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Euler's Gem: The Polyhedron Formula and the Birth of Topology
by David S. RichesonHow a simple equation reshaped mathematicsLeonhard Euler’s polyhedron formula describes the structure of many objects—from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. Yet Euler’s theorem is so simple it can be explained to a child. From ancient Greek geometry to today’s cutting-edge research, Euler’s Gem celebrates the discovery of Euler’s beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical idea’s many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a who’s who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem’s development, Euler’s Gem will fascinate every mathematics enthusiast. This paperback edition contains a new preface by the author.
Eulerian Numbers
by T. Kyle PetersenThis text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian polynomials, as well as the weak order and the shard intersection order of the symmetric group. The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian numbers are replaced with Narayana numbers. Again there is a progression from combinatorics to geometry, including discussion of the associahedron and the lattice of noncrossing partitions. The final chapters discuss how both the Eulerian and Narayana numbers have analogues in any finite Coxeter group, with many of the same enumerative and geometric properties. There are four supplemental chapters throughout, which survey more advanced topics, including some open problems in combinatorial topology. This textbook will serve a resource for experts in the field as well as for graduate students and others hoping to learn about these topics for the first time.
Eureka Math - A Story of Functions: Algebra I (9) Student Edition Book #1 (modules 1-3)
by Great MindsEureka Math helps students truly understand mathematics and connect it to the real world, preparing them to solve problems they have not encountered.
Eureka Math 2, [Grade] 1, Learn: Units of Ten, Module 5: Place Value Concepts to Compare, Add, and Substract
by Great MindsEureka Math 2, [Grade] 1, Learn: Units of Ten, Module 5: Place Value Concepts to Compare, Add, and Substract
Eureka Math Algebra I Study Guide
by Great MindsThe Eureka Math curriculum provides detailed daily lessons and assessments to support teachers in integrating the Common Core State Standards for Mathematics (CCSSM) into their instruction. The companion guides to Eureka Math gather the key components of the curriculum for each grade into a single location. Both users and non-users of Eureka Math can benefit equally from the content presented. The CCSSM require careful study. A thorough study of the Guidebooks is a professional development experience in itself as users come to better understand the standards and the associated content. Each book includes narratives that provide educators with an overview of what students learn throughout the year, information on alignment to the instructional shifts and the standards, design of curricular components, and descriptions of mathematical models. The Guidebooks can serve as either a self-study professional development resource or as the basis for a deep group study of the standards for a particular grade. For teachers who are either brand new to the classroom or to the Eureka Math curriculum, the Grade Level Guidebooks introduce them not only to Eureka Math but also to the content of the grade level in a way they will find manageable and useful. Teachers already familiar with the curriculum will also find this resource valuable as it allows for a meaningful study of the grade level content in a way that highlights the coherence between modules and topics. The Guidebooks allow teachers to obtain a firm grasp on what it is that students should master during the year.
Eureka Math Curriculum Guide
by Great MindsEureka Math is a comprehensive, content-rich PreK-12 curriculum that follows the focus and coherence of the Common Core State Standards in Mathematics (CCSSM) and carefully sequences the mathematical progressions into expertly crafted instructional modules. The companion Study Guides to Eureka Math gather the key components of the curriculum for each grade into a single location, unpacking the standards in detail so that both users and non-users of Eureka Math can benefit equally from the content presented. Each of the Eureka Math Curriculum Study Guides includes narratives that provide educators with an overview of what students should be learning throughout the year, information on alignment to the instructional shifts and the standards, design of curricular components, approaches to differentiated instruction, and descriptions of mathematical models. The Study Guides can serve as either a self-study professional development resource or as the basis for a deep group study of the standards for a particular grade. For teachers who are new to the classroom or the standards, the Study Guides introduce them not only to Eureka Math but also to the content of the grade level in a way they will find manageable and useful. Teachers familiar with the Eureka Math curriculum will also find this resource valuable as it allows for a meaningful study of the grade level content in a way that highlights the coherence between modules and topics. The Study Guides allow teachers to obtain a firm grasp on what it is that students should master during the year. The Eureka Math Curriculum Study Guide, Grade 2 provides an overview of all of the Grade 2 modules, including Sums and Differences to 20; Addition and Subtraction of Length Units; Place Value, Counting, and Comparison of Numbers to 1,000; Addition and Subtraction Within 200 with Word Problems to 100; Addition and Subtraction Within 1,000 with Word Problems to 100; Foundations of Multiplication and Division; Problem Solving with Length, Money, and Data; and Time, Shapes, and Fractions as Equal Parts of Shapes.
Eureka Math Geometry Study Guide
by Great MindsThe Eureka Math curriculum provides detailed daily lessons and assessments to support teachers in integrating the Common Core State Standards for Mathematics (CCSSM) into their instruction. The companion guides to Eureka Math gather the key components of the curriculum for each grade into a single location. Both users and non-users of Eureka Math can benefit equally from the content presented. The CCSSM require careful study. A thorough study of the Guidebooks is a professional development experience in itself as users come to better understand the standards and the associated content. Each book includes narratives that provide educators with an overview of what students learn throughout the year, information on alignment to the instructional shifts and the standards, design of curricular components, and descriptions of mathematical models. The Guidebooks can serve as either a self-study professional development resource or as the basis for a deep group study of the standards for a particular grade. For teachers who are either brand new to the classroom or to the Eureka Math curriculum, the Grade Level Guidebooks introduce them not only to Eureka Math but also to the content of the grade level in a way they will find manageable and useful. Teachers already familiar with the curriculum will also find this resource valuable as it allows for a meaningful study of the grade level content in a way that highlights the coherence between modules and topics. The Guidebooks allow teachers to obtain a firm grasp on what it is that students should master during the year.
Eureka Math Grade 6 Study Guide
by Great MindsEureka Math is a comprehensive, content-rich PreK-12 curriculum that follows the focus and coherence of the Common Core State Standards in Mathematics (CCSSM) and carefully sequences the mathematical progressions into expertly crafted instructional modules. The companion Study Guides to Eureka Math gather the key components of the curriculum for each grade into a single location, unpacking the standards in detail so that both users and non-users of Eureka Math can benefit equally from the content presented. Each of the Eureka Math Curriculum Study Guides includes narratives that provide educators with an overview of what students should be learning throughout the year, information on alignment to the instructional shifts and the standards, design of curricular components, approaches to differentiated instruction, and descriptions of mathematical models. The Study Guides can serve as either a self-study professional development resource or as the basis for a deep group study of the standards for a particular grade. For teachers who are new to the classroom or the standards, the Study Guides introduce them not only to Eureka Math but also to the content of the grade level in a way they will find manageable and useful. Teachers familiar with the Eureka Math curriculum will also find this resource valuable as it allows for a meaningful study of the grade level content in a way that highlights the coherence between modules and topics. The Study Guides allow teachers to obtain a firm grasp on what it is that students should master during the year. The Eureka Math Curriculum Study Guide, Grade 6 provides an overview of all of the Grade 6 modules, including Ratios and Unit Rates; Arithmetic Operations Including Dividing by a Fraction; Rational Numbers; Expressions and Equations; Area, Surface Area, and Volume Problems; Statistics.
Eureka Math Grade 7 Study Guide
by Great MindsEureka Math is a comprehensive, content-rich PreK-12 curriculum that follows the focus and coherence of the Common Core State Standards in Mathematics (CCSSM) and carefully sequences the mathematical progressions into expertly crafted instructional modules. The companion Study Guides to Eureka Math gather the key components of the curriculum for each grade into a single location, unpacking the standards in detail so that both users and non-users of Eureka Math can benefit equally from the content presented. Each of the Eureka Math Curriculum Study Guides includes narratives that provide educators with an overview of what students should be learning throughout the year, information on alignment to the instructional shifts and the standards, design of curricular components, approaches to differentiated instruction, and descriptions of mathematical models. The Study Guides can serve as either a self-study professional development resource or as the basis for a deep group study of the standards for a particular grade. For teachers who are new to the classroom or the standards, the Study Guides introduce them not only to Eureka Math but also to the content of the grade level in a way they will find manageable and useful. Teachers familiar with the Eureka Math curriculum will also find this resource valuable as it allows for a meaningful study of the grade level content in a way that highlights the coherence between modules and topics. The Study Guides allow teachers to obtain a firm grasp on what it is that students should master during the year. The Eureka Math Curriculum Study Guide, Grade 7 provides an overview of all of the Grade 7 modules, including Ratios and Proportional Relationships; Rational Numbers; Expressions and Equations; Percent and Proportional Relationships; Statistics and Probability; Geometry.
Eureka Math Practice: Grade 3 Fluency, Modules 5-7
by Great MindsEureka Math fluency activities provide differentiated practice through a variety of formats--some are conducted orally, some use manipulatives, others use a personal whiteboard, and still others use a handout and paper-and-pencil format. Eureka Math Practice provides each student with the printed fluency exercises for his or her grade level.
Eureka Math Study Guide
by Great MindsEureka Math is a comprehensive, content-rich PreK-12 curriculum that follows the focus and coherence of the Common Core State Standards in Mathematics (CCSSM) and carefully sequences the mathematical progressions into expertly crafted instructional modules. The companion Study Guides to Eureka Math gather the key components of the curriculum for each grade into a single location, unpacking the standards in detail so that both users and non-users of Eureka Math can benefit equally from the content presented. Each of the Eureka Math Curriculum Study Guides includes narratives that provide educators with an overview of what students should be learning throughout the year, information on alignment to the instructional shifts and the standards, design of curricular components, approaches to differentiated instruction, and descriptions of mathematical models. The Study Guides can serve as either a self-study professional development resource or as the basis for a deep group study of the standards for a particular grade. For teachers who are new to the classroom or the standards, the Study Guides introduce them not only to Eureka Math but also to the content of the grade level in a way they will find manageable and useful. Teachers familiar with the Eureka Math curriculum will also find this resource valuable as it allows for a meaningful study of the grade level content in a way that highlights the coherence between modules and topics. The Study Guides allow teachers to obtain a firm grasp on what it is that students should master during the year. The Eureka Math Curriculum Study Guide, Grade 1 provides an overview of all of the Grade 1 modules, including Sums and Differences to 10; Introduction to Place Value Through Addition and Subtraction Within 20; Ordering and Comparing Length Measurements as Numbers; Place Value, Comparison, Addition and Subtraction to 40; Identifying, Composing, and Partitioning Shapes; and Place Value, Comparison, Addition and Subtraction to 100.
Eureka Math Study Guide: A Story of Units, Grade 3 (Common Core Mathematics)
by Great MindsEureka Math is a comprehensive, content-rich PreK–12 curriculum that follows the focus and coherence of the Common Core State Standards in Mathematics (CCSSM) and carefully sequences the mathematical progressions into expertly crafted instructional modules. The companion Study Guides to Eureka Math gather the key components of the curriculum for each grade into a single location, unpacking the standards in detail so that both users and non-users of Eureka Math can benefit equally from the content presented. <P><P> Each of the Eureka Math Curriculum Study Guides includes narratives that provide educators with an overview of what students should be learning throughout the year, information on alignment to the instructional shifts and the standards, design of curricular components, approaches to differentiated instruction, and descriptions of mathematical models. The Study Guides can serve as either a self-study professional development resource or as the basis for a deep group study of the standards for a particular grade. For teachers who are new to the classroom or the standards, the Study Guides introduce them not only to Eureka Math but also to the content of the grade level in a way they will find manageable and useful. Teachers familiar with the Eureka Math curriculum will also find this resource valuable as it allows for a meaningful study of the grade level content in a way that highlights the coherence between modules and topics. The Study Guides allow teachers to obtain a firm grasp on what it is that students should master during the year.<P> The Eureka Math Curriculum Study Guide, Grade 3 provides an overview of all of the Grade 3 modules, including Properties of Multiplication and Division and Solving Problems with Units of 2–5 and 10; Place Value and Problem Solving with Units of Measure; Multiplication and Division with Units of 0, 1, 6–9, and Multiples of 10; Multiplication and Area; Fractions as Numbers on the Number Line; and Collecting and Displaying Data.
Eureka Math Study Guide: A Story of Units, Grade 5 (Common Core Mathematics)
by Great MindsEureka Math is a comprehensive, content-rich PreK–12 curriculum that follows the focus and coherence of the Common Core State Standards in Mathematics (CCSSM) and carefully sequences the mathematical progressions into expertly crafted instructional modules. The companion Study Guides to Eureka Math gather the key components of the curriculum for each grade into a single location, unpacking the standards in detail so that both users and non-users of Eureka Math can benefit equally from the content presented. <P><P> Each of the Eureka Math Curriculum Study Guides includes narratives that provide educators with an overview of what students should be learning throughout the year, information on alignment to the instructional shifts and the standards, design of curricular components, approaches to differentiated instruction, and descriptions of mathematical models. The Study Guides can serve as either a self-study professional development resource or as the basis for a deep group study of the standards for a particular grade. For teachers who are new to the classroom or the standards, the Study Guides introduce them not only to Eureka Math but also to the content of the grade level in a way they will find manageable and useful. Teachers familiar with the Eureka Math curriculum will also find this resource valuable as it allows for a meaningful study of the grade level content in a way that highlights the coherence between modules and topics. The Study Guides allow teachers to obtain a firm grasp on what it is that students should master during the year.<P> The Eureka Math Curriculum Study Guide, Grade 5 provides an overview of all of the Grade 5 modules, including Place Value and Decimal Fractions; Multi-Digit Whole Number and Decimal Fraction Operations; Addition and Subtraction of Fractions; Multiplication and Division of Fractions and Decimal Fractions; Addition and Multiplication with Volume and Areal; Problem Solving with the Coordinate Plane.
Eureka Math, Grade 2, Modules 1, 2, & 3: Grade 2 Student Edition Book #2 (modules 1-3)
by Great MindsNIMAC-sourced textbook
