This document discusses the concept of functions in linguistics and syntactic theory. It provides examples of how functions have been modeled in different theories, such as grammars representing functions that map inputs to outputs. The document also discusses problems that have arisen with modeling language as computational functions, and proposes moving toward an interactive computation paradigm that allows for bidirectional information flow and adaptation to inputs.
Recent developments on SMT solvers for non-linear polynomial constraints have become crucial to make the template-based (or constraint-based) method for program analysis effective in practice. Moreover, using Max-SMT (its optimization version) is the key to extend this approach to develop an automated compositional program verification method based on generating conditional inductive invariants. We build a bottom-up program verification framework that propagates preconditions of small program parts as postconditions for preceding program parts and can recover from failures when some precondition is not proved. These techniques have successfully been implemented within the VeryMax tool which currently can check safety, reachability and termination properties of C++ code. In this talk we will provide an overview of the Max-SMT solving techniques and its application to compositional program analysis.
Dear students, get JNU 2021 Solved assignments and case study help by professionals.
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Evaluation of subjective answers using glsa enhanced with contextual synonymyijnlc
Evaluation of subjective answers submitted in an exam is an essential but one of the most resource consuming educational activity. This paper details experiments conducted under our project to build a software that evaluates the subjective answers of informative nature in a given knowledge domain. The paper first summarizes the techniques such as Generalized Latent Semantic Analysis (GLSA) and Cosine Similarity that provide basis for the proposed model. The further sections point out the areas of improvement in the previous work and describe our approach towards the solutions of the same. We then discuss the implementation details of the project followed by the findings that show the improvements achieved. Our approach focuses on comprehending the various forms of expressing same entity and thereby capturing the subjectivity of text into objective parameters. The model is tested by evaluating answers submitted by 61 students of Third Year B. Tech. CSE class of Walchand College of Engineering Sangli in a test on Database Engineering.
This document discusses using the concept of a metric space to determine if a sequence of languages converges. It introduces the idea of a metric space as a set where a distance function is defined that satisfies specific properties. As an example, it shows that a sequence of languages where each language is a finite union of regular languages converges in the limit to a context-free language. Determining if sequences of languages converge depends on understanding the properties of the spaces involved and how to define a suitable distance metric between languages.
Algorithm Design and Complexity - Course 6Traian Rebedea
This document provides an overview of algorithm design and complexity. It discusses different classes of problems including P vs NP problems. P problems can be solved in polynomial time, while NP problems can be verified in polynomial time but may not be solvable in polynomial time. NP-hard problems are at least as hard as NP problems, and NP-complete problems are NP-hard problems that are also in NP. The document describes techniques for solving difficult problems like backtracking and discusses examples like the n-queens problem.
NP-hard and NP-complete problems deal with the distinction between problems that can be solved in polynomial time versus those where no polynomial time algorithm is known. The document discusses key concepts like P vs NP problems, the theory of NP-completeness, nondeterministic algorithms, reducibility, Cook's theorem stating that satisfiability is in P if and only if P=NP, and examples of NP-hard graph problems like graph coloring. Cook's theorem shows that the satisfiability problem is in NP and is NP-complete, meaning that if any NP-complete problem can be solved in polynomial time, then NP would equal P.
This document discusses the concept of functions in linguistics and syntactic theory. It provides examples of how functions have been modeled in different theories, such as grammars representing functions that map inputs to outputs. The document also discusses problems that have arisen with modeling language as computational functions, and proposes moving toward an interactive computation paradigm that allows for bidirectional information flow and adaptation to inputs.
Recent developments on SMT solvers for non-linear polynomial constraints have become crucial to make the template-based (or constraint-based) method for program analysis effective in practice. Moreover, using Max-SMT (its optimization version) is the key to extend this approach to develop an automated compositional program verification method based on generating conditional inductive invariants. We build a bottom-up program verification framework that propagates preconditions of small program parts as postconditions for preceding program parts and can recover from failures when some precondition is not proved. These techniques have successfully been implemented within the VeryMax tool which currently can check safety, reachability and termination properties of C++ code. In this talk we will provide an overview of the Max-SMT solving techniques and its application to compositional program analysis.
Dear students, get JNU 2021 Solved assignments and case study help by professionals.
Mail us at : help.mbaassignments@gmail.com
Call us at : 08263069601
Evaluation of subjective answers using glsa enhanced with contextual synonymyijnlc
Evaluation of subjective answers submitted in an exam is an essential but one of the most resource consuming educational activity. This paper details experiments conducted under our project to build a software that evaluates the subjective answers of informative nature in a given knowledge domain. The paper first summarizes the techniques such as Generalized Latent Semantic Analysis (GLSA) and Cosine Similarity that provide basis for the proposed model. The further sections point out the areas of improvement in the previous work and describe our approach towards the solutions of the same. We then discuss the implementation details of the project followed by the findings that show the improvements achieved. Our approach focuses on comprehending the various forms of expressing same entity and thereby capturing the subjectivity of text into objective parameters. The model is tested by evaluating answers submitted by 61 students of Third Year B. Tech. CSE class of Walchand College of Engineering Sangli in a test on Database Engineering.
This document discusses using the concept of a metric space to determine if a sequence of languages converges. It introduces the idea of a metric space as a set where a distance function is defined that satisfies specific properties. As an example, it shows that a sequence of languages where each language is a finite union of regular languages converges in the limit to a context-free language. Determining if sequences of languages converge depends on understanding the properties of the spaces involved and how to define a suitable distance metric between languages.
Algorithm Design and Complexity - Course 6Traian Rebedea
This document provides an overview of algorithm design and complexity. It discusses different classes of problems including P vs NP problems. P problems can be solved in polynomial time, while NP problems can be verified in polynomial time but may not be solvable in polynomial time. NP-hard problems are at least as hard as NP problems, and NP-complete problems are NP-hard problems that are also in NP. The document describes techniques for solving difficult problems like backtracking and discusses examples like the n-queens problem.
NP-hard and NP-complete problems deal with the distinction between problems that can be solved in polynomial time versus those where no polynomial time algorithm is known. The document discusses key concepts like P vs NP problems, the theory of NP-completeness, nondeterministic algorithms, reducibility, Cook's theorem stating that satisfiability is in P if and only if P=NP, and examples of NP-hard graph problems like graph coloring. Cook's theorem shows that the satisfiability problem is in NP and is NP-complete, meaning that if any NP-complete problem can be solved in polynomial time, then NP would equal P.
Connectionist language models offer many advantages over their statistical counterparts, but they also have some drawbacks like a much more expensive computational cost. This paper describes a novel method to overcome this problem. A set of normalization values associated to the most frequent N-grams is pre-computed and the model is smoothed with lower N-gram connectionist or statistical models. The
proposed approach is favourably compared to standard connectionist language models and with statistical back-off language models.
1) The document discusses the complexity classes P, NP, NP-hard and NP-complete. P refers to problems that can be solved in polynomial time, while NP includes problems that can be verified in polynomial time.
2) NP-hard problems are at least as hard as the hardest problems in NP. NP-complete problems are the hardest problems in NP. If any NP-complete problem could be solved in polynomial time, then P would be equal to NP.
3) Common NP-complete problems discussed include the traveling salesman problem and integer knapsack problem. Reductions are used to show that one problem is at least as hard as another.
The document discusses the theory of NP-completeness. It begins by defining the complexity classes P, NP, NP-hard, and NP-complete. It then explains the concepts of reduction and how none of the NP-complete problems can be solved in polynomial time deterministically. The document provides examples of NP-complete problems like satisfiability (SAT), vertex cover, and the traveling salesman problem. It shows how nondeterministic algorithms can solve these problems and how they can be transformed into SAT instances. Finally, it proves that SAT is the first NP-complete problem by showing it is in NP and NP-hard.
FP is the set of function problems that can be solved by a deterministic Turing machine in polynomial time. It is the function problem equivalent of P. The difference between FP and P is that FP problems can have any output that can be computed in polynomial time, while P problems only have yes/no answers. FNP is the set of function problems that can be solved by a non-deterministic Turing machine in polynomial time. Whether FP equals FNP depends on whether P equals NP - FP equals FNP if and only if P equals NP.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
pptphrase-tagset-mapping-for-french-and-english-treebanks-and-its-application...Lifeng (Aaron) Han
The document presents a method for unsupervised machine translation evaluation using universal phrase tags. It designs a mapping between phrase tags from different treebanks to 9 universal tags. An unsupervised metric called HPPR is introduced to measure similarity between the universal phrase sequences of the source and translated sentences. Experiments on French-English data show HPPR achieves promising correlations with human judgments without using reference translations.
This document discusses algorithms and problem solving. It covers exploring the algorithmic approach to problem solving, learning about algorithm development, and becoming aware of the problem solving process. Key points include:
- An algorithm is a step-by-step process for solving a problem in a finite number of steps.
- The problem solving process involves analyzing the problem, designing an algorithm to solve it, implementing the algorithm in code, and maintaining the program if needed.
- Object-oriented design methodologies like brainstorming, filtering, scenarios, and responsibility algorithms can help discover algorithms to solve problems.
Harnessing Deep Neural Networks with Logic RulesSho Takase
This document summarizes a method for harnessing deep neural networks with logic rules. The goal is to incorporate general rules and human intuitions into neural networks. Rules are expressed using first-order predicate logic and incorporated into training as constraints. The method alternates between calculating the model distribution subject to constraints (q(y|x)) and updating the model parameters (θ). Experiments on sentiment analysis and named entity recognition show the approach improves performance by enforcing linguistic rules during training.
This document provides an introduction to NP-completeness, including: definitions of key concepts like decision problems, classes P and NP, and polynomial time reductions; examples of NP-complete problems like satisfiability and the traveling salesman problem; and approaches to dealing with NP-complete problems like heuristic algorithms, approximation algorithms, and potential help from quantum computing in the future. The document establishes NP-completeness as a central concept in computational complexity theory.
This document discusses NP-hard and NP-complete problems. It begins by defining the classes P, NP, NP-hard, and NP-complete. It then provides examples of NP-hard problems like the traveling salesperson problem, satisfiability problem, and chromatic number problem. It explains that to show a problem is NP-hard, one shows it is at least as hard as another known NP-hard problem. The document concludes by discussing how restricting NP-hard problems can result in problems that are solvable in polynomial time.
The document provides an overview of theory of computation. It defines computation as any type of information processing that can be represented as a precise algorithm. The theory of computation seeks to define algorithms formally and determine the capabilities and limitations of computation. It comprises three main areas: automata theory, computability, and complexity. Automata theory deals with solving simple decision problems. Computability determines which problems can be solved by computers. Complexity analyzes which problems can be computed efficiently. The document outlines a course on theory of computation covering these topics through examining machines, complexity classes, and the objectives of introducing different computation models and demonstrating uncomputable problems.
This document provides an overview of a course on the design and analysis of computer algorithms taught by Professor David Mount at the University of Maryland in Fall 2003. The course will cover algorithm design techniques like dynamic programming and greedy algorithms. Major topics will include graph algorithms, minimum spanning trees, shortest paths, and computational geometry. Later sections will discuss intractable problems and approximation algorithms. When designing algorithms, students are expected to provide a description, proof of correctness, and analysis of time and space efficiency. Mathematical background on algorithm analysis, including asymptotic notation and recurrences, will be reviewed.
The document discusses NP-complete problems and polynomial-time reductions between them. It summarizes several permutation and subset problems that are known to be NP-complete, including Hamiltonian path/cycle, vertex cover, and 3-SAT. It then describes polynomial-time algorithms for solving some of these problems exactly using a "decision box" that can determine in polynomial time whether an instance has a solution. For example, it presents an O(n) algorithm for finding a minimum vertex cover using a decision box to iteratively test subset sizes.
This document discusses temporal logics for verification including Linear Temporal Logic (LTL) and Metric Temporal Logic (MTL) and their applications to different models like words, timed words, and data words. It introduces the syntax and semantics of LTL, MTL, and extensions of MTL to these different models. It also discusses different decision problems like satisfiability, model checking, and path checking for these logics and complexity results for different classes of structures. Finally, it advertises an open call for a research training group on quantitative logics and automata.
The document summarizes the concepts of P vs NP complexity classes. It states that P problems can be solved in polynomial time, like searching an array, while NP problems are solved in non-deterministic polynomial time, like the knapsack problem. It then defines different types of algorithms and complexity classes. The key classes discussed are P, NP, NP-Complete, and NP-Hard. It provides examples like sorting being in P, while the Hamiltonian problem is NP-Complete. A graphical representation is also included to illustrate the relationships between the complexity classes.
1. An algorithm is a sequence of unambiguous instructions to solve a problem within a finite amount of time. It takes an input, processes it, and produces an output.
2. Designing an algorithm involves understanding the problem, choosing a computational model and problem-solving approach, designing and proving the algorithm's correctness, analyzing its efficiency, coding it, and testing it.
3. Important algorithm design techniques include brute force, divide and conquer, decrease and conquer, transform and conquer, dynamic programming, and greedy algorithms.
This document provides information about a coding session for primary school students. It will introduce students to various coding apps like Scratch Jr, Bee-Bot and Hopscotch. The session is divided into levels for foundation stage, key stage 1 and key stage 2. It includes lesson plans, curriculum links and classroom activities for each app. The goal is to give students an understanding of coding concepts and how these apps can support teaching and learning across different key stages.
Technology Lesson Plan Assignment: Quadratice Functionsdart11746
This technology-infused lesson plan teaches 9th grade students about quadratic functions through a week-long unit. Students will learn to solve and graph quadratic equations and functions algebraically and graphically using tools like graphing calculators, online graphing calculators, and SMART Notebook software. Formative and summative assessments include group presentations and a unit test on quadratic functions. The lesson incorporates student-centered learning and supports various learning styles.
This lesson uses TI-Nspire software to demonstrate quadratic transformations. Students will explore how varying the coefficients a, b, and c affects the graph of the quadratic function. By manipulating sliders to change coefficient values, students can observe the transformations and develop an understanding of each coefficient's impact on the graph. The technology allows students to quickly test conjectures and analyze multiple functions simultaneously. This interactive, exploration-based approach aims to help students discern the relationships between algebraic and graphical representations of quadratics.
The document describes an artifact analyzing quadratic function transformations using Ti-Nspire software, noting how varying the coefficients a, b, and c affects the graph by changing the slope, translating the parabola, or moving it up and down. Students observed the behavior of the graphs under different transformations and noticed that the roots remained at 3 and 5 regardless of the transformations.
Connectionist language models offer many advantages over their statistical counterparts, but they also have some drawbacks like a much more expensive computational cost. This paper describes a novel method to overcome this problem. A set of normalization values associated to the most frequent N-grams is pre-computed and the model is smoothed with lower N-gram connectionist or statistical models. The
proposed approach is favourably compared to standard connectionist language models and with statistical back-off language models.
1) The document discusses the complexity classes P, NP, NP-hard and NP-complete. P refers to problems that can be solved in polynomial time, while NP includes problems that can be verified in polynomial time.
2) NP-hard problems are at least as hard as the hardest problems in NP. NP-complete problems are the hardest problems in NP. If any NP-complete problem could be solved in polynomial time, then P would be equal to NP.
3) Common NP-complete problems discussed include the traveling salesman problem and integer knapsack problem. Reductions are used to show that one problem is at least as hard as another.
The document discusses the theory of NP-completeness. It begins by defining the complexity classes P, NP, NP-hard, and NP-complete. It then explains the concepts of reduction and how none of the NP-complete problems can be solved in polynomial time deterministically. The document provides examples of NP-complete problems like satisfiability (SAT), vertex cover, and the traveling salesman problem. It shows how nondeterministic algorithms can solve these problems and how they can be transformed into SAT instances. Finally, it proves that SAT is the first NP-complete problem by showing it is in NP and NP-hard.
FP is the set of function problems that can be solved by a deterministic Turing machine in polynomial time. It is the function problem equivalent of P. The difference between FP and P is that FP problems can have any output that can be computed in polynomial time, while P problems only have yes/no answers. FNP is the set of function problems that can be solved by a non-deterministic Turing machine in polynomial time. Whether FP equals FNP depends on whether P equals NP - FP equals FNP if and only if P equals NP.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
pptphrase-tagset-mapping-for-french-and-english-treebanks-and-its-application...Lifeng (Aaron) Han
The document presents a method for unsupervised machine translation evaluation using universal phrase tags. It designs a mapping between phrase tags from different treebanks to 9 universal tags. An unsupervised metric called HPPR is introduced to measure similarity between the universal phrase sequences of the source and translated sentences. Experiments on French-English data show HPPR achieves promising correlations with human judgments without using reference translations.
This document discusses algorithms and problem solving. It covers exploring the algorithmic approach to problem solving, learning about algorithm development, and becoming aware of the problem solving process. Key points include:
- An algorithm is a step-by-step process for solving a problem in a finite number of steps.
- The problem solving process involves analyzing the problem, designing an algorithm to solve it, implementing the algorithm in code, and maintaining the program if needed.
- Object-oriented design methodologies like brainstorming, filtering, scenarios, and responsibility algorithms can help discover algorithms to solve problems.
Harnessing Deep Neural Networks with Logic RulesSho Takase
This document summarizes a method for harnessing deep neural networks with logic rules. The goal is to incorporate general rules and human intuitions into neural networks. Rules are expressed using first-order predicate logic and incorporated into training as constraints. The method alternates between calculating the model distribution subject to constraints (q(y|x)) and updating the model parameters (θ). Experiments on sentiment analysis and named entity recognition show the approach improves performance by enforcing linguistic rules during training.
This document provides an introduction to NP-completeness, including: definitions of key concepts like decision problems, classes P and NP, and polynomial time reductions; examples of NP-complete problems like satisfiability and the traveling salesman problem; and approaches to dealing with NP-complete problems like heuristic algorithms, approximation algorithms, and potential help from quantum computing in the future. The document establishes NP-completeness as a central concept in computational complexity theory.
This document discusses NP-hard and NP-complete problems. It begins by defining the classes P, NP, NP-hard, and NP-complete. It then provides examples of NP-hard problems like the traveling salesperson problem, satisfiability problem, and chromatic number problem. It explains that to show a problem is NP-hard, one shows it is at least as hard as another known NP-hard problem. The document concludes by discussing how restricting NP-hard problems can result in problems that are solvable in polynomial time.
The document provides an overview of theory of computation. It defines computation as any type of information processing that can be represented as a precise algorithm. The theory of computation seeks to define algorithms formally and determine the capabilities and limitations of computation. It comprises three main areas: automata theory, computability, and complexity. Automata theory deals with solving simple decision problems. Computability determines which problems can be solved by computers. Complexity analyzes which problems can be computed efficiently. The document outlines a course on theory of computation covering these topics through examining machines, complexity classes, and the objectives of introducing different computation models and demonstrating uncomputable problems.
This document provides an overview of a course on the design and analysis of computer algorithms taught by Professor David Mount at the University of Maryland in Fall 2003. The course will cover algorithm design techniques like dynamic programming and greedy algorithms. Major topics will include graph algorithms, minimum spanning trees, shortest paths, and computational geometry. Later sections will discuss intractable problems and approximation algorithms. When designing algorithms, students are expected to provide a description, proof of correctness, and analysis of time and space efficiency. Mathematical background on algorithm analysis, including asymptotic notation and recurrences, will be reviewed.
The document discusses NP-complete problems and polynomial-time reductions between them. It summarizes several permutation and subset problems that are known to be NP-complete, including Hamiltonian path/cycle, vertex cover, and 3-SAT. It then describes polynomial-time algorithms for solving some of these problems exactly using a "decision box" that can determine in polynomial time whether an instance has a solution. For example, it presents an O(n) algorithm for finding a minimum vertex cover using a decision box to iteratively test subset sizes.
This document discusses temporal logics for verification including Linear Temporal Logic (LTL) and Metric Temporal Logic (MTL) and their applications to different models like words, timed words, and data words. It introduces the syntax and semantics of LTL, MTL, and extensions of MTL to these different models. It also discusses different decision problems like satisfiability, model checking, and path checking for these logics and complexity results for different classes of structures. Finally, it advertises an open call for a research training group on quantitative logics and automata.
The document summarizes the concepts of P vs NP complexity classes. It states that P problems can be solved in polynomial time, like searching an array, while NP problems are solved in non-deterministic polynomial time, like the knapsack problem. It then defines different types of algorithms and complexity classes. The key classes discussed are P, NP, NP-Complete, and NP-Hard. It provides examples like sorting being in P, while the Hamiltonian problem is NP-Complete. A graphical representation is also included to illustrate the relationships between the complexity classes.
1. An algorithm is a sequence of unambiguous instructions to solve a problem within a finite amount of time. It takes an input, processes it, and produces an output.
2. Designing an algorithm involves understanding the problem, choosing a computational model and problem-solving approach, designing and proving the algorithm's correctness, analyzing its efficiency, coding it, and testing it.
3. Important algorithm design techniques include brute force, divide and conquer, decrease and conquer, transform and conquer, dynamic programming, and greedy algorithms.
This document provides information about a coding session for primary school students. It will introduce students to various coding apps like Scratch Jr, Bee-Bot and Hopscotch. The session is divided into levels for foundation stage, key stage 1 and key stage 2. It includes lesson plans, curriculum links and classroom activities for each app. The goal is to give students an understanding of coding concepts and how these apps can support teaching and learning across different key stages.
Technology Lesson Plan Assignment: Quadratice Functionsdart11746
This technology-infused lesson plan teaches 9th grade students about quadratic functions through a week-long unit. Students will learn to solve and graph quadratic equations and functions algebraically and graphically using tools like graphing calculators, online graphing calculators, and SMART Notebook software. Formative and summative assessments include group presentations and a unit test on quadratic functions. The lesson incorporates student-centered learning and supports various learning styles.
This lesson uses TI-Nspire software to demonstrate quadratic transformations. Students will explore how varying the coefficients a, b, and c affects the graph of the quadratic function. By manipulating sliders to change coefficient values, students can observe the transformations and develop an understanding of each coefficient's impact on the graph. The technology allows students to quickly test conjectures and analyze multiple functions simultaneously. This interactive, exploration-based approach aims to help students discern the relationships between algebraic and graphical representations of quadratics.
The document describes an artifact analyzing quadratic function transformations using Ti-Nspire software, noting how varying the coefficients a, b, and c affects the graph by changing the slope, translating the parabola, or moving it up and down. Students observed the behavior of the graphs under different transformations and noticed that the roots remained at 3 and 5 regardless of the transformations.
The document describes an artifact analyzing quadratic function transformations using Ti-Nspire software, noting how varying the coefficients a, b, and c affects the graph by changing the slope, translating the parabola, or moving it up and down. Students observed the behavior of the graphs under different transformations and noticed that the roots remained at 3 and 5 regardless of the transformations.
The document provides guidance on creating an effective board plan for a mathematics lesson. It explains that a board plan is a systematic placement of tasks, problems, and accompanying responses on the board during lesson delivery and discussion. It should anticipate different student responses and tell a storylike progression from objectives to tasks to responses that demonstrates the key concepts without clearing the board. The sample board plan shows tasks, responses, and space for student work and conjectures to generalize concepts and make connections between ideas. The goal is to make the mathematical thinking processes and features of concepts visible through a sequenced set of examples and problems.
This document provides a Flexible Instruction Delivery Plan (FIDP) for a Grade 11 General Mathematics course. The course is delivered over one semester for a total of 80 hours. The core subject aims to teach students how to solve problems involving rational, exponential, and logarithmic functions as well as business-related problems. By the end of the course, students will be able to apply their mathematical knowledge to real-life situations. The FIDP outlines 4 quarters of content covering Functions, Rational Functions, Inverse Functions, Exponential and Logarithmic Functions, and Business Mathematics. Each section includes learning competencies, assessment strategies, and performance standards to measure student understanding.
1. The document discusses various ways to incorporate technology into math teaching including applets, blogging, collaborative projects, fractals, GPS navigation, and online math practice tools.
2. It provides examples of math-related activities and lessons involving topics like cryptology, dance, earth science, estimation, history, and weather that integrate math concepts.
3. The document emphasizes that developing students' mathematical understanding is more important than rote computation skills and that challenging gifted students with advanced concepts does not have to wait until basic skills are mastered.
The document discusses designing a systemic K-12 Common Core State Standards mathematics curriculum. It outlines a multi-phase process for task forces to collaboratively design units that vertically and horizontally align standards across grades. Specifically, it describes designing unit names, enduring understandings, essential questions, standards for mathematical practice, and vocabulary before integrating these elements into units of study. The document provides examples of how other states have structured their CCSS math course design and unit mapping.
This document summarizes a computer science lesson on algorithms and flowcharts. It discusses defining sequential, selective, and repetitive constructs to represent program flow. Sequential constructs execute steps strictly in order. Selection constructs execute code conditionally. Iterative constructs allow statements to repeat until a condition is met. Examples are given of algorithms and flowcharts for calculating averages, finding the largest of two numbers, and counting from 1 to 10. Students are asked to complete homework on algorithm characteristics, summing 10 numbers, and the Fibonacci series.
This lesson plan describes a 30-minute lesson for secondary school students on graphs of quadratic equations. Students will learn about the properties of quadratic graphs like maximum/minimum points and lines of symmetry. They will also learn about the effects of the a, b, and c coefficients in the quadratic equation y=ax^2 + bx + c. Students will work in pairs using the Nspire graphing calculator software to explore quadratic graphs. The teacher will assess students informally through their worksheet answers and formally through their graphed assignments and an upcoming test.
1. The document discusses logarithmic functions, including graphing logarithmic functions, determining their domain and range, and finding intercepts, zeros, and asymptotes.
2. It provides an example of graphing the function y = log2x and discusses key features of logarithmic graphs like being defined only for positive x-values and having a vertical asymptote at x = 0.
3. Determining the domain of a logarithmic function involves setting the argument greater than 0 and solving the inequality to find the domain interval. The range of a logarithmic function is all real numbers.
Here are the answers to the drill questions:
1. y = log2 X ; if x = 2
Given: x = 2
To find: y
Using the definition of logarithm: logb x is the power to which the base b must be raised to produce the value x.
Since 2 = 20, y = 0
2. y = log1/2 X
Given: No value of x is given
To find: y
Using the definition of logarithm: logb x is the power to which the base b must be raised to produce the value x.
Since the base is 1/2, which is less than 1, there is no value of x that can satisfy this
This document provides an overview of the Maple T.A. system, which is a web-based tool for automatically generating, assessing, and providing feedback on mathematical exercises. It can generate various question types and uses Maple to evaluate symbolic responses. The document demonstrates the student, instructor, and author interfaces and discusses strengths such as the variety of questions that can be created, as well as weaknesses like limited feedback and usability issues. Major challenges for CAS-based assessment tools are also outlined.
This lesson plan teaches secondary 3 students how to sketch exponential and logarithmic graphs using Graphmatica software. Students will work individually on computers to sketch graphs, indicating asymptotes and intercepts. They will analyze patterns to deduce shapes of other graphs. The lesson aims to develop analytical and problem solving skills. Students are assessed based on their ability to correctly complete a homework worksheet applying concepts from the lesson.
This document provides an overview of the CS760 Machine Learning course taught by David Page at the University of Wisconsin. The course will cover a broad survey of machine learning algorithms and applications over 30 class meetings. Topics will include both theoretical and practical aspects of supervised learning algorithms like naive Bayes, decision trees, neural networks, and support vector machines. Students will complete programming homework assignments applying various machine learning algorithms and a midterm exam. The primary goals of the course are to understand what learning systems should do and how existing systems work.
This document outlines the syllabus for a machine learning course. It introduces the instructor, teaching assistant, required textbook, and meeting schedule. It describes the course style as primarily algorithmic and experimental, covering many ML subfields. The goals are to understand what a learning system should do and how existing systems work. Background knowledge in languages, AI topics, and math is assumed, but no prior ML experience is needed. Requirements include biweekly programming homework, a midterm exam, and a final project. Grading will be based on homework, exam, project, and discussion participation. Policies on late homework and academic misconduct are also provided.
This document provides an overview of object-oriented programming (OOP) including:
- The history and key concepts of OOP like classes, objects, inheritance, polymorphism, and encapsulation.
- Popular OOP languages like C++, Java, and Python.
- Differences between procedural and OOP like top-down design and modularity.
In the last few decades the field of Information and Communication Technology (ICT) has made a swift progress. The growing role of computers in education is beyond doubt and has become essential for higher educational institutions for teaching and instructional purposes to improve the quality and efficiency of both teaching and learning
Fosdem 2013 petra selmer flexible querying of graph dataPetra Selmer
These are the slides from a talk I presented at the Graph Processing room at FOSDEM 2013, in which I discussed my PhD topic: a query language allowing for the flexible querying of complex paths within graph structured data
Similar to Teaching algebra through functional programming (20)
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...Diana Rendina
Librarians are leading the way in creating future-ready citizens – now we need to update our spaces to match. In this session, attendees will get inspiration for transforming their library spaces. You’ll learn how to survey students and patrons, create a focus group, and use design thinking to brainstorm ideas for your space. We’ll discuss budget friendly ways to change your space as well as how to find funding. No matter where you’re at, you’ll find ideas for reimagining your space in this session.
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
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This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
9. With support from the US Office of
Naval Research, Logo was pilot-
tested in the summer of 1967 with
fifth- and sixth-grade math students.
10. The reason that a laboratory is not traditionally used in
mathematical study is not that it would be less valuable there
than in biology, chemistry, or physics; rather, the idea of a
mathematical experiment was, until recently, unrealizable, and
barely conceivable, except in very special or superficial senses.
How could a person set in motion a sequence of
mathematical events or a mathematical process, and then see
its effects unfold? Using a computer with an appropriate
programming language adds this extra dimension to mathe-
matical experience; the important contribution of the computer
is a new and powerful operational universe for mathematical
experiment
By W. Feurzeig, S. Papert, Mo Bloom, R. Grant, C. Solomon.
Taken from the Final Report on the first fifteen months of the LOGO Project,
November 30, 1969.
Submitted to the National Science Foundation on Contract NSF-C 558.
Copies will be available from ERIC
11. Programming can be used to give students very
specific insights into a number of key concepts.
Ideas such as variable and function remain, to say
the least, obscure for many high school students.
Indeed, college students often have trouble with the
many roles of the “x” in algebra: sometimes it
appears to be a number, sometimes a subtly
different kind of object called a variable, and on
other occasions it is to be treated as a function…
In programming, the distinctions arise concretely.
By W. Feurzeig, S. Papert, Mo Bloom, R. Grant, C. Solomon.
Taken from the Final Report on the first fifteen months of the LOGO Project,
November 30, 1969.
Submitted to the National Science Foundation on Contract NSF-C 558.
Copies will be available from ERIC
19. Definition of a function
› a relationship or expression involving one or more
variables (dictionary.com)
› a mathematical correspondence that assigns exactly one
element of one set to each element of the same or
another set (merriam-webster.com)
› a process or a relation that associates each element x of
a set X, the domain of the function, to a single
element y of another set Y (wikipedia)
24. Students create a simple, 3-character game involving a
player, a target and a danger. They design what each
character looks like, and use algebraic concepts to detect
collisions.
25. Introduction to Scheme
› Prefix language with parenthesis
› (+ 1 2)
› (define (foo (a b)) (+ a b))
› (define (foo (a b c)) (+ a (- b c)))
26. WeScheme (a subset of Scheme)
› Students are given
predefined functions for
– IO
– higher-order functions
› Are able to focus on
calculations
33. double distance(int x, int y, int x1, int y1) {
double aSquared = Math.pow(x - x1, 2);
double bSquared = Math.pow(y - y1, 2);
double cSquared = aSquared + bSquared;
return Math.sqrtc(cSquared);
}
Why Scheme? Why not Java?
A first course in computer programming should not be about the current “hot”
language in industry – which may be obsolete by the time today’s freshmen
graduate – but rather about lasting, transferable concepts and practices of good
programming. Yet beginning programming students spend much of their time
wrestling with the language, and often mistake that as the subject of the course; the
programming language distracts from the course material. – Stephen Bloch
(Math/CS Department Adelphi University)
34. Why Scheme?
› Syntax is simple
– Parenthesis
– Operators
– define keyword
› Functional
– Not imperative
35. Study on Bootstrap Curriculum
› The Bootstrap curriculum was taught at two schools
› An assessment on math skills was given before and after
the course to both the study and control groups
› Assessments were statistically analyzed
› Interviews were conducted with all the participants in the
Bootstrap course
36. Bootstrap course #1
› Taught at a middle school as an after school class
› Participants volunteered
– 14 started the course, 9 finished
› The course lasted about 6 weeks
– Twice a week
– 1 ½ hours each class
› Control group was a CTE (Careers, Technology,
Engineering) class
37. Bootstrap course #2
› Taught at a high school during school
› Participants where chosen by administration
– juniors and seniors who could not pass basic algebra
– students received ½ math credit for participation in math
– 14 started the course, 9 finished
› The course lasted about 6 weeks
– Twice a week
– 1 ½ hours each class
› Control group was a CTE (Careers, Technology,
Engineering) class
38. A friend sees the word “function” in your math book
and asks what it means. In terms of mathematics,
how do you explain “function” to them?
Given 𝑓 𝑥 = 5(𝑥 + 3), find 𝑓(5 − 𝑛)
Assessment Questions for understanding of
Functions
42. Transfer from Scheme to Algebra
(define distance (x y x1 y1)
(sqrt
(+ (sq (-(x x1) sq(- (b b1)))))
𝑓 𝑥, 𝑥1
, 𝑦, 𝑦1
= (𝑥1 − 𝑥)2+(𝑦1 − 𝑦)2
43. Consider the following function:
On a graph, plot and label and .
How far apart are the two points?
Show your work.
f (x) = 3
4 x + 2
f (0) f (4)
Using the following two functions,
find the value of the composite function, f (g(5)).
Show your work.
f (x) = 2x
g(y) = y2
Questions on Transferring Programming
Functions to Algebra Functions
47. Observations
› Students in both study and control groups didn’t answer
the harder questions
› In interviews with the study group
– when asked why they didn’t answer the hard questions
– did not remember what the syntax meant
– said the algebra syntax looked scary
– students very comfortable with the Scheme syntax
48. 𝑓 𝑎, 𝑏 = 𝑎2 + 𝑏2
Students found math syntax confusing or
scary – despite some brief coaching
49. (define distance (a b)
(sqrt
(+ (sq a) sq(b))))
Students showed in interview they were comfortable with
Scheme Syntax, probably because they had worked with it
in building their games.
50.
51. Conclusions
› Programming in most languages can teach some math
principles
– PEMDAS
– Cartesian Planes
– Formulas like Pythagorean Theorem
› Programming does not transfer well to math
symbols/syntax
– Unfamiliarity
– The term scary is used
› Programming can teach Computational Thinking
52. Conclusions
› Functional Programming is very good at teaching
functions
› The understanding of functions gained may help with the
concept in later education
53. The demonstration of positive transfer from
programming into algebra is exciting, but the
findings should not be generalized to suggest that
merely “learning to program” would result in
mathematical gains for students. Bootstrap’s
success rests on a conscious selection of
programming language, software tools, curriculum
and pedagogical practice that are drawn from
the algebraic domain.
-Emanuel Schanzer in his Doctoral Thesis