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PHYS771 Lecture 9: Quantum Scott Aaronson There are two ways to teach quantum mechanics. The first way -- which for most physicists today is still the only way -- follows the historical order in which the ideas were discovered. So, you start with classical mechanics and electrodynamics, solving lots of grueling differential equations at every step. Then you learn about the "blackbody paradox" and various strange experimental results, and the great crisis these things posed for physics. Today, in the quantum information age, the fact that all the physicists had to learn quantum this way seems increasingly humorous. As a direct result of this "QWERTY" approach to explaining quantum mechanics - which you can see reflected in almost every popular book and article, down to the present -- the subject acquired an undeserved reputation for being hard. So, what is quantum mechanics? Ray Laflamme: That's very much a computer-science point of view. Scott: Yes, it is. A Less Than 0% Chance (p1,.... . ? PHYS771 Lecture 9: Quantum PHYS771 Lecture 9: Quantum
Interactive Processes
Free Printable Graph Paper in 18 Sizes. Includes a special file designed for six 3x4 square foot garden plots. Page also includes centimeter graph paper in 3 styles. Graph Paper has graph paper. I will name the graph paper based on the number of squares in width and length, except for the tiny graph paper. Set One - Basic Graph Papers Set Two - Graph papers with a darker line at either the 5th or the 10th cell Set Three - Graph papers marked at the 3rd cell - Includes a Square Foot Garden Plotted Graph Set Four - Centimeter Graph Paper - in 3 styles, each with 3 variations The Grid Note - List This is a generator. Graph Paper, Set One I recently inspected this set of graph paper files, printed them, and measured them. Basic information: The files in this set are black and white. FTP stands for Fit to Paper The Files for the First Set Of Graph Paper 10x14 Approximate Square Size Printer settings: None: 3/4 inch FTP: 11/16 inch 20x26 Approximate Square Size Printer settings: None: 3/8 inch FTP: 9mm 30x40 Approximate Square Size Printer settings: None: 1/4 inch FTP: 6mm Graph Paper, Set Two Graph papers in set two have these features Free Printable Graph Paper in 18 Sizes. Includes a special file designed for six 3x4 square foot garden plots. Page also includes centimeter graph paper in 3 styles.
How a matchmaking algorithm saved lives How a matchmaking algorithm saved lives Long before dating sites, a pair of economists delved into the question of matchmaking, and hit upon a formula with applications far beyond romance. Would you let an economist set you up on a date? Economics is often associated with the idea of money. In the 1960s, researchers David Gale and Lloyd Shapley embarked upon federally-funded research to take up an unlikely subject: matchmaking. They were interested in the math behind pairing people up with partners who returned their affections. Suppose you had a group of men and a group of women who wanted to get married. Here’s an example inspired by Jane Austen’s “Pride and Prejudice”: The goal is to find stable matches between two sets of people who have different preferences and opinions on who is their best match. The central concept is that the matches should be stable: There should be no two people who prefer each other to the partners they actually got. The men and women each rank their preferences. How a matchmaking algorithm saved lives
The story might well be true, and there is certainly, as we shall see, a solid germ of truth in it, but there is very little evidence for the best bits."... Bill Casselman University of British Columbia, Vancouver, Canada Email Bill Casselman The myth It makes a great story. The year is 1943. American bombers are suffering badly from German air defense. The SRG was one of several collaborating groups of scientists formed soon after America joined the war. Wald was born in the former Austrian-Hungarian empire in 1902, in the city now called Cluj. The problem of armoring planes is assigned to Wald. The Internet loves this tale. "Abraham Wald" aircraft to see what Mr. ABRAHAM WALD AND THE MISSING BULLET HOLES Seeing is Disbelieving How A Story From World War II Shapes Facebook Today The hole story: What you don't see will kill you The reason for this excitement is that the aircraft damage is an example of what is known as "survivorship bias." The autobiographical memoir by W. Comments? Postcript Feature Column Feature Column
MRI Math Connections: Intel Math + MLC

Intel Math is an 80-hour professional development course in mathematics content for K-8 teachers. The program was adapted from the Vermont Math Initiative developed by Dr. Ken Gross. The course is collaboratively taught by a practicing mathematician and a mathematics educator. One of the goals of Intel Math is that teacher participants deepen their own understanding of math through problem-solving. Intel Math “is designed to close the gap between insufficient mathematics training of elementary school teachers and the demands of the contemporary mathematics classroom” (Kenneth Gross, on VMI ) and places emphasis on deepening the teacher participants’ understanding of core K-8 mathematics concepts. Intel Math is grounded in a problem-solving approach to topics such as integer arithmetic, the decimal number system, place value, rational number arithmetic, rates, linear equations, and functions. Pedagogy comprises approximately 10% of the course. The University of Arizona - Intel Math The University of Arizona - Intel Math
K-8 Math Progressions (formerly known as Intel Math) Stephani Burton, who just started her fourth year as a pre-kindergarten teacher at John Winthrop Elementary School in Boston, decided during her first year on the job that she wanted an extra dose of professional development in mathematics. So she chose to hone her skills with a program called K-8 Math Progressions. Burton was looking for a challenge. 80 Hours of Training Altogether it amounts to 80 hours of training -- roughly the time it takes to walk 240 miles, watch four seasons of Lost, or in Burton’s case, make an entire collection of 70 to 80 pieces of jewelry. Burton learned what it’s like to be in her students’ shoes, grappling with unfamiliar mathematical concepts. Burton, like most teachers who take K-8 Math Progressions, walked away from the 80-hour course knowing much more about math and how to teach it. New Insights on Mathematics K-8 Math Progressions is relatively new. Moving the Dial on Math Achievement K-8 Math Progressions K-8 Math Progressions
Library of 2009-10 Interdisciplinary Colloquium Series Title: What is Stem Education?President Jack M. Wilson University of Massachusetts Thursday 8th October 2009; 4:30-8pm, Advanced Technology & Manufacturing Center, Fall RiverAbstract and further details Watch the Talk Title: Sensible TechnologyDr Nathalie Sinclair Simon Fraser University Monday 30th November 2009; 3:30-5pmAbstract Title: Building Mathematics Learning Communities: A Focus on Looking at Student WorkDona Apple Consultant & Professional Development Provider Wednesday 16th December 2009; 3:30-5pmAbstract Download Presentation Watch the Talk Title: Multiple Dimensions Involved in the Design of Teaching Learning Situations Taking Advantage of Technology: Examples in Dynamic Mathematics TechnologyDr Colette Laborde University Joseph Fourier and IUFM of Grenoble, France Wednesday 3rd March 2010; 3:30-5pmAbstract Kaput Center for Research and Innovation in STEM Education Kaput Center for Research and Innovation in STEM Education
Game Dev Math

Essential Math for Games Programmers As the quality of games has improved, more attention has been given to all aspects of a game to increase the feeling of reality during gameplay and distinguish it from its competitors. Mathematics provides much of the groundwork for this improvement in realism. And a large part of this improvement is due to the addition of physical simulation. Creating such a simulation may appear to be a daunting task, but given the right background it is not too difficult, and can add a great deal of realism to animation systems, and interactions between avatars and the world. This tutorial deepens the approach of the previous years' Essential Math for Games Programmers, by spending one day on general math topics, and one day focusing in on the topic of physical simulation. It, like the previous tutorials, provides a toolbox of techniques for programmers, with references and links for those looking for more information. Topics for the various incarnations of this tutorial can be found below. Slides Essential Math for Games Programmers
Game Development Math Recipes One of the most daunting aspects of game development for many people is the mathematics involved. The following are a collection of recipes that go into detail on how to perform a number of common math related tasks. Each example ships with at least one working demonstration application (written in JavaScript using EaselJS), with complete source code. Don’t worry if your language of choice is C++, C# or Java, the JavaScript code is easily ported to any C derived language. In every case the code is written to favour readability over performance. Velocity and angular velocity Got something you want to make move? Tutorial Link Rotating one object relative to another Rotating about the origin is easy, but sometimes you want to rotate relative to the location of another object. Tutorial Link Rotating to face another object Sometimes you want to rotate to look at another object. Tutorial Link Collision detection using a bounding circle Tutorial Link Handling sprite based shooting Tutorial Link Game Development Math Recipes
Fourth Revision, July 2009 This is a tutorial on vector algebra and matrix algebra from the viewpoint of computer graphics. It covers most vector and matrix topics needed to read college-level computer graphics text books. A mirror site that contains this material is: Mirror Site Computer graphics requires more math than is covered here. Although primarily aimed at university computer science students, this tutorial is useful to any programmer interested in 3D computer graphics or 3D computer game programming. This tutorial is useful for more than computer graphics. These notes assume that you have studied plane geometry and trigonometry sometime in the past. These pages were designed at 800 by 600 resolution. Some sections are years old and have been used in class many times (and hence are "classroom tested" and likely to be technically correct and readable). The zip file contains all the above instructional material as of August 22, 2003. Vector Math Tutorial for 3D Computer Graphics Vector Math Tutorial for 3D Computer Graphics

Electrical Engineering News, Resources, and Community | EEWeb
Exapuni 05/04/14, 00:01 @Anónimo No tengo la guía a mano, entiendo que la inecuación es 3X(2X + 3) > 0 2X - 5Para que el termino de la izquierda sea mayor a 0 tanto numerador (3X(2X + 3)) como denominador (2X - 5) tienen que tener el mismo signo ( + o - ). Entonces expresas el ejercicio de está manera 3X(2X + 3) > 0 y 2X - 5 > 0 o 3X(2X + 3) < 0 y 2X - 5 < 0 Tene en cuenta que en primer termino de ambas posibilidades (3X(2X + 3)) te vuelve a pasar lo mismo. Para la primera posibilidad: 3X > 0 y 2X + 3 > 0 y 2X - 5 > 0 o 3X < 0 y 2X + 3 < 0 y 2X - 5 > 0 Para la segunda posibilidad 3X(2X + 3) debe ser menor a 0. 3X > 0 y 2X + 3 < 0 y 2X - 5 < 0 o 3X < 0 y 2X + 3 > 0 y 2X - 5 < 0 El ejercicio es un poco mareador, se abren muchas posibilidades. El resultado final (te lo escribo en forma de uniones) es: (-3/2;0) U (5/2;+infinito), espero que haya quedado claro. Apunte Guia 1 Numeros Reales.pdf de Matemática de la carrera Medicina de la Universidad de Buenos Aires - UBA
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Dwarf Galaxies Dim Hopes of Dark Matter | Quanta Magazine Once again, a shadow of a signal that scientists hoped would amplify into conclusive evidence of dark matter has instead flatlined, repeating a maddening refrain in the search for the invisible, omnipresent particles. The Fermi Large Area Telescope (LAT) failed to detect the glow of gamma rays emitted by annihilating dark matter in miniature “dwarf” galaxies that orbit the Milky Way, scientists reported Friday at a meeting in Nagoya, Japan. The hint of such a glow showed up in a Fermi analysis last year, but the statistical bump disappeared as more data accumulated. “We were obviously somewhat disappointed not to see a signal,” said Matthew Wood, a postdoctoral researcher at Stanford University who was centrally involved in the Fermi-LAT collaboration’s new analysis, in an email. However, scientists knew that the same glow could also originate from an unknown population of millisecond pulsars in the galactic center — bright, rapidly spinning stars that spew gamma rays into space. J.
The question is deceptively simple: Given a geometric space — a sphere, perhaps, or a doughnut-like torus — is it possible to divide it into smaller pieces? In the case of the two-dimensional surface of a sphere, the answer is clearly yes. Anyone can tile a mosaic of triangles over any two-dimensional surface. Likewise, any three-dimensional space can be cut up into an arbitrary number of pyramids. But what about spaces in higher dimensions? Subdividing a space in this way, a process known as triangulation, is a basic tool that topologists can use to tease out the properties of manifolds. Reed Hutchinson/UCLA Ciprian Manolescu realized that work from his student years could be used to solve a century-old problem in topology. Ciprian Manolescu remembers hearing about the triangulation conjecture for the first time as a graduate student at Harvard University in the early 2000s. Others kept working on the problem, however, clawing toward a solution that remained stubbornly out of reach. Triangulation Conjecture Disproved | Quanta Magazine
Artur Avila Is First Brazilian Mathematician to Win Fields Medal It was pouring rain on a chilly spring day, and Artur Avila was marooned at the University of Paris Jussieu campus, minus the jacket he had misplaced before boarding a red-eye from Chicago. “Let’s wait,” said the Brazilian mathematician in a sleep-deprived drawl, his snug black T-shirt revealing the approximate physique of a sturdy World Cup midfielder. “I don’t want to get sick.” In everyday matters, Avila steers clear of complications and risk. Soon the conversation turned to a different kind of worry for Avila — that public reminders of Brazil’s apparent lack of intellectual achievement will discourage students there from pursuing careers in pure math and science research. To Avila, the criticism stings. Even then, in May, the native son of Rio de Janeiro had a secret weapon, a compelling argument that Brazil belongs among elite math nations like the United States, France and Russia. “He has high geometric vision. Math on the Beach Thomas Lin/Quanta Magazine Dynamical Systems | Oppikirjoja avoimella lähdekoodilla!
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A few weeks ago I (Jo Boaler) was working in my Stanford office when the silence of the room was interrupted by a phone call. A mother called me to report that her 5-year-old daughter had come home from school crying because her teacher had not allowed her to count on her fingers. This is not an isolated event—schools across the country regularly ban finger use in classrooms or communicate to students that they are babyish. This is despite a compelling and rather surprising branch of neuroscience that shows the importance of an area of our brain that “sees” fingers, well beyond the time and age that people use their fingers to count. In a study published last year, the researchers Ilaria Berteletti and James R. Booth analyzed a specific region of our brain that is dedicated to the perception and representation of fingers known as the somatosensory finger area. Give the students colored dots on their fingers and ask them to touch the corresponding piano keys: Math Teachers Should Encourage Their Students to Count Using Their Fingers in Class
Numberless Word Problems | Teaching to the Beat of a Different Drummer
More Lessons Learned from Research, Volume 1
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Talking Math with Your Kids | Because children enjoy using their minds
Drawing On Math
The MathEd Out Podcast | Searching for Better Mathematics Education
Learning Games: Rolling the Dice Math
Dividing Two-Digit Numbers
Dividing Two-Digit Numbers
Can you solve the control room riddle? - Dennis Shasha
The LEMMA series
Extension Maths

A level maths teaching resources | Underground Mathematics
The Myth of 'I'm Bad at Math' - Miles Kimball & Noah Smith
Inspiring Students to Math Success and a Growth Mindset
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Easier Fibonacci Number puzzles
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