Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Some Applications of Geometric Thinking is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. But this book isn't a “course” in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves. The goal of Some Applications of Geometric Thinking is to help teachers see that geometric ideas can be used throughout the secondary school curriculum, both as a hub that connects ideas from all parts of secondary school and beyond—algebra, number theory, arithmetic, and data analysis—and as a locus for applications of results and methods from these fields. Some Applications of Geometric Thinking is a volume of the book series “IAS/PCMI—The Teacher Program Series” published by the American Mathematical Society. Each volume in this series covers the content of one Summer School Teacher Program year and is independent of the rest. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Fractions, Tilings, and Geometry is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. The overall goal of the course is an introduction to non-periodic tilings in two dimensions and space-filling polyhedra. While the course does not address quasicrystals, it provides the underlying mathematics that is used in their study. Because of this goal, the course explores Penrose tilings, the irrationality of the golden ratio, the connections between tessellations and packing problems, and Voronoi diagrams in 2 and 3 dimensions. These topics all connect to precollege mathematics, either as core ideas (irrational numbers) or enrichment for standard topics in geometry (polygons, angles, and constructions). But this book isn't a “course” in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes. These materials provide participants with the opportunity for authentic mathematical discovery—participants build mathematical structures by investigating patterns, use reasoning to test and formalize their ideas, offer and negotiate mathematical definitions, and apply their theories and mathematical machinery to solve problems. Fractions, Tilings, and Geometry is a volume of the book series “IAS/PCMI—The Teacher Program Series” published by the American Mathematical Society. Each volume in this series covers the content of one Summer School Teacher Program year and is independent of the rest.
Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Probability and Games is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. This course leads participants through an introduction to probability and statistics, with particular focus on conditional probability, hypothesis testing, and the mathematics of election analysis. These ideas are tied together through low-threshold entry points including work with real and fake coin-flipping data, short games that lead to key concepts, and inroads to connecting the topics to number theory and algebra. But this book isn't a “course” in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes. These materials provide participants with the opportunity for authentic mathematical discovery—participants build mathematical structures by investigating patterns, use reasoning to test and formalize their ideas, offer and negotiate mathematical definitions, and apply their theories and mathematical machinery to solve problems. Probability and Games is a volume of the book series “IAS/PCMI—The Teacher Program Series” published by the American Mathematical Society. Each volume in this series covers the content of one Summer School Teacher Program year and is independent of the rest.
Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Famous Functions in Number Theory is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. But this book isn't a "course" in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves. Famous Functions in Number Theory introduces readers to the use of formal algebra in number theory. Through numerical experiments, participants learn how to use polynomial algebra as a bookkeeping mechanism that allows them to count divisors, build multiplicative functions, and compile multiplicative functions in a certain way that produces new ones. One capstone of the investigations is a beautiful result attributed to Fermat that determines the number of ways a positive integer can be written as a sum of two perfect squares. Famous Functions in Number Theory is a volume of the book series "IAS/PCMI-The Teacher Program Series" published by the American Mathematical Society. Each volume in that series covers the content of one Summer School Teacher Program year and is independent of the rest. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Applications of Algebra and Geometry to the Work of Teaching is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. But this book isn't a "course" in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves. The specific theme developed in Applications of Algebra and Geometry to the Work of Teaching is the use of complex numbers--especially the arithmetic of Gaussian and Eisenstein integers--to investigate some questions that are at the intersection of algebra and geometry, like the classification of Pythagorean triples and the number of representations of an integer as the sum of two squares. Applications of Algebra and Geometry to the Work of Teaching is a volume of the book series "IAS/PCMI-The Teacher Program Series" published by the American Mathematical Society. Each volume in that series covers the content of one Summer School Teacher Program year and is independent of the rest. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
This is the eighth book in the Teacher Program Series. Each book includes a full course in a mathematical focus topic. The topic for this book is the study of continued fractions, including important results involving the Euclidean algorithm, the golden ratio, and approximations to rational and irrational numbers. The course includes 14 problem sets designed for low-threshold, high-ceiling access to the topic, building on one another as the concepts are explored. The book also includes solutions for all the main problems and detailed facilitator notes for those wanting to use this book with students at any level. The course is based on one delivered at the Park City Math Institute in Summer 2018.
This book collects all the relevant material regarding the process of adjudication in construction. It provides clarity for those involved in the adjudication process or related proceedings with detailed and reliable analysis of them supported by statutory provisions and judicial observations. Adjudication in Construction Law discusses the role of ‘true value’ adjudications following smash and grab decisions on the basis of the absence of a pay less notice, the restraint of adjudication by injunction, hybrid contracts dealing with both construction operations and other operations and timing and content of payment notices and pay less notices. Additionally, this book includes a summary of the different procedures adopted in other jurisdictions, as well as an explanation of the payment procedures under the statutory framework. It also goes on to append all the relevant statutory material, contractual adjudication procedures and forms. A new feature of this edition is a detailed analysis and discussion of the development and of the ‘rules’ relating to the acceptability of a wrong answer provided that the right question has been dealt with, only one dispute being susceptible to adjudication and the necessity or otherwise of a dispute ‘arising under’ the construction contract. A clear and comprehensive aid, this book is an essential read for lawyers or construction professionals involved in adjudication.
Mystery fiction takes place in a centered world, one whose most distinctive characteristic is motivation (of behavior and signs). Built on a faith in foundations, it insists upon the solidity of social life, the validity of social conventions, and the sanctity of signs. Mystery assures us that motives exist for both words and deeds.".
Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Probability and Games is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. This course leads participants through an introduction to probability and statistics, with particular focus on conditional probability, hypothesis testing, and the mathematics of election analysis. These ideas are tied together through low-threshold entry points including work with real and fake coin-flipping data, short games that lead to key concepts, and inroads to connecting the topics to number theory and algebra. But this book isn't a “course” in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes. These materials provide participants with the opportunity for authentic mathematical discovery—participants build mathematical structures by investigating patterns, use reasoning to test and formalize their ideas, offer and negotiate mathematical definitions, and apply their theories and mathematical machinery to solve problems. Probability and Games is a volume of the book series “IAS/PCMI—The Teacher Program Series” published by the American Mathematical Society. Each volume in this series covers the content of one Summer School Teacher Program year and is independent of the rest.
Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Moving Things Around is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. But this book isn't a “course” in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves. The goal of Moving Things Around is to help participants make what might seem to be surprising connections among seemingly different areas: permutation groups, number theory, and expansions for rational numbers in various bases, all starting from the analysis of card shuffles. Another goal is to use these connections to bring some coherence to several ideas that run throughout school mathematics—rational number arithmetic, different representations for rational numbers, geometric transformations, and combinatorics. The theme of seeking structural similarities is developed slowly, leading, near the end of the course, to an informal treatment of isomorphism. Moving Things Around is a volume of the book series “IAS/PCMI—The Teacher Program Series” published by the American Mathematical Society. Each volume in this series covers the content of one Summer School Teacher Program year and is independent of the rest.
Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Fractions, Tilings, and Geometry is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. The overall goal of the course is an introduction to non-periodic tilings in two dimensions and space-filling polyhedra. While the course does not address quasicrystals, it provides the underlying mathematics that is used in their study. Because of this goal, the course explores Penrose tilings, the irrationality of the golden ratio, the connections between tessellations and packing problems, and Voronoi diagrams in 2 and 3 dimensions. These topics all connect to precollege mathematics, either as core ideas (irrational numbers) or enrichment for standard topics in geometry (polygons, angles, and constructions). But this book isn't a “course” in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes. These materials provide participants with the opportunity for authentic mathematical discovery—participants build mathematical structures by investigating patterns, use reasoning to test and formalize their ideas, offer and negotiate mathematical definitions, and apply their theories and mathematical machinery to solve problems. Fractions, Tilings, and Geometry is a volume of the book series “IAS/PCMI—The Teacher Program Series” published by the American Mathematical Society. Each volume in this series covers the content of one Summer School Teacher Program year and is independent of the rest.
Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Moving Things Around is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. But this book isn't a "course" in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves. The goal of Moving Things Around is to help participants make what might seem to be surprising connections among seemingly different areas: permutation groups, number theory, and expansions for rational numbers in various bases, all starting from the analysis of card shuffles. Another goal is to use these connections to bring some coherence to several ideas that run throughout school mathematics-rational number arithmetic, different representations for rational numbers, geometric transformations, and combinatorics. The theme of seeking structural similarities is developed slowly, leading, near the end of the course, to an informal treatment of isomorphism. Moving Things Around is a volume of the book series "IAS/PCMI-The Teacher Program Series" published by the American Mathematical Society. Each volume in this series covers the content of one Summer School Teacher Program year and is independent of the rest
Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Fractions, Tilings, and Geometry is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. The overall goal of the course is an introduction to non-periodic tilings in two dimensions and space-filling polyhedra. While the course does not address quasicrystals, it provides the underlying mathematics that is used in their study. Because of this goal, the course explores Penrose tilings, the irrationality of the golden ratio, the connections between tesse.
Proceedings of the 23rd annual conference of the Australasian Association for Engineering Education, held in Melbourne in December 2012. The conference theme was 'the profession of engineering education: advancing teaching, research and careers' and the conference explored opportunities for improving teaching and scholarship, rigorous research in engineering education and career advancement as an engineering educator.
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