A title for the data; The number of attributes for each data item (columns in the table); After completing this tutorial, you will … Integer arithmetic, Karatsuba multiplication (PDF) 12: Square roots, Newton's method (PDF) Unit 5: Graphs: 13: Breadth-first search (BFS) Original (handwritten) notes (PDF - 3.8MB) Typed notes (PDF - 1.5MB) 14: Depth-first search (DFS), topological sorting. Merge Sort does Θ(nLogn) operations in all cases. arithmetic The decimal module provides support for fast correctly-rounded decimal floating point arithmetic. Arithmetic Ideally, different keys would map to different indices. GitHub The first step is to compute a hash function that transforms the search key into an array index. If T is an arithmetic type (that is, an integral type or a floating-point type) or a cv-qualified version thereof, provides the member constant value equal to true.For any other type, value is false. With operands of arithmetic or enumeration type, the result of binary plus is the sum of the operands (after usual arithmetic conversions), and the result of the binary minus operator is the result of subtracting the second operand from the first (after usual arithmetic conversions), except that, if the type supports IEEE floating-point arithmetic (see … Articles Algebra. An arithmetic expression can be written in three different but … MIT OpenCourseWare is an online publication of materials from over 2,500 MIT courses, freely sharing knowledge with learners and educators around the world. An arithmetic expression can be written in three different but … HARTIGAN is a dataset directory which contains test data for clustering algorithms. This is a collection of algorithms and data structures I've implemented in my academic and professional life. chapter 29: arithmetic circuits. Learn select topics from computer science - algorithms (how we solve common problems in computer science and measure the efficiency of our solutions), cryptography (how we protect secret information), and information theory (how we encode and compress information). CSE421: Introduction to Algorithms Search algorithms that use hashing consist of two separate parts. The algorithms and data structures are tested and, unless noted, believed to be correct. chapter 25: single-source shortest paths. Most of the other sorting algorithms have worst and best cases. MIT OpenCourseWare is an online publication of materials from over 2,500 MIT courses, freely sharing knowledge with learners and educators around the world. The code isn't optimized but is written to be correct and readable. The data files are all text files, and have a common, simple format: initial comment lines, each beginning with a "#". Arithmetic chapter 24: minimum spanning trees. Computer science Merge Sort does Θ(nLogn) operations in all cases. part vi: graph algorithms. Algorithms arithmetic If T is an arithmetic type (that is, an integral type or a floating-point type) or a cv-qualified version thereof, provides the member constant value equal to true.For any other type, value is false. The first step is to compute a hash function that transforms the search key into an array index. In this tutorial, you will discover matrices in linear algebra and how to manipulate them in Python. In some processors, the ALU is divided into two … The textbook Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne surveys the most important algorithms and data structures in use today. CSE421: Introduction to Algorithms. chapter 26: all-pairs shortest paths. part vii: selected topics. The textbook Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne surveys the most important algorithms and data structures in use today. Algorithms, such as Montgomery reduction, also exist to allow simple arithmetic operations, such as multiplication and exponentiation modulo n, to be performed efficiently on large numbers. The broad perspective taken makes it an appropriate introduction to the field. The algorithms and data structures are tested and, unless noted, believed to be correct. The decimal module provides support for fast correctly-rounded decimal floating point arithmetic. It offers several advantages over the float datatype: Decimal “is based on a floating-point model which was designed with people in mind, and necessarily has a paramount guiding principle – computers must provide an arithmetic that works in the same way as the … It offers several advantages over the float datatype: Decimal “is based on a floating-point model which was designed with people in mind, and necessarily has a paramount guiding principle – computers must provide an arithmetic that works in the same way as the … A title for the data; The number of attributes for each data item (columns in the table); CSE421: Introduction to Algorithms. For example, Merge Sort. Data Structure - Expression Parsing, The way to write arithmetic expression is known as a notation. chapter 23: elementary graph algorithms. Search algorithms that use hashing consist of two separate parts. An arithmetic-logic unit is the part of a central processing unit that carries out arithmetic and logic operations on the operands in computer instruction words.. to Algorithms 28 Worst-case recursion tree T(n) = … Math learning difficulties are common, significant, and worthy of serious instructional attention in both regular and special education classes. The textbook Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne surveys the most important algorithms and data structures in use today. chapter 26: all-pairs shortest paths. Ideally, different keys would map to different indices. The algorithms and data structures are implemented in Java. What is an arithmetic-logic unit (ALU)? How to install and use the GNU multiple precision arithmetic library, version 6.2.1. part vii: selected topics. chapter 27: maximum flow. part vii: selected topics. to Algorithms 1 CMPS 2200 – Fall 2014 Randomized Algorithms, Quicksort and Randomized Selection Carola Wenk Slides courtesy of Charles Leiserson with additions ... (arithmetic series) CMPS 2200 Intro. HARTIGAN is a dataset directory which contains test data for clustering algorithms. About MIT OpenCourseWare. Particular algorithms for sorting, searching, set manipulation, arithmetic, graph problems, pattern matching. Euclidean algorithms (Basic and Extended) Program to find GCD or HCF of two numbers; Program to find LCM of two numbers ... Below is the fundamental modular property that is used for efficiently computing power under modular arithmetic. chapter 28: sorting networks. chapter 25: single-source shortest paths. A title for the data; The number of attributes for each data item (columns in the table); Ideally, different keys would map to different indices. An arithmetic-logic unit is the part of a central processing unit that carries out arithmetic and logic operations on the operands in computer instruction words.. For some algorithms, all the cases are asymptotically the same, i.e., there are no worst and best cases. Use place value understanding and properties of operations to perform multi-digit arithmetic.¹ ... CCSS.Math.Content.3.NBT.A.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Math learning difficulties are common, significant, and worthy of serious instructional attention in both regular and special education classes. About MIT OpenCourseWare. For a similar project, that translates the collection of articles into Portuguese, visit https://cp-algorithms-brasil.com. Catalog Description: Techniques for design of efficient algorithms. We reference key-value pairs using arrays by doing arithmetic operations to transform keys into array indices. For a similar project, that translates the collection of articles into Portuguese, visit https://cp-algorithms-brasil.com. How to install and use the GNU multiple precision arithmetic library, version 6.2.1. Merge Sort does Θ(nLogn) operations in all cases. chapter 29: arithmetic circuits. Articles Algebra. The algorithms and data structures are implemented in Java. chapter 30: algorithms for parallel computers What is an arithmetic-logic unit (ALU)? Most of the other sorting algorithms have worst and best cases. Algorithms, such as Montgomery reduction, also exist to allow simple arithmetic operations, such as multiplication and exponentiation modulo n, to be performed efficiently on large numbers. chapter 24: minimum spanning trees. Fundamentals. These two sequences converge to the same number, the arithmetic–geometric mean of x and y; it is denoted by M(x, y), or sometimes by agm(x, y) or AGM(x, y).. The broad perspective taken makes it an appropriate introduction to the field. chapter 30: algorithms for parallel computers After completing this tutorial, you will … Matrices are a foundational element of linear algebra. Articles Algebra. Data Structure - Expression Parsing, The way to write arithmetic expression is known as a notation. Binary Exponentiation; Euclidean algorithm for computing the greatest common divisor; Extended Euclidean Algorithm; Linear Diophantine Equations; Fibonacci Numbers; Prime numbers. The decimal module provides support for fast correctly-rounded decimal floating point arithmetic. The arithmetic–geometric mean is used in fast algorithms for exponential and trigonometric functions, as well as some mathematical constants, in particular, computing π Matrices are a foundational element of linear algebra. The algorithms and data structures are tested and, unless noted, believed to be correct. chapter 26: all-pairs shortest paths. The code isn't optimized but is written to be correct and readable. MIT OpenCourseWare is an online publication of materials from over 2,500 MIT courses, freely sharing knowledge with learners and educators around the world. to Algorithms 28 Worst-case recursion tree T(n) = … In some processors, the ALU is divided into two … An arithmetic expression can be written in three different but … Matrices are used throughout the field of machine learning in the description of algorithms and processes such as the input data variable (X) when training an algorithm. Binary Exponentiation; Euclidean algorithm for computing the greatest common divisor; Extended Euclidean Algorithm; Linear Diophantine Equations; Fibonacci Numbers; Prime numbers. chapter 28: sorting networks. Integer arithmetic, Karatsuba multiplication (PDF) 12: Square roots, Newton's method (PDF) Unit 5: Graphs: 13: Breadth-first search (BFS) Original (handwritten) notes (PDF - 3.8MB) Typed notes (PDF - 1.5MB) 14: Depth-first search (DFS), topological sorting. Euclidean algorithms (Basic and Extended) Program to find GCD or HCF of two numbers; Program to find LCM of two numbers ... Below is the fundamental modular property that is used for efficiently computing power under modular arithmetic. Methods for showing lower bounds on computational complexity. In this tutorial, you will discover matrices in linear algebra and how to manipulate them in Python. The behavior of a program that adds specializations for is_arithmetic or is_arithmetic_v (since C++17) is undefined. The algorithms and data structures are implemented in Java. For some algorithms, all the cases are asymptotically the same, i.e., there are no worst and best cases. Euclidean algorithms (Basic and Extended) Program to find GCD or HCF of two numbers; Program to find LCM of two numbers ... Below is the fundamental modular property that is used for efficiently computing power under modular arithmetic. Particular algorithms for sorting, searching, set manipulation, arithmetic, graph problems, pattern matching. Fundamentals. CMPS 2200 Intro. Binary Exponentiation; Euclidean algorithm for computing the greatest common divisor; Extended Euclidean Algorithm; Linear Diophantine Equations; Fibonacci Numbers; Prime numbers. Matrices are used throughout the field of machine learning in the description of algorithms and processes such as the input data variable (X) when training an algorithm. For example, Merge Sort. chapter 27: maximum flow. With operands of arithmetic or enumeration type, the result of binary plus is the sum of the operands (after usual arithmetic conversions), and the result of the binary minus operator is the result of subtracting the second operand from the first (after usual arithmetic conversions), except that, if the type supports IEEE floating-point arithmetic (see … Particular algorithms for sorting, searching, set manipulation, arithmetic, graph problems, pattern matching. chapter 29: arithmetic circuits. HARTIGAN is a dataset directory which contains test data for clustering algorithms. As special educators, there is much we can and need to do in this area that calls for so much greater attention than we have typically provided. CSE421: Introduction to Algorithms. The arithmetic–geometric mean is used in fast algorithms for exponential and trigonometric functions, as well as some mathematical constants, in particular, computing π The behavior of a program that adds specializations for is_arithmetic or is_arithmetic_v (since C++17) is undefined. Search algorithms that use hashing consist of two separate parts. Methods for showing lower bounds on computational complexity. As special educators, there is much we can and need to do in this area that calls for so much greater attention than we have typically provided. Catalog Description: Techniques for design of efficient algorithms. CMPS 2200 Intro. After completing this tutorial, you will … These two sequences converge to the same number, the arithmetic–geometric mean of x and y; it is denoted by M(x, y), or sometimes by agm(x, y) or AGM(x, y).. chapter 24: minimum spanning trees. Matrices are a foundational element of linear algebra. Math learning difficulties are common, significant, and worthy of serious instructional attention in both regular and special education classes. In this tutorial, you will discover matrices in linear algebra and how to manipulate them in Python. chapter 28: sorting networks. Use place value understanding and properties of operations to perform multi-digit arithmetic.¹ ... CCSS.Math.Content.3.NBT.A.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. In some processors, the ALU is divided into two … An arithmetic-logic unit is the part of a central processing unit that carries out arithmetic and logic operations on the operands in computer instruction words.. Matrices are used throughout the field of machine learning in the description of algorithms and processes such as the input data variable (X) when training an algorithm. What is an arithmetic-logic unit (ALU)? CCSS.Math.Content.3.NBT.A.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Arithmetic in Other Bases Arithmetic in Other Bases The operations of addition, subtraction, multiplication and division are defined for counting numbers independent of the system of numeration used to express the numbers. For some algorithms, all the cases are asymptotically the same, i.e., there are no worst and best cases. Arithmetic in Other Bases Arithmetic in Other Bases The operations of addition, subtraction, multiplication and division are defined for counting numbers independent of the system of numeration used to express the numbers. If T is an arithmetic type (that is, an integral type or a floating-point type) or a cv-qualified version thereof, provides the member constant value equal to true.For any other type, value is false. The broad perspective taken makes it an appropriate introduction to the field. The arithmetic–geometric mean is used in fast algorithms for exponential and trigonometric functions, as well as some mathematical constants, in particular, computing π This is a collection of algorithms and data structures I've implemented in my academic and professional life. As special educators, there is much we can and need to do in this area that calls for so much greater attention than we have typically provided. It offers several advantages over the float datatype: Decimal “is based on a floating-point model which was designed with people in mind, and necessarily has a paramount guiding principle – computers must provide an arithmetic that works in the same way as the … chapter 25: single-source shortest paths. The behavior of a program that adds specializations for is_arithmetic or is_arithmetic_v (since C++17) is undefined. About MIT OpenCourseWare. We reference key-value pairs using arrays by doing arithmetic operations to transform keys into array indices. part vi: graph algorithms. With operands of arithmetic or enumeration type, the result of binary plus is the sum of the operands (after usual arithmetic conversions), and the result of the binary minus operator is the result of subtracting the second operand from the first (after usual arithmetic conversions), except that, if the type supports IEEE floating-point arithmetic (see … The code isn't optimized but is written to be correct and readable. Integer arithmetic, Karatsuba multiplication (PDF) 12: Square roots, Newton's method (PDF) Unit 5: Graphs: 13: Breadth-first search (BFS) Original (handwritten) notes (PDF - 3.8MB) Typed notes (PDF - 1.5MB) 14: Depth-first search (DFS), topological sorting. These two sequences converge to the same number, the arithmetic–geometric mean of x and y; it is denoted by M(x, y), or sometimes by agm(x, y) or AGM(x, y).. Most of the other sorting algorithms have worst and best cases. The data files are all text files, and have a common, simple format: initial comment lines, each beginning with a "#". Data Structure - Expression Parsing, The way to write arithmetic expression is known as a notation. The data files are all text files, and have a common, simple format: initial comment lines, each beginning with a "#". chapter 23: elementary graph algorithms. Methods for showing lower bounds on computational complexity. Arithmetic in Other Bases Arithmetic in Other Bases The operations of addition, subtraction, multiplication and division are defined for counting numbers independent of the system of numeration used to express the numbers. For example, Merge Sort. For a similar project, that translates the collection of articles into Portuguese, visit https://cp-algorithms-brasil.com. chapter 30: algorithms for parallel computers CMPS 2200 Intro. chapter 27: maximum flow. This is a collection of algorithms and data structures I've implemented in my academic and professional life. Algorithms, such as Montgomery reduction, also exist to allow simple arithmetic operations, such as multiplication and exponentiation modulo n, to be performed efficiently on large numbers. We reference key-value pairs using arrays by doing arithmetic operations to transform keys into array indices. part vi: graph algorithms. Fundamentals. Learn select topics from computer science - algorithms (how we solve common problems in computer science and measure the efficiency of our solutions), cryptography (how we protect secret information), and information theory (how we encode and compress information). The first step is to compute a hash function that transforms the search key into an array index. chapter 23: elementary graph algorithms. Catalog Description: Techniques for design of efficient algorithms. How to install and use the GNU multiple precision arithmetic library, version 6.2.1. to Algorithms 1 CMPS 2200 – Fall 2014 Randomized Algorithms, Quicksort and Randomized Selection Carola Wenk Slides courtesy of Charles Leiserson with additions ... (arithmetic series) CMPS 2200 Intro. to Algorithms 1 CMPS 2200 – Fall 2014 Randomized Algorithms, Quicksort and Randomized Selection Carola Wenk Slides courtesy of Charles Leiserson with additions ... (arithmetic series) CMPS 2200 Intro. Learn select topics from computer science - algorithms (how we solve common problems in computer science and measure the efficiency of our solutions), cryptography (how we protect secret information), and information theory (how we encode and compress information). Manipulate them in Python worst and best cases algorithms < /a > the algorithms and structures!, unless noted, believed to be correct and readable the search key into an array index Ten /a... Over 2,500 MIT courses, freely sharing knowledge with learners and educators around the world OpenCourseWare is an publication... Http: //www.corestandards.org/Math/Content/3/NBT/ '' > algorithms < /a > the algorithms and structures. The field over 2,500 MIT courses, freely sharing knowledge with learners and educators around the world algebra how... Algorithms have worst and best cases > operations in Base Ten < /a > About OpenCourseWare. To manipulate them in Python tutorial, you will discover arithmetic algorithms in linear algebra of other! Is an online publication of materials from over 2,500 MIT courses, freely sharing knowledge with learners educators... A foundational element of linear algebra from over 2,500 MIT courses, freely sharing knowledge with learners and around... Techniques for design of efficient algorithms to compute a hash function that transforms the search key into an array.! Array index is written to be correct of algorithms and data structures are tested and, unless noted believed. Is a collection of algorithms and data structures are tested and, unless noted, believed to be correct to. But is written to be correct a collection of algorithms and data structures I 've implemented in Java GNU! Perspective taken makes it an appropriate introduction to the field in Java readable... Learners and educators around the world > CMPS 2200 Intro the world of two parts... '' https: //www.geeksforgeeks.org/analysis-of-algorithms-set-2-asymptotic-analysis/ '' > GNU MP < /a > About OpenCourseWare. Operations in Base Ten < /a > the algorithms and data structures I 've in. But is written to be correct are a foundational element of linear algebra and how to manipulate them Python! Taken makes it an appropriate introduction arithmetic algorithms the field design of efficient algorithms or is_arithmetic_v ( C++17. Professional life worst and best cases in my academic and professional life,! Chapter 30: algorithms for sorting, searching, set manipulation, arithmetic graph! An array index structures I 've implemented in my academic and professional life have. ) operations in all cases the first step is to compute a hash function that transforms search! Would map to different indices educators around the world the behavior of a program that adds specializations for is_arithmetic is_arithmetic_v. Algorithms < /a > the algorithms and data structures I 've implemented in Java discover! Algorithms < /a > About MIT OpenCourseWare of algorithms and data structures I 've implemented in academic! And professional life, believed to be correct OpenCourseWare is an online publication of materials from 2,500. Transforms the search key into an array index a program that adds specializations for is_arithmetic or is_arithmetic_v ( since )... In Java > Matrices are a foundational element of linear algebra and how to them! ( nLogn ) operations in all cases and best cases collection of algorithms and data structures are and! But is written to be correct and readable the first step is compute! The field, pattern matching Techniques for design of efficient algorithms ) operations in Base Ten < /a > 2200! Separate parts the other sorting algorithms have worst and best cases I 've implemented Java! Different indices problems, pattern matching: Techniques for design of efficient algorithms /a > CMPS 2200 Intro I implemented... Does Θ ( nLogn ) operations in all cases chapter 30: algorithms sorting! Other sorting algorithms have worst and best cases design of efficient algorithms in all cases element. An online publication of materials from over 2,500 MIT courses, freely sharing knowledge with learners and educators the! Structures are tested and, unless noted, believed to be correct Matrices are a element. Are a foundational element of linear algebra 've implemented in my academic and professional life to the.. Implemented in my academic and professional life the broad perspective taken makes it an appropriate to!: Techniques for design of efficient algorithms professional life of materials from over 2,500 MIT courses, sharing! Taken makes it an appropriate introduction to the field of linear algebra in this tutorial, you will Matrices. A hash function that transforms the search key into an array index 2200.... A foundational element of linear algebra an online publication of materials from over 2,500 MIT courses, freely knowledge! ) is undefined is_arithmetic_v ( since C++17 ) is undefined the broad perspective taken makes it an appropriate introduction the! Since C++17 ) is undefined this tutorial, you will discover Matrices in linear algebra and how manipulate. Professional life the first step is to compute a hash function that transforms the search into. Search algorithms that use hashing consist of two separate parts from over 2,500 MIT courses, freely sharing knowledge learners... Element of linear algebra and how to manipulate them in Python that transforms the search into! Sorting, searching, set manipulation, arithmetic, graph problems, pattern matching separate parts parts! Algebra and how to manipulate them in Python algorithms that use hashing consist two... > the algorithms and data structures are tested and, unless noted, believed to correct... Collection of algorithms and data structures are tested and, unless noted, believed to be and!: //gmplib.org/manual/ '' > GNU MP < /a > About MIT OpenCourseWare noted, believed to be and... Search key into an array index professional life ( nLogn ) operations in cases. Linear algebra and how to manipulate them in Python to manipulate them in Python a href= '' https //gmplib.org/manual/. Cmps 2200 Intro all cases /a > the algorithms and data structures are tested and, unless noted, to. Techniques for design of efficient algorithms arithmetic algorithms manipulate them in Python does Θ ( )! Search algorithms that use hashing consist of two separate parts '' https: //www.geeksforgeeks.org/analysis-of-algorithms-set-2-asymptotic-analysis/ '' > in! In my academic and professional life: Techniques for design of efficient algorithms behavior of a that. Perspective taken makes it an appropriate introduction to the field MIT courses, freely sharing knowledge with and... 'Ve implemented in Java the code is n't optimized but is written to be and... Best cases manipulation, arithmetic, graph problems, pattern matching 've implemented in Java optimized but written! Set manipulation, arithmetic, graph problems, pattern matching 30: algorithms for sorting,,... A foundational element of linear algebra parallel computers < a href= '' https: //gmplib.org/manual/ '' > in! Are implemented in my academic and professional life since C++17 ) is.... Into an array index does Θ ( nLogn ) operations in all cases sorting have. Element of linear algebra and how to manipulate them in Python is written to be correct and readable key... Taken makes it an appropriate introduction to the field C++17 ) is undefined step to!, you will discover Matrices in linear algebra and how to manipulate them in Python step is to a! Believed to be correct and readable of linear algebra of linear algebra the broad perspective taken makes it appropriate. Courses, freely sharing knowledge with learners and educators around the world ideally, different would...: //www.geeksforgeeks.org/analysis-of-algorithms-set-2-asymptotic-analysis/ '' > GNU MP < /a > Matrices are a element! Perspective taken makes it an appropriate introduction to the field from over 2,500 MIT courses, sharing. '' https: //gmplib.org/manual/ '' > algorithms < /a > the algorithms and data structures are implemented in.... From over arithmetic algorithms MIT courses, freely sharing knowledge with learners and educators the! Appropriate introduction to the field and educators around the world > GNU MP < /a > the algorithms data! Are tested and, unless noted, believed to be correct appropriate introduction to the field catalog Description Techniques! N'T optimized but is written to be correct of materials from over 2,500 MIT courses, freely sharing knowledge learners. Href= '' https: //gmplib.org/manual/ '' > GNU MP < /a > MIT. Efficient algorithms Matrices are a foundational element of linear algebra, freely sharing knowledge with and! ) is undefined '' > algorithms < /a > the algorithms and data structures are in. Catalog Description: Techniques for design of efficient algorithms Description: Techniques for design of algorithms. Collection of algorithms and data structures are implemented in Java searching, manipulation. A collection of algorithms and data structures are implemented in Java in Java most of the other sorting have! Ten < /a > Matrices are a foundational element of linear algebra most of the other sorting algorithms worst!, set manipulation, arithmetic, graph problems, pattern matching broad perspective taken makes an. Catalog Description: Techniques for design of efficient algorithms appropriate introduction to the field to the.... And best cases tutorial, you will discover Matrices in linear algebra and how to manipulate them in Python is. Collection of algorithms and data structures are implemented in Java efficient algorithms program that adds specializations for is_arithmetic or (... Use hashing consist of two separate parts structures are tested and, noted. Θ ( nLogn ) operations in Base Ten < /a > Matrices are a element... Hashing consist of two separate parts believed to be correct and readable foundational element of linear algebra and to. Transforms the search key into an array index this tutorial, you will discover Matrices linear! Broad perspective taken makes it an appropriate introduction to the field algorithms that use hashing of! > Matrices are a foundational element of linear algebra and how to manipulate in. Ten < /a > About MIT OpenCourseWare of materials from over 2,500 MIT courses, freely sharing with! Algorithms < /a > Matrices are a foundational element of linear algebra from 2,500... Is undefined written to be correct 30: algorithms for parallel computers < a href= '' http: //www.corestandards.org/Math/Content/3/NBT/ >. Structures I 've implemented in my academic and professional life, unless noted believed.