs &...
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Nov 14, 2013 Kiran S. Kedlaya
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In this unit, we consider a relatively simple example of a large sieve inequality, of the sort introduced by Linnik. This is a setup for the multiplicative large sieve inequality we will need for Bombieri-Vinogradov.
Topics: Maths, Algebra, Number Theory, Mathematics
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Nov 14, 2013 Mr. Travis Byington;Lawrence Evans;Mr. Ryan Magee;Hao Zhang
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Calculating E from Gauss�s law- In a few cases the charge distribution has suf�cient geometric symmetry that one can use Gauss's law to calculate the E-�eld. The trick is to...
Topics: Physics, Electromagnetism and Electromagnetic Radiation, Classical Electromagnetism�,...
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Nov 14, 2013 Jared Speck
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We now discuss a technique, known as separation of variables, that can be used to explicitly solve certain PDEs. It is especially useful in the study of linear PDEs. Although this technique is applicable to some important PDEs, it is unfortunately far from universally applicable.
Topics: Maths, Differential Equations (ODEs & PDEs), Partial Differential Equations (PDEs), Mathematics
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Nov 14, 2013 Jin Au Kong
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In the previous lecture, we wrote the EFIE for an incident TE plane wave on a PEC surface.The solution was then obtained by some types of �intuitive� arguments, such as dividing the integration domain into small elements and supposing that the unknown does not vary too much over each elementary cell. We shall now see more rigorously what we actually did, and show that it was in fact a simple version of the Method of Moments.
Topics: Physics, Electromagnetism and Electromagnetic Radiation, Nuclear, Atomic and Molecular Physics,...
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Nov 14, 2013 Edward A. Bender;S. Gill Williamson
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Topics: Maths, Mathematics
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Nov 14, 2013 Daniel H. Rothman
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We now study the �routes� or �scenarios� towards chaos.
Topics: Maths, Dynamics and Relativity, Dynamical Systems, Bifurcations in Flows and Maps, Chaos, The...
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Nov 14, 2013 Jeff Viaclovsky
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Fundamental theorem of calculus. Let f : [a, b] R be continuous and let ... Then F is di_erentiable and F'(x) = f(x).
Topics: Maths, Analysis and Calculus, Analysis, Integration, Fundamental Theorem of Calculus, Mathematics
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Nov 14, 2013 Richard Melrose
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Poisson Summation: This is really a correlation between fourier transforms and fourier series
Topics: Maths, Differential Equations (ODEs & PDEs), Methods, Fourier Analysis, Mathematics
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Nov 14, 2013 Alan Guth;Barton Zwiebach
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Topic: Maths
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Nov 14, 2013 Dmitry Panchenko
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Given the joint distribution of (X, Y), the individual distributions of X, Y are marginal distributions.
Topics: Maths, Statistics and Probability, Mathematics
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Nov 14, 2013 Richard M. Dudley
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Topics: Maths, Statistics and Probability, Statistics, Mathematics
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Nov 14, 2013 Peter M. Neumann
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These notes are intended as a rough guide to the eight-lecture course Introduction to Pure Mathematics which is a part of the Oxford 1st-year undergraduate course for the Preliminary Examination in Mathematics. Please do not expect a polished account. They are my personal lecture notes, not a carefully checked textbook. Nevertheless, I hope they may be of some help.
Topic: Maths
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Nov 14, 2013 Dmitry Panchenko
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Topics: Maths, Statistics and Probability, Stochastic Analysis, Probability, Stochastic Processes, Brownian...
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Nov 14, 2013 Laurent Demanet
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Fourier�s analysis was tremendously successful in the 19th century for formulating series expansions for solutions of some very simple ODE and PDE. This class shows that in the 20th century, Fourier analysis has established itself as a central tool for numerical computations as well, for vastly more general ODE and PDE when explicit formulas are not available
Topics: Maths, Numerical Analysis, Mathematics
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Nov 14, 2013 Prof. Carl Stitz;Prof. Jeff Zeager
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Topics: Algebra, Mathematics
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Nov 14, 2013 Daniel Kleitman;Peter Shor
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To do a 2^k FFT mod a prime p you need to choose a prime p whose remainders include 2^k-th roots of unity, and you need to find one such root that is not a 2^(k-1)-th root of unity
Topics: Maths, Mathematics
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Nov 14, 2013 Kiran S. Kedlaya
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Topics: Maths, Linear Algebra and Geometry, Algebraic Geometry, Mathematics
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Nov 14, 2013 Peter Ouwehand
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Topic: Maths
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Nov 14, 2013 Igor Vilfan
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Some typical results of MC simulations of a d = 2 Ising ferromagnet are shownin Fig. 4.9. At high T (T = 2TC), there is only short-range order, the spins form small clusters. The correlation length (approximately equal to the linear size of the largest cluster) is small. Close (but above) TC, somewhat larger patches in which most of the spins are lined up in the same direction begin to develop. ...
Topic: Maths
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Nov 14, 2013 Jacob Lurie
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Topics: Maths, Algebra, Topology and Metric Spaces, Mathematics
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Nov 14, 2013 Lawrence Evans;Mr. J. Edward Ladenburger
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Kepler�s laws Explanations of the motion of the celestial bodies � sun, moon, planets and stars � are among the oldest scienti�c theories. The apparent rotation of these bodies around the earth every day was attributed by the ancients to their place in "celestial spheres" which revolved daily around the stationary earth, assumed to be at the center of the universe.
Topics: Physics, Physics
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Nov 14, 2013 Markus Zahn
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Topics: Physics, Condensed Matter, Electromagnetism and Electromagnetic Radiation, Structural, Mechanical,...
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Nov 14, 2013 Pekka Pyykk�
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The energy-expression: Subtracting the rest energy mc2 from E, the one-electron Dirac Hamiltonian...and the Dirac-Fock Hamiltonian...,The total wave function is the Slater determinant. ...
Topics: Physics, Quantum Physics, Physics
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Nov 14, 2013 J. Bernstein;A. Rita
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Topics: Maths, Linear Algebra and Geometry, Geometry, Mathematics
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Nov 14, 2013 John Lewis;Arthur Mattuck;Haynes Miller;Jeremy Orloff
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Topics: Maths, Differential Equations (ODEs & PDEs), Mathematics
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Nov 14, 2013 Rodolfo R. Rosales
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Contents 1. Physical setup, assumptions, and notation. 2. Derivation of the governing equations. 3. Linearized governing equations.
Topics: Maths, Differential Equations (ODEs & PDEs), Partial Differential Equations (PDEs), Mathematics
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Nov 14, 2013 Tomasz S. Mrowka
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Topics: Maths, Linear Algebra and Geometry, Geometry of Manifolds, Mathematics
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Nov 14, 2013 Jeff Viaclovsky
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Topics: Maths, Analysis and Calculus, Differential Equations (ODEs & PDEs), Mathematics
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Nov 14, 2013 John Lewis;Arthur Mattuck;Haynes Miller;Jeremy Orloff
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In this note we will only consider linear systems of the form x = Ax. Such a system always has a critical point at the origin.
Topics: Maths, Differential Equations (ODEs & PDEs), Mathematics
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Nov 14, 2013 Kiran S. Kedlaya
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In this unit, we convert the additive large sieve inequality from the previous unit, which concerned characters of the additive group, into a result about Dirichlet characters.
Topics: Maths, Algebra, Number Theory, Mathematics
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Nov 14, 2013 Gregg Musiker
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De�nition: If a vertex v has at least as many chips on it as its degree, i.e. C(v) � deg(v), we say that v is ready to �re. A vertex v that is ready to �re may send chips to its neighbors by sending one chip along each of its incident edges. Given graph G, we say that a chip con�guration C is stable if no vertex is ready to �re, i.e. if C(v) < deg(v) for all vertices v _ V (G).
Topics: Maths, Algebra, Statistics and Probability, Probability, Combinatorics, Mathematics
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Nov 14, 2013 John Lewis;Arthur Mattuck;Haynes Miller;Jeremy Orloff
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In summary, the procedure of sketching trajectories of the 2 _ 2 linear homogeneous system x_ = Ax, where A is a constant matrix
Topics: Maths, Differential Equations (ODEs & PDEs), Mathematics
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Nov 14, 2013 Hung Cheng
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In this chapter, we shall discuss the method of separation of variables and demonstrate this method with several PDEs examples.
Topic: Maths
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Nov 14, 2013 Abhinav Kumar
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Topics: Maths, Algebra, Number Theory, Mathematics
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Nov 14, 2013 Roland Speicher
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I will present the basic de�nitions and properties of non-crossing partitions and free cumulants and outline its relations with freeness and random matrices. As examples, I will consider the problems of calculating the eigenvalue distribution of the sum of randomly rotated matrices and of the compression (upper left corner) of a randomly rotated matrix.
Topics: Maths, Linear Algebra and Geometry, Vectors and Matrices, Matrices, Mathematics
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Nov 14, 2013 Hung Cheng
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In this chapter we give a short discussion of complex numbers and the theory of a function of a complex variable.
Topics: Maths, Mathematics
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Nov 14, 2013 R. E. Showalter
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Chapter I presents all the elementary Hilbert space theory that is needed for the book. Chapter II is an introduction to distributions and Sobolev spaces. Chapter III is an exposition of the theory of linear elliptic boundary value problems in variational form. (The meaning of \variational form" is explained in Chapter VII.). Chapter IV is an exposition of the generation theory of linear semigroups of contractions and its applications to solve initial-boundary value problems for partial...
Topics: Maths, Mathematics
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Nov 14, 2013 Abhinav Kumar
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Factorization If n is composite, how do we factor in poly(log n) time. The obvious way is to divide by all, which is O(�n)
Topics: Maths, Logic, Numbers and Set Theory, Algebra, Elementary Number Theory, Coding and Cryptography,...
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Nov 14, 2013 James Nearing
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When the idea of negative numbers was broached a couple of thousand years ago, they were considered suspect, in some sense not �real.� Later, when probably one of the students of Pythagoras discovered that numbers such as �2 are irrational and cannot be written as a quotient of integers, legends have it that the discoverer su_ered dire consequences. Now both negatives and irrationals are taken forgranted as ordinary numbers of no special consequence. Why should �_1 be any di_erent? Yet...
Topics: Physics, Mathematical Methods in Physics, Logic, Set Theory, and Algebra, Rings and Algebras,...
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Nov 14, 2013 J. Bernstein
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Topics: Maths, Linear Algebra and Geometry, Geometry, Mathematics
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Nov 14, 2013 Ben Simons
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How are the properties of an electron gas in�uenced by weak Coulomb interaction? _ Qualitative considerations: When is the intereaction weak? De�ning
Topics: Physics, Condensed Matter, Particle Physics and Fields, Quantum Physics, General Theory of Fields...
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Nov 14, 2013 Peter Dourmashkin
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Topics: Physics, Classical Mechanics, Classical Mechanics of Discrete Systems, General Theory of Classical...
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Nov 14, 2013 Richard Fitzpatrick
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These lecture notes are designed to accompany a lower-division college survey course covering electricity, magnetism, and optics. Students are expected to be familiar with calculus and elementary mechanics.
Topic: Maths
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Nov 14, 2013 Kiran S. Kedlaya
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This unit begins the second part of the course, in which we will investigate a class of methods in analytic number theory known as sieves. (For non-native speakers of English: in ordinary life, a sieve is a device through which you pour a powder, like �our, to �lter out large impurities.) Whereas the �rst part of the course leaned heavily on methods from complex analysis, here the emphasis will be more combinatorial.
Topics: Maths, Algebra, Number Theory, Mathematics
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Nov 14, 2013 Michel X. Goemans
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In this lecture we will cover: 1. Topics related to Edmonds-Gallai decompositions 2. Factor critica-raphs and ear-decompositions.
Topics: Maths, Graph Theory, Optimization and Control, Statistics and Probability, Connectivity and...
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Nov 14, 2013 Emma Carberry
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We�ll assume that the curves are in R3 unless otherwise noted. We start o_ by quoting the following useful theorem about self adjoint linear maps over R2:
Topics: Maths, Linear Algebra and Geometry, Differential Geometry, Mathematics
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Nov 14, 2013 Dmitry Panchenko
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Topic: Maths
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Nov 14, 2013 Jonathan Kelner
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Topics: Maths, Mathematics
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Nov 14, 2013 Sigurdur Helgason
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Topics: Maths, Analysis and Calculus, Complex Analysis, Mathematics