PPT-Complexity & the O-Notation

Computability So far we talked about Turing Machines that decide languages and compute functions We only cared about making the machine decide the languagecompute the function We didnt care about the machines performance. Consider the coordinate system illustrated in Figure 1 Instead of using the typical axis labels and we use and or 1 The corresponding unit basis vectors are then and or 1 The basis vectors and have the following properties 1 1 0 2 Figu Shantanu. . Dutt. ECE Dept.. UIC. Time Complexity. An algorithm time complexity is a function T(n) of problem size n that represents how much time the algorithm will take to complete its task.. Note that there could be more than one problem size parameter n, in which case we can denote the time complexity function as T(S), where S is the set of size parameters. E.g., for the shortest path problem on a graph G, we have 2 size parameters, n the # of vertices and e the # of edges (thus T(S) = T(. Defining sustainable development. Sustainability : Defining sustainable development in broader terms. Sustainability Science: Criticisms of current approaches. Complexity and complex adaptive systems. English Language Arts Common Core State Standards. Illinois State Board of Education . English Language Arts Content Specialists. Hosted by Erik Iwersen, June, 2012. . Text Complexity. . “. The Common Core Standards hinge on students encountering appropriately complex texts at each grade level in order to develop the mature language skills and the conceptual knowledge they need for success in school and life. Objectives. Express numbers in scientific notation.. Convert from standard form to scientific notation.. Convert from scientific notation to standard form.. Add, Subtract, Multiply, and Divide with scientific notation.. ECF Arbiter Seminar - Material by CAA. Notation. Algebraic notation should be used as given in Appendix C of the Laws of Chess.. Some older British players still use descriptive. Therefore knowing descriptive is useful but will not be taught in this course (though these notes will show the moves in descriptive for info).. Slide . 2. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. . 3.1. Decimal Notation, Order, and Rounding. 3.2. Addition and Subtraction. 3.3. Multiplication. 3.4. Division. 3.5. Converting from Fraction Notation to Decimal Notation. Angle . Notation – Three Possibilities. A. B. C. Vertex. Congruent Angles & Angle Measure. 30˚. A. B. C. D. E. Angle Bisector. A. B. C. D. “ If . . bisects. . .  . Using your Protractor. REALLY, REALLY . BIG . OR. . REALLY, REALLY . SMALL. . NUMBERS.. Mathematicians . are Lazy!!!. They decided that by using powers of 10, they can create short versions of long numbers.. Rules for Scientific Notation. Lijie. Chen. MIT. Today’s Topic. Background. . What is Fine-Grained Complexity?. The Methodology of Fine-Grained Complexity. Frontier: Fine-Grained Hardness for Approximation Problems. The Connection. 210,000,000,000,000,000,000,000 miles. (22 zeros). This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.. Scientific Notation. A number is expressed in scientific notation when it is in the form. the execution time required or. the space used in memory or in disk by an algorithm . Big O notation is used describe the rough estimate of the number of “steps” to complete the algorithm. Definition. 4. 3. 2. 1. 0. In addition to 3, student will be able to go above and beyond by applying what they know about working with . integer . exponents..  .  .  .  .  . The student will be able to work with . LO: To use and understand the notation used for functions.. 3, 5, 7, 8 ….. Functions. 11, 15, 19, 21. 3. 11. We sometimes use a function machine to illustrate how functions behave ..