This document contains notes from several coding lectures and labs. It discusses using loops to draw different shapes on a 2D grid, including lines, squares, and diagonals using only a single loop. Methods for drawing horizontal, vertical, and diagonal lines are explained. Transformations like moving, flipping, and rotating shapes on the grid are also covered through examples of changing the row and column indices in the drawing loops.
This document summarizes a slide presentation on string methods and debugging in Java. It provides examples of common string methods like charAt, compareTo, indexOf, replace, and substring. It also briefly explains how to debug programs using breakpoints and stepping through code line-by-line.
This document provides a summary of lecture 4 of the MIT OpenCourseWare course 6.094 Introduction to MATLAB. The lecture covers advanced MATLAB methods including probability and statistics, data structures like cells and structs, images and animation, debugging tools, and an introduction to symbolic math and various MATLAB toolboxes. Key concepts are demonstrated through examples and exercises.
1st prep.sheet فى الجبر والهندسة للصف الأول الإعدادى لغات أمنية وجدى
This document contains a series of math exercises involving rational numbers, integers, algebraic expressions, and basic operations. It includes tasks like completing statements, representing numbers on a number line, comparing rational numbers using symbols, writing rational numbers between given values, finding sums and differences of algebraic expressions, factorizing expressions, and calculating mean, median, and mode from data sets. The exercises cover topics such as properties of rational numbers, operations on integers and algebraic expressions, and basic statistics.
9-7 Graphing Points in Coordinate PlaneRudy Alfonso
The document explains how to graph points on a coordinate grid using ordered pairs. It defines the x-axis as the horizontal axis and y-axis as the vertical axis. The first number in an ordered pair represents the distance from the origin on the x-axis, while the second number represents the distance from the origin on the y-axis. Several examples are given of locating points from their ordered pair coordinates.
The document contains various math problems including:
- Choosing the correct answers to multiple choice questions about numbers and place values
- Identifying whether number sentences are true or false
- Arranging numbers in ascending order
- Identifying shapes
- Writing out number words
- Comparing numbers using inequality signs
- Continuing number patterns
- Solving word problems involving addition, subtraction, and finding totals/remainders
The document tests a variety of math skills ranging from numbers and operations to problem solving.
The document provides steps for solving rational inequalities. It shows how to:
1) Sketch the graph of the function.
2) Write the interval where the function is under/on or over the boundary.
3) Solve the equation to determine the values for the intervals.
This document discusses concepts in coordinate geometry and graphics. It covers topics like points, lines, circles, coordinate systems, color wheels, and using trigonometric functions to generate graphical patterns. Randomness is explored through defining multiple rules with the same name to randomly select shapes. The document encourages exercises to design patterns in a 3x3 grid and create tiles combining basic patterns with randomness.
"Incremental Lossless Graph Summarization", KDD 2020지훈 고
A presentation slides of Jihoon Ko*, Yunbum Kook* and Kijung Shin, "Incremental Lossless Graph Summarization", KDD 2020.
Given a fully dynamic graph, represented as a stream of edge insertions and deletions, how can we obtain and incrementally update a lossless summary of its current snapshot?
As large-scale graphs are prevalent, concisely representing them is inevitable for efficient storage and analysis. Lossless graph summarization is an effective graph-compression technique with many desirable properties. It aims to compactly represent the input graph as (a) a summary graph consisting of supernodes (i.e., sets of nodes) and superedges (i.e., edges between supernodes), which provide a rough description, and (b) edge corrections which fix errors induced by the rough description. While a number of batch algorithms, suited for static graphs, have been developed for rapid and compact graph summarization, they are highly inefficient in terms of time and space for dynamic graphs, which are common in practice.
In this work, we propose MoSSo, the first incremental algorithm for lossless summarization of fully dynamic graphs. In response to each change in the input graph, MoSSo updates the output representation by repeatedly moving nodes among supernodes. MoSSo decides nodes to be moved and their destinations carefully but rapidly based on several novel ideas. Through extensive experiments on 10 real graphs, we show MoSSo is (a) Fast and 'any time': processing each change in near-constant time (less than 0.1 millisecond), up to 7 orders of magnitude faster than running state-of-the-art batch methods, (b) Scalable: summarizing graphs with hundreds of millions of edges, requiring sub-linear memory during the process, and (c) Effective: achieving comparable compression ratios even to state-of-the-art batch methods.
This document summarizes a slide presentation on string methods and debugging in Java. It provides examples of common string methods like charAt, compareTo, indexOf, replace, and substring. It also briefly explains how to debug programs using breakpoints and stepping through code line-by-line.
This document provides a summary of lecture 4 of the MIT OpenCourseWare course 6.094 Introduction to MATLAB. The lecture covers advanced MATLAB methods including probability and statistics, data structures like cells and structs, images and animation, debugging tools, and an introduction to symbolic math and various MATLAB toolboxes. Key concepts are demonstrated through examples and exercises.
1st prep.sheet فى الجبر والهندسة للصف الأول الإعدادى لغات أمنية وجدى
This document contains a series of math exercises involving rational numbers, integers, algebraic expressions, and basic operations. It includes tasks like completing statements, representing numbers on a number line, comparing rational numbers using symbols, writing rational numbers between given values, finding sums and differences of algebraic expressions, factorizing expressions, and calculating mean, median, and mode from data sets. The exercises cover topics such as properties of rational numbers, operations on integers and algebraic expressions, and basic statistics.
9-7 Graphing Points in Coordinate PlaneRudy Alfonso
The document explains how to graph points on a coordinate grid using ordered pairs. It defines the x-axis as the horizontal axis and y-axis as the vertical axis. The first number in an ordered pair represents the distance from the origin on the x-axis, while the second number represents the distance from the origin on the y-axis. Several examples are given of locating points from their ordered pair coordinates.
The document contains various math problems including:
- Choosing the correct answers to multiple choice questions about numbers and place values
- Identifying whether number sentences are true or false
- Arranging numbers in ascending order
- Identifying shapes
- Writing out number words
- Comparing numbers using inequality signs
- Continuing number patterns
- Solving word problems involving addition, subtraction, and finding totals/remainders
The document tests a variety of math skills ranging from numbers and operations to problem solving.
The document provides steps for solving rational inequalities. It shows how to:
1) Sketch the graph of the function.
2) Write the interval where the function is under/on or over the boundary.
3) Solve the equation to determine the values for the intervals.
This document discusses concepts in coordinate geometry and graphics. It covers topics like points, lines, circles, coordinate systems, color wheels, and using trigonometric functions to generate graphical patterns. Randomness is explored through defining multiple rules with the same name to randomly select shapes. The document encourages exercises to design patterns in a 3x3 grid and create tiles combining basic patterns with randomness.
"Incremental Lossless Graph Summarization", KDD 2020지훈 고
A presentation slides of Jihoon Ko*, Yunbum Kook* and Kijung Shin, "Incremental Lossless Graph Summarization", KDD 2020.
Given a fully dynamic graph, represented as a stream of edge insertions and deletions, how can we obtain and incrementally update a lossless summary of its current snapshot?
As large-scale graphs are prevalent, concisely representing them is inevitable for efficient storage and analysis. Lossless graph summarization is an effective graph-compression technique with many desirable properties. It aims to compactly represent the input graph as (a) a summary graph consisting of supernodes (i.e., sets of nodes) and superedges (i.e., edges between supernodes), which provide a rough description, and (b) edge corrections which fix errors induced by the rough description. While a number of batch algorithms, suited for static graphs, have been developed for rapid and compact graph summarization, they are highly inefficient in terms of time and space for dynamic graphs, which are common in practice.
In this work, we propose MoSSo, the first incremental algorithm for lossless summarization of fully dynamic graphs. In response to each change in the input graph, MoSSo updates the output representation by repeatedly moving nodes among supernodes. MoSSo decides nodes to be moved and their destinations carefully but rapidly based on several novel ideas. Through extensive experiments on 10 real graphs, we show MoSSo is (a) Fast and 'any time': processing each change in near-constant time (less than 0.1 millisecond), up to 7 orders of magnitude faster than running state-of-the-art batch methods, (b) Scalable: summarizing graphs with hundreds of millions of edges, requiring sub-linear memory during the process, and (c) Effective: achieving comparable compression ratios even to state-of-the-art batch methods.
1. The document is a mathematics assignment on differentiation from pages 33-40. It was prepared by 4 students for their 1st semester class at the Polytechnic Manufacturing State University of Bangka Belitung.
2. The assignment contains the solutions to 10 differentiation problems finding the derivatives of various functions.
The document is a mathematics calculus homework assignment in Bahasa Indonesia. It contains 10 calculus problems asking students to find the derivatives of various functions. The functions include exponential functions like f(x) = 20ex, logarithmic functions like g(x) = ln(5x3), and combinations of exponentials, logarithms, and polynomials. The document provides the solutions to each problem in steps showing the use of logarithmic differentiation to find the derivatives.
1. This document provides the solutions to differentiation problems for a group mathematics assignment on pages 33-40 regarding differentiation. It lists the names of the group members and provides the solutions to 10 differentiation problems.
2. The solutions find the derivatives of various functions involving exponents, logarithms, and other operations. Derivatives are found using logarithmic differentiation and power rule.
3. The document is part of a mathematics assignment from the Polytechnic Manufacturing State University of Bangka Belitung in Indonesia for the class and semester noted.
This document summarizes research on deficient quartic spline interpolation. It begins by introducing the topic and defining deficient quartic splines. It then proves the existence and uniqueness of a spline interpolation that matches given functional values and derivatives at interior points, with specified boundary conditions. Specifically, it shows there is a unique spline if the mesh size is greater than or equal to the interval length divided by 2. Next, the document derives error bounds for the spline interpolation. It obtains pointwise bounds for the error function and shows the error is bounded above by a function involving the fifth modulus of smoothness of the given function. In conclusion, best possible error bounds are obtained for the deficient quartic spline interpolation method presented.
1. The document shows methods for calculating the area of rectangles by splitting them into smaller rectangles.
2. It demonstrates that the area of the original rectangle equals the sum of the areas of the smaller rectangles.
3. Algebraic formulas are developed to represent splitting rectangles and multiplying sums and differences.
The document discusses hypergraph motifs, which describe connectivity patterns between three connected hyperedges in a hypergraph. It proposes MoCHy, a family of parallel algorithms for counting instances of hypergraph motifs in large hypergraphs. Experimental results on real-world hypergraphs from different domains show that their motif distributions differ significantly from randomized hypergraphs, and MoCHy can efficiently count motifs in large hypergraphs.
"SSumM: Sparse Summarization of Massive Graphs", KDD 2020KyuhanLee4
A presentation slides of Kyuhan Lee, Hyeonsoo Jo, Jihoon Ko, Sungsu Lim, Kijung Shin, "SSumM: Sparse Summarization of Massive Graphs", KDD 2020.
Given a graph G and the desired size k in bits, how can we summarize G within k bits, while minimizing the information loss?
Large-scale graphs have become omnipresent, posing considerable computational challenges. Analyzing such large graphs can be fast and easy if they are compressed sufficiently to fit in main memory or even cache. Graph summarization, which yields a coarse-grained summary graph with merged nodes, stands out with several advantages among graph compression techniques. Thus, a number of algorithms have been developed for obtaining a concise summary graph with little information loss or equivalently small reconstruction error. However, the existing methods focus solely on reducing the number of nodes, and they often yield dense summary graphs, failing to achieve better compression rates. Moreover, due to their limited scalability, they can be applied only to moderate-size graphs.
In this work, we propose SSumM, a scalable and effective graph-summarization algorithm that yields a sparse summary graph. SSumM not only merges nodes together but also sparsifies the summary graph, and the two strategies are carefully balanced based on the minimum description length principle. Compared with state-of-the-art competitors, SSumM is (a) Concise: yields up to 11.2X smaller summary graphs with similar reconstruction error, (b) Accurate: achieves up to 4.2X smaller reconstruction error with similarly concise outputs, and (c) Scalable: summarizes 26X larger graphs while exhibiting linear scalability. We validate these advantages through extensive experiments on 10 real-world graphs.
Odd Permutations - Part 5 of The Mathematics of Professor Alan's Puzzle SquareAlan Dix
In the previous part of The Mathematics of Professor Alan's Puzzle Square, we saw that the patterns of tiles in 3x3 squares fall into exactly two families, we called them odd and even. Any square in the same family can be transformed into any other with the basic moves. In this part we use Group Theory to see why this is the case ... and to prove it is so!
https://magisoft.co.uk/alan/misc/game/maths/
The Puzzle Square is an online puzzle that is a bit like a two-dimensional version of Rubik's Cube. This series of presentations introduces various aspects of mathematics that are useful for learning about the square and other puzzles.
This article presents a generalization of Schur's inequality for three non-negative real numbers a, b, c, x, y, z such that the sequences (a, b, c) and (x, y, z) are monotone. The generalized Schur inequality states that x(a - b)(a - c) + y(b - a)(b - c) + z(c - a)(c - b) ≥ 0. Several examples are provided to demonstrate how this simple inequality can be used to easily solve more complex inequalities. The generalized Schur inequality allows transforming inequalities into a standard form where the solution follows immediately.
This document discusses solving quadratic equations by factoring. It begins by defining a quadratic equation in standard form and explaining the zero factor property. It then provides examples of solving quadratic equations through factoring and setting each factor equal to zero. Finally, it demonstrates solving word problems by setting up and solving the resulting quadratic equation.
This chapter introduces complex numbers. It defines a complex number as having the form x + iy, where x and y are real numbers. It describes how to represent complex numbers graphically on an Argand diagram and defines the modulus and argument of a complex number. It explains how to perform arithmetic operations like addition, subtraction, multiplication and division on complex numbers in both Cartesian (x + iy) and polar forms. It also introduces concepts like the conjugate of a complex number and using real and imaginary parts to solve equations. The chapter aims to explain the basic properties and manipulations of complex numbers.
1) The document discusses properties of real numbers including integers, rational numbers, decimals, and fractions. It covers the four fundamental operations on integers - addition, subtraction, multiplication, and division.
2) Key properties of integer addition and subtraction are discussed, including closure, commutativity, associativity, and additive identity. Addition is commutative and associative, while subtraction is not commutative or associative.
3) Examples are provided to illustrate performing the four operations on integers and evaluating expressions involving integers. Rules for multiplying and dividing positive and negative integers are also explained.
This document introduces coordinate graphs and ordered pairs. It defines a coordinate grid as a set of uniformly spaced horizontal and vertical lines used to locate points by their distance from two intersecting lines. The x-axis is the horizontal number line representing the dependent variable, while the y-axis is the vertical number line representing the independent variable. An ordered pair identifies a point's location by its x and y coordinates, with the x value found first by moving horizontally along the x-axis and then the y value found by moving vertically.
CAPE PURE MATHEMATICS UNIT 2 MODULE 1 PRACTICE QUESTIONSCarlon Baird
dy/dx = (x - 3y)/(6x - 4)
The stationary points on the curve C occur when tan(x) = 2.
The equation of the tangent to C at the point where x=0 is y = 2ex.
This document discusses linear programming and optimization. It begins with essential questions about finding maximum and minimum values of functions over regions. Key vocabulary is defined, including linear programming, feasible region, bounded, unbounded, and optimize. Two examples are provided to demonstrate how to graph inequality systems, identify feasible regions, and find the maximum and minimum values of an objective function over those regions using linear programming techniques.
CAPE PURE MATHEMATICS UNIT 2 MODULE 2 PRACTICE QUESTIONSCarlon Baird
This document contains practice questions on sequences, series, and approximations from a CAPE Pure Mathematics unit. Question 1 covers finding terms of sequences defined recursively and evaluating finite sums. Question 2 involves finding expressions for terms of sequences defined recursively and finding their sums. Later questions cover topics like proving identities using induction, evaluating infinite series, approximating functions using Taylor series, and finding roots of equations numerically. The questions provide worked examples of key concepts in sequences, series, and approximations.
Application of subQuan to Algebra: 3rd-8th grade and beyond...Dream Realizations
NWMC12 3-8 presentation demonstrating the visual link of subQuan understanding and Algebra. Looks at the forms of numbers as seen on our website @ dreamrealizations.org
1) The document discusses solving quadratic equations by factoring, including using the zero factor property.
2) It provides examples of solving quadratic equations by factoring them into two binomial factors and setting each factor equal to zero.
3) The document also shows how to solve word problems by setting up and solving quadratic equations derived from the problem information.
The document discusses solving systems of linear equations. It provides examples of solving systems graphically and algebraically. Example 1 shows solving the system x + y = 3 and -2x + y = -6 by graphing the lines defined by each equation on the same xy-plane and finding their point of intersection, which is the solution to the system.
Two-dimensional arrays in C++ allow the creation of arrays with multiple rows and columns. A 2D array is initialized and accessed using two indices, one for the row and one for the column. 2D arrays can be processed using nested for loops, with the outer loop iterating through each row and the inner loop iterating through each column. Functions can accept 2D arrays as parameters, but the number of columns must be specified since arrays are stored in row-major order.
There are two types of ciphers - Block and Stream. Block is used to .docxrelaine1
This document provides an overview of different modes of operation for ciphers including Electronic Code Book (ECB) mode, Cipher Block Chaining (CBC) mode, Output Feedback (OFB) mode, and Counter (CTR) mode. It explains the basic operations of each mode, such as how plaintext blocks are encrypted and how subsequent blocks depend on previous encrypted blocks. Weaknesses of the DES cipher are also discussed, noting it was withdrawn in 2005 due to insufficient security. The document then provides an example of applying CBC mode to DES encryption.
1. The document is a mathematics assignment on differentiation from pages 33-40. It was prepared by 4 students for their 1st semester class at the Polytechnic Manufacturing State University of Bangka Belitung.
2. The assignment contains the solutions to 10 differentiation problems finding the derivatives of various functions.
The document is a mathematics calculus homework assignment in Bahasa Indonesia. It contains 10 calculus problems asking students to find the derivatives of various functions. The functions include exponential functions like f(x) = 20ex, logarithmic functions like g(x) = ln(5x3), and combinations of exponentials, logarithms, and polynomials. The document provides the solutions to each problem in steps showing the use of logarithmic differentiation to find the derivatives.
1. This document provides the solutions to differentiation problems for a group mathematics assignment on pages 33-40 regarding differentiation. It lists the names of the group members and provides the solutions to 10 differentiation problems.
2. The solutions find the derivatives of various functions involving exponents, logarithms, and other operations. Derivatives are found using logarithmic differentiation and power rule.
3. The document is part of a mathematics assignment from the Polytechnic Manufacturing State University of Bangka Belitung in Indonesia for the class and semester noted.
This document summarizes research on deficient quartic spline interpolation. It begins by introducing the topic and defining deficient quartic splines. It then proves the existence and uniqueness of a spline interpolation that matches given functional values and derivatives at interior points, with specified boundary conditions. Specifically, it shows there is a unique spline if the mesh size is greater than or equal to the interval length divided by 2. Next, the document derives error bounds for the spline interpolation. It obtains pointwise bounds for the error function and shows the error is bounded above by a function involving the fifth modulus of smoothness of the given function. In conclusion, best possible error bounds are obtained for the deficient quartic spline interpolation method presented.
1. The document shows methods for calculating the area of rectangles by splitting them into smaller rectangles.
2. It demonstrates that the area of the original rectangle equals the sum of the areas of the smaller rectangles.
3. Algebraic formulas are developed to represent splitting rectangles and multiplying sums and differences.
The document discusses hypergraph motifs, which describe connectivity patterns between three connected hyperedges in a hypergraph. It proposes MoCHy, a family of parallel algorithms for counting instances of hypergraph motifs in large hypergraphs. Experimental results on real-world hypergraphs from different domains show that their motif distributions differ significantly from randomized hypergraphs, and MoCHy can efficiently count motifs in large hypergraphs.
"SSumM: Sparse Summarization of Massive Graphs", KDD 2020KyuhanLee4
A presentation slides of Kyuhan Lee, Hyeonsoo Jo, Jihoon Ko, Sungsu Lim, Kijung Shin, "SSumM: Sparse Summarization of Massive Graphs", KDD 2020.
Given a graph G and the desired size k in bits, how can we summarize G within k bits, while minimizing the information loss?
Large-scale graphs have become omnipresent, posing considerable computational challenges. Analyzing such large graphs can be fast and easy if they are compressed sufficiently to fit in main memory or even cache. Graph summarization, which yields a coarse-grained summary graph with merged nodes, stands out with several advantages among graph compression techniques. Thus, a number of algorithms have been developed for obtaining a concise summary graph with little information loss or equivalently small reconstruction error. However, the existing methods focus solely on reducing the number of nodes, and they often yield dense summary graphs, failing to achieve better compression rates. Moreover, due to their limited scalability, they can be applied only to moderate-size graphs.
In this work, we propose SSumM, a scalable and effective graph-summarization algorithm that yields a sparse summary graph. SSumM not only merges nodes together but also sparsifies the summary graph, and the two strategies are carefully balanced based on the minimum description length principle. Compared with state-of-the-art competitors, SSumM is (a) Concise: yields up to 11.2X smaller summary graphs with similar reconstruction error, (b) Accurate: achieves up to 4.2X smaller reconstruction error with similarly concise outputs, and (c) Scalable: summarizes 26X larger graphs while exhibiting linear scalability. We validate these advantages through extensive experiments on 10 real-world graphs.
Odd Permutations - Part 5 of The Mathematics of Professor Alan's Puzzle SquareAlan Dix
In the previous part of The Mathematics of Professor Alan's Puzzle Square, we saw that the patterns of tiles in 3x3 squares fall into exactly two families, we called them odd and even. Any square in the same family can be transformed into any other with the basic moves. In this part we use Group Theory to see why this is the case ... and to prove it is so!
https://magisoft.co.uk/alan/misc/game/maths/
The Puzzle Square is an online puzzle that is a bit like a two-dimensional version of Rubik's Cube. This series of presentations introduces various aspects of mathematics that are useful for learning about the square and other puzzles.
This article presents a generalization of Schur's inequality for three non-negative real numbers a, b, c, x, y, z such that the sequences (a, b, c) and (x, y, z) are monotone. The generalized Schur inequality states that x(a - b)(a - c) + y(b - a)(b - c) + z(c - a)(c - b) ≥ 0. Several examples are provided to demonstrate how this simple inequality can be used to easily solve more complex inequalities. The generalized Schur inequality allows transforming inequalities into a standard form where the solution follows immediately.
This document discusses solving quadratic equations by factoring. It begins by defining a quadratic equation in standard form and explaining the zero factor property. It then provides examples of solving quadratic equations through factoring and setting each factor equal to zero. Finally, it demonstrates solving word problems by setting up and solving the resulting quadratic equation.
This chapter introduces complex numbers. It defines a complex number as having the form x + iy, where x and y are real numbers. It describes how to represent complex numbers graphically on an Argand diagram and defines the modulus and argument of a complex number. It explains how to perform arithmetic operations like addition, subtraction, multiplication and division on complex numbers in both Cartesian (x + iy) and polar forms. It also introduces concepts like the conjugate of a complex number and using real and imaginary parts to solve equations. The chapter aims to explain the basic properties and manipulations of complex numbers.
1) The document discusses properties of real numbers including integers, rational numbers, decimals, and fractions. It covers the four fundamental operations on integers - addition, subtraction, multiplication, and division.
2) Key properties of integer addition and subtraction are discussed, including closure, commutativity, associativity, and additive identity. Addition is commutative and associative, while subtraction is not commutative or associative.
3) Examples are provided to illustrate performing the four operations on integers and evaluating expressions involving integers. Rules for multiplying and dividing positive and negative integers are also explained.
This document introduces coordinate graphs and ordered pairs. It defines a coordinate grid as a set of uniformly spaced horizontal and vertical lines used to locate points by their distance from two intersecting lines. The x-axis is the horizontal number line representing the dependent variable, while the y-axis is the vertical number line representing the independent variable. An ordered pair identifies a point's location by its x and y coordinates, with the x value found first by moving horizontally along the x-axis and then the y value found by moving vertically.
CAPE PURE MATHEMATICS UNIT 2 MODULE 1 PRACTICE QUESTIONSCarlon Baird
dy/dx = (x - 3y)/(6x - 4)
The stationary points on the curve C occur when tan(x) = 2.
The equation of the tangent to C at the point where x=0 is y = 2ex.
This document discusses linear programming and optimization. It begins with essential questions about finding maximum and minimum values of functions over regions. Key vocabulary is defined, including linear programming, feasible region, bounded, unbounded, and optimize. Two examples are provided to demonstrate how to graph inequality systems, identify feasible regions, and find the maximum and minimum values of an objective function over those regions using linear programming techniques.
CAPE PURE MATHEMATICS UNIT 2 MODULE 2 PRACTICE QUESTIONSCarlon Baird
This document contains practice questions on sequences, series, and approximations from a CAPE Pure Mathematics unit. Question 1 covers finding terms of sequences defined recursively and evaluating finite sums. Question 2 involves finding expressions for terms of sequences defined recursively and finding their sums. Later questions cover topics like proving identities using induction, evaluating infinite series, approximating functions using Taylor series, and finding roots of equations numerically. The questions provide worked examples of key concepts in sequences, series, and approximations.
Application of subQuan to Algebra: 3rd-8th grade and beyond...Dream Realizations
NWMC12 3-8 presentation demonstrating the visual link of subQuan understanding and Algebra. Looks at the forms of numbers as seen on our website @ dreamrealizations.org
1) The document discusses solving quadratic equations by factoring, including using the zero factor property.
2) It provides examples of solving quadratic equations by factoring them into two binomial factors and setting each factor equal to zero.
3) The document also shows how to solve word problems by setting up and solving quadratic equations derived from the problem information.
The document discusses solving systems of linear equations. It provides examples of solving systems graphically and algebraically. Example 1 shows solving the system x + y = 3 and -2x + y = -6 by graphing the lines defined by each equation on the same xy-plane and finding their point of intersection, which is the solution to the system.
Two-dimensional arrays in C++ allow the creation of arrays with multiple rows and columns. A 2D array is initialized and accessed using two indices, one for the row and one for the column. 2D arrays can be processed using nested for loops, with the outer loop iterating through each row and the inner loop iterating through each column. Functions can accept 2D arrays as parameters, but the number of columns must be specified since arrays are stored in row-major order.
There are two types of ciphers - Block and Stream. Block is used to .docxrelaine1
This document provides an overview of different modes of operation for ciphers including Electronic Code Book (ECB) mode, Cipher Block Chaining (CBC) mode, Output Feedback (OFB) mode, and Counter (CTR) mode. It explains the basic operations of each mode, such as how plaintext blocks are encrypted and how subsequent blocks depend on previous encrypted blocks. Weaknesses of the DES cipher are also discussed, noting it was withdrawn in 2005 due to insufficient security. The document then provides an example of applying CBC mode to DES encryption.
This document contains summaries of solutions to various LeetCode problems in Java. It begins with a 3-sentence summary of the Rotate Array problem and its solutions, followed by shorter 1-sentence summaries of other problems and their solutions, including Evaluate Reverse Polish Notation, Longest Palindromic Substring, Word Break, and more. Dynamic programming and recursion are discussed as approaches for some of the problems.
The document describes a Tic Tac Toe game created in C++. It includes the introduction of Tic Tac Toe, the C++ code to create the game board and logic, and explanations of various programming concepts used like functions, loops, arrays and switch statements. The C++ code allows two players to alternate placing X and O markers on a 3x3 grid until someone wins by getting 3 in a row, or it ends in a draw if all spaces are filled without a winner.
Python 101++: Let's Get Down to Business!Paige Bailey
You've started the Codecademy and Coursera courses; you've thumbed through Zed Shaw's "Learn Python the Hard Way"; and now you're itching to see what Python can help you do. This is the workshop for you!
Here's the breakdown: we're going to be taking you on a whirlwind tour of Python's capabilities. By the end of the workshop, you should be able to easily follow any of the widely available Python courses on the internet, and have a grasp on some of the more complex aspects of the language.
Please don't forget to bring your personal laptop!
Audience: This course is aimed at those who already have some basic programming experience, either in Python or in another high level programming language (such as C/C++, Fortran, Java, Ruby, Perl, or Visual Basic). If you're an absolute beginner -- new to Python, and new to programming in general -- make sure to check out the "Python 101" workshop!
Efficient realization for geometric transformation of digital images in run l...Shlomo Pongratz
The document describes algorithms for efficiently transforming digital images represented in run length encoding under various geometric transformations like rotation, flipping, and shearing. It presents several existing algorithms for performing such transformations in linear time or better and identifies limitations in those algorithms. Improved algorithms are proposed that can perform rotations and other transformations in one pass of the run length encoded image data in linear or near-linear time.
7th maths-1.concept , addition and subtraction properties of intergers-sanghLiveOnlineClassesInd
The document discusses integers and their properties. It begins by defining natural numbers, whole numbers, and integers. It then discusses integer addition and subtraction on a number line, including moving right for positive integers and left for negative integers. Key terms like additive inverse are also defined. Several practice problems are included about temperature differences and determining which options represent magic squares. Finally, the properties of integers like closure, commutativity, and associativity are explained.
7th maths-1.concept , addition and subtraction properties of intergersLiveOnlineClassesInd
The document discusses integers and their properties. It begins by defining natural numbers, whole numbers, and integers as collections of numbers that include negative numbers. It then discusses integer addition and subtraction on a number line, defining properties like additive inverses. Several practice problems are included to test understanding of integer concepts and properties like closure, commutativity, and associativity of addition and subtraction. The overall purpose is to revise and test understanding of integers and their properties.
This document appears to be pages from a mathematics textbook. It contains over 80 numbered problems and explanations related to skills like rounding, order of operations, fractions, decimals, percentages and more. The problems range in complexity from basic rounding to multiple step word problems. The document provides worked examples and explanations to help students learn essential math concepts and skills.
This document discusses nested loop logic and patterns for printing shapes using nested loops. It begins by conceptualizing a grid with rows and columns that can be used to print patterns. Examples are given of simple right triangles printed using nested loops. Formulas are provided for determining the middle of a grid and the number of rows needed based on the number of columns to print isosceles triangles. The document also discusses starting indexes at zero instead of one and algorithms for printing shapes centered with diagonals.
This document discusses arrays and functions. It covers various topics related to arrays including declaring and manipulating multidimensional arrays, array parameters in functions, and converting between array types. It also provides an overview of functions, describing them as subparts of a program for obtaining input, performing calculations, and displaying output. Examples are given throughout to demonstrate array and function concepts.
The document discusses different number systems including decimal, binary, octal, and hexadecimal. It explains how each system uses a different set of digits to represent values and how numbers are expressed as a sum of weighted place values. Conversion between different number systems like binary to decimal is demonstrated. Gray codes and binary codes for representing decimal digits are also covered. Boolean algebra concepts such as logic gates, truth tables, and identities are defined.
Robotic Manipulator with Revolute and Prismatic JointsTravis Heidrich
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1. Oct 8th
Lab08.
Quiz review
Triangle and Stripes
http://www.slideshare.net/takyeon
2. Quiz review
No
i++
++i
Use and then increase
Increase and then use
int i = 3;
int a = i++; // a = 3, i = 4
int b = ++a; // b = 4, a = 4
3. Quiz review
str
maxCount 100
• Whenever a new variable is declared, it is
added to STACK.
• Primitive data types are stored in STACK
• byte, short, int, long, float, double, boolean, char
• Other data types are stored in HEAP.
• String, Integer, Scanner, …
"Hello"
"HELLO"
• Data in HEAP are not immediately
deleted but unlinked, and will be
garbage-collected.
4. public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int size = sc.nextInt();
for(int row=1;row<=size;row++) {
for(int col=1;col<=size;col++) {
System.out.print(row*col + " ");
}
System.out.println();
}
}
5. Lab – 2D drawing
Two methods.
0,0 0,1 0,2 0,3 0,4
1,0 1,1 1,2 1,3 1,4
2,0 2,1 2,2 2,3 2,4
3,0 3,1 3,2 3,3 3,4
4,0 4,1 4,2 4,3 4,4
M1. Iterate pixels to paint
for (int i=0; i<size; i++) {
grid.setColor(i, i, Color.BLUE);
}
Intuitive and efficient
M2. Iterate every pixel, use if conditionals to
check pixels to paint
for (int row=0; row<size; row++) {
for (int col=0; col<size; col++) {
if(row==col) {
grid.setColor(row, col, Color.BLUE);
}
}
}
Complex and inefficient
BUT! More generalizable
6. Lab – 2D drawing
Two methods.
0,0 0,1 0,2 0,3 0,4
1,0 1,1 1,2 1,3 1,4
2,0 2,1 2,2 2,3 2,4
3,0 3,1 3,2 3,3 3,4
M1. Iterate pixels to paint
Very difficult
4,0 4,1 4,2 4,3 4,4 M2. Iterate every pixel, use if conditionals to
check pixels to paint
for (int row=0; row<size; row++) {
for (int col=0; col<size; col++) {
if(row!=col) {
grid.setColor(row, col, Color.BLUE);
}
}
}
You can simply inverse the conditional logic
Now you want to
paint all the pixels
except the diagonal
line.
13. Finding common factors of two numbers
Common factors can divide both numbers.
E.g. Common factors of 9 and 12 1 and 3
public void commonFactor(int n1, int n2) {
for(int i=1; i<=min(n1,n2); i++) {
if(n1%i==0 && n2%i==0) {
System.out.println(i);
}
}
}
Common factors of 24 and 78 1, 2, 3, and 6
14. compareTo method
String s1 = "aaa";
String s2 = "aac";
int k = s1.compareTo(s2); // k => -2
Compares s1 and s2 lexicographically.
Negative if s1 precedes s2
Positive if s1 follows s2
Zero if s1 is equal to s2
15. Get multiple words, find the first and the last words
1) Using while loop, keep asking words until "STOP"
2) Using compareTo, update the first and the last words
3) Print out
18. SquareGrid.java
Drawing shapes on 2D grid
ExampleDriver.java
• Prompt a shape question
• Create an empty grid
• Draw the requested shape
OperatorMaker.java
drawOp (SquareGrid grid, int symbol)
minus, plus, divide, multiply (SquareGrid grid)
You will change only these methods
19. Single loop for drawing a line
0 1) How can we get the middle row number?
3
size : 7
int size = grid.getHt();
int midRow = size / 2;
0,0 0,1 0,2 0,3 0,4
1,0 1,1 1,2 1,3 1,4
2,0 2,1 2,2 2,3 2,4
3,0 3,1 3,2 3,3 3,4
4,0 4,1 4,2 4,3 4,4
2) How to draw a line?
• Iterate over columns (0 – 4)
• Paint the middle cell
for (int iCol=0; iCol<size; iCol++) {
grid.setColor(midRow, iCol, Color.BLUE);
}
20. Single loop for drawing a line
0,0 0,1 0,2 0,3 0,4 1) How can we get the middle column number?
1,0 1,1 1,2 1,3 1,4
2,0 2,1 2,2 2,3 2,4
3,0 3,1 3,2 3,3 3,4
4,0 4,1 4,2 4,3 4,4
int size = grid.getWd();
int midCol = size / 2;
2) How to draw a line?
• Iterate over rows (0 – 4)
• Paint the middle cell
for (int iRow=0; iRow<size; iRow++) {
grid.setColor(iRow, midCol, Color.BLUE);
}
Notice that drawing horizontal and vertical lines are quite similar.
We just switched row and column variables.
21. Single loop for drawing a line
0,0 0,1 0,2 0,3 0,4
1,0 1,1 1,2 1,3 1,4
2,0 2,1 2,2 2,3 2,4
3,0 3,1 3,2 3,3 3,4
4,0 4,1 4,2 4,3 4,4
1) How to draw a line?
• Iterate over rows or columns (0-4)
• Paint diagonal cells.
for (int iRow=0; iRow<size; iRow++) {
grid.setColor(iRow, iRow, Color.BLUE);
}
23. Single loop for drawing a line
Iterating over
the columns,
paint the middle
cell.
Iterating over
the columns,
paint the middle
cell.
Iterating over
the rows,
paint the center
cell.
Iterating over
the columns,
paint i-th cell.
Draw Plus,
Divide,
and Divide (rotated).
24.
25. Sep 29th
Lab05.
1. Recap the quiz #1
2. String Class
3. static vs. instance method
26. Recap quiz #1.
PRINT your names in
the grade server.
NO nicknames.
27. Recap quiz #1.
Use specific technical keywords
e.g. What does CVS “do” for us?
1. Check out / Download the starter files
2. Store / Save multiple versions of the source code
share, deliver, get, access, connected people, ...
Penalties for inaccurate extra info
e.g. CVS runs our code and give us grades. -1 for incorrect extra info.
28.
29. String Class
Create a new String object with an
initial value “hello”
String s = “hello”;
String objects have many convenient methods,
upperS = s.toUpperCase(); // will set upperS to “HELLO”
whereIsl= s.indexOf(‘l’); // will find the position of the first ‘l’
newS = s.replace(‘e’,’a’); // will set newS to “hallo”
30. int type vs. Integer Class
int i=0;
Primitive data type
Integer i = 17;
Wrapper Class
Faster A little slower
don’t have much method provide methods
- convert to string
- generate hash codes
31. Static vs. Instance method
Intance methods need a sheep as a subject.
bob.eat();
bob.smileTo(clara);
bob.getPenNumber();
Static methods are about all the sheeps.
Sheep.getTotalSheep();
Sheep.removeAll();
Sheep.addSheep(‘evan’);
33. Flow of Control
1. Top-to-bottom statements
2. Method calls
3. Conditional statements
4. Iteration (loop)
for, while, ...
34. Two goals of iteration
1. Automation
Reduce repetition of code
System.out.println(“****”);
System.out.println(“****”);
System.out.println(“****”);
How can we reduce?
for(int i=0;i<3;i++) {
System.out.println(“****”);
}
2. Abstraction
Code for various situations
System.out.println(“****”);
How can we print n-number of “*”?
35. From manual & concrete to automatic & abstract
Level 1. Draw 30 by 10 rectangle (hard-coded)
System.out.println(“**********”);
System.out.println(“**********”);
System.out.println(“**********”);
... 27 more lines
Too many copy & paste. Hard to modify.
Level 2. Draw 30 by 10 rectangle (single-loop)
int row=0;
while(row<30) {
System.out.println(“**********”);
row++;
}
A little more compact.
Still too many * for each line.
36. From manual & concrete to automatic & abstract
Level 3. Draw 30 by 10 rectangle (nested-loop)
int row=0, col=0;
while(row<30) {
while(col<10) {
System.out.print(“*”);
}
System.out.println();
}
Much compact.
Cannot change # of row and col
Level 4. Draw height by width (nested-loop, parameterized)
int row=0, col=0;
int height=30, width=10;
while(row<height) {
while(col<width) {
System.out.print(“*”);
}
System.out.println();
}
Compact
Can draw any sized rectangle