# LaTeX Symbols

From AoPSWiki This article will provide a short list of commonly used LaTeX symbols. Operators Relations Negations of many of these relations can be formed by just putting \not before the symbol, or by slipping an n between the \ and the word. To use other relations not listed here, such as =, >, and <, in LaTeX, you may just use the symbols on your keyboard. Greek Letters Headline text Arrows (For those of you who hate typing long strings of letters, \iff and \implies can be used in place of \Longleftrightarrow and \Longrightarrow respectively.) Dots Accents When applying accents to i and j, you can use \imath and \jmath to keep the dots from interfering with the accents: \tilde and \hat have wide versions that allow you to accent an expression: Others Command Symbols Some symbols are used in commands so they need to be treated in a special way. (Warning: Using \$for will result in . European Language Symbols Bracketing Symbols (\frac{a}{x} )^2 the parentheses don't come out the right size: gives Examples Related: math 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. The Octave language is quite similar to Matlab so that most programs are easily portable. Octave is distributed under the terms of the GNU General Public License. March 7, 2014 — Octave 3.8.1 Released Version 3.8.1 is a bug fixing release and is now available for download. One of the biggest new features for the Octave 3.8.x release series is a graphical user interface. Given the length of time and the number of bug fixes and improvements since the last major release Octave, we also decided against delaying the release any longer. A First Course in Linear Algebra (A Free Textbook) Open-Source Textbooks Instead I am concentrating recommendations and examples within the undergraduate mathematics curriculum, so please visit the Open Math Curriculum page. If you are linking to this site, please use that page for a broad list, or link to linear.pugetsound.edu specifically for the Linear Algebra text. This page contains some links to similar open-source textbooks. Free Textbooks Abstract Algebra: Theory and Applications, by Thomas W. Freedom Some thoughts on open-content, intellectual property, open-source software and books.The Economy of Ideas An essay on intellectual property, copyright and digital media. Sources of Open-Content Textbook Revolution Careful capsule descriptions of free textbooks in many disciplines. Licensing Open-Content Free Software Foundation GNU licenses, popular for software projects. Sampling Terminology « PreviousHomeNext » As with anything else in life you have to learn the language of an area if you're going to ever hope to use it. Here, I want to introduce several different terms for the major groups that are involved in a sampling process and the role that each group plays in the logic of sampling. The major question that motivates sampling in the first place is: "Who do you want to generalize to?" Once you've identified the theoretical and accessible populations, you have to do one more thing before you can actually draw a sample -- you have to get a list of the members of the accessible population. People often confuse what is meant by random selection with the idea of random assignment. At this point, you should appreciate that sampling is a difficult multi-step process and that there are lots of places you can go wrong. Copyright ï¿½2006, William M.K. Introduction to Scilab Terence Leung Ho Yin, Tsing Nam Kiu Table of Contents About Scilab Installing and Running Scilab Documentation and Help Scilab Basics Common Operators Common Functions Special Constants The Command Line Data Structures Strings Saving and Loading Variables Dealing with Matrices Entering Matrices Calculating Sums Subscripts The Colon Operator Simple Matrix Generation Concatenation Deleting Rows and Columns Matrix Inverse and Solving Linear Systems Entry-wise operations, Matrix Size The Programming Environment Creating Functions Flow Control Some Programming Tips Debugging Plotting Graphs 2D Graphs 3D Surfaces Scilab versus Matlab References 1. About Scilab Scilab is a freely distributed open source scientific software package, first developed by researchers from INRIA and ENPC, and now by the Scilab Consortium. an interpreter libraries of functions (Scilab procedures) libraries of Fortran and C routines For further information and documentation, visit the Scilab homepage: 2. scilex What's Special About This Number? What's Special About This Number? If you know a distinctive fact about a number not listed here, please e-mail me. primes graphs digits sums of powers bases combinatorics powers/polygonal Fibonacci geometry repdigits algebra perfect/amicable pandigital matrices divisors games/puzzles 0 is the additive identity . 1 is the multiplicative identity . 2 is the only even prime . 3 is the number of spatial dimensions we live in. 4 is the smallest number of colors sufficient to color all planar maps. 5 is the number of Platonic solids . 6 is the smallest perfect number . 7 is the smallest number of sides of a regular polygon that is not constructible by straightedge and compass. 8 is the largest cube in the Fibonacci sequence . 9 is the maximum number of cubes that are needed to sum to any positive integer . 10 is the base of our number system. 11 is the largest known multiplicative persistence . 12 is the smallest abundant number . 13 is the number of Archimedian solids . 17 is the number of wallpaper groups . Develop Willpower Details Category: Chuck Gallozzi Published on Sunday, 19 April 2009 19:46 Written by Chuck Gallozzi He who lives without discipline dies without honor If we are to be the master of our destiny, we need self-discipline, self-control, willpower, or self-mastery. However, not everyone wants to improve. All right, so we agree willpower is necessary, but how do we strengthen it? You can also deliberately do what you'd rather not. Suppose I were to place a 15-foot long by 2-foot wide plank, 6 inches above the ground and offer you$500 to walk across it, would you do so? Another hurdle for willpower to overcome is the extra effort that is needed when doing something unpleasant. We know what is best for us.

Math Help An Engineers Quick References to Mathematics Algebra Help Math SheetThis algebra reference sheet contains the following algebraic operations addition, subtraction, multiplication, and division. It also contains associative, commutative, and distributive properties. There are example of arithmetic operations as well as properties of exponents, radicals, inequalities, absolute values, complex numbers, logarithms, and polynomials. This sheet also contains many common factoring examples. There is a description of the quadratic equation as well as step by step instruction to complete the square.Download PDFDownload Image Geometry Math SheetThis geometry help reference sheet contains the circumference and area formulas for the following shapes: square, rectangle, circle, triangle, parallelogram, and trapezoid.

An Intuitive Explanation of Fourier Theory Steven Lehar slehar@cns.bu.edu Fourier theory is pretty complicated mathematically. But there are some beautifully simple holistic concepts behind Fourier theory which are relatively easy to explain intuitively. Basic Principles: How space is represented by frequency Higher Harmonics: "Ringing" effects An Analog Analogy: The Optical Fourier Transform Fourier Filtering: Image Processing using Fourier Transforms Basic Principles Fourier theory states that any signal, in our case visual images, can be expressed as a sum of a series of sinusoids. These three values capture all of the information in the sinusoidal image. The magnitude of the sinusoid corresponds to its contrast, or the difference between the darkest and brightest peaks of the image. There is also a "DC term" corresponding to zero frequency, that represents the average brightness across the whole image. Different Fourier coefficients combine additively to produce combination patterns. Back to top The Optical Fourier Transform

Constructivism Definition Constructivism is a philosophy of learning founded on the premise that, by reflecting on our experiences, we construct our own understanding of the world we live in. Each of us generates our own “rules” and “mental models,” which we use to make sense of our experiences. Learning, therefore, is simply the process of adjusting our mental models to accommodate new experiences. Discussion There are several guiding principles of constructivism: 1. How Constructivism Impacts Learning Curriculum–Constructivism calls for the elimination of a standardized curriculum. Instruction–Under the theory of constructivism, educators focus on making connections between facts and fostering new understanding in students. Assessment–Constructivism calls for the elimination of grades and standardized testing. Reading Jacqueline and Martin Brooks, The Case for Constructivist Classrooms.

Figures for &quot;Impossible fractals&quot; Figures for "Impossible fractals" Cameron Browne Figure 1. The tri-bar, the Koch snowflake and the Sierpinski gasket. Figure 2. Figure 3. Figure 4. Figure 5. Figure 6. Figure 7. Figure 8. Figure 9. Figure 10. Figure 11. Figure 12. Figure 13. 45° Pythagorean tree, balanced 30° Pythagorean tree and extended tri-bar. Figure 14. Figure 15. Figure 16.

Impress your friends with mental Math tricks » Fun Math Blog See Math tricks on video at the Wild About Math! mathcasts page. Being able to perform arithmetic quickly and mentally can greatly boost your self-esteem, especially if you don't consider yourself to be very good at Math. And, getting comfortable with arithmetic might just motivate you to dive deeper into other things mathematical. This article presents nine ideas that will hopefully get you to look at arithmetic as a game, one in which you can see patterns among numbers and pick then apply the right trick to quickly doing the calculation. The tricks in this article all involve multiplication. Don't be discouraged if the tricks seem difficult at first. As you learn and practice the tricks make sure you check your results by doing multiplication the way you're used to, until the tricks start to become second nature. 1. Multiplying by 9 is really multiplying by 10-1.So, 9x9 is just 9x(10-1) which is 9x10-9 which is 90-9 or 81. Let's try a harder example: 46x9 = 46x10-46 = 460-46 = 414. 2. 3.

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