Statistical Formulas For Programmers By Evan Miller DRAFT: May 19, 2013 Being able to apply statistics is like having a secret superpower. Where most people see averages, you see confidence intervals. When someone says “7 is greater than 5,” you declare that they're really the same. In a cacophony of noise, you hear a cry for help. Unfortunately, not enough programmers have this superpower. As my modest contribution to developer-kind, I've collected together the statistical formulas that I find to be most useful; this page presents them all in one place, a sort of statistical cheat-sheet for the practicing programmer. Most of these formulas can be found in Wikipedia, but others are buried in journal articles or in professors' web pages. Send suggestions and corrections to emmiller@gmail.com Table of Contents 1. One of the first programming lessons in any language is to compute an average. 1.1 Corrected Standard Deviation The standard deviation is a single number that reflects how spread out the data actually is. Where: SE=s√N 2. 3.
Platforms The Aalto University Platforms are designed to initiate and coordinate multi- and interdisciplinary research and teaching in some thematic area. The Platforms bring together Aalto's competences in the area, and increase Aalto's external visibility. Primary purposes of the Platforms are to facilitate and strengthen the industry-academia collaboration, and to increase the internal cooperation within the University. The Platforms and their agendas are born through a bottom-up process, and aim at concrete benefits for the participating actors.
Big-O Algorithm Complexity Cheat Sheet GRADO DE ESTADÍSTICA Universitat de Barcelona Informació sobre: Idiomes Cercador Serveis Estudis de grau Inicio > Estudios y Docencia > Oferta formativa > Grados > E > GRADO DE ESTADÍSTICA ¿Qué se pretende con esta enseñanza? Formar profesionales de la estadística, capacitados para llevar a cabo las tareas específicas del proceso de análisis de la información y toma de decisiones, incidiendo en: La obtención y el tratamiento de datos. Imprimir la ficha del grado Enlaces de interés Acceso directo a: Omitir los accesos directos Mas información Servicio de Atención al EstudianteTel. 933 556 000 Fax 934 035 917Buzón de consultasHorarios, localización y transportes Síguenos: Miembro de: Dos Campus de Excelencia Internacional Footer © Universitat de Barcelona
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. Topics for the various incarnations of this tutorial can be found below. Current Materials Slides The latest available versions of the slides for the math tutorials at GDC 2015 are as follows: Past Materials Core Mathematics
Radically Cheap: The Story of Pat Delany, Open Source Machine Tools Advocate The ex-rancher felt empathy push his problem-solving mind into a new direction. He looked back at all those years he had tinkered with junk-built machine tools in his workshop — all that time spent poring over scans of antique how-to magazines looking for clever hacks to avoid having to buy new tools. It was fun and sometimes necessary for me, he thought, but what I’ve created here can also help many people. This is the story of Pat Delany, one of the leading creative voices in Appropriate Technology — technology that is small-scale, decentralized, labor-intensive, energy-efficient, environmentally sound, and locally controlled. This 78-year-old grandfather came to the field as an outsider, inspired by a second-hand description of a news photo. But his visionary home-built machine-tool designs now have the potential to help millions bootstrap themselves out of poverty. Delany had worked with machines for his entire life and built many machines for himself. The MultiMachine Lost Wisdom
Bit Twiddling Hacks By Sean Eron Anderson seander@cs.stanford.edu Individually, the code snippets here are in the public domain (unless otherwise noted) — feel free to use them however you please. The aggregate collection and descriptions are © 1997-2005 Sean Eron Anderson. The code and descriptions are distributed in the hope that they will be useful, but WITHOUT ANY WARRANTY and without even the implied warranty of merchantability or fitness for a particular purpose. As of May 5, 2005, all the code has been tested thoroughly. Contents About the operation counting methodology When totaling the number of operations for algorithms here, any C operator is counted as one operation. Compute the sign of an integer The last expression above evaluates to sign = v >> 31 for 32-bit integers. Alternatively, if you prefer the result be either -1 or +1, then use: sign = +1 | (v >> (sizeof(int) * CHAR_BIT - 1)); // if v < 0 then -1, else +1 On the other hand, if you prefer the result be either -1, 0, or +1, then use:
IEEE Global Humanitarian Technology Conference (GHTC) Public Domain Aeronautical Software (PDAS) The R Project for Statistical Computing Octave GNU Octave is a high-level interpreted language, primarily intended for numerical computations. It provides capabilities for the numerical solution of linear and nonlinear problems, and for performing other numerical experiments. It also provides extensive graphics capabilities for data visualization and manipulation. Octave is normally used through its interactive command line interface, but it can also be used to write non-interactive programs. Octave is distributed under the terms of the GNU General Public License. Version 4.0.0 has been released and is now available for download. An official Windows binary installer is also available from A list of important user-visible changes is availble at by selecting the Release Notes item in the News menu of the GUI, or by typing news at the Octave command prompt. Thanks to the many people who contributed to this release!
Introduction to Algorithms Table of Contents I Foundations Introduction 3 1 The Role of Algorithms in Computing 5 1.1 Algorithms 5 1.2 Algorithms as a technology 11 2 Getting Started 16 2.1 Insertion sort 16 2.2 Analyzing algorithms 23 2.3 Designing algorithms 29 3 Growth of Functions 43 3.1 Asymptotic notation 43 3.2 Standard notations and common functions 53 4 Divide-and-Conquer 65 4.1 The maximum-subarray problem 68 4.2 Strassen's algorithm for matrix multiplication 75 4.3 The substitution method for solving recurrences 83 4.4 The recursion-tree method for solving recurrences 88 4.5 The master method for solving recurrences 93 4.6 Proof of the master theorem 97 5 Probabilistic Analysis and Randomized Algorithms 114 5.1 The hiring problem 114 5.2 Indicator random variables 118 5.3 Randomized algorithms 122 5.4 Probabilistic analysis and further uses of indicator random variables 130 II Sorting and Order Statistics Introduction 147 6 Heapsort 151 6.1 Heaps 151 6.2 Maintaining the heap property 154 6.3 Building a heap 156 7 Quicksort 170 Index
Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne Quaternions This page is an introduction to Quaternions, the pages below this have more detail about their algebra and how to use them to represent 3D rotations. Introduction Quaternions were discovered on 16 October 1843 by William Rowan Hamilton. He spent years trying to find a three dimensional number systems, but with no success, when he looked in 4 dimensions instead of 3 it worked. Quaternions form an interesting algebra where each object contains 4 scalar variables (sometimes known as Euler Parameters not to be confused with Euler angles), these objects can be added and multiplied as a single unit in a similar way to the usual algebra of numbers. However, there is a difference, unlike the algebra of scalar numbers qa * qb is not necessarily equal to qb * qa (where qa and qb are quaternions). The arithmetic of quaternions, such as how to do addition and multiplication, is explained on this page. a + i b + j c + k d Use of quaternions to represent transformations in 3D. where: sfrotation Index