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Guide to Teaching Data Science: An Interdisciplinary Approach
by Orit Hazzan Koby MikeData science is a new field that touches on almost every domain of our lives, and thus it is taught in a variety of environments. Accordingly, the book is suitable for teachers and lecturers in all educational frameworks: K-12, academia and industry.This book aims at closing a significant gap in the literature on the pedagogy of data science. While there are many articles and white papers dealing with the curriculum of data science (i.e., what to teach?), the pedagogical aspect of the field (i.e., how to teach?) is almost neglected. At the same time, the importance of the pedagogical aspects of data science increases as more and more programs are currently open to a variety of people.This book provides a variety of pedagogical discussions and specific teaching methods and frameworks, as well as includes exercises, and guidelines related to many data science concepts (e.g., data thinking and the data science workflow), main machine learning algorithms and concepts (e.g., KNN, SVM, Neural Networks, performance metrics, confusion matrix, and biases) and data science professional topics (e.g., ethics, skills and research approach).Professor Orit Hazzan is a faculty member at the Technion’s Department of Education in Science and Technology since October 2000. Her research focuses on computer science, software engineering and data science education. Within this framework, she studies the cognitive and social processes on the individual, the team and the organization levels, in all kinds of organizations.Dr. Koby Mike is a Ph.D. graduate from the Technion's Department of Education in Science and Technology under the supervision of Professor Orit Hazzan. He continued his post-doc research on data science education at the Bar-Ilan University, and obtained a B.Sc. and an M.Sc. in Electrical Engineering from Tel Aviv University.
A Guide to the Classification Theorem for Compact Surfaces (Geometry and Computing #9)
by Dianna Xu Jean GallierThis welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy and formal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example. Ideal for students whose mastery of algebraic topology may be a work-in-progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincaré characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learning where it is required, without interrupting the carefully planned structure of the core exposition. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuine confidence in its use and in so doing encourage readers to move on to a deeper exploration of the versatile and valuable techniques available in algebraic topology.
Guidebook to R Graphics Using Microsoft® Windows
by Kunio TakezawaIntroduces the graphical capabilities of R to readers new to the software Due to its flexibility and availability, R has become the computing software of choice for statistical computing and generating graphics across various fields of research. Guidebook to R Graphics Using Microsoft® Windows offers a unique presentation of R, guiding new users through its many benefits, including the creation of high-quality graphics. Beginning with getting the program up and running, this book takes readers step by step through the process of creating histograms, boxplots, strip charts, time series graphs, steam-and-leaf displays, scatterplot matrices, and map graphs. In addition, the book presents: Tips for establishing, saving, and printing graphs along with essential base-package plotting functions Interactive R programs for carrying out common tasks such as inputting values, moving data on a natural spline, adjusting three-dimensional graphs, and understanding simple and local linear regression Various external packages for R that help to create more complex graphics like rimage, gplots, ggplot2, tripack, rworldmap, and plotrix packages Throughout the book, concise explanations of key concepts of R graphics assist readers in carrying out the presented procedures, and any coverage of functions is clearly written out and displayed in the text as demos. The discussed techniques are accompanied by a wealth of screenshots and graphics with related R code available on the book's FTP site, and numerous exercises allow readers to test their understanding of the presented material. Guidebook to R Graphics Using Microsoft® Windows is a valuable resource for researchers in the fields of statistics, public health, business, and the life and social sciences who use or would like to learn how to use R to create visual representations of data. The book can also be used as a supplement for courses on statistical analysis at the upper-undergraduate level.
Guided Math in Action: Building Each Student's Mathematical Proficiency with Small-Group Instruction
by Nicki NewtonLearn how to help elementary students build mathematical proficiency with purposeful, standards-based, differentiated, engaging small-group instruction. This best-selling book from Dr. Nicki Newton provides a repertoire of in-depth strategies for conducting effective guided math lessons, scaffolding and managing learning in small groups, and assessing learning. Dr. Newton shows you the framework for guided math lessons and then helps you develop an action plan to get started. This fully updated second edition features helpful new sections on beliefs, teacher moves, planning, talking and questioning, and kidwatching. It also contains a brand new study guide to help you get the most out of the book and use it with your colleagues. Perfect for teachers, coaches, and supervisors, this popular resource is filled with tools you can use immediately, including anchor charts, schedules, templates, and graphic organizers. With the practical help throughout, you’ll be able to implement Tier 1 and 2 lessons easily. This book will help you guide all your students to becoming more competent, flexible, and confident mathematicians!
Guided Math Lessons in Fifth Grade: Getting Started
by Nicki NewtonGuided Math Lessons in Fifth Grade provides detailed lessons to help you bring guided math groups to life. Based on the bestselling Guided Math in Action, this practical book offers 16 lessons, taught in a round of 3—concrete, pictorial and abstract. The lessons are based on the priority standards and cover fluency, word problems, fractions, and decimals. Author Dr. Nicki Newton shows you the content, as well as the practices and processes, that should be worked on in the lessons so that students not only learn the content but also how to solve problems, reason, communicate their thinking, model, use tools, use precise language and see structure and patterns. Throughout the book, you’ll find tools, templates and blackline masters so that you can instantly adapt the lesson to your specific needs and use it right away. With the easy-to-follow plans in this book, students can work more effectively in small guided math groups—and have loads of fun along the way! Remember that guided math groups are about doing the math. So throughout these lessons, you will see students working with manipulatives to make meaning, doing mathematical sketches to show what they understand and can make sense of the abstract numbers. When students are given the opportunities to make sense of the math in hands-on and visual ways, then the math begins to make sense to them!
Guided Math Lessons in First Grade: Getting Started
by Nicki NewtonGuided Math Lessons in First Grade provides detailed lessons to help you bring guided math groups to life. Based on the bestselling Guided Math in Action, this practical book offers 16 lessons, taught in a round of 3—concrete, pictorial, and abstract. The lessons are based on the priority standards and cover fluency, word problems, operations and algebraic thinking, and place value. Author Dr. Nicki Newton shows you the content as well as the practices and processes that should be worked on in the lessons, so that students not only learn the content but also how to solve problems, reason, communicate their thinking, model, use tools, use precise language, and see structure and patterns. Throughout the book, you’ll find tools, templates, and blackline masters so that you can instantly adapt the lesson to your specific needs and use it right away. With the easy-to-follow plans in this book, students can work more effectively in small guided math groups—and have loads of fun along the way!
Guided Math Lessons in Fourth Grade: Getting Started
by Nicki NewtonGuided Math Lessons in Fourth Grade provides detailed lessons to help you bring guided math groups to life. Based on the bestselling Guided Math in Action, this practical book offers 16 lessons, taught in a round of three–concrete, pictorial and abstract. The lessons are based on the priority standards and cover fluency, word problems, fractions and place value. Author Dr. Nicki Newton shows you the content as well as the practices and processes that should be worked on in the lessons, so that students not only learn the content but also how to solve problems, reason, communicate their thinking, model, use tools, use precise language, and see structure and patterns. Throughout the book, you’ll find tools, templates and blackline masters so that you can instantly adapt the lesson to your specific needs and use it right away. With the easy-to-follow plans in this book, students can more work effectively in small guided math groups—and have loads of fun along the way! Remember that guided math groups are about doing the math. So doing mathematical sketches to show what they understand and can make sense of the abstract numbers. When students are given the opportunities to make sense of the math in hands-on and visual ways, then the math begins to make sense!
Guided Math Lessons in Kindergarten: Getting Started
by Nicki NewtonGuided Math Lessons in Kindergarten provides detailed lessons to help you bring guided math groups to life. Based on the bestselling Guided Math in Action, this practical book offers 16 lessons, taught in a round of three—concrete, pictorial and abstract. The lessons are based on the priority standards and cover fluency, word problems, counting and cardinality, and place value. Author Dr. Nicki Newton shows you the content as well as the practices and processes that should be worked on in the lessons, so that students not only learn the content but also how to solve problems, reason, communicate their thinking, model, use tools, use precise language, and see structure and patterns. Throughout the book, you’ll find tools, templates and blackline masters so that you can instantly adapt the lesson to your specific needs and use it right away. With the easy-to-follow plans in this book, students can more work effectively in small guided math groups—and have loads of fun along the way! Remember that guided math groups are about doing the math. So throughout these lessons you will see students working with manipulatives to make meaning, doing mathematical sketches to show what they understand and can make sense of the abstract numbers. When students are given the opportunities to make sense of the math in hands-on and visual ways, then the math begins to make sense to them!
Guided Math Lessons in Second Grade: Getting Started
by Nicki NewtonGuided Math Lessons in Second Grade provides detailed lessons to help you bring guided math groups to life. Based on the bestselling Guided Math in Action, this practical book offers 16 lessons, taught in a round of 3—concrete, pictorial, and abstract. The lessons are based on the priority standards and cover fluency, word problems, operations and algebraic thinking, and place value. Author Dr. Nicki Newton shows you the content as well as the practices and processes that should be worked on in the lessons, so that students not only learn the content but also how to solve problems, reason, communicate their thinking, model, use tools, use precise language, and see structure and patterns. Throughout the book, you’ll find tools, templates, and blackline masters so that you can instantly adapt the lesson to your specific needs and use it right away. With the easy-to-follow plans in this book, students can work more effectively in small guided math groups—and have loads of fun along the way!
Guided Math Lessons in Third Grade: Getting Started
by Nicki NewtonGuided Math Lessons in Third Grade provides detailed lessons to help you bring guided math groups to life. Based on the bestselling Guided Math in Action, this practical book offers 16 lessons, taught in a round of 3—concrete, pictorial and abstract. The lessons are based on the priority standards and cover fluency, word problems, fractions and place value. Author Dr. Nicki Newton shows you the content as well as the practices and processes that should be worked on in the lessons, so that students not only learn the content but also how to solve problems, reason, communicate their thinking, model, use tools, use precise language, and see structure and patterns. Throughout the book, you’ll find tools, templates and blackline masters so that you can instantly adapt the lesson to your specific needs and use it right away. With the easy-to-follow plans in this book, students can work more effectively in small guided math groups—and have loads of fun along the way! Remember that guided math groups are about doing the math. So throughout these lessons you will see students working with manipulatives to make meaning, doing mathematical sketches to show what they understand and can make sense of the abstract numbers. When students are given the opportunities to make sense of the math in hands-on and visual ways, then the math begins to make sense to them!
Guidelines for Applying Cohesive Models to the Damage Behaviour of Engineering Materials and Structures
by Karl-Heinz Schwalbe Ingo Scheider Alfred CornecThis brief provides guidance for the application of cohesive models to determine damage and fracture in materials and structural components. This can be done for configurations with or without a pre-existing crack. Although the brief addresses structural behaviour, the methods described herein may also be applied to any deformation induced material damage and failure, e.g. those occurring during manufacturing processes. The methods described are applicable to the behaviour of ductile metallic materials and structural components made thereof. Hints are also given for applying the cohesive model to other materials.
El gumbo más delicioso / Yumbo Gumbo (Storytelling Math)
by Keila V. Dawson¡Celebra la diversidad, las matemáticas y el poder de contar cuentos en esta edición bilingüe (español e inglés)!Celebrate diversity, math, and the power of storytelling with this bilingual (Spanish and English) edition!¡Los abuelos de Annabelle finalmente le enseñarán a cocinar gumbo! Pero la familia no puede ponerse de acuerdo sobre qué tipo de gumbo hacer. Votan por su favorito, pero el resultado de la votación es un empate. ¿Y ahora qué? Una exploración lúdica de los datos y el razonamiento socioemocional, presentando personajes criollos de Luisiana y un glosario de palabras criollas de Luisiana.Storytelling Math celebra a los niños usando las matemáticas en sus aventuras diarias mientras juegan, construyen y descubren el mundo que les rodea. Historias alegres y actividades manuales hacen que sea fácil para los niños y sus adultos explorar las matemáticas cotidianas juntos. Desarrollado en colaboración con expertos en matemáticas de TERC, una organización educativa educativa sin fines de lucro con enfoque en en ciencia, tecnología, ingeniería y matemáticas (STEM, por sus siglas en inglés), bajo una subvención de la Fundación Heising-Simons.Annabelle's grandparents are finally going to teach her how to cook gumbo! But the family can't agree on what type of gumbo to make. They vote for their favorite, but the vote results in a tie. Now what? A playful exploration of data and social-emotional reasoning, featuring Louisiana Creole characters and a glossary of Louisiana Creole words.Storytelling Math celebrates children using math in their daily adventures as they play, build, and discover the world around them. Joyful stories and hands-on activities make it easy for kids and their grown-ups to explore everyday math together. Developed in collaboration with math experts at STEM education nonprofit TERC, under a grant from the Heising-Simons Foundation.
Gut gepackt – Kein Bit zu viel: Kompression digitaler Daten verständlich erklärt (essentials)
by Olaf ManzBei der heutigen Datenflut, die auf Speichermedien und im Internet kursiert, ist die Kompression digitaler Daten nach wie vor ein immens wichtiger Aspekt bei Datenübertragung und -speicherung. Dieses essential erläutert ohne theoretischen Überbau und mit elementaren mathematischen und informatischen Methoden die wichtigsten Kompressionsverfahren, so unter anderem die Entropiecodierungen von Shannon-Fano und von Huffman, sowie die Wörterbuchcodierungen der Lempel-Ziv-Familie. Ausführlich eingegangen wird auch auf Irrelevanzreduktion und die Quantisierung bei optischen und akustischen Signalen, die die Unzulänglichkeiten des menschlichen Auges und Ohres zur Datenkompression ausnutzen. Illustriert wird das Ganze anhand gängiger Praxisanwendungen aus dem alltäglichen Umfeld. Die Aufbereitung erlaubt den Einsatz beispielsweise in Arbeitsgruppen an MINT-Schulen, bei Einführungskursen an Hochschulen und ist auch für interessierte Laien geeignet.
Guts of Surfaces and the Colored Jones Polynomial
by David Futer Efstratia Kalfagianni Jessica PurcellThis monograph derives direct and concrete relations between colored Jones polynomials and the topology of incompressible spanning surfaces in knot and link complements. Under mild diagrammatic hypotheses, we prove that the growth of the degree of the colored Jones polynomials is a boundary slope of an essential surface in the knot complement. We show that certain coefficients of the polynomial measure how far this surface is from being a fiber for the knot; in particular, the surface is a fiber if and only if a particular coefficient vanishes. We also relate hyperbolic volume to colored Jones polynomials. Our method is to generalize the checkerboard decompositions of alternating knots. Under mild diagrammatic hypotheses, we show that these surfaces are essential, and obtain an ideal polyhedral decomposition of their complement. We use normal surface theory to relate the pieces of the JSJ decomposition of the complement to the combinatorics of certain surface spines (state graphs). Since state graphs have previously appeared in the study of Jones polynomials, our method bridges the gap between quantum and geometric knot invariants.
The H-Function
by Ram Kishore Saxena Hans J. Haubold A. M. MathaiThe two main topics emphasized in this book, special functions and fractional calculus, are currently under fast development in theory and application to many problems in statistics, physics, and engineering, particularly in condensed matter physics, plasma physics, and astrophysics. The book begins by setting forth definitions, contours, existence conditions, and particular cases of the H-function. The authors then deal with Laplace, Fourier, Hankel, and other transforms. As these relations are explored, fractional calculus and its relations to H-functions emerge with important results on fractional differentiation and fractional integral operators. The latter chapters explore applications of H-functions in statistical distribution theory, structures of random variables, generalized distributions, Mathai's pathway models, and versatile integrals. The authors also present an introduction to functions of matrix argument, with special focus on the space of Hermitian positive matrices. The book concludes with the most recent applications of H-functions and fractional calculus to physical problems in reactions, diffusion, reaction-diffusion theory, statistics, superstatistics, and generalized entropies.
H-Transforms: Theory and Applications
by Anatoly A. KilbasAlong with more than 2100 integral equations and their solutions, this handbook outlines exact analytical methods for solving linear and nonlinear integral equations and provides an evaluation of approximate methods. Each section provides examples that show how methods can be applied to specific equations.
Haar Wavelets
by Ülo Lepik Helle HeinThis is the first book to present a systematic review of applications of the Haar wavelet method for solving Calculus and Structural Mechanics problems. Haar wavelet-based solutions for a wide range of problems, such as various differential and integral equations, fractional equations, optimal control theory, buckling, bending and vibrations of elastic beams are considered. Numerical examples demonstrating the efficiency and accuracy of the Haar method are provided for all solutions.
Hadamard Matrices: Constructions using Number Theory and Linear Algebra
by Jennifer Seberry Mieko YamadaUp-to-date resource on Hadamard matrices Hadamard Matrices: Constructions using Number Theory and Algebra provides students with a discussion of the basic definitions used for Hadamard Matrices as well as more advanced topics in the subject, including: Gauss sums, Jacobi sums and relative Gauss sums Cyclotomic numbers Plug-in matrices, arrays, sequences and M-structure Galois rings and Menon Hadamard differences sets Paley difference sets and Paley type partial difference sets Symmetric Hadamard matrices, skew Hadamard matrices and amicable Hadamard matrices A discussion of asymptotic existence of Hadamard matrices Maximal determinant matrices, embeddability of Hadamard matrices and growth problem for Hadamard matrices The book can be used as a textbook for graduate courses in combinatorics, or as a reference for researchers studying Hadamard matrices. Utilized in the fields of signal processing and design experiments, Hadamard matrices have been used for 150 years, and remain practical today. Hadamard Matrices combines a thorough discussion of the basic concepts underlying the subject matter with more advanced applications that will be of interest to experts in the area.
Hadamard Products of Projective Varieties (Frontiers in Mathematics)
by Cristiano Bocci Enrico CarliniThis monograph deals with the Hadamard products of algebraic varieties. A typical subject of study in Algebraic Geometry are varieties constructed from other geometrical objects. The most well-known example is constituted by the secant varieties, which are obtained through the construction of the join of two algebraic varieties, which, in turn, is based on the operation of summing two vectors. However, other constructions are possible through a change of the basic operation. One remarkable case is based on the Hadamard product of two vectors. While secant varieties of algebraic varieties have been studied extensively and systematically, the same is not yet true for the Hadamard products of algebraic varieties. This monograph aims to bridge this gap in the literature.The topic is presented in a self-contained manner, and it is accessible to all readers with sound knowledge of Commutative Algebra and Algebraic Geometry. Both experienced researchers and students can profit from this monograph, which will guide them through the subject. The foundational aspects of the Hadamard products of algebraic varieties are covered and some connections both within and outside Algebraic Geometry are presented. The theoretical and algorithmic aspects of the subject are considered to demonstrate the effectiveness of the results presented. Thus, this monograph will also be useful to researchers in other fields, such as Algebraic Statistics, since it provides several algebraic and geometric results on such products.
Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities
by Bashir Ahmad Ahmed Alsaedi Sotiris K. Ntouyas Jessada TariboonThis book focuses on the recent development of fractional differential equations, integro-differential equations, and inclusions and inequalities involving the Hadamard derivative and integral. Through a comprehensive study based in part on their recent research, the authors address the issues related to initial and boundary value problems involving Hadamard type differential equations and inclusions as well as their functional counterparts. The book covers fundamental concepts of multivalued analysis and introduces a new class of mixed initial value problems involving the Hadamard derivative and Riemann-Liouville fractional integrals. In later chapters, the authors discuss nonlinear Langevin equations as well as coupled systems of Langevin equations with fractional integral conditions. Focused and thorough, this book is a useful resource for readers and researchers interested in the area of fractional calculus.
Hahalis and the Labour of Love: A Social Movement on Buka Island (Explorations In Anthropology Ser.)
by Eleanor Rimoldi Max RimoldiThis book studies the Hahalis Welfare Society, a Bougainville movement which worked for many years to maintain and reform traditional practices and to retain a degree of autonomy in a world of rapid political change and economic dependency. The first extended ethnography of Buka published in nearly sixty years, this book will be of particular interest to Melanesian specialists.
Hajnal Andréka and István Németi on Unity of Science: From Computing to Relativity Theory Through Algebraic Logic (Outstanding Contributions to Logic #19)
by Judit Madarász Gergely SzékelyThis book features more than 20 papers that celebrate the work of Hajnal Andréka and István Németi. It illustrates an interaction between developing and applying mathematical logic. The papers offer new results as well as surveys in areas influenced by these two outstanding researchers. They also provide details on the after-life of some of their initiatives.Computer science connects the papers in the first part of the book. The second part concentrates on algebraic logic. It features a range of papers that hint at the intricate many-way connections between logic, algebra, and geometry. The third part explores novel applications of logic in relativity theory, philosophy of logic, philosophy of physics and spacetime, and methodology of science. They include such exciting subjects as time travelling in emergent spacetime. The short autobiographies of Hajnal Andréka and István Németi at the end of the book describe an adventurous journey from electric engineering and Maxwell’s equations to a complex system of computer programs for designing Hungary’s electric power system, to exploring and contributing deep results to Tarskian algebraic logic as the deepest core theory of such questions, then on to applications of the results in such exciting new areas as relativity theory in order to rejuvenate logic itself.
The Half-Life of Facts: Why Everything We Know Has an Expiration Date
by Samuel ArbesmanNew insights from the science of science Facts change all the time. Smoking has gone from doctor recommended to deadly. We used to think the Earth was the center of the universe and that Pluto was a planet. For decades, we were convinced that the brontosaurus was a real dinosaur. In short, what we know about the world is constantly changing. But it turns out there’s an order to the state of knowledge, an explanation for how we know what we know. Samuel Arbesman is an expert in the field of scientometrics-literally the science of science. Knowledge in most fields evolves systematically and predictably, and this evolution unfolds in a fascinating way that can have a powerful impact on our lives. Doctors with a rough idea of when their knowledge is likely to expire can be better equipped to keep up with the latest research. Companies and governments that understand how long new discoveries take to develop can improve decisions about allocating resources. And by tracing how and when language changes, each of us can better bridge generational gaps in slang and dialect. Just as we know that a chunk of uranium can break down in a measurable amount of time-a radioactive half-life-so too any given field’s change in knowledge can be measured concretely. We can know when facts in aggregate are obsolete, the rate at which new facts are created, and even how facts spread. Arbesman takes us through a wide variety of fields, including those that change quickly, over the course of a few years, or over the span of centuries. He shows that much of what we know consists of "mesofacts”-facts that change at a middle timescale, often over a single human lifetime. Throughout, he offers intriguing examples about the face of knowledge: what English majors can learn from a statistical analysis of The Canterbury Tales, why it’s so hard to measure a mountain, and why so many parents still tell kids to eat their spinach because it’s rich in iron. The Half-life of Facts is a riveting journey into the counterintuitive fabric of knowledge. It can help us find new ways to measure the world while accepting the limits of how much we can know with certainty. .
Haltungen von Sechstklässlern im Umgang mit Vermutungen in mathematisch-forschenden Kontexten: Theoriebildung und Unterrichtsentwicklung
by Carolin DanzerCarolin Danzer nimmt mit dieser Arbeit den Übergang von der Entwicklung einer Vermutung zur Überprüfung und Begründung oder Widerlegung dieser im Zuge mathematischer Erkenntnisprozesse von Lernenden in den Blick. Im Rahmen einer qualitativen Interviewstudie wird hierbei das Konzept der Haltung sowohl aus theoretischer als auch aus unterrichtspraktischer Perspektive ausdifferenziert. Es gelingt der Autorin, vier idealtypische Haltungen von Mathematiklernenden im Umgang mit Vermutung zu rekonstruieren, die Auswirkungen dieser auf den mathematischen Erkenntnisprozess der Lernenden zu erklären sowie Schlussfolgerungen für das Konzept einer tragfähigen Grundhaltung und die Konzeption von Mathematikunterricht zu ziehen. Damit leistet die Arbeit einen Beitrag sowohl zur mathematikdidaktischen Theoriebildung als auch zur konkreten Unterrichtsentwicklung.
Hamilton-Jacobi Equations: Paola Loreti, Nicoletta Anna Tchou
by Yves Achdou Paola Loreti Nicoletta Tchou Guy Barles Grigory L. Litvinov Hitoshi IshiiThese Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These lecture notes contain four contributions by Yves Achdou (Finite Difference Methods for Mean Field Games), Guy Barles (An Introduction to the Theory of Viscosity Solutions for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations).