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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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by Edward A. Bender;S. Gill Williamson
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Topics: Maths, Mathematics
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by Prof. Charles Grinstead;Prof. Laurie Snell
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This text is designed for an introductory probability course taken by sophomores, juniors, and seniors in mathematics, the physical and social sciences, engineering, and computer science. It presents a thorough treatment of probability ideas and techniques necessary for a �rm understanding of the subject. The text can be used in a variety of course lengths, levels, and areas of emphasis
Topics: Maths, Mathematics
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by Richard Fitzpatrick
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What is classical mechanics? Classical mechanics is the study of the motion of bodies (including the special case in which bodies remain at rest) in accordance with the general principles �rst enunciated by Sir Isaac Newton in his Philosophiae Naturalis Principia Mathematica (1687), commonly known as the Principia. Classical mechanics was the �rst branch of Physics to be discovered, and is the foundation upon which all other branches of Physics are built. Moreover, classical mechanics has...
Topic: Maths
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by Prof. Carl Stitz;Prof. Jeff Zeager
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Topics: Maths, Mathematics
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by 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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by Prof. Michael Corral
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This book covers elementary trigonometry. It is suitable for a one-semester course at the college level, though it could also be used in high schools
Topics: Maths, Mathematics
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by Sigurdur Helgason
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Theorem 1 Let � _ C be a region, F a family of holomorphic functions on � such that for each compact E _ �, F is uniformly bounded on E. Then F has a subsequence converging uniformly on each compact subset of �.
Topics: Maths, Analysis and Calculus, Complex Analysis, Mathematics
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by Dmitry Panchenko
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_(_), parameter _ > 0, random variable takes values: {0, 1, 2, ...} p.f. ... Moment generating function:
Topics: Maths, Statistics and Probability, Probability, Statistics, Random Variables, Useful Distributions,...
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by Dmitry Panchenko
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Topics: Maths, Statistics and Probability, Mathematics
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by Dmitry Panchenko
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Topics: Maths, Analysis and Calculus, Statistics and Probability, Mathematics
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by Donald E. Knuth;Tracy Larrabee;Paul M. Roberts
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The �rst three lectures were a �minicourse� that summarized the basics. About two hundred people attended those three sessions, which were devoted primarily to a discussion of the points in �1 of this report. An exercise (�2) and a suggested solution (�3) were also part of the mini course. The remaining 28 lectures covered these and other issues in depth. We saw many examples of �before� and �after� from manuscripts in progress. We learned how to avoid excessive subscripts...
Topics: Maths, Analysis and Calculus|Maths, Study Guides, Study Skills and Assignment Guidelines, Learning...
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by Denis Auroux
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Topics: Maths, Analysis and Calculus, Calculus, Mathematics
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by Edward A. Bender;S. Gill Williamson
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Parts I and II deal with two fundamental aspects of combinatorics: enumeration and graph theory. �Enumeration� can mean either counting or listing things. Mathematicians have generally limited their attention to counting, but listing plays an important role in computer science, so we discuss both aspects. After introducing the basic concepts of �graph theory� in Part II, we present a variety of applications of interest in computer science and mathematics. Induction and recursion play a...
Topics: Combinatorics, Mathematics
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by Dmitry Panchenko
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Topics: Maths, Analysis and Calculus, Statistics and Probability, Mathematics
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by Prof. Kiran S. Kedlaya
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Aside from this introduction, the book is divided into four parts. The �rst part, �Rudiments�, is devoted to the foundations of Euclidean geometry and to some of the most pervasive ideas within the subject. The second part, �Special situations�, treats some common environments of classical synthetic geometry; it is here where one encounters many of the challenging Olympiad problems which helped inspire this book. The third part, �The roads to modern geometry�, consists of two 4...
Topics: Maths, Mathematics
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by Richard Fitzpatrick
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These set of lecture notes are designed for an upper-division undergraduate course on computational physics. The purpose of this course is demonstrate to students how computers can enable us to both broaden and deepen our understanding of physics by vastly increasing the range of mathematical calculations which we can conveniently perform.
Topics: Physics, Physics
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by Markus Zahn
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Topics: Physics, Electromagnetism and Electromagnetic Radiation, Classical Electromagnetism�, Physics
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by Jeff Viaclovsky
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Topics: Maths, Analysis and Calculus, Differential Equations (ODEs & PDEs), Mathematics
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by Roberto Casalbuoni
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Aim of this course is to extend ordinary quantum mechanics, which describes nonrelativistic particles in interaction with given forces, to the relativistic case where forces are described by �elds, as for the electromagnetic case. The most relevant di_erences between the two cases are that the forces become dynamical degrees of freedom, and that one needs a relativistic treatment of the problem. In order to get a consistent description we will need to quantize the �eld degrees of freedom....
Topics: Physics, Particle Physics and Fields, Quantum Physics, General Theory of Fields and Particles,...
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by Hans de Vries
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In this section we use a more elementary approach using the Klein Gordon equation. Each component of the Dirac/Weyl spinor obeys separately also the Klein Gordon equation. To show this �rst we start of with the Dirac equation.
Topic: Maths
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by Gilbert Strang
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This book begins with four special families of matrices�simple and useful, absolutely basic. We look �rst at the properties of these particular matrices Kn,Cn, Tn,and Bn. (Some properties are obvious, others are hidden.) It is terri�c to practice linear algebra by working with genuinely important matrices.
Topics: Maths, Linear Algebra and Geometry, Numerical Analysis, Linear Algebra, Linear Algebraic Systems,...
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by Denis Auroux
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1. Pseudoholomorphic Curves ...
Topics: Maths, Linear Algebra and Geometry, Geometry, Mathematics
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by David Lippman;Jeff Eldridge;Mike Kenyon;Lawrence Morales;Melonie Rasmussen
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Topics: Maths, Mathematics
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by Prof. Dave Witte Morris;Prof. Joy Morris
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well as in the application of mathematics to the rest of the world involve many variables
Topics: Maths, Mathematics
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by Prof. John Erdman
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The current set of notes is an activity-oriented companion to the study of real analysis. It is intended as a pedagogical companion for the beginner, an introduction to some of the main ideas in real analysis, a compendium of problems I think are useful in learning the subject, and an annotated reading/reference list
Topics: Maths, Mathematics
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by Sigurdur Helgason
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While integrals like _ f(z) dz and _ M dx+ N dy have been de�ned in the text (p.101), di_erential forms like dx, dy and dz = dx + i dy have not been de�ned (and the de�nition is more subtle), we shall develop the theory of harmonic functions (p.162-170) without di_erential forms.
Topics: Maths, Analysis and Calculus, Complex Analysis, Mathematics
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by 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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by Richard Fitzpatrick
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The purpose of this course is to present quantum mechanics in a systematic fashion, starting from the fundamental postulates, and developing the theory in as logical a manner as possible.
Topics: Physics, Quantum Physics, Quantum Mechanics, Foundations of Quantum Mechanics, Measurement Theory,...
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by Denis Auroux
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1. Differential forms - Given M a smooth manifold, one has two natural bundles: the tangent bundle TM =...
Topics: Maths, Linear Algebra and Geometry, Geometry of Manifolds, Mathematics
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by Barbara Illowsky;Susan Dean
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The textbook was developed over several years and has been used in regular and honors-level classroom settings and in distance learning classes. This textbook is intended for introductory statistics courses being taken by students at two� and four�year colleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite. The book focuses on applications of statistical knowledge rather than the theory behind it.
Topics: Maths, Mathematics
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by Ji_� Lebl
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This book is a one semester course in basic analysis
Topics: Maths, Mathematics
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by Jeff Viaclovsky
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Topics: Maths, Analysis and Calculus, Differential Equations (ODEs & PDEs), Mathematics
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by Dmitry Panchenko
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Topics: Maths, Statistics and Probability, Statistics, Statistical Tables, Contingency Tables, Mathematics
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by David Joyner;Minh Van Nguyen;Dr Nathann Cohen
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This is an introductory book on algorithmic graph theory. Theory and algorithms are illustrated using the Sage open source mathematics software. To get an overview of the book, you can view the table of contents as shown below or download the complete book. This book is more commonly known as the "DaMN" book if you notice the first letter of the first name of each author. So feel free to call it the DaMN book :-)
Topics: Maths, Graph Theory, Statistics and Probability, Basics, Connectivity and Matchings, Probabilistic...
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by Denis Auroux
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1. Homological Mirror Symmetry - Conjecture 1. X, X_ are mirror Calabi-Yau varieties
Topics: Maths, Linear Algebra and Geometry, Geometry, Mathematics
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by James S. Milne
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The �rst version of these notes was written for a �rst-year graduate algebra course. As in most such courses, the notes concentrated on abstract groups and, in particular, on �nite groups.
Topic: Maths
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by Prof. Michael Corral
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This book covers calculus in two and three variables. It is suitable for a one-semester course, normally known as �Vector Calculus�, �Multivariable Calculus�, or simply �Calculus III�. The prerequisites are the standard courses in single-variable calculus (a.k.a. Calculus I and II).
Topics: Maths, Mathematics
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by R. Mainieri;Predrag Cvitanovi�c;E.A. Spiegel
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We define a dynamical system (M, f) and classify its solutions as equilibria, periodic, and aperiodic. An �aperiodic� solution is either �wandering� or belongs to a non�wandering set, which in turn can be decomposed into chain-recurrent sets. Various cases are illustrated with concrete examples, such as the Rossler and Lorenz systems.
Topics: Physics, Quantum Physics, Quantum Mechanics, Physics
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by Kiran S. Kedlaya
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In this unit, we introduce some special multiplicative functions, the Dirichlet characters, and study their corresponding Dirichlet series. We will use these in a subsequent unit to prove Dirichlet�s theorem on primes in arithmetic progressions, and the prime number theorem in arithmetic progressions.
Topics: Maths, Algebra, Number Theory, Mathematics
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by Prof. Joseph Fields
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f(x). However, many of the functions of importance both within mathematics itself as
Topics: Maths, Mathematics
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by Prof. Kenneth P. Bogart
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This book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially but not exclusively on the part of combinatorics that mathematicians refer to as �counting.� The book consists almost entirely of problems.
Topics: Maths, Mathematics
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by Sigurdur Helgason
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Topics: Maths, Analysis and Calculus, Complex Analysis, Mathematics
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by Dmitry Panchenko
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De�nition: A Maximum likelihood estimator (M.L.E.): ... such that ...
Topics: Maths, Statistics and Probability, Probability, Statistics, Sampling Theory, Estimation Techniques,...
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by Denis Auroux
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Flux through general surfaces: For a general surface, we will use xyz-coordinates. It turns out that here it is simpler to calculate the in�nitesimal vector dS = n dS directly, rather than calculate n and dS separately and multiply them, as we did in the previous section
Topics: Maths, Analysis and Calculus, Calculus, Mathematics
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by Jir� Lebl
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The laws of physics are generally written down as differential equations. Therefore, all of science and engineering use differential equations to some degree. Understanding differential equations is essential to understanding almost anything you will study in your science and engineering classes. You can think of mathematics as the language of science, and differential equations are one of the most important parts of this language as far as science and engineering are concerned.
Topic: Maths
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by Prof. Carl Stitz;Prof. Jeff Zeager
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Topics: Maths, Mathematics
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by Edward A. Bender;S. Gill Williamson
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Topics: Maths, Mathematics
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by Dr Thomas W. Judson
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The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second-half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory
Topics: Group Theory, Permutations, Cosets, Mathematics
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by 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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by G.'t Hooft;S. Vandoren
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Prologue General relativity is a beautiful scheme for describing the gravitational �eld and the equations it obeys. Nowadays this theory is often used as a prototype for other, more intricate constructions to describe forces between elementary particles or other branches of fundamental physics. This is why in an introduction to general relativity it is of importance to separate as clearly as possible the various ingredients that together give shape to this paradigm. After explaining the...
Topic: Maths
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by Daniel H. Rothman
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Thus we seek a geometric depiction of the trajectories in a lower-dimensional space�in essence, a view of phase space without all the detail.
Topics: Maths, Dynamics and Relativity, Dynamical Systems, Mathematics
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by Dmitry Panchenko
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De�nition: Conditional probability of Event A given Event B: ...
Topics: Maths, Statistics and Probability, Mathematics
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by Luis Alvarez-Gaume;Miguel A. Vazquez-Mozo
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In these lectures we present a few topics in Quantum Field Theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to Particle Physics and String Theory.
Topic: Maths
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by Prof. Jim Hefferon
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on functions involving a single independent variable and a single dependent variable. For
Topics: Maths, Mathematics
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by Prof. David Guichard
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The emphasis in this course is on problems�doing calculations and story problems. To master problem solving one needs a tremendous amount of practice doing problems.
Topics: Maths, Mathematics
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by Jeff Viaclovsky
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Normed space and Banach spaces. A normed space is a vector space V together with a function ||�|| : V_R such that ...
Topics: Maths, Analysis and Calculus, Analysis, Integration, Mathematics
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by Matthias Beck;Gerald Marchesi;Dennis Pixton;Lucas Sabalka
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These are the lecture notes of a one-semester undergraduate course which we taught at SUNY Binghamton. For many of our students, Complex Analysis is their first rigorous analysis (if not mathematics) class they take, and these notes reflect this very much. We tried to rely on as few concepts from real analysis as possible. In particular, series and sequences are treated ``from scratch." This also has the (maybe disadvantageous) consequence that power series are introduced very late in the...
Topics: Complex Analysis, Residue Theorem, Second Order Ordinary Differential Equations in the Complex...
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The purpose of this course, Physics 582, is two fold. Here I will to introduce Field Theory as a framework for the study of systems with a very large number of degrees of freedom, N _ �. On the other hand, I will also introduce and develop the tools that will allow us to treat such systems. Systems that involve a large (in fact in�nite) number of coupled degrees of freedom arise in many areas of Physics, notably in High Energy and in Condensed Matter Physics, among others. Although the...
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Field Theory, Physics
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by John W. Norbury
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Chapter 1. Lagrangian Field Theory 1.1 Units. We start with the most basic thing of all, namely units and concentrate on the units most widely used in particle physics and quantum �eld theory (natural units). We also mention the units used in General Relativity, because these days it is likely that students will study this subject as well.
Topic: Maths
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by David H. Collingwood;K. David Prince;Matthew M. Conroy
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This book is full of worked out examples. We use the the notation �Soluttion.� to indicate where the reasoning for a problem begins; the symbol is used to indicate the end of the solution to a problem. There is a Table of Contents that is useful in helping you �nd a topic treated earlier in the course. It is also a good rough outline when it comes time to study for the �nal examination. The book also includes an index at the end. Finally, there is an appendix at the end of the text with...
Topic: Mathematics
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by Matt Boelkins
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Topics: Calculus, Mathematics
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by Dmitry Panchenko
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Topics: Maths, Statistics and Probability, Mathematics
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by Kiran S. Kedlaya
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In this unit, we derive some results about the location of the zeroes of the Riemann zeta function, including a small zero-free region inside the critical strip.
Topics: Maths, Algebra, Number Theory, Mathematics
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In the past lectures we have considered the properties of a number of �eld theories that describe physical systems isolated from the outside world. However,the only way to investigate the properties of a physical system is to interact withit. Thus, we must consider physical systems which somehow are coupled to theirsurroundings. We will have two situations in mind. In one case, we will look atthe problem of the interaction of states of an isolated system, i.e., a scatteringproblem. In this...
Topics: Physics, Particle Physics and Fields, General Theory of Fields and Particles, Field Theory, Physics
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by Pieter Kok
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Topics: Physics, Quantum Physics, Quantum Mechanics, Formalism, Foundations of Quantum Mechanics,...
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by Keijo Ruohonen
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The notes form the base text for the course �MAT-41196 Graph Theory�. They containan introduction to basic concepts and results in graph theory, with a special emphasis put onthe network-theoretic circuit-cut dualism. In many ways a model was the elegant and carefulpresentation of SWAMY & THULASIRAMAN, especially the older (and better) edition. There areof course many modern text-books with similar contents, e.g. the popular GROSS & YELLEN.
Topics: Graph Theory, Basics, Connectivity and Matchings, Graph Colouring, Planar Graphs, Matchings in...
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by Eric Poisson
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Topics: Physics, Physics
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by Arthur Mattuck;Haynes Miller;Jeremy Orloff;John Lewis
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De�nition of Laplace Transform: The Laplace transform of a function f(t) of a real variable t is another function depending on a new variables, which is in general complex. We will denote the Laplace transform of f by L f.
Topics: Maths, Analysis and Calculus, Complex Analysis, Fourier and Laplace Transforms, Laplace Transform,...
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by Dmitry Panchenko
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Topic: Maths
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by Benjamin McKay
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These notes are drawn from lectures given at University College Cork in the spring of 2006, for a �rst year introduction to linear algebra. The course aims for a complete proof of the spectral theorem. Problems appear throughout the text, which you must learn to solve. They often provide vital results used in the course. Most of these problems have hints, particularly the more important ones. There are also review problems at the end of each section, and you should try to solve a few from...
Topics: Maths, Linear Algebra and Geometry, Algebra, Numerical Analysis, Vectors and Matrices, Linear...
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by Sergei Treil
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Topics: Linear Algebra, Vectors, Eigenvalues and Eigenvectors, Determinant and Trace, Dual of a...
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by David W. Hogg
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These notes have three (perhaps ambitious) aims: (a) to introduce undergraduates to special relativity from its founding principle to its varied consequences, (b) to serve as a reference for those of us who need to use special relativity regularly but have no long-term memory, and (c) to provide an illustration of the methods of theoretical physics for which the elegance and simplicity of special relativity are ideally suited. History is a part of all science�I will mention some of the...
Topic: Maths
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by Jeff Viaclovsky
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Topics: Maths, Analysis and Calculus, Differential Equations (ODEs & PDEs), Mathematics
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by Jerry Griffiths
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In this chapter we will present an analysis of the colliding wave problem using a method that has become familiar in the study of stationary axisymmetric space-times. In this case the �eld is described in terms of a complex potential function that is referred to as the Ernst potential (see Ernst 1968a). This approach leads directly to various methods for generating further exact solutions.
Topics: Physics, Special Relativity, General Relativity and Gravitation, Classical General Relativity,...