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## Algorithm Strategies Of Problem Solving

Accept Reject Read More. If not, then you must look for an alternative solution and start the process over again. Problem Solving Problem solving is a valuable skill that can really only be learnt, and perfected, through continual practice. 6 Exercises 243. GE8151 - PROBLEM SOLVING AND PYTHON PROGRAMMING - PSPP - SYLLABUS (REGULATION 2017) ANNA UNIVERSITY UNIT I ALGORITHMIC PROBLEM SOLVING (GE8151) Algorithms, building blocks of algorithms (statements, state, control flow, functions), notation (pseudo code, flow chart, programming language), algorithmic problem solving, simple strategies for developing algorithms (iteration, recursion). These strategies depend on using readily accessible, though loosely applicable, information to control problem solving in human beings, machines and abstract issues. Math texts, online classes, and more for students in grades 5-12. Translate the problem into a visual one. You may still be struggling with some of the basic ideas and skills from a first computer science course and yet be ready to further explore the discipline and continue to practice problem solving. otherwise a new algorithm has to be devised. Hambrick and Randall W. ENTIRE BOOK : Algorithmic Problem Solving with Python by John B. How to use problem-solving in a sentence. The cognitive approach to problem solving Problem space theory. Design and Analysis of Algorithm is very important for designing algorithm to solve different types of problems in the branch of computer science and information technology. 5) Apply Backtracking technique to solve the following instance of the subset sum problems. For example, software developers can use them to work out how the automated and manual parts of a process join up. 17 Individual Problem set - warmup Lab 01, Problem Set 01 Mon. In particular, I develop a double set method for the single point strategy which resolves an ordering problem associated with the standard algorithm. Some Problem-Solving Strategies. Problem Solving: Guess and Check What Is It? "Guess and Check" is a problem-solving strategy that students can use to solve mathematical problems by guessing the answer and then checking that the guess fits the conditions of the problem. By repeatedly asking the question “why” on a problem, you can dig into the root cause of a problem, and that’s how you can find the best solution to tackle the root problem once and for all. ALGORITHS is a step by step procedure that will always produce correct solutions. One of the things I that drove me crazy about Sudoku is how difficult it is to return to a puzzle if you get interupted. But PSCT is an evolving beast. It symobilizes a website link url. Computer Scientists classify problems by how hard they are 2. , c ij ≥ 0 for all (i,j) ∈ E • Bellman-Ford algorithm • Applicable to problems with arbitrary costs • Floyd-Warshall algorithm • Applicable to problems with arbitrary costs • Solves a more general all-to-all shortest path problem. This document presents some guidelines to approach the solution of a great variety of problems, particularly those presented in computer programming. 4 Problem-Solving Tactics Of Great Leaders. Problem Solving Rubric. After all, when professional services firms can deliver a product that solves a portion of customers’ problems quickly, they make a strong case for being the right partner to help guide the rest of a transformation. You can’t just simply jump into trying to solve it. Such algorithms provide an accurate solution to Equation 2. There are 4 types of Problem Solving Strategies: Algorithm: this is step by step strategies for how to solve the problem (pseudo-code) Heuristic: the general strategies used to make quick short-cut solutions to the problems that sometimes lead to solutions but sometimes lead to errors. In this process the teacher develops a problem, carefully accesses skills needed to solve the problem, and creates conditions and/or parameters that act as guidelines for products or solutions, These same conditions and parameters also serve as evaluation criteria. Look at each column, row and 3x3 box and try to break it down into preemptive sets. Some example tricks. A partial list of strategies is included: Guess and check Look for a pattern Make an orderly list Draw a picture Eliminate possibilities Solve a simpler problem Use symmetry Use a model. However, those who attain exceptional insights into problem-solving can gain success in the long run. Heuristic Techniques for Problem Solving. For example, software developers can use them to work out how the automated and manual parts of a process join up. Reasoning strategies are organized into two categories—those appropriate and those not appropriate to the numbers at hand in the problem. Since students learn in different way, some student may wish to use a strategy other than suggested in the math challenge. As someone who uses this problem solving algorithm far too often. For example, if for every length x the worst input of size x takes time x then this problem has linear runtime. Develop Alternative Solutions. To a cook, the objects are the various types of vegetables, meat and sauce. Algo-heuristics is a way of prescribing instruction for problem solving. Thus the guessing is not an arbitrary guessing but an educated one. A well-defined problem is one that has a clear goal or solution, and problem solving strategies are easily developed. Ask questions B. The objective of a heuristic algorithm is to apply a rule of thumb approach to produce a solution in a reasonable time frame that is good enough for solving the problem at hand. The Inferential System does nothing more -- and nothing less -- than construct a conclusion consistent with its inputs. Other problems are large and may require significant time and effort to solve. Strategies are usually how students approach and manipulate the numbers. Solving problems is a key component of many science, math, and engineering classes. The focus now is their role in problem solving, strategies for developing the, techniques for following and testing them. Algorithms are ﬁnite processes that if followed will solve the problem. Negotiation and Collaborative Problem Solving Negotiators can invent new strategies, create new alternatives, and develop new ways of implementing agreements. 14 Jan 2004 CS 3243 - Blind Search Solving problems by searching Chapter 3 Outline Problem-solving agents Problem types Problem formulation Example problems Basic search algorithms Problem-solving agents Example: Romania On holiday in Romania; currently in Arad. They aim to identify the differential use of visuo-spatial strategies and the availability of analytical strategies for scientific problem solving by students and instructors, individuals with high and low spatial ability, and men and women. After a student understands a problem, he or she is able to search his or her memory to identify problems that are comparable, and then apply or adapt the solutions to those remembered problems to the current problem. In this video, I taught Problem solving methods (Algorithm and its Strategies) Class 10th Computer, Ch. strategy that guarantees a solution to a problem B. There are many ways to write an algorithm. Nakhleh and Richard C. This article presents nine such techniques; in increasing difficulty. • In a networking or telecommunication applications, Dijkstra’s algorithm has been used for solving the min-delay path problem (which is the shortest path problem). otherwise a new algorithm has to be devised. One can use one to two tools to write down an algorithm – Flowcharts or Pseudocode. Divide and conquer 1. representation of the average or ideal member of a concept C. It presupposes that students can take on some of the responsibility for their own learning and can take personal action to solve problems, resolve conflicts, discuss alternatives, and focus on thinking as a vital element of the curriculum. Sequencing suggestions, pacing guides, and orienting activities for students are included in our Introduction to the Activity Series [pdf]. Rational agents or Problem-solving agents in AI mostly used these search strategies or algorithms to solve a. Problem solving is a process in which we perceive and resolve a gap between a present situation and a desired goal, with the path to the goal blocked by known or unknown obstacles. The fitness function should quantitatively measure how fit a given solution is in solving the problem. , what the problem is about) 2. Think, think, think of some solutions. The multi-armed bandit problem is a classic reinforcement learning example where we are given a slot machine with n arms (bandits) with each arm having its own rigged probability distribution of success. In 1972, Allen Newell and Herbert Simon published the book Human Problem Solving, in which they outlined their problem space theory of problem solving. understanding the question 2. Some problems are small and can be resolved quickly. Phil does 3 sit-ups on the first day of school. Students need to develop the ability to apply problem-solving skills when faced with issues or problems that are new to them. Adapt 5 Whys to Clearly Define the Problem. This is essentially a very brief summary of Volume I by the Nocco et al. An algorithm is a step-by-step analysis of the process, while a flowchart explains the steps of a program in a graphical way. Thought experiments like “what is the algorithm for making coffee” may be interesting as a way to introduce the topic, but aren’t really useful because the problem is too under-constrained to really be “algorithimizable”. Benefits Of Algorithm. Trouble Shooting - Micro Plant. ALGORITHS is a step by step procedure that will always produce correct solutions. , to find any one element in a set of acceptable choices which constitute a fraction f of the total number of choices in an unsorted data base. In essence, a problem is a situation that confronts a person, that requires resolution, and for which the path to the solution is not immediately known. Practicing Problem SolvingPracticing Problem Solving The problems must be challenging enough so there is a real advantage to using a problem solving framework 1 The problem must be advantage to using. Here are three common programming strategies:. This is the second in a six-part blog series on teaching 21st century skills, including problem solving , metacognition, critical thinking, and collaboration, in classrooms. If a goal of a class is for students to emerge with the ability to solve new kinds of problems or to use new problem-solving techniques, then students need numerous opportunities to develop the skills necessary to approach and answer different types of problems. You will nd choosing a strategy increasingly easy. Identifying the problem. Solving problems is the core of computer science. Chemical educators have often assumed that success in. problem solving: the process of recognizing a problem, defining it, identifying alternative plans to resolve the problem, selecting a plan, organizing steps of the plan, implementing the plan, and evaluating the outcome; a performance component of occupational therapy. In this video, I taught Problem solving methods (Algorithm and its Strategies) Class 10th Computer, Ch. What Is A 'Problem-Solving Approach'? As the emphasis has shifted from teaching problem solving to teaching via problem solving (Lester, Masingila, Mau, Lambdin, dos Santon and Raymond, 1994), many writers have attempted to clarify what is meant by a problem-solving approach to teaching mathematics. Many times you will need to take the answer you get from the equation and use it in some other way to answer the question originally given in the problem. How many sit-ups will Phil do on the fifth day?. You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. ① State the problem and identify the measures that most clearly indicate the problem you are seeking to solve, and the time over which the problem has changed, and will be solved. The purpose of a word-problem mnemonic is to provide students with a framework for solving word problems. 4 games The total number of games for 5 people = 1+2+3+4 = 10 games. Or, if you could implement a solution that really works, or seize upon opportunities before it is too late. The first step in the problem-solving process is to get to the root of the problem and understand what you need to overcome. Study them carefully so you know how to use them to solve other math problems. The ability to solve problem comes from doing it. 5) Apply Backtracking technique to solve the following instance of the subset sum problems. Problem-solving skills are a set of soft skills to use in difficult, unexpected, or complicated matters that arise in the workplace. Read the problem carefully. Source code from second edition. Thoughts on Problem Solving Critical and Creative Thinking Getting Unstuck Closed-Ended Algorithm Open-Ended Algorithm: ICM's - Introduction - Definition 1 - Definition 2 - Brainstorming - Planning - Evaluate. Roditi and Steinberg (2007) recommended gathering all math strategies that students with executive function weakness have been taught into a "strategy. These 9 problem solving worksheets allow students to practice different problem solving strategies. Specific, measurable goals motivate by defining the enabling us to measure our progress and our achievements. Math Problem Solving Resources Laura Candler’s Math Problem Solving page is where you’ll find great resources for teaching problem solving as well as a variety of math problem activity pages. There is no guarantee that the solution found will be the most accurate or optimal solution for the given problem. Critical Thinking and Strategic Problem Solving Skills for Leaders Learn how to creatively manage strategic dilemmas and solve business problems Organizational success rests in the hands of executives who can deliver superior problem solving strategies. One can use one to two tools to write down an algorithm – Flowcharts or Pseudocode. ALGORITHMIC PROBLEM SOLVING 1. Requires a Java 5 or higher compiler. Police Enforcement Strategies to Prevent Crime in Hot Spot Areas Summarizes the findings from all rigorous academic studies evaluating police enforcement strategies in hot spot areas: Problem-Solving Tips: A Guide to Reducing Crime and Disorder through Problem-Solving Partnerships Contains information and insights into the problem-solving approach. A partial list of strategies is included: Guess and check Look for a pattern Make an orderly list Draw a picture Eliminate possibilities Solve a simpler problem Use symmetry Use a model. 2 Rule-Based Expert Systems 286. From the many numerical algo-rithms developed by the ancient Babylonians to the founding of graph theory by Euler, algorithmic problem solving has been a popular intellectual pursuit during the last few thousand years. The term DMAIC stands for the five main steps in the process: Define, Measure, Analyze, Improve, and Control. How do I use an algorithm to solve real life problem? An algorithm is just a set of steps to solve a problem. A historical meaning of this word is basically a procedure used for solving an arithmetic problem, like the procedure required for finding square roots. The first strategy to use when given a problem. But for platforms this is doubly true, thanks to the chicken-and-egg problem. 3 games Case 4: The 5th person plays the 1st, 2nd, 3rd and 4th i. This scale evaluates the process employed in response to a problem-solving task. With practice, all of us can get much better at it. Read the next article: The skills of problem solving. Keywords (Audience): High. the best leaders use four similar problem-solving tactics, Instant MBA Problem Solving Strategy & Tactics Conflict Resolution. A problem is like a curve in the road. Evolutionary algorithms have won games of chess and solved huge optimization problems that overwhelm most computational resources. We often refer the solution as "good enough" in. 3 Model-Based, Case Based, and Hybrid Systems 298 8. Use a variable and choose helpful names for variables or unknowns. JavaScript Algorithms and Data Structures Masterclass is a fantastic course and really solidified my understanding of these core CS concepts. These larger problems are often tackled by turning them into formal projects. Indeed, really, really understanding the problem is sometimes the only hard bit: once you really, really understand the problem, the answer may be obvious. Algorithm We'll solve the problem of finding and marking a solution path using recursion. Besides, it makes the problem almost impossible to solve. Differentiate Word Problems. An important step in the design is to specify an in- stance of the problem. Problem-solving skills are a set of soft skills to use in difficult, unexpected, or complicated matters that arise in the workplace. Problem Solving: Guess and Check What Is It? "Guess and Check" is a problem-solving strategy that students can use to solve mathematical problems by guessing the answer and then checking that the guess fits the conditions of the problem. I would also like to thank the reviewers of the manuscript for their suggestions. Blind (uninformed, brute force) strategies 3 Problem Solving as Search In the state space view of the world, finding a solution is finding a path through the state space When we (as humans) solve a problem like the 8-puzzle we have some idea of what constitutes the next best move It is hard to program this kind of approach. Divide and conquer 1. Describe the steps of the analytical problem-solving model. The purpose of a word-problem mnemonic is to provide students with a framework for solving word problems. Creativity/Problem Solving/Critical Thinking Lesson Plans and Resources This page was scanned for broken links and updated on 8-15-2019. The broad perspective taken makes it an appropriate introduction to the field. Common Core Standards: 3. Such algorithms provide an accurate solution to Equation 2. The standard algorithm of multiplication is based on the principle that you already know: multiplying in parts (partial products): simply multiply ones and tens separately, and add. Pulling any one of the arms gives you a stochastic reward of either R=+1 for success, or R=0 for failure. The D-Wave annealer then iteratively optimizes each subproblem to eventually solve the original larger one. Problem solving models are used to address the many challenges that arise in the workplace. The key idea of the proposed NDE is the use of new triangular mutation rule. , 2014), where the authors present the results of a 4-month experiment whose main aim was to change pupils’ culture of problem solving by using heuristic strategies suitable for problem solving in mathematics. This post “7 Strategies for Solving the Chicken and Egg Problem as a Startup” originally appeared in the Huffington Post. Macleod, 1994). Test and verify the completed program (Testing). An algorithm is a methodical, logical rule or procedure (such as a step-by-step description for evacuating a building during a fire) that guarantees a solution to a problem. Hambrick and Randall W. There are a wide range of ways in which a given algorithm can be used to solve a problem. Solving a mathematics problem requires more than understanding a description of the problem, that is, more than understanding the quantities, the data, the conditions, the unknowns and all other mathematical facts related to the problem. This is a solver for the "24 ® Game" by Suntex International Inc. Searching is the universal technique of problem solving in AI. In this case linprog. The early work on problem solving was concerned with problems that were puzzles or games such as the Tower of Hanoi task (see below for a description of the task). Look at each column, row and 3x3 box and try to break it down into preemptive sets. Define the problem. Divide and conquer. Any nine symbols would serve just as well to create and solve the puzzles. Taylor2 1Bangor University, 2Tufts University Research on problem solving typically does not address tasks that involve following detailed and/or illustrated step-by-step instructions. For problem-solving, this is usually straightforward. Each of these examples demonstrates a quick transition to a symbolic rule. Demonstrate, with and without concrete materials, an understanding of multiplication (2-digit by 2-digit) to solve problems. [email protected] Step Through the Sample Data. A Seven Step Approach to Solving Programming Problems. However, in the same ways that we teach strategies for other areas of maths, we can also teach strategies to solve maths problems. See the box below for a description of the STAR acronym. Applications of Software Development Methods in Problem Solving 12. Free rubric builder and assessment tools. o Emphasize thinking about problem solving strategies. Analysis of Algorithms Lectures at Princeton-- Applets & Demos based on CLR. IMPACT OF HEURISTIC STRATEGIES ON PUPILS’ ATTITUDES TO PROBLEM SOLVING Abstract The paper is a sequel to the article (Novotná et al. Their success rests on the power of generating diversity by introducing randomness and parallelization into the search procedure and quickly filtering out suboptimal solutions. For example, you could probably discover the insertion sort or selection sort algorithms by trying to sort an a list of numbers on your own. Developing and refining these skills through training, practice and learning can provide the ability to solve problems more effectively and over time address problems with a greater degree of complexity and difficulty. Diagnose the situation so that your focus is on the problem, not just its symptoms. Three evenly spaced dots forming an ellipsis. Chapter 3 Problem Solving Methods. Don't reinvent the wheel. Problem solving (with in the context of developing programs) refers to analyzing a problem with the intention of deriving a solution for the problem. Developing a problem-solving process doesn't just help you make more informed decisions. A proximal algorithm is an algorithm for solving a convex optimization problem that uses the proximal operators of the objective terms. What is the basic approach to problem solving Step 1: Identify small problems. Before we talk about the stages of problem solving, it's important to have a definition of what it is. 0 International License. A pen and a pencil cost Problem Case 1: The 2nd person plays the 1st i. The solution to instilling these thinking skills lies in problem solving lesson plans. While solving a problem, this should be known that what will be out ultimate aim. 5 Epilogue and References 240. Psuedocode the Solution. Ask questions B. The following diagram illustrates solving the N=4 problem using this recursive strategy. In 1972, Allen Newell and Herbert Simon published the book Human Problem Solving, in which they outlined their problem space theory of problem solving. problem models to solving Minesweeper. Creating an algorithm is an art which may never be fully automated. Understanding the problem:The problem given should be understood completely. You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. , considers different strategies and approaches to a problem, restates problem from various perspectives) 3. Another type of strategy is an algorithm. This topic will explain all about the search algorithms in AI. Algorithm Notation: ----- F = turn front side clockwise by 90 degrees F' = turn front side counter-clockwise by 90 degrees U = turn upper side clockwise by 90 degrees U' = turn upper side counter-clockwise by 90 degrees 2U = turn upper side by 180 degrees (clockwise or counter-clockwiseit doesn't matter) R = turn right side clockwise by 90 degrees (clockwise, as if you were facing it) R' = turn right side counter-clockwise by 90 degrees etc. Problem Solving Agent An agent that tries to come up with a sequence of actions that will bring the environment into a desired state. It is used when the solution can be recursively described in terms of solutions to subproblems (optimal substructure). Great programmers are able to conceptually come up with solutions by visualizing and breaking down the problem into smaller parts. The fact that the outcome of applying a heuristic is unpredictable means that the strategy can be either more or less effective than using an algorithm. Algorithmic Problem Solving. • Apply standard problem-solving heuristics to aid in problem solving related • to computer science. Problem Solving. A partial list of strategies is included: Guess and check Look for a pattern Make an orderly list Draw a picture Eliminate possibilities Solve a simpler problem Use symmetry Use a model. Using the guess and check problem solving strategy to help solve math word problems. Often this is just as hard as the next step. Benefits Of Algorithm. Approach of the algorithm is iterative and also maintains shortest path with each intermediate nodes. An algorithm is a defined set of step-by-step procedures that provides the correct answer to a particular problem. This includes formulae and theorems that have been tested and proven to work. The strategies included are: -draw a picture -make a list or table -work backward -guess and check -find a pattern -write an equation Each worksheet is 4 questions and is either organized by the problem solving strategy or as a mixed review. Describe and analyze a sequence of instructions being followed. Blelloch; Algorithmic Solutions (formerly LEDA Library) -- a library of the data types and algorithms ( number types and linear algebra, basic data types, dictionaries, graphs, geometry, graphics). “Being able to use your body in problem solving alters the way you solve the problems,” said University of Wisconsin psychologist Dr. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). An alternative to PDCA, the 5 step approach is a simpler alternative, which may help a team quickly understand and try new ideas to resolve the problem at hand. the way in which information is processed and manipulated in the decision making process. The first step in teaching problem solving skills to kids is to ensure they are calm. 17 Individual Problem set - warmup Lab 01, Problem Set 01 Mon. Problem solving methods include areas such as scientific methods, analysis, logic, rational thought, intuition, creativity and design thinking. Pengertian Problem Solving problem-solving-strategies-algorithms Sebuah Metode Baru Heuristik untuk Menyelesaikan Spasial Dibatasi Perencanaan Hutan Masalah Berdasarkan Mitigasi Infeasibilities Memancarkan Outward dari Pilihan Paksa. Skilled mathematical thinkers have a variety of problem. The next line executed is “print the value of product” which outputs a = 0, the correct answer to the problem 0 $\times$ 0. Disadvantages: There are several things that could lead to problem solving disadvantages. Requires a Java 5 or higher compiler. Philip Ball 08 January 2015. Algorithms, building blocks of algorithms (statements, state, control flow, functions), notation (pseudo code, flow chart, programming language), algorithmic problem solving, simple strategies for developing algorithms (iteration, recursion). This is a Quantitative Comparison question. and algorithm of the example follows (in fig. representation of the average or ideal member of a concept C. Davidson 6 The Role of Working Memory in Problem Solving 176 David Z. When used in conjunction with reasoning and decision-making skills, the process works well for one or more participants. Problems are the issues which comes across any system. The algorithm works by partitioning an original large problem into a group of subproblems. These lessons are usually outside the main flow of the curriculum; indeed, they are purposely independent of any. In essence, a problem is a situation that confronts a person, that requires resolution, and for which the path to the solution is not immediately known. One of the important aspects of solving a problem is forming a good strategy. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). ) Inappropriate use of algorithms. Models are how the strategies are organized on paper so that students can. Even a simple problem like twenty-four puzzle contains almost 10^25 nodes. An algorithm whether directed on a computer, or foreseen as verbal instructions, will tell us the process or method. Solve a problem by applying the problem-solving process. This activity helps students to develop proficiency in using analogical problem solving. Solving Every Sudoku Puzzle by Peter Norvig In this essay I tackle the problem of solving every Sudoku puzzle. The D-Wave annealer then iteratively optimizes each subproblem to eventually solve the original larger one. The proposed computation appears to be considerably more efficient than the specialized form of the simplex method which is in common use. Strategies to help students. The step by step procedure involved in solving a mathematical problem using math formula is a perfect example of a problem-solving algorithm. The Six-Step Problem-Solving Process is an easy approach to dealing with issues and problems that you face. Practicing Problem SolvingPracticing Problem Solving The problems must be challenging enough so there is a real advantage to using a problem solving framework 1 The problem must be advantage to using. A significant feature of these strategies is that they reflect a careful analysis of the problems to which they are applied. In this study, the model for school bus routing problem is proposed, and a heuristic algorithm for solving the proposed model is suggested. Rather than directing a lesson, the teacher needs to provide time for students to grapple with problems, search for strategies and solutions on their own, and learn to evaluate their own results. As someone who uses this problem solving algorithm far too often. Instead, it learned to delete the list, so that it was no longer technically unsorted. The cognitive approach to problem solving Problem space theory. A well-defined problem is one that has a clear goal or solution, and problem solving strategies are easily developed. A stylized bird with an open mouth, tweeting. There are several strategies you can apply while trying to solve a problem. Solving a hard Sudoku puzzle will require quite a different set of techniques compared to an easy one. There are many ways to write an algorithm. September 4, 2011, Harri Daniel, Comments Off on Benefits Of Algorithm. Keywords (Audience): High. Read the problem carefully. com ISBN: 978-0-02-111965-3 MHID: 0-02-111965-1 Homework Practice and Problem-Solving Practice Workbook Contents Include: • 117 Homework Practice worksheets-. These plans reflect general rules for developing skills used in solving problems. 15 Individual Problem Set Session 05, Problem Set 05 10 Mon. Problem solving is an important component of mathematics education because it is the single vehicle which seems to be able to achieve at school level all three of the values of mathematics listed at the outset of this article: functional, logical and aesthetic. Cognitive flexibility is the ability to shift thinking easily in order to solve problems. For Exercises 1-6, match the problem solving strategy with the definition or example. However, in general, as one gains experience in solving problems, one develops one's own techniques and strategies, though they are often intangible. Problem-solving strategies; The role of algorithms in the problem-solving process; Implementation strategies for algorithms; Debugging strategies; The concept and properties of algorithms; Learning outcomes. The artificial intelligence (AI) technique employs a problem solving strategy for project planning that can be beneficial to project managers. When solving maths problems, students should be encouraged to follow a general problem solving procedure. A problem is a tuple $(S, s, A, \rho, G, P)$ where. The efficiency of problem-solving is strongly determined by the way the problem is analysed into separate components: objects, predicates, state space, operators, selection criteria. In Artificial Intelligence, Search techniques are universal problem-solving methods. 0 Introduction 277. I will provide the standard algorithms for each model before presenting my own implementation. 18 Review of Problem Set 04 and Lab 05. Cognitive flexibility is the ability to shift thinking easily in order to solve problems. The following diagram illustrates solving the N=4 problem using this recursive strategy. Problem solving (with in the context of developing programs) refers to analyzing a problem with the intention of deriving a solution for the problem. After a student understands a problem, he or she is able to search his or her memory to identify problems that are comparable, and then apply or adapt the solutions to those remembered problems to the current problem. , 5+7=12, 12–5=7, 12–7=5 and 5×7=35, 35÷5=7, 35÷7=5). ALGORITHMIC PROBLEM SOLVING 1. In the activity guide, students describe strategies for solving problems. Those classrooms are beautiful, but they seem to be few and far between. - Chapter 2 covers dynamic memory allocation. problem solving strategies Get your students familiarized with these steps and strategies for problem solving. A focus on problems that do not respond to algorithmic solutions. In general, searching refers to as finding information one needs. 3 Lab 1 Fri. Computer languages, frameworks, and algorithms are tools that you can learn by studying. 1 game Case 2: The 3rd person plays the 1st and 2nd i. In the 20th century, there has been an advancement of research on mathematical problem solving and findings about possibilities to promote problem solving with varying priorities (c. Solving Every Sudoku Puzzle by Peter Norvig In this essay I tackle the problem of solving every Sudoku puzzle. Then, I provided them. Algorithms are used when there is a clear, systematic pathway to solving the problem. It will also help you prioritize your time so you can get back to what really matters. While solving a problem, this should be known that what will be out ultimate aim. Problem Solving Strategies Lesson. This method usually allows us to reduce the time complexity to a large extent. Inductive Reasoning Examples In psychology, inductive reasoning or 'induction' is defined as reasoning based on detailed facts and general principles, which are eventually used to reach a specific conclusion. The solution to instilling these thinking skills lies in problem solving lesson plans. The kinds of problems that have yielded to the technique range from developing novel strategies in game theory to designing complex mechanical systems. Learn which problem solving techniques and strategies can help you effectively handle the challenges you face in your projects. At least as important, though, is that the student must also possess the necessary metacognitive. hill cl… Get the answers you need, now!. 4 Agent Based and Distributed Problem Solving 235 7. , operation counts) The role of algorithms in the problem-solving process Problem-solving strategies Iterative and recursive mathematical functions. When most programmers are given a programming problem in an interview, they make several key mistakes. This strategy is not practical for. Trouble Shooting - Micro Plant. The Math Behind Sudoku Solving Strategy. a chemical concept. Look for familiar things. Finally, a problem-solving question, which I consider to be at a "higher level" than the previous two, might briefly describe a scenario, and list the requirements of the problem. This site supplements our 1-on-1 teaching consultations. 1, minimizes a convex function fby repeatedly applying proxf to some initial point x0. Guess and Check " Guess and Check " is a problem-solving strategy that students can use to solve mathematical problems by guessing the answer and then checking that the guess fits the conditions of the problem. The next line executed is “print the value of product” which outputs a = 0, the correct answer to the problem 0 $\times$ 0. We cover abstract data types and data structures, writing algorithms, and solving problems. Synonyms for problem-solving at Thesaurus. Examine problems and proposed solutions from multiple perspectives 7. The three common strategies are: Divide and conquer strategy - This is the most widely used strategy. Problem solving skills and the problem-solving process are a critical part of daily life both as individuals and organizations. When Cobb discussed the answer of 15 with one. What is my problem? 2. Definition of Algorithm. Oct 29, 2017 - Explore wileyteaching's board "Math - Problem Solving", followed by 1479 people on Pinterest. Greedy algorithms work by recursively constructing a set of objects from the smallest possible constituent parts. After you see a few examples, it's going to start making sense! The first thing we do is change the way the problem is written The first math step is to look at that first number of the guy we are dividing into that 6. The second step of the beginner's Rubik's Cube tutorial doesn't require long algorithms. IDEAL is just one problem solving strategy. Problem solving is a systematic search through a range of possible actions in order to reach a predefined goal. This is a book designed to make up this role in the categorization; learning the algorithmic problem solving by analyzing and practicing interview problems -- a reciprocal relationship that makes 1+1=4: Algorithms, Interviews, Passion, and Confidence. Use methods 2 and 3 alternatingly to complete the puzzle as much as you can, until those methods lead no further. Algorithm : In computing (Computer science and Information Technology) algorithm is a statement(s) outlining the operation of a computer program, written in. The strategy is highly time consuming, and involves taking lots of steps. Another type of strategy is an algorithm. Recursive parts. Another reason the role of algorithms is changing is that researchers have identified a number of serious problems with the traditional approach to teaching computation. Such algorithms provide an accurate solution to Equation 2. Below given are the core strategies involved in solving every problem. Think Gutenberg, James Watt, and Thomas Edison. Dynamic programming (usually referred to as DP ) is a very powerful technique to solve a particular class of problems. Several approximation and heuristic strategies, based on Equation 2, have been proposed in the literature (and ). In Team-Based Problem Solving, students form collaborative teams to solve a problem or undertake a project. A Seven Step Approach to Solving Programming Problems. Through the use of think-alouds, teachers model each stage of the problem-solving process, which can be best understood as following four steps: 1. The goal of this document is to provide recommendations which can help remove technical blockers to disabling TLS 1. com ISBN: 978-0-02-111965-3 MHID: 0-02-111965-1 Homework Practice and Problem-Solving Practice Workbook Contents Include: • 117 Homework Practice worksheets-. [email protected] Three evenly spaced dots forming an ellipsis. word or story problem suited to the age and interests of your students. Think, think, think of some solutions. Indeed, really, really understanding the problem is sometimes the only hard bit: once you really, really understand the problem, the answer may be obvious. Describe a time you had to solve a problem without managerial input. at choosing an appropriate strategy is best learned by solving many problems. How to use the FeynmanAlgorithm: Write the problem down, in an unambiguous way. Algoriths 2. A mathematical formula such as πR2 is a special case of an algorithm. It presupposes that students can take on some of the responsibility for their own learning and can take personal action to solve problems, resolve conflicts, discuss alternatives, and focus on thinking as a vital element of the curriculum. This process is summarized in Figure 1. 1 Overview of Expert System Technology 279 8. On Line 2, the Boolean expression is true, so we set product = 0 and skip the entire else clause. Posted on December 6, 2017 by Nguyễn Viết Hiền. o Emphasize thinking about problem solving strategies. LP 9A Problem Solving 1 3/12/2017 Problem Solving: Strategies and Obstacles • Algorithms • Heuristics • Insight Barriers to Problem Solving • Confirmation Bias • Mental Sets • Functional fixedness (not in your textbook) o Examples of overcoming functional fixedness • Mental Representations (not in your textbook). The strategy tools available here, a set of ideas already tested but constantly evolving, are to help you think about the A-Z of "problem-solving with others," from picking issues and winning attention for them to planning and implementing to get results, from bargaining to learning and back again. 1 (327 ratings) Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately. Second grade is a very important year where students develop fluency with two-digit addition and subtraction. In a top-down approach an overview of the system is formulated, specifying but not detailing any first-level subsystems. Check if it is similar to some standard problems & if a Known algorithm exists. Data Structures and Problem Solving Using Java (Fourth Edition) Data Structures and Problem Solving Using C++ (Second Edition) Published by Addison-Wesley, 2010; ISBN: 0-321-54140-5; CS-2 Text ; Errata (last update: 8/29/16) Source code. ; The sites listed below provide lesson plans and resources for promoting problem solving, creativity, and critical thinking. Heuristic techniques are not a formal problem-solving model as such, but can be used as an approach to problem solving, where solutions are not expected to produce a perfect or optimal solution. This is a book designed to make up this role in the categorization; learning the algorithmic problem solving by analyzing and practicing interview problems -- a reciprocal relationship that makes 1+1=4: Algorithms, Interviews, Passion, and Confidence. 70-71) By means of introspection (Polya's method) or by making systematic observations of experts solving large number of problems, it might be possible to identify and characterize the heuristic strategies that are used by expert problem solvers. The school year is off to a roaring start, and this is the year that I figure out how to teach problem solving strategies (and continue making students show their problem solving strategies). A state space consists of the tree of symbolic states that are generated when all possible operators are iteratively applied to the current state of symbols representing objects composing the. She paid for the items using $10,$5 and \$1 bills. These 9 problem solving worksheets allow students to practice different problem solving strategies. In general, searching refers to as finding information one needs. It indicates the ability to send an email. Recursive parts. IDEAL is just one problem solving strategy. These researchers conclude that young children's problem-solving abilities have been seriously underestimated. There is no guarantee that the solution found will be the most accurate or optimal solution for the given problem. Chapter 3 Problem Solving Methods. Uncovering essential information as part of your problem-solving strategy will prevent you from:. Rather than directing a lesson, the teacher needs to provide time for students to grapple with problems, search for strategies and solutions on their own, and learn to evaluate their own results. For example, if for every length x the worst input of size x takes time x then this problem has linear runtime. Pólya, 1945 Developing problem solving skills is like learning to play a musical instrument—a book or a teacher can point you in the right direction, but only your. Classroom Cognitive and Meta-Cognitive Strategies for Teachers: Research-Based Strategies for Problem-Solving in Mathematics, K-12 PDF Download Edible Math — Hands On Math Strategies (Primary). Usually, a problem is stated in words, either orally or written. I would like to thank the participants of the study who volunteered their time. Inside each directory, you'll find instructions for that problem, along with a test file as well as an empty skeleton file. This work considers a generalization of Grover’s search problem, viz. can be put to better use on such topics as problem solving, estimation, mental arithmetic, geometry, and data analysis (NCTM, 1989). The random mouse, wall follower, Pledge, and Trémaux's algorithms are designed to be used inside the maze by a traveler with no prior knowledge of the maze, whereas the dead-end filling and shortest path algorithms are designed to be used by a person or computer program that can see. Define the problem. Choose the best strategy. This is a Quantitative Comparison question. Constructing a clear objective assists both the execution of change, the delivery and the communication and engagement of the people involved. A state space consists of the tree of symbolic states that are generated when all possible operators are iteratively applied to the current state of symbols representing objects composing the. and algorithm of the example follows (in fig. A solution is needed to. Algorithm We'll solve the problem of finding and marking a solution path using recursion. Some common problem-solving strategies are: compute; simplify; use an equation; make a model, diagram, table, or chart; or work backwards. When students answer incorrectly, praise the student for his/her risk-taking and effort while also describing and modeling the correct response. Getting Started (Stage One) Pre Deliberation. The teacher also participates, explaining his or her drawings to the class or group. Solving the problem and understanding the content is. Destructive problem-solving. In everyday life,. The sections below help explain key problem-solving steps. can be put to better use on such topics as problem solving, estimation, mental arithmetic, geometry, and data analysis (NCTM, 1989). It indicates the ability to send an email. Police Enforcement Strategies to Prevent Crime in Hot Spot Areas Summarizes the findings from all rigorous academic studies evaluating police enforcement strategies in hot spot areas: Problem-Solving Tips: A Guide to Reducing Crime and Disorder through Problem-Solving Partnerships Contains information and insights into the problem-solving approach. On Similarities and Differences Between Proving and Problem Solving. Algorithms are solutions. Selecting a state space. Ask questions B. The search algorithms help you to search for a particular position in such games. A "problem" is a task, activity, or situation for which a solution is not immediately identified, known, or obtainable. An algorithm for finding your total grocery bill, for example, would direct you to add up the costs of individual items to find the total. At least as important, though, is that the student must also possess the necessary metacognitive. Also dependent on the problem is whether this approach, by itself, will yield a solution or whether the approach will simply help you generate a hypothesis that requires further exploration using another strategy. Algorithm design is fluid and subject to individual plans. Based on a model by Pólya (), in a first phase of research on problem solving, particularly in the 1960s and the 1970s, a series of studies on problem-solving processes placing emphasis on the. If you are familiar with my Addition & Subtraction Word Problems, you may have noticed that I make a big distinction between the strategies used when solving problems and the models students employ with those strategies. There are 4 types of Problem Solving Strategies: Algorithm: this is step by step strategies for how to solve the problem (pseudo-code) Heuristic: the general strategies used to make quick short-cut solutions to the problems that sometimes lead to solutions but sometimes lead to errors. Site Map This is the Site Map for Problem-Solving-Techniques. Traveling Salesman Problem (TSP) The TSP problem is defined as follows: Given a set of cities and distances between every pair of cities, find the shortest way of visiting all the cities exactly once and returning to the starting city. So, you get 2 conceptual models - one for problem solving and other for decision-making - and 5 techniques. indd i0i_0iv_CAG2FM_111966. muses either the simplex algorithm or the active-set algorithm. Unfortunately, the method requires you to do something that, at least to me, seems so insane that I literally want to laugh out loud. If students are having trouble with the concept of algorithms, have them use the worksheet to guide their thinking. Young children may not always be able to say exactly what the problem is. One feature that distinguishes AI search algorithms from other graph-searching algorithms is the size of the graph involved. Problem Solving Process : A typical collaborative process has three well-defined stages, each containing a number of steps, tasks or objectives. Posted on December 6, 2017 by Nguyễn Viết Hiền. Problem solving, Uncategorized. The better you become at the different types of strategies and at determining which type to use in which situation, the easier you will find not only your college studies but navigating the world at large. 8‐Step Model Drawing: Singapore's Best Problem‐Solving MATH Strategies, by Bob Hogan and Char Forsten; ISBN 13‐973‐1‐88458‐95‐6 Word Problems for Model Drawing Practice, by Catherine Jones Kuhns; ISBN 978‐1‐934026‐53‐3 Article: Marjorie Montague. The most severe of those is the improper allocation of time. Classrooms in which students engage in problem solving and have the opportunity to invent strategies do exist. Repeat the same process with this half, until you only have two people and you can ask if one of the two has the token. Heuristics in Problem Solving: The Role of Direction in Controlling Search Space Yun Chu1, Zheng Li2, Yong Su3, and Zygmunt Pizlo4 Abstract: Isomorphs of a puzzle called m+m resulted in faster solution times and an easily repro-duced solution path in a labeled version of the problem compared to a more difficult. There are different strategies you can use to solve multiplication problems: repeated addition, break-apart, arrays, and partial. Algorithms are solutions. Solve a problem. Trouble Shooting - Micro Plant. Well an algorithm is a step by step procedure for solving a problem. You can use this formula to find the last term in the sequence or the number of. There are 4 types of Problem Solving Strategies: Algorithm: this is step by step strategies for how to solve the problem (pseudo-code) Heuristic: the general strategies used to make quick short-cut solutions to the problems that sometimes lead to solutions but sometimes lead to errors. Problem solving methods include areas such as scientific methods, analysis, logic, rational thought, intuition, creativity and design thinking. Indeed, really, really understanding the problem is sometimes the only hard bit: once you really, really understand the problem, the answer may be obvious. The searching algorithm helps us to search for solution of particular problem. This site provides practical strategies to address teaching problems across the disciplines. This type of problem solving strategy involves asking questions in order to clarify the task and your understanding of the problem. Problem-solving skills are a set of soft skills to use in difficult, unexpected, or complicated matters that arise in the workplace. 215) represents a more complex approach to problem-solving that requires a deeper level of understanding about mathematics. Linear programming - solution. In contrast, a poorly-defined problem is the opposite. By Brad Miller and David Ranum, Luther College. Look for familiar things C. C construct and problem solving strategies. The importance of algorithm can not be undermined. HEC Paris & McGill professors of strategy have identified five pitfalls that. A stylized bird with an open mouth, tweeting. This article explains the five problem solving steps and provides strategies on how to execute each one. For example, you could probably discover the insertion sort or selection sort algorithms by trying to sort an a list of numbers on your own. The idea is very simple, If you have solved a problem with the given input, then save the result for future reference, so. One can use one to two tools to write down an algorithm – Flowcharts or Pseudocode. When our emotions are high, it's much more challenging to see things rationally, making impulsive reactions more likely. When utilizing these techniques, the way the pros prefer to do it, is to start with the basic ones. Tier 1: SDF/Algorithms and Design [11 hours]: The concept and properties of algorithms Informal comparison of algorithm efficiency (e. Problem solving and posing to students can have many benefits: Problem solving and posing strategy is a way of presenting material to teach students to pose and solve problem with given tools and knowledgeable guidance. It is plausible to suggest that if the information is presented in. Recursive part(s) that call the same algorithm (i. Ask questions B. In this study, the model for school bus routing problem is proposed, and a heuristic algorithm for solving the proposed model is suggested. Identifying the problem. Problem solving in mathematics education has been a prominent research field that aims at understanding and relating the processes involved in solving problems to students’ development of mathematical knowledge and problem solving competencies. I would like to thank the participants of the study who volunteered their time. I will provide the standard algorithms for each model before presenting my own implementation. Problem Solving as Searching a State Space Cognitivist explanations of problem solving are based on a generalized model of searching in a state space. It turns out to be quite easy (about one page of code for the main idea and two pages for embellishments) using two ideas: constraint propagation and search. Accept Reject Read More. The strategy consists of five big steps: Read and comprehend the problem statement. LP 9A Problem Solving 1 3/12/2017 Problem Solving: Strategies and Obstacles • Algorithms • Heuristics • Insight Barriers to Problem Solving • Confirmation Bias • Mental Sets • Functional fixedness (not in your textbook) o Examples of overcoming functional fixedness • Mental Representations (not in your textbook). Figure 1 shows an example of a direct modeling strategy on the Rob’s rocks problem. For example, the proximal minimization algorithm, discussed in more detail in §4. , factorial(1)) • Recursive step(s): • A function calling itself on a smaller problem. Ken Watanbe, former McKinsey consultant and author of "Problem Solving 101," teaches that practicing good problem-solving skills develops a mindset that drives people to bring out the best in themselves and to shape the world in a positive way. This put legitimate companies and brands in a bind as they have had to adapt their Facebook marketing strategies accordingly. Many made errors – ones that primary teachers would recognize – such as 15 or 115. Develop a simple understanding of an algorithm using computer-free exercises. ARIZ is an acronym for the Russian phrase “Algorithm for Inventive Problem Solving,” ARIZ is a logical structured process that incrementally evolves a complex problem to a point where it is simple to solve. Basic Strategy for Algorithmic Problem Solving. The idea is very simple, If you have solved a problem with the given input, then save the result for future reference, so. Even though problem solving does not necessarily follow these exact steps (and not all problems have a specific solution), you can use these guidelines to encourage and assist children as they solve the problems they meet each day. Ian Whitacre is a faculty member in the School of Teacher Education at Florida State University in Tallahassee. Another type of strategy is an algorithm. You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. For example, if for every length x the worst input of size x takes time x then this problem has linear runtime. They will also develop and evaluate methods of training these strategies. Selecting the right search strategy for your Artificial Intelligence, can greatly amplify the quality of results. Mar 21, 2020 - Explore drnicki7's board "word problems", followed by 14100 people on Pinterest. Title: Microsoft Word - POOCH PROBLEM SOLVING STRATEGY. Here are three common programming strategies:. Problem Solving Strategies Trial and Improvement Draw a Diagram Look for a Pattern Act It Out Draw a Table Simplify the Problem Use an Equation Work Backwards Eliminate Possibilities. L12: Problem Solving Strategy and Test Prep: Act it Out - Make a Model (Ch 7, Gr 5) L9: Problem Solving Strategy and Test Prep: Act it Out (Ch 1, G3) L9: Problem Solving Strategy and Test Prep: Act it Out (Ch 13, Gr 3). Problem Case 1: The 2nd person plays the 1st i. Algorithm definition is - a procedure for solving a mathematical problem (as of finding the greatest common divisor) in a finite number of steps that frequently involves repetition of an operation; broadly : a step-by-step procedure for solving a problem or accomplishing some end. The problem space consists of the initial (current) state. Heuristic techniques are not a formal problem-solving model as such, but can be used as an approach to problem solving, where solutions are not expected to produce a perfect or optimal solution. These plans reflect general rules for developing skills used in solving problems. It is now well-known that positive emotional state helps cognitive flexibility and makes creative problem-solving easy in many situations (The American Heritage Dictionary, Second College Edition, 1983). Function Optimization and Function Approximation were presented as two general classes of problems to which the algorithms from the fields of Metaheuristics, Computational Intelligence, and Biologically Inspired Computation are applied. Read the next article: The skills of problem solving. We have to move through the process but on the positive side an algorithm guarantees that we’ll get to the solution. Through the use of think-alouds, teachers model each stage of the problem-solving process, which can be best understood as following four steps: 1. 215) represents a more complex approach to problem-solving that requires a deeper level of understanding about mathematics. It is important to point out at this stage, that though we are concentrating here on mathematical problem solving, many of the strategies and techniques that are used in mathematics are used in any type of problem. Those most effective at debugging draw from extensive experience, as well as refined problem-solving skills. Algorithms are usually executed by computer programs but the term can also apply to steps in domains such as mathematics for human problem solving. Adapt 5 Whys to Clearly Define the Problem. Our problem solving pages provide a simple and structured approach to problem solving. 5 Problem Solving Steps – Process & Strategies for Success 1. The purpose of a word-problem mnemonic is to provide students with a framework for solving word problems. You are allowed to slip a flipper under one of the pancakes and flip over the whole stack above the flipper. Good algorithms take less time and memory to perform a task. The efficiency of problem-solving is strongly determined by the way the problem is analysed into separate components: objects, predicates, state space, operators, selection criteria. A partial list of strategies is included: Guess and check Look for a pattern Make an orderly list Draw a picture Eliminate possibilities Solve a simpler problem Use symmetry Use a model. NOTE: This strategy appears to be more effective when used in later, rather than earlier, elementary grades. Students constructed their own strategies that. Now, you have identified and studied your problem. You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Constructing a clear objective assists both the execution of change, the delivery and the communication and engagement of the people involved. What concepts and terms are important in solving this problem?. com Abstract This paper explains genetic algorithm for novice in this field. However, problem solving is also seen in the animal kingdom through the use of mazes and testing to obtain hidden rewards. Figure 1 shows an example of a direct modeling strategy on the Rob’s rocks problem. How to solve a Dynamic Programming Problem ? D ynamic P rogramming (DP) is a technique that solves some particular type of problems in Polynomial Time. Using a known method isn't fun, and it isn't creative. The problem must be. Reconsider your initial solution and. Colt explains the material in a clear and concise way with diagrams and exercises which were really helpful for visualizing and getting real world practice. Rather than directing a lesson, the teacher needs to provide time for students to grapple with problems, search for strategies and solutions on their own, and learn to evaluate their own results. However, the research of Flower, Hayes, and. can be put to better use on such topics as problem solving, estimation, mental arithmetic, geometry, and data analysis (NCTM, 1989). It is used when the solution can be recursively described in terms of solutions to subproblems (optimal substructure). There Is a Difference. (written in Italian). This article explains the five problem solving steps and provides strategies on how to execute each one. There are some single-player games such as tile games, Sudoku, crossword, etc. However, they require time proportional to several factorizations of H. Problem Solving.


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# Find triangle rectangle opposite side length

In the right-angled triangle below, is it possible to find length $BC$ with only length $AC$ and angle $A$?

• $BC=(AC)f(A)$, where $f$ is one of the basic trig functions. I'll leave you to work out which one. – David May 25 '18 at 1:36
• "Triangle rectangle" was a new phrase to me. It makes perfect sense (at least once I see the picture), but it's more common in English to use the less latin-ified "right-angled triangle". – Arthur May 25 '18 at 1:58
• Thanks, I translated literally I didn't know the english term. – Manspider May 25 '18 at 2:38

$\tan\theta = \frac O A$
$\tan A = \frac{BC}{AC}$
$BC=\tan A\times AC$

format: plain


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[Recommended]Industrial Espionage  David Doe is a network administrator for the ABC Company. David is passed over for promotion three times. He is quite vocal in his dissatisfaction with this situation.

Industrial Espionage David Doe is a network administrator for the ABC Company. David is passed over for promotion three times. He is quite vocal in…

Industrial Espionage
David Doe is a network administrator for the ABC Company. David is passed over for promotion three times. He is quite vocal in his dissatisfaction with this situation. In fact, he begins to express negative opinions about the organization in general. Eventually, David quits and begins his own consulting business. Six months after David’s departure, it is discovered that a good deal of the ABC Company’s research has suddenly been duplicated by a competitor. Executives at ABC suspect that David Doe has done some consulting work for this competitor and may have passed on sensitive data. However, in the interim since David left, his computer has been formatted and reassigned to another person. ABC has no evidence that David Doe did anything wrong.
What steps might have been taken to detect David’s alleged industrial espionage?
What steps might have been taken to prevent his perpetrating such an offense?

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Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.767819
Title: Regulation of oligodendrocyte lineage cell function by the RXRγ nuclear receptor
Author: Di Canio, Ludovica
ISNI:       0000 0004 7661 1895
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2019
Availability of Full Text:
 Access from EThOS: Full text unavailable from EThOS. Please try the link below. Access from Institution:
Abstract:
Remyelination is a spontaneous regenerative process whereby myelin sheaths are restored to demyelinated axons. Key players in this process are oligodendrocyte progenitor cells (OPCs), a widespread population of CNS progenitor cells which persist into adulthood. Remyelination is impaired in patients with chronic demyelinating conditions such as Multiple Sclerosis, and as with other regenerative processes, its efficiency declines with increasing age. Hence, there is a need for the development of therapeutic interventions that will aid in promoting endogenous remyelination when the endogenous regenerative potential is compromised. The nuclear receptor RXR$\gamma$ is an important positive regulator of OPC differentiation and an accelerator of endogenous remyelination in aged rats. RXR$\gamma$ functions as a ligand-induced transcription factor and is able to regulate gene transcription. It does so by heterodimerising with other nuclear receptors and recruiting co-regulators involved in chromatin remodelling. However, we lack understanding on the specific mechanism by which RXR$\gamma$ promotes OPC differentiation. With the work presented in this thesis I demonstrate that RXR$\gamma$ function is regulated at multiple signalling levels. Proximity ligation assays revealed that RXR$\gamma$ remains consistently bound to its partners throughout the oligodendrocyte lineage, and the biological relevance of each heterodimer is determined by the dynamic association of co-regulators. This is in turn influenced by ligand presence and subcellular receptor localisation. To identify the genes controlled by RXR$\gamma$ in OPCs I carried out ChIP sequencing, which revealed genes involved in proliferation and cell cycle control. Further functional assessments aided me in the development of a hypothesis whereby RXR$\gamma$ activation does not directly influence oligodendrocyte formation, but rather promotes cell cycle exit thereby accelerating and facilitating OPC differentiation. Altered nuclear receptor expression and ligand presence in ageing OPCs may consequently impair this process. My thesis provides an alternative hypothesis to how RXR$\gamma$ regulates lineage cell progression, highlighting a new avenue in the development of therapeutic interventions targeting generic stem cell functions for which drugs are already FDA approved, rather than oligodendrocyte-specific pathways.
Supervisor: Franklin, Robin J. M. ; Wayne, Gareth Sponsor: BBSRC ; GlaxoSmithKline
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.767819  DOI:
Keywords: oligodendrocyte ; nuclear receptors ; remyelination ; rxr ; opc
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# Smaller Elixir Docker Images

Posted 22 Feb 2019 to elixir, docker and has Comments

When running Elixir in production, I was surprised how large the Docker images were and how long they took to build. In an effort to keep those images smaller, and reduce the build time for those images, I spent a while testing different options. The solution I came up with seems obvious in retrospect - but took a long while to test all the different options. I’ve made liberal use of multi-stage builds, which allow you to pull artifacts from intermediary images into later stages. The final image can then be significantly smaller. These steps assume you’re using Distillery for packaging your Elixir application for deployment using OTP releases.

I’ll go through all of the three stages in order below, each Dockerfile snippet is a part of a single file that I put together in the last section.

## Dependency Stage

The first stage (which I name base) just consists of adding the mix file and lock, fetching dependencies, and building them. This will happen irrespective of your application files, meaning your app files can be updated and this stage will remain the same. Changing your dependencies list in mix.exs will result in this whole stage being rebuilt, but hopefully that’s not something that happens frequently. In my experience, building the dependencies was the primary cause for how long it took to build new images, so I wanted this time penalty to be rare.

Here’s the first part that just builds the deps into a base intermediate image:

# First, download and compile all dependencies in an intermediate base image
FROM elixir:1.8.1-alpine as base
# Your dependencies for the OS may differ
RUN apk update && apk --no-cache add --virtual builds-deps build-base libressl libressl-dev
WORKDIR /app
ENV MIX_ENV prod
RUN mix local.rebar --force
RUN mix local.hex --if-missing --force
RUN mix deps.get --only prod
RUN mix deps.compile

## Release Build

The next stage builds the actual release using Distillery. It compiles your application code, creates a release, and then ungzip’s the release package into a folder to be picked up by the subsequent stage. For the smallest image, you should include the Erlang Runtime System via Distillery (instead of using a docker image that includes the Erlang VM). Based on testing, this option can help reduce the size of the final image significantly. Just make sure your rel/config.exs has the following options:

environment :prod do
set include_erts: true
set include_src: false
...
end

Here’s the next section in the Dockerfile to build the release and ungzip it into a folder for pickup in the next stage:

# Now build a release from our app files
FROM elixir:1.8.1-alpine as intermediate
COPY --from=base /app /app
ENV MIX_ENV prod
RUN mix local.hex --if-missing --force
WORKDIR /app
RUN mix compile
RUN mix release
WORKDIR /release
# replace 'my_app' below with your application name, and possibly your app version
RUN tar -zxf /app/_build/prod/rel/my_app/releases/0.1.0/my_app.tar.gz -C /release

## Release Artifact

The last step just copies the release to a base alpine image to run, and then runs the result in the foreground.

# now run the release.  Make sure the alpine version below matches the alpine version
# included by erlang included by elixir:1.8-alpine
FROM alpine:3.9
RUN apk update && apk add --no-cache bash openssl
ENV MIX_ENV prod
ENV LANG C.UTF-8
COPY --from=intermediate /release /app
EXPOSE 4001
CMD ["/app/bin/my_app", "foreground"]

## Putting It All Together

And here’s the final Dockerfile with all of the parts in order. My final release is ~50M, which is significantly smaller than the ~200MB when not using intermediate stages.

# First, download and compile all dependencies in an intermediate base image
FROM elixir:1.8.1-alpine as base
# Your dependencies for the OS may differ
RUN apk update && apk --no-cache add --virtual builds-deps build-base libressl libressl-dev
WORKDIR /app
ENV MIX_ENV prod
RUN mix local.rebar --force
RUN mix local.hex --if-missing --force
RUN mix deps.get --only prod
RUN mix deps.compile

# Now build a release from our app files
FROM elixir:1.8.1-alpine as intermediate
COPY --from=base /app /app
ENV MIX_ENV prod
RUN mix local.hex --if-missing --force
WORKDIR /app
RUN mix compile
RUN mix release
WORKDIR /release
# replace 'my_app' below with your application name, and possibly your app version
RUN tar -zxf /app/_build/prod/rel/my_app/releases/0.1.0/my_app.tar.gz -C /release

# now run the release.  Make sure the alpine version below matches the alpine version
# included by erlang included by elixir:1.8-alpine
FROM alpine:3.9
RUN apk update && apk add --no-cache bash openssl
ENV MIX_ENV prod
ENV LANG C.UTF-8
COPY --from=intermediate /release /app
EXPOSE 4001
CMD ["/app/bin/my_app", "foreground"]


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# Sieve of Eratosthenes: making it quicker

I was thinking about doing problem 23 of Project Euler. It includes the difficulty where you have to factorize primes. I had already done that in problems I solved earlier, but it was only necessary to have a prime list until a relative small number.

So I had already implemented the algorithm when I took a look at this problem. I stored numbers in a list, flagged the ones that weren't prime numbers and removed them from the list, al of this in Python. It worked well for small lists, but when I went big, the memory usage was just too much.

I still wanted to use the algorithm of Eratosthenes, but I still needed a solution to my memory issue. So I decided, I don't know if it is the best solution, to write the list to a file and to constantly rewrite this file.

I succeeded in making this algorithm, but it's not really fast. To find primes up to the number 20 000 it took my program 405 seconds, or 6'45".

Is there any way I can improve this implementation? No file rewriting, cashing data in the RAM, etc.?

SieveCash.py (Python 3)

import tempfile
import os
import sys

def createSieve(outputFile, maxp, logging=0):
"""Creates a sieve and stores one prime per line in file outputFile."""
# Write a list of all numbers to check to a file
myNumFile = createBeginNumberList(maxp, outputFile)

# Do the looping
rfh = open(myNumFile, "r")
try:
for i in range(maxp+1):
# log if necessary
if logging > 0 and i % logging == 0:
print("Checking number", i, "(" + str(int(i/(maxp+1)*100)) + "%)")

# do thingy
break

if myNum != 0:
rfh.close()
rfh = None

rfh = open(myNumFile, "r")

finally:
if rfh != None:
rfh.close()

# Remove zeros
removeZerosInFile(outputFile)

return myNumFile

def createBeginNumberList(maxn, fileName):
"""@return value: the file path"""

tfh = open(fileName, "w")
try:
writeLineToFile(tfh, "0")
writeLineToFile(tfh, "0")
for i in range(2, maxn+1):
writeLineToFile(tfh, str(i))
finally:
tfh.close()

return fileName

def rewriteFileWithoutMultiples(inputFilename, multiple, startPos):
rfh = open(inputFilename, "r")
try:
writeFile = tempfile.mkstemp()
os.close(writeFile[0])
wfh = open(writeFile[1], "w")
except:
rfh.close()
raise

# Rewrite file
try:
writeLineToFile(wfh, str(aNum))

while True:
if aNum == None:
break

if aNum % multiple == 0:
writeLineToFile(wfh, "0")
else:
writeLineToFile(wfh, str(aNum))
finally:
rfh.close()
wfh.close()

# Copy
copyFile(writeFile[1], inputFilename)

def copyFile(source, dest):
rfh = open(source, "r")
try:
wfh = open(dest, "w")
except:
rfh.close()
raise

try:
while len(aLine) != 0:
wfh.write(aLine)
finally:
rfh.close()
wfh.close()

def removeZerosInFile(inputFile):
rfh = open(inputFile, "r")
try:
writeFile = tempfile.mkstemp()
os.close(writeFile[0])
wfh = open(writeFile[1], "w")
except:
rfh.close()
raise

# Rewrite file
try:
while True:
if aNum == None:
break

if aNum != 0:
writeLineToFile(wfh, str(aNum))

finally:
rfh.close()
wfh.close()

# Copy
copyFile(writeFile[1], inputFile)

def writeLineToFile(fh, l):
try:
fh.write(l)
fh.write('\n')
except:
fh.close()
raise

numb = len(mynum)
mynum = mynum.strip('\n')

if len(mynum) == 0:
return (0, None)

return (numb, int(mynum))

if __name__ == "__main__":
if len(sys.argv) < 2:
print("Usage:", sys.argv[0], "MAX_PRIME [LOG_INTERVAL]")
sys.exit(1)

maxp = int(sys.argv[1])
logging = int(maxp / 100)
try:
logging = int(sys.argv[2])
except:
pass

print("Creating seive until number", maxp, "with logging interval", logging)
createSieve(os.path.expanduser("~/Desktop/Sieve-" + str(maxp) + ".txt"),
maxp, logging)

Program Output (On an iMac 2.16 GHz Intel Core 2 Duo, 1GB RAM)

imac-van-ief2:23 ief2$SECONDS=0; python3 SieveCash.py 20000 2000; echo$SECONDS
Creating seive until number 20000 with logging interval 2000
Checking number 0 (0%)
Checking number 2000 (9%)
Checking number 4000 (19%)
Checking number 6000 (29%)
Checking number 8000 (39%)
Checking number 10000 (49%)
Checking number 12000 (59%)
Checking number 14000 (69%)
Checking number 16000 (79%)
Checking number 18000 (89%)
Checking number 20000 (99%)
405

## migrated from stackoverflow.comDec 2 '11 at 21:12

This question came from our site for professional and enthusiast programmers.

Writing to disk is going to be really slow. Don't do that.

If you are running out of memory, try using the standard array module or the numpy library. Both of those provide efficient arrays for holding large numbers of values. Your only running out of memory because python's lists don't store their values in a memory efficient manner.

If you are running out of memory for some reason even taking that into account, post that code here and we'll be glad to point out how to improve the memory usage.

If space is the problem, a bit-array may help. Straightforward and unoptimised (I don't know Python so well),

import sys
import array

def sieve(n):
sieveBits = (n-1) // 2
sieveInts = (sieveBits+31) // 32
sieveBound = int(n**0.5) // 2
arr = array.array('I')
arr.extend((0,)*sieveInts)
for i in xrange(sieveBound):
if (arr[i >> 5] & (1 << (i&31))) == 0:
for j in xrange(2*i*(i+3)+3,sieveBits,2*i+3):
arr[j >> 5] |= 1 << (j&31)
return arr

def primes(n):
arr = sieve(n)
primes = [2] + [2*i+3 for i in xrange((n-1)//2) if arr[i >> 5] & (1 << (i & 31)) == 0]
return primes

if __name__ == "__main__":
if len(sys.argv) > 1:
up = int(sys.argv[1])
else:
up = 100000
print len(primes(up))

It's dog-slow (4.6 seconds to sieve up to 10,000,000), but the sieving doesn't take much memory.

• Yeah… my advice was basically going to be to use a typed array. :) That speeds up things quite a bit as it removed the equivalent of millions of “if” statements. – veryfoolish Dec 4 '11 at 12:08

Here is my version of the sieve. Ideone finds the 2262 primes less than 20000 in 0.02 seconds.

def sieve(n):
m = (n-1) // 2
b = [True]*m
i,p,ps = 0,3,[2]
while p*p < n:
if b[i]:
ps.append(p)
j = 2*i*i + 6*i + 3
while j < m:
b[j] = False
j = j + 2*i + 3
i+=1; p+=2
while i < m:
if b[i]:
ps.append(p)
i+=1; p+=2
return ps
• way faster DUDE! please explain ur code so that many user will learn – sundar nataraj Jun 12 '14 at 6:43

One minor improvement is to use xrange instead of range. In your case, you don't need range, and xrange has better memory performance, which might make a little difference.

• Sorry, I should've mentioned I use Python 3 – Ief2 Dec 2 '11 at 19:51
• OK, then nevermind. Definitely removing all file IO would help – TJD Dec 2 '11 at 19:52
• That's my initial problem. If I try to loop through 20 000 numbers, my computer can't handle anymore! – Ief2 Dec 2 '11 at 19:53


text:
Convergence of gradient-based algorithms for the Hartree-Fock equations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 46 (2012) no. 6, pp. 1321-1336.

The numerical solution of the Hartree-Fock equations is a central problem in quantum chemistry for which numerous algorithms exist. Attempts to justify these algorithms mathematically have been made, notably in [E. Cancès and C. Le Bris, Math. Mod. Numer. Anal. 34 (2000) 749-774], but, to our knowledge, no complete convergence proof has been published, except for the large-Z result of [M. Griesemer and F. Hantsch, Arch. Rational Mech. Anal. (2011) 170]. In this paper, we prove the convergence of a natural gradient algorithm, using a gradient inequality for analytic functionals due to Łojasiewicz [Ensembles semi-analytiques. Institut des Hautes Études Scientifiques (1965)]. Then, expanding upon the analysis of [E. Cancès and C. Le Bris, Math. Mod. Numer. Anal. 34 (2000) 749-774], we prove convergence results for the Roothaan and Level-Shifting algorithms. In each case, our method of proof provides estimates on the convergence rate. We compare these with numerical results for the algorithms studied.

DOI : https://doi.org/10.1051/m2an/2012008
Classification : 35Q40,  65K10
Mots clés : Hartree-Fock equations, Łojasiewicz inequality, optimization on manifolds
@article{M2AN_2012__46_6_1321_0,
author = {Levitt, Antoine},
title = {Convergence of gradient-based algorithms for the Hartree-Fock equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
pages = {1321--1336},
publisher = {EDP-Sciences},
volume = {46},
number = {6},
year = {2012},
doi = {10.1051/m2an/2012008},
zbl = {1269.82008},
mrnumber = {2996329},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2012008/}
}
Levitt, Antoine. Convergence of gradient-based algorithms for the Hartree-Fock equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 46 (2012) no. 6, pp. 1321-1336. doi : 10.1051/m2an/2012008. http://archive.numdam.org/articles/10.1051/m2an/2012008/

[1] F. Alouges and C. Audouze, Preconditioned gradient flows for nonlinear eigenvalue problems and application to the Hartree-Fock functional. Numer. Methods Partial Differ. Equ. 25 (2009) 380-400. | MR 2483772 | Zbl 1166.65039

[2] G.B. Bacskay, A quadratically convergent Hartree-Fock (QC-SCF) method. Application to closed shell systems. Chem. Phys. 61 (1981) 385-404.

[3] E. Cancés, SCF algorithms for Hartree-Fock electronic calculations, in Mathematical models and methods for ab initio quantum chemistry, edited by M. Defranceschi and C. Le Bris. Lect. Notes Chem. 74 (2000). | MR 1857459 | Zbl 0992.81103

[4] E. Cancès and C. Le Bris, Can we outperform the DIIS approach for electronic structure calculations? Int. J. Quant. Chem. 79 (2000) 82-90.

[5] E. Cancès and C. Le Bris, On the convergence of SCF algorithms for the Hartree-Fock equations. Math. Mod. Numer. Anal. 34 (2000) 749-774. | Numdam | MR 1784484 | Zbl 1090.65548

[6] E. Cancès and K. Pernal, Projected gradient algorithms for Hartree-Fock and density matrix functional theory calculations. J. Chem. Phys. 128 (2008) 134-108.

[7] E. Cancès, M. Defranceschi, W. Kutzelnigg, C. Le Bris and Y. Maday, Computational quantum chemistry : a primer. Handbook Numer. Anal. 10 (2003) 3-270. | MR 2008386 | Zbl 1070.81534

[8] A. Edelman, T.A. Arias and S.T. Smith, The geometry of algorithms with orthogonality constraints. SIAM J. Matrix Anal. Appl. 20 (1998) 303. | MR 1646856 | Zbl 0928.65050

[9] J.B. Francisco, J.M. Martínez and L. Martínez, Globally convergent trust-region methods for self-consistent field electronic structure calculations. J. Chem. Phys. 121 (2004) 10863. | Zbl 1110.92069

[10] M. Griesemer and F. Hantsch, Unique solutions to Hartree-Fock equations for closed shell atoms. Arch. Ration. Mech. Anal. 203 (2012) 883-900. | MR 2928136 | Zbl 1256.35101

[11] A. Haraux, M.A. Jendoubi and O. Kavian, Rate of decay to equilibrium in some semilinear parabolic equations. J. Evol. Equ. 3 (2003) 463-484. | MR 2019030 | Zbl 1036.35035

[12] S. Høst, J. Olsen, B. Jansík, L. Thøgersen, P. Jørgensen and T. Helgaker, The augmented Roothaan-Hall method for optimizing Hartree-Fock and Kohn-Sham density matrices. J. Chem. Phys. 129 (2008) 124-106.

[13] K.N. Kudin, G.E. Scuseria and E. Cancès, A black-box self-consistent field convergence algorithm : one step closer. J. Chem. Phys. 116 (2002) 8255.

[14] E.H. Lieb and B. Simon, The Hartree-Fock theory for Coulomb systems. Commun. Math. Phys. 53 (1977) 185-194. | MR 452286

[15] P.L. Lions, Solutions of Hartree-Fock equations for Coulomb systems. Commun. Math. Phys. 109 (1987) 33-97. | MR 879032 | Zbl 0618.35111

[16] S. Łojasiewicz, Ensembles semi-analytiques. Institut des Hautes Études Scientifiques (1965).

[17] R. McWeeny,. The density matrix in self-consistent field theory. I. Iterative construction of the density matrix, in Proc. of R. Soc. Lond. A. Math. Phys. Sci. 235 (1956) 496. | MR 81755 | Zbl 0071.42302

[18] P. Pulay, Improved SCF convergence acceleration. J. Comput. Chem. 3 (1982) 556-560.

[19] J. Salomon, Convergence of the time-discretized monotonic schemes. ESAIM : M2AN 41 (2007) 77-93. | Numdam | MR 2323691 | Zbl 1124.65059

[20] V.R. Saunders and I.H. Hillier, A “Level-Shifting” method for converging closed shell Hartree-Fock wave functions. Int. J. Quant. Chem. 7 (1973) 699-705.

[21] R.B. Sidje, Expokit : a software package for computing matrix exponentials. ACM Trans. Math. Softw. 24 (1998) 130-156. | Zbl 0917.65063


text:
## Light

$c=\lambda v$

Duby3L
Posts: 72
Joined: Fri Sep 28, 2018 12:26 am

### Light

How does amplitude affect frequency? And what is the relationship between the wavelength and frequency?

Samantha Man 1L
Posts: 63
Joined: Fri Sep 28, 2018 12:22 am

### Re: Light

I'm pretty sure amplitude and frequency aren't dependent on each other since amplitude is like how high/low the wave goes and frequency is how fast the wave travels. I know that wavelength and frequency are inversely proportional of each other based on c=(wavelength)(frequency).

Melody Zhang 3L
Posts: 35
Joined: Fri Sep 28, 2018 12:21 am

### Re: Light

The amplitude is the height of the wave and it corresponds with he intensity of the light. I don't believe amplitude is related to frequency because the intensity of light is different from the energy of each photon, which is related to the wavelength and frequency.

Searra Harding 4I
Posts: 68
Joined: Fri Sep 28, 2018 12:29 am

### Re: Light

Duby3L wrote:How does amplitude affect frequency? And what is the relationship between the wavelength and frequency?

Amplitude doesn't necessarily affect frequency. When thinking of amplitude you can think "How large?" and when thinking about frequency think "How fast?" Wavelength and frequency have an inverse relationship because of c=wavelength x frequency. For example, if wavelength decreases, then frequency increases.

Archana Biju 1G
Posts: 29
Joined: Fri Sep 28, 2018 12:18 am

### Re: Light

Amplitude and frequency are related in that they are inversely proportional to one another.

So, if the amplitude increases, the frequency decreases, or if the amplitude decreases, the frequency increases. This relationship is derived from the equation v = c/(lamda).

805098281
Posts: 30
Joined: Fri Sep 28, 2018 12:26 am

### Re: Light

Amplitude is distance divided by the frequency. The wavelength can be found by dividing the speed of light by the frequency.

LaurenJuul_1B
Posts: 65
Joined: Fri Sep 28, 2018 12:17 am

### Re: Light

Archana Biju 1G wrote:Amplitude and frequency are related in that they are inversely proportional to one another.

So, if the amplitude increases, the frequency decreases, or if the amplitude decreases, the frequency increases. This relationship is derived from the equation v = c/(lamda).

Actually, amplitude and frequency are not inverses! Frequency is the inverse of wavelength, since frequency is equal to the velocity of the wave divided by lambda, which is wavelength.

Alyssa Wilson 2A
Posts: 65
Joined: Fri Sep 28, 2018 12:18 am

### Re: Light

805098281 wrote:Amplitude is distance divided by the frequency. The wavelength can be found by dividing the speed of light by the frequency.

The amplitude is how tall a wave can get, where the frequency means how quick a wave can be, as well as how many peaks are in the cycle. I believe that frequency and amplitude aren't dependent on one another, because of the formula that states that the wavelength and the frequency are inversely related. c=(wavelength)(frequency)

Rosha Mamita 2H
Posts: 63
Joined: Fri Sep 28, 2018 12:19 am

### Re: Light

Archana Biju 1G wrote:Amplitude and frequency are related in that they are inversely proportional to one another.

So, if the amplitude increases, the frequency decreases, or if the amplitude decreases, the frequency increases. This relationship is derived from the equation v = c/(lamda).

I believe its the frequency and wavelength that are inversely proportional to one another rather than frequency and wavelength. Equations we went over in class relating to the frequency and wavelength show that one will increase as the other decreases

Samantha Chang 2K
Posts: 69
Joined: Fri Sep 28, 2018 12:17 am

### Re: Light

Amplitude measures the height of each wave and equates to the energy or intensity of the light. The amplitude does not have any effect on the frequency. Wavelength and frequency are inverses of one another, so if one increases the other one decreases. This is based off of the equation c(speed of light)=(wavelength)(frequency). It helped me to draw out a picture to understand the concept.

### Who is online

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text:
## Featured resource

### Fractions

“Oh no! Not fractions!” The anxiety that students (and teachers) experience with this core mathematical topic prompted the editors to bring together research on the teaching and learning of fractions.

Members: $36.00 inc.GST Others:$ 45.00 inc.GST

Home > Topdrawer > Patterns > Good teaching > Familiar situations

# Familiar situations

Mathematics is abstract but it is based on a particular way of looking at our everyday environment.

Learning will therefore be more effective if it can be related to students' experience.

In particular, good teaching always relates patterns to the students' world.

The result is not only increased student interest and motivation but also a greater likelihood that they will understand the underlying ideas and be able to apply mathematics to everyday situations.

Patterns are everywhere in our environment so it is easy to use familiar examples for teaching about patterns.

Examples of patterns can be found both within the classroom and outside.

For example, patterns that students may have made with counters, beads, numerals or cut-out shapes can also be seen in floor tiles, school fencing, brick walls and butterfly wings.

## A pattern hunt

A pattern hunt is an excellent way for students to explore familiar patterns.


text:
# Classification

## In words...

In classification, the learning algorithm is used to discriminate between a finite number of categories of patterns. In this setting, the model is a classifier which predicts labels corresponding to the categories (often identified with $Q$ integers for a problem with $Q$ categories).

For example, we could build a classifier that given the picture of a fruit tells us if it is an apple or a banana. Such a classifier can be trained to recognize the fruits correctly from a set of labeled pictures.

When the number of categories is 2, then we have a binary classification problem, which we distinguish from multi-class problems that have more than 2 categories.

The typical loss function used in classification is the 0-1 loss, which merely assigns a cost of 1 to misclassifications and 0 to correct predictions. Given that loss function, the risk of a classifier corresponds to its probabilty of misclassifying a random pattern.

The optimal classifier minimizing this probability is the Bayes classifier, which assigns a pattern to the most likely category. But in order to do so, the classifier needs access to the probability distribution of the data, which is unknown by assumption. Therefore, we have to use learning algorithms that aim at this optimal classifier but will not be able to obtain it (unless we are given an infinite number of training data).

Perhaps the most straightforward algorithm for classification is the $K$-nearest-beighbors algorithm. Another simple and very famous algorithm at the origin of the family of neural networks is the perceptron. More recently, the Support Vector Machine became very popular.

Classification algorithms can be distinguished according to whether they build linear classifiers or nonlinear classifiers. Depending on how these classifiers are built, the algorithms are said to be discriminative (as the ones mentioned above) or generative.

## In pictures...

### A small pattern recognition demo

This is a simple demo of binary classification, in which the machine tries to recognize patterns drawn by hand. It shows how one can build a training set by labeling examples and then make predictions for pictures of unknown patterns.

This demo implements the following classifiers: $K$-nearest neighbors, the perceptron and the support vector machine.

#### Build a training set

Start by drawing a pattern and .
Then, draw a different pattern and .
Do this multiple times to collect a sample of drawings (of these 2 different patterns).

#### Make predictions

When you have enough data, draw a new example and ask the machine to or or .

At any time, you can or

### More examples

This other demo shows how a generative classifier known as the naive Bayes classifier can be used to filter spams in mailboxes.

## In maths...

In classification, the labels belong to a finite set of categories, which can be identified with the set of integers $\Y = \{1,\dots,Q\}$. In this case, the most common choice is to use the 0-1 loss function, which is defined as the indicator function of the event corresponding to a misclassification: $$\ell(y, \hat{y}) = \I{\hat{y} \neq y} .$$ Using this loss function, the risk of a classifier $f$ becomes the probability of misclassification by this classifier: $$R(f) = \E_{X,Y} [ \I{f(X) \neq Y} ] = P_{X,Y} (f(X) \neq Y)$$ since it computes the expectation of the indicator function.

### Binary classification

When $Q=2$ we have a binary classification problem and it is more convenient to use $Y\in\Y = \{-1,+1\}$. With this convention, any binary classifier $f : \X \rightarrow \{-1,+1\}$ can be defined via a real-valued function $g : \X \rightarrow \R$ as $$f(\g x) = \sign( g (\g x) ) .$$ Many classification algorithms focus on learning $g$ rather than $f$ directly.


text:
# Show that the function f(x)=4x^2-5x has a zero between 1 and 2.

Feb 16, 2016

As the value of function $f \left(x\right)$ changes from negative to positive and as is continuous, it has a zero between $a$ and $b$.

#### Explanation:

The function is $f \left(x\right) = 4 {x}^{2} - 5 x$.

Its derivative being $8 x - 5$, $f \left(x\right)$ is a continuous function.

Further, at $a$ i.e. $x = 1$, the value of function is $4 \cdot {1}^{2} - 5 \cdot 1$ or is $- 1$.

At $b$, i.e. $x = 2$, the value of function is $4 \cdot {2}^{2} - 5 \cdot 2$ or is $6$.

It is obvious that between $a$ and $b$, value of function changes from negative to positive and as it is continuous, it has a zero between $a$ and $b$.

We may apply the Bolzano Theorem

Bolzano Theorem (BT)

Let, for two real a and b, a < b, a function f be continuous on a closed interval [a, b] such that f(a) and f(b) are of opposite signs. Then there exists a number ${x}_{o}$,in $\left[a , b\right]$ with $f \left({x}_{o}\right) = 0$.

Hence we have that

$f \left(1\right) = 4 \cdot {1}^{2} - 5 \cdot 1 = - 1$

$f \left(2\right) = 4 \cdot {2}^{2} - 5 \cdot 2 = 6$

Because $f \left(1\right) \cdot f \left(2\right) < 0$ then from Bolzano Theorem we have that there is a value ${x}_{o}$ in $\left[1 , 2\right]$ for which $f \left({x}_{o}\right) = 0$