PPT-Algebra, Structure and Solving Algorithms

Rubiks Cube Jasmine DeZeeuw Adam Douthwright Colby Fraser History The R ubiks Cube was invented by a Hungarian named Erno Rubik He was born on July 13 1944 Rubik was a professor at a school for applied . Arithmetic Operations The real numbers have the following properties Commutative Law Associative Law Distributive law In particular putting in the Distributive Law we get and so EXAMPLE 1 a b c If we use the Distributive Law three times we get This for Linear Algebra and Beyond. Jim . Demmel. EECS & Math Departments. UC Berkeley. 2. Why avoid communication? (1/3). Algorithms have two costs (measured in time or energy):. Arithmetic (FLOPS). Communication: moving data between . Probabilistic Process Algebra. Suzana Andova. Outline of the lecture. Semantics of non-determinism in probabilistic setting. Analysing. probabilistic systems and schedulers. Probabilistic branching . Abstraction . and Recursions in . Process . Algebra . Suzana Andova. Outline of the lecture. Combining silent steps with recursion. Fairness rules. Some examples . Fairness: is this what it is really about?. Tony Hoare. Feb 2012. With Ideas from. Ian Wehrman. John Wickerson. Stephan van . Staden. Peter O’Hearn. Bernhard Moeller. Georg Struth. Rasmus Petersen. …and others. and Calculi from. Robin Milner. Factorising (add brackets). This is the inverse (opposite) of expanding brackets 2x(3x + 1) = . 6x. ² . + 2x. 2 terms. Example 1: . Factorise completely . . 4x. 2. + 12x . Method: HCF. 4x. ² . Introduction. This chapter focuses on basic manipulation of Algebra. It also goes over rules of Surds and Indices. It is essential that you understand this whole chapter as it links into most of the others!. Developing Relational Thinking in the Primary Grades. Relational Thinking. Students who can express a number in terms of other numbers and operations on those numbers hold a . relational understanding of the number. Susan Staats. Associate Professor-Math. University of Minnesota. staats@umn.edu. Interdisciplinary math is…. Different from “math in context.”. Different from an application.. Must support learning that is significant in a partner discipline.. is a set . B. of values together with: . - two binary operations, commonly denoted by and ∙ , . - a unary operation, usually denoted by . ˉ or ~ or . ’. ,. - two elements usually called . Problem - a well defined task.. Sort a list of numbers.. Find a particular item in a list.. Find a winning chess move.. Algorithms. A series of precise steps, known to stop eventually, that solve a problem.. AF Practical Problem Solving Model (PPSM). 8 Step . Model. Overview. Objective. Help Airmen focus on problem solving skills that affect:. Mission. Workcenters. People. Approach aimed at:. Increasing combat capability. 10 Bat Algorithms Xin-She Yang, Nature-Inspired Optimization Algorithms, Elsevier, 2014 The bat algorithm (BA) is a bio-inspired algorithm developed by Xin-She Yang in 2010. 10.1 Echolocation of Bats -4 x - 2 y = -12 4 x + 8 y = -24 2) 4 x + 8 y = 20 -4 x + 2 y = -30 3) x - y = 11 2 x + y = 19 4) -6 x + 5 y = 1 6 x + 4 y = -10 5) -2 x - 9 y = -25 -4 x - 9 y = -23 6)