The Traveling Salesman Problem Explained in under 5 mins | Graph Theory Basics
Welcome to our Graph Theory Basics series! In this video, we explain the Traveling Salesman Problem (TSP) in under 5 minutes. The TSP is a classic optimization problem that seeks the shortest possible route for a salesman to visit each city once and return to the starting point. We'll break down the problem, discuss its significance in graph theory and real-world applications, and provide clear examples to help you understand this fundamental concept. Whether you're a student, a math enthusiast, or simply curious about graph theory, this video will give you a concise and comprehensive overview of the Traveling Salesman Problem. Don't forget to like, comment, and subscribe for more insightful videos on graph theory and other mathematical concepts! #GraphTheory #TravelingSalesmanProblem #TSP #Mathematics #Optimization #GraphTheoryBasics #MathTutorial #EducationalVideo
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
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How many possible Circuits in a Complete Graph? | Graph Theory Basics
Welcome to our Graph Theory Basics series! In this video, we explore the fascinating question: how many possible circuits are there in a complete graph? We'll break down the concept of circuits, explain their significance in graph theory, and demonstrate how to calculate the number of possible circuits in a complete graph with illustrative examples. Whether you're a student, a math enthusiast, or just curious about graph theory, this video will provide you with a clear understanding of circuits in complete graphs. Don't forget to like, comment, and subscribe for more insightful videos on graph theory and other mathematical concepts! #GraphTheory #CompleteGraph #Circuits #Mathematics #GraphTheoryBasics #MathTutorial #EducationalVideo
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
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What is a Complete Graph? | Graph Theory Basics
Welcome to our Graph Theory Basics series! In this video, we delve into the concept of complete graphs. What exactly is a complete graph? We'll provide a clear and concise definition, explore its key properties, and offer illustrative examples to help you understand this fundamental element of graph theory. Whether you're a student, a math enthusiast, or simply curious about graph theory, this video will give you a solid understanding of complete graphs. Don't forget to like, comment, and subscribe for more insightful videos on graph theory and other mathematical concepts! #GraphTheory #CompleteGraph #Mathematics #GraphTheoryBasics #MathTutorial #EducationalVideo
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
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Does a Hamiltonian path or circuit exist on this graph? | Graph Theory Basics
Dive deep into graph theory with our educational video, "Does a Hamiltonian Path or Circuit Exist on this Graph? | Graph Theory Basics". This tutorial explores the critical task of identifying Hamiltonian Paths and Circuits in various graphs, essential for understanding more complex graph structures. Perfect for both beginners and advanced learners, this video breaks down the criteria and techniques used to analyze graphs for Hamiltonian features. Through detailed explanations and practical examples, you'll gain the skills needed to tackle these challenges in your studies or professional projects. Subscribe now for more comprehensive guides on graph theory essentials!
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
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Hamiltonian Circuits and Paths Explained | Graph Theory Basics
Unlock the mysteries of graph theory with our insightful video, "Hamiltonian Circuits and Paths Explained | Graph Theory Basics". In this video, we delve into Hamiltonian Circuits and Paths, crucial concepts for understanding complex network traversals in graph theory. Ideal for students and enthusiasts, this guide explains what Hamiltonian Circuits and Paths are, how to determine their existence in a graph, and their significance in solving real-world problems. With clear examples and detailed explanations, this video is your go-to resource for mastering these important topics. Subscribe to our channel for more tutorials that make learning advanced concepts simple and fun!
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
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Euler's Path and Circuit Theorems Explained | Graph Theory Basics
Explore essential concepts in graph theory with our video, "Euler's Path and Circuit Theorems Explained | Graph Theory Basics". This comprehensive guide illuminates Euler's Path and Circuit Theorems, key insights that are foundational to understanding how paths and circuits function within various types of graphs. Ideal for students, educators, and professionals, this video explains the theorems in an accessible manner, provides historical context, and demonstrates their application through practical examples. Whether you're just starting out or brushing up on your knowledge, this video is a valuable resource. Subscribe for more educational content on mathematical theories and their real-world applications!
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
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Does an Euler Path or Circuit Exist on this Graph? | Graph Theory Basics
Join us in our latest educational video, "Does an Euler Path or Circuit Exist on this Graph? | Graph Theory Basics". In this tutorial, we tackle one of the key questions in graph theory: identifying whether a given graph supports an Euler Path or an Euler Circuit. Perfect for students and professionals alike, this video explains the necessary conditions for the existence of these paths and circuits, offers step-by-step methods to analyze different graphs, and provides practical examples to solidify your understanding. Enhance your graph theory skills and learn to apply these concepts effectively in your studies or work. Subscribe for more insightful mathematical content!
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
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What is an Euler Circuit? | Graph Theory Basics
Dive into the fascinating world of graph theory with our detailed video, "What is an Euler Circuit? | Graph Theory Basics". This video delves into the concept of Euler Circuits, a fundamental principle crucial for understanding complex networks and solving logistical problems. Learn about the criteria that differentiate Euler Circuits from Euler Paths, explore their historical roots, and see how they apply in modern-day challenges. Perfect for both novices and experienced learners, this guide offers definitions, visual demonstrations, and examples to enhance your grasp of Euler Circuits. Subscribe to our channel for more insightful tutorials on graph theory essentials!
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
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What is a Euler Path? | Graph Theory Basics
Unlock the secrets of graph theory with our educational video on "What is an Euler Path? | Graph Theory Basics". This video provides a comprehensive explanation of Euler Paths, a key concept in graph theory that are essential for solving problems like the historic Seven Bridges of Königsberg. Ideal for students and professionals looking to deepen their understanding of mathematical theories and their applications in real-world scenarios. Dive into examples, definitions, and much more. Whether you're a beginner or looking to refresh your knowledge, this video is your ultimate guide to mastering Euler Paths. Subscribe for more content on graph theory and beyond!
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
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What makes a Graph Connected or Disconnected in Graph Theory? | Graph Theory Basics
Welcome to our educational video on "What Makes a Graph Connected or Disconnected in Graph Theory?" Are you intrigued by how elements within a network are linked or, conversely, how they might remain isolated? Do you wonder what it means for a graph to be connected or disconnected and why this distinction is crucial in graph theory? Whether you're a student delving into complex mathematical concepts, a software engineer dealing with network structures, or just a curious mind eager to understand the underpinnings of connectivity, this video is perfectly suited for you. Today, we're going to explore the definitions of connected and disconnected graphs, demonstrate their characteristics through examples, and discuss the implications of each in practical scenarios. By the end of this video, you'll have a clear understanding of what keeps a graph together or what breaks it apart, enriching your knowledge of how graphs operate in theory and in real-world applications. Let’s get connected with the details of graph connectivity!
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
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What is the difference between a Path and a Circuit? | Graph Theory Basics
Welcome to our detailed tutorial on "What is the Difference Between a Path and a Circuit in Graph Theory?" Have you ever puzzled over the terms "path" and "circuit" when studying graphs, and wondered exactly what distinguishes these concepts? Whether you’re a student tackling graph theory for the first time, a professional in computer networking, or simply someone with a keen interest in mathematical structures, this video is designed with you in mind. Today, we're going to clarify these fundamental concepts by exploring what paths and circuits are, how they differ, and why understanding these differences is essential for analyzing and solving problems in graphs. We’ll provide clear examples and visual illustrations to ensure you grasp the nuances of these concepts. So, if you’re ready to dive deeper into graph theory and enhance your analytical skills, stay tuned as we unfold everything you need to know about paths and circuits!
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
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What is the Degree of a Vertex? | Graph Theory Basics
Welcome to our educational video on "What is the Degree of a Vertex in Graph Theory?" Are you curious about how to measure the connectivity of nodes within a network? Have you ever wondered what the term "degree of a vertex" means and why it's crucial in graph theory? Whether you're a mathematics student, a computer science enthusiast, or someone interested in network analysis, this video is tailored for you. We'll delve into the concept of the degree of a vertex, which indicates the number of edges connected to a vertex, and explain its significance in understanding the structure and complexity of graphs. By the end of this video, you'll have a firm grasp of vertex degrees and see how this fundamental concept is applied in solving real-world problems across various disciplines. So, get ready to enhance your understanding of graphs with our straightforward and engaging explanations!
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
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What is a Loop in Graph Theory? | Graph Theory Basics
Welcome to our informative session on "What is a Loop in Graph Theory?" Have you ever come across a graph and noticed an edge that begins and ends at the same vertex? Wondering what this feature is called and what role it plays in graph theory? Whether you’re a student, a software developer, or just someone with a keen interest in understanding the structures of networks, this video is designed for you. Today, we’re going to explore the concept of loops, their significance in graphs, and how they influence the behavior and analysis of networks. By explaining loops in a clear and engaging manner, we'll help you grasp their applications in various fields such as computer science, biology, and social network analysis. So, if you're ready to dive deep into graph theory and unlock new insights, stay tuned as we uncover everything you need to know about loops!
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
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What are the Weights of a Graph in Graph Theory? | Graph Theory Basics
Welcome to our detailed tutorial on "What are the Weights of a Graph in Graph Theory?" Are you intrigued by how graphs can be used to model real-world scenarios? Do you find yourself asking, "What exactly is a weight in a graph, and why is it important?" Whether you're a student gearing up for complex graph theory topics, a budding data scientist, or just someone fascinated by the mathematics of networks, this video is crafted for you. We'll delve into the concept of weights in a graph, demonstrating how they add another layer of information to the basic structure of nodes and edges. By understanding weights, you'll see how graphs are utilized to solve problems in networking, optimization, and beyond. Join us as we unfold the critical role of weights in graph theory with clear explanations and practical examples. Let’s unravel these concepts together and see how they apply to everyday challenges!
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
33
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Vertices and Edges Explained | Graph Theory Basics
Welcome to our comprehensive guide on the essentials of graph theory, focusing on "Vertices and Edges Explained." Are you curious about the building blocks of graphs? Ever wondered, "What is a vertex?" or "What is an edge?" Whether you're a student looking to ace your next exam, a professional in computer science, or simply intrigued by the mathematics that underpin complex networks, this video is tailored for you. We'll break down the concepts of vertices (or nodes) and edges in a simple, engaging way, illustrating how they form the backbone of graph theory. This exploration will not only answer your fundamental questions but also show you the practical applications of these concepts in various fields. So, if you're ready to demystify the basics of graphs and discover how they can be applied in real-world scenarios, let's dive in and learn together!
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
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Probability Calculation: Shared Birthdays Among 30 People
Join us as we delve into probability theory to explore the likelihood of shared birthdays among a group of 30 individuals in a room. In this tutorial, we investigate the probability of at least one shared birthday among the 30 people present. Through a systematic explanation, we elucidate the steps involved in calculating this probability. Whether you're interested in probability or intrigued by coincidental events, this video provides valuable insights into understanding the likelihood of shared birthdays in large groups. Tune in to uncover the probability of shared birthdays among 30 people!
In this video we solve the problem:
Suppose 30 people are in a room. What is the probability that there is at least one shared birthday among these 30 people?
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
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Probability Calculation: Shared Birthdays Among Five People
Join us in exploring probability theory as we investigate the likelihood of shared birthdays among five individuals in a room. In this tutorial, we delve into the probability of at least one shared birthday among the five people present. Through a systematic explanation, we elucidate the steps involved in calculating this probability. Whether you're intrigued by probability or fascinated by coincidental events, this video provides valuable insights into understanding the likelihood of shared birthdays in small groups. Tune in to uncover the probability of shared birthdays among five people!
In this video we solve the problem:
Suppose five people are in a room. What is the probability that there is at least one shared birthday among these five people?
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
27
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Probability Calculation: Shared Birthdays Among Three People
Delve into probability theory with us as we explore the likelihood of shared birthdays among three individuals in a room. In this tutorial, we analyze the probability of at least one shared birthday among the three people present. Through a systematic explanation, we elucidate the steps involved in calculating this probability. Whether you're intrigued by probability or curious about coincidental events, this video provides valuable insights into understanding the likelihood of shared birthdays in small groups. Tune in to uncover the probability of shared birthdays among three people!
The problem we solve in this video is:
Suppose three people are in a room. What is the probability that there is at least one shared birthday among these three people?
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
7
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Probability Computation: Drawing Two Aces from a Deck of Cards
Explore the realm of probability with us as we tackle a card-based scenario. In this tutorial, we delve into computing the probability of randomly drawing five cards from a deck and obtaining exactly two Aces. Through a systematic explanation, we elucidate the steps involved in calculating this probability. Whether you're a card game enthusiast or interested in probability theory, this video offers valuable insights into understanding the likelihood of specific outcomes in card games. Join us to learn about the probability of drawing two Aces from a deck of cards!
In the video we solve the problem:
Compute the probability of randomly drawing five cards from a deck and getting exactly two Aces.
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
8
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Probability Calculation: Drawing One Ace from a Deck of Cards
Join us as we delve into the fascinating world of probability with a card-based scenario. In this tutorial, we analyze the probability of randomly drawing five cards from a deck and obtaining exactly one Ace. Through a systematic explanation, we elucidate the steps involved in computing this probability. Whether you're a card enthusiast or interested in probability theory, this video provides valuable insights into understanding the likelihood of specific outcomes in card games. Tune in to learn about the probability of drawing one Ace from a deck of cards!
The problem we solve in this video is:
Compute the probability of randomly drawing five cards from a deck and getting exactly one Ace.
#probability #MathHelp #MinuteMath #MathMadeSimple #MathTutorial #mathinsociety #oer #MathSkills #Education #math
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
2
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Probability of Winning the Second Prize in the State Lottery
Explore the likelihood of winning the second prize in the state lottery through this tutorial. We delve into the mechanics of the lottery, where six numbers are drawn from a pool of 48 balls, and winning requires matching five of the chosen numbers. Through a step-by-step explanation, we compute the probability of winning the $1,000 second prize with a single lottery ticket purchase. Whether you're a lottery player or interested in probability analysis, this video provides valuable insights into understanding your chances of winning secondary prizes in lottery games. Join us to uncover the probability of winning big!
The problem we solve in this video is:
In the state lottery from the previous example, if five of the six numbers drawn match the numbers that a player has chosen, the player wins a second prize of $1,000. Compute the probability that you win the second prize if you purchase a single lottery ticket.
#probability #MathHelp #MinuteMath #MathMadeSimple #MathTutorial #mathinsociety #oer #MathSkills #Education #math
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
6
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Probability of Winning the Million-Dollar Lottery Prize
Join us as we explore the probability of winning the million-dollar prize in a state lottery. In this tutorial, we analyze the mechanics of the lottery, where 48 balls are placed in a machine and six of them are drawn at random. Through a systematic explanation, we elucidate how to compute the probability of winning the grand prize with a single lottery ticket purchase. Whether you're a lottery enthusiast or interested in probability theory, this video provides valuable insights into understanding probabilities in lottery games. Tune in to learn about your chances of hitting the jackpot!
The problem we solve in this video is:
In a certain state's lottery, 48 balls numbered 1 through 48 are placed in a machine and six of them are drawn at random. If the six numbers drawn match the numbers that a player had chosen, the player wins $1,000,000. In this lottery, the order the numbers are drawn in doesn’t matter. Compute the probability that you win the million-dollar prize if you purchase a single lottery ticket.
#probability #MathHelp #MinuteMath #MathMadeSimple #MathTutorial #mathinsociety #oer #MathSkills #Education #math
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
6
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Probability of No Repeated Digits in a 4-Digit PIN
Dive into probability with us as we tackle the problem of selecting a 4-digit PIN without repeated digits. In this tutorial, we explore how to calculate the probability of creating a PIN with no repeated digits. Through a step-by-step explanation, we elucidate the concept of probability and provide a clear understanding of the solution process. Whether you're concerned about PIN security or interested in probability theory, this video offers valuable insights into understanding probabilities in practical scenarios. Join us to deepen your appreciation for probability and its applications in everyday life!
In this video we solve the problem:
A 4-digit PIN number is selected. What is the probability that there are no repeated digits?
#probability #mathhelp #MinuteMath #MathMadeSimple #MathTutorial #mathinsociety #oer #MathSkills #Education #math
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
Combinations: Selecting Student Council Representatives
Join us as we explore combinations in the context of selecting student council representatives from a class. In this tutorial, we tackle the problem of determining how many different ways a group of four students can be chosen from a 35-member class to represent the class on the student council. Through a systematic explanation, we elucidate the concept of combinations and provide a clear understanding of the solution process. Whether you're involved in student leadership or interested in combinatorial mathematics, this video offers valuable insights into understanding combinations in practical scenarios. Tune in to deepen your appreciation for combinations and their role in forming representative groups!
In this video we solve this problem:
A group of four students is to be chosen from a 35-member class to represent the class on the student council. How many ways can this be done?
#probability #MathHelp #MinuteMath #MathMadeSimple #MathTutorial #mathinsociety #oer #MathSkills #Education #math
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.
4
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Permutations: Selecting an Executive Committee
Explore permutations in organizational structure as we tackle the problem of selecting an executive committee from a board of directors. In this tutorial, we analyze how many different ways a four-person executive committee (president, vice-president, secretary, treasurer) can be chosen from a 16-member board of directors of a non-profit organization. Through a systematic explanation, we elucidate the concept of permutations and provide a clear understanding of the solution process. Whether you're involved in organizational management or interested in combinatorial mathematics, this video offers valuable insights into understanding permutations in practical contexts. Join us to deepen your appreciation for permutations and their role in forming executive committees!
In this video we solve this problem:
How many ways can a four-person executive committee (president, vice-president, secretary, treasurer) be selected from a 16-member board of directors of a non-profit organization?
#probability #MathHelp #MinuteMath #MathMadeSimple #MathTutorial #mathinsociety #oer #MathSkills #Education #math
Visit our website Math Help and Math Merch:
https://minutemath.com/
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Personal Instagram: https://www.instagram.com/gannonforpresident/
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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.