Exponential Sums, Hypergeometric Sheaves, and Monodromy Groups
An examination of some of the remarkable connections between group theory and arithmetic algebraic geometry over finite fields Exponential sums have been of great interest ever since Gauss, and their importance in analytic number theory goes back a century to Kloosterman. Grothendieck's creation of the machinery of l-adic cohomology led to the understanding that families of exponential sums give rise to local systems, while Deligne, who gave his general equidistribution theorem after proving the Riemann hypothesis part of the Weil conjectures, established the importance of the monodromy groups of these local systems. Deligne's theorem shows that the monodromy group of the local system incarnating a given family of exponential sums determines key statistical properties of the family of exponential sums in question. Despite the apparent simplicity of this relation of monodromy groups to statistical properties, the actual determination of the monodromy group in any particular situation is highly nontrivial and leads to many interesting questions. This book is devoted to the determination of the monodromy groups attached to various explicit families of exponential sums, especially those attached to hypergeometric sheaves, arguably the simplest local systems on G_m, and to some simple (in the sense of simple to write down) one-parameter families of one-variable sums. These last families turn out to have surprising connections to hypergeometric sheaves. One of the main technical advances of this book is to bring to bear a group-theoretic condition (S+), which, when it applies, implies very strong structural constraints on the monodromy group, and to show that (S+) does indeed apply to the monodromy groups of most hypergeometric sheaves.
L-Functions
This book provides an accessible introduction to the theory of L-functions, emphasising their central role in number theory and their direct applications to key results. Designed to be elementary, it offers readers a clear pathway into the subject, starting from minimal background. It describes several important classes of L-functions -- Riemann and Dedekind zeta functions, Dirichlet L-functions, and Hecke L-functions (for characters with finite image) -- by showing how they are all special cases of the construction, due to Artin, of the L-function of a Galois representation. The analytic properties of abelian L-functions are presented in detail, including the full content of Tate's thesis, which establishes analytic continuation and functional equations via harmonic analysis. General Hecke L-functions are also discussed, using the modern perspective of id癡les and ad癡les to connect their analytic theory with the representation-theoretic approach of Artin's L-functions. A distinguishing feature of this book is its accessibility: while largely avoiding arithmetic geometry, it provides introductions to both algebraic number theory and key aspects of representation theory. This approach ensures that the material is accessible to both beginning graduate students and advanced undergraduates. Applications play a central role throughout, highlighting how L-functions underpin significant results in number theory. The book provides complete proofs of the prime number theorem, Dirichlet's theorem on primes in arithmetic progressions, Chebotarev's density theorem, and the analytic class number formula, demonstrating the power of the theory in solving classical problems. It serves as an ideal introduction for advanced undergraduates and beginning graduate students and can also be a useful reference for preparing a course on the subject.
How Did You Count?
"I hope that this Teacher's Guide supports your own inquiry into children's mathematics, and I hope that the images elicit brilliance from the children you do math with--wherever you and they may count."From the author of the award-winning Which One Doesn't Belong? and How Many? comes How Did You Count?, the latest title in Christopher Danielson's collection that is sure to spark conversation, questioning, and wondering amongst both younger and older students alike.In this innovative Teacher's Guide, Danielson gives you the tools you need to both begin and dig deeper into the How Did You Count? routine. In clear, accessible language, Danielson discusses the mathematical ideas likely to emerge on each page of the How Did You Count? picture book and helps you anticipate and understand your students' likely answers. Through classroom stories, he models listening to, talking about, and delighting in students' ideas around counting, numbers, and operations.Reading this Teacher's Guide alongside your copy of the How Did You Count? children's picture book will help you and your students discover together how the beauty of counting and numerical relationships and structure extends far beyond 1, 2, 3.This listing is for the Teacher's Guide only. There is also a Teacher's Guide and How Did You Count? picture book set available.
How Did You Count?
From the author of the award-winning Which One Doesn't Belong? and How Many? comes How Did You Count?, the latest title in Christopher Danielson's collection that is sure to spark conversation, questioning and wondering amongst both younger and older students alike.This listing is for a hard cover copy of the children's picture book. There is also a Teacher's Guide / Picture book set and a 5-pack of the softcover picture book available.
Math Mammoth Grade 3 Answer Keys, International Version
Math Mammoth Grade 3 Tests and Cumulative Revisions, International Version
Fractions for Dummies
An easy, straightforward, and fun guide for learning fractions and its counterparts Fractions For Dummies is the perfect strategy guide for both understanding and using one of math's most common (and most challenging) topic areas. You'll explore current solving strategies for fraction-related problems, and you'll also discover how to solve problems involving fractions' closely related cousins, decimals and percentages. Dive deep into the basics of these topics before moving on to more advanced uses, such as word problems, with the help of author and experienced math teacher Mark Zegarelli. This straightforward and intuitive book also includes: Techniques for working with mixed numbers (numbers that include whole amounts and fractions) and more Ways to add, subtract, multiply, and divide fractions with whole numbers and with each other Strategies for helping and supporting the young student in your life who's struggling with fractions, decimals, and/or percentages It's time you showed these math areas who's boss. Fractions For Dummies shows you just how easy fractions and the like can be!
Catalan Numbers
Catalan numbers, named after the French-Belgian mathematician Eug癡ne Charles Catalan (1814-1894), arise in a variety of combinatorial problems. They have many interesting properties, a rich history, and numerous arithmetic, number-theoretical, analytical, and combinatorial connections, as well as a variety of classical and modern applications. Considering the long list of open problems and questions related to the classical case, its relatives (Bell numbers, Motzkin numbers, Narayana numbers, etc.) and its generalizations, this book provides a broad perspective on the theory of this class of special numbers that will be of interest to professionals, students, and a general audience.The book begins with the history of the problem, before defining the considered numerical sets. The recurrence equation, closed formula, and generating function are then presented, followed by the simplest properties and number-theoretical properties. Later chapters discuss the relationships between Catalan numbers and other special numbers, as well as their applications and open problems.
Mathtastic Foundation Numbers 1-6
Mathtastic is an off the shelf intervention for teaching number sense. A book for Learning Support Teachers as an intervention at Tier 2 and 3 for students requiring additional support learning number sense skills. The book has an explicit teaching section plus lots of games and activities to practice the skills to fluency. Mathtastic Foundation Level focuses on teaching foundation numbers 1-6 including counting and number formation. The concepts of addition and subtraction are taught and practiced through both and worded problems and number-based. Patterning, doubling and sharing skills are also included as these are key skills. Levels 1,2 & 3 follow on from this and are also available for purchase. Each module can be used as a lesson or can be split over several lessons depending on the time you have available and the speed the student works through the number sense strategies. Lesson components: Thinking problems - these are designed to be open ended and challenge the student to think mathematically. Subitizing - this is the skills of recognising a set of objects without counting and is a key skill which is not always established in students with difficulties in maths.Counting patterns and objects - students need to develop a sense of the number line. Number sense - each session there is a different focus working through the 8 areas of number sense. These are explained and modelled before applying the number sense concept to problems. Games - many students with math difficulties can get anxious about maths and practicing the skills through games is a less threatening way to gain the repetition they need. The games have been chosen to specifically practice the skill in focus and also allow for reasoning skills. Word problems - students need to apply their knowledge in problems. In the Foundation Level only addition: part part whole and joining are taught. For subtraction only separate result unknown is taught, Number problems - each session there are number problems related to the focus area and for modules 7 and 8 spaced retrieval of focus areas is included.
Math Mammoth Grade 3 Skills Review Workbook
Some students benefit from spiral review, and that is exactly what Math Mammoth Grade 3 Skills Review Workbook offers! It has been designed to complement the lessons in Math Mammoth Grade 3 complete curriculum, providing spiral review of the concepts in the grade 3 curriculum.Math Mammoth Grade 3 Skills Review Workbook is divided into chapters, which correspond to the chapters in Math Mammoth Grade 3 curriculum. It is meant to be used during the school year, alongside the main curriculum. Spiral reviewing means that after a particular concept or skill has been studied in the main curriculum, it is then reviewed repeatedly over time in several different worksheets of this book.You can choose exactly when to use the worksheets within the chapter, and how many of them to use. Not all students need all of these worksheets to help them keep their math skills fresh, so please vary the amount of worksheets you assign your student(s) according to their need.Each worksheet is designed to be one page, and includes a variety of exercises in a fun way without becoming too long and tedious. Please see the sample file (PDF) to get a good idea of what the worksheets look like.The problems and exercises in this book are completely new and different from any other Math Mammoth series of books.The answer key is available as a separate book.This is the 2024 edition.
Math Mammoth Grade 3 Skills Review Workbook Answer Key
Math Mammoth Grade 3 Skills Review Workbook Answer Key contains answers to all the worksheets in Math Mammoth Grade 3 Skills Review Workbook. The workbook itself is available separately. This is the 2024 edition.
Math Mammoth Grade 3 Tests and Cumulative Reviews, Canadian Version
Math Mammoth Grade 3 Tests and Cumulative Reviews (Canadian Version) includes consumable student copies of end-of-chapter tests, the end-of-year test, and additional cumulative review lessons that match the Math Mammoth Grade 3 curriculum. This is the 2024 edition.
Math Mammoth Grade 3-B Worktext, Canadian Version
Math Mammoth Grade 3-B Worktext (2024 edition) is the student book for the latter half of grade 3, and part of the Math Mammoth Grade 3 complete curriculum. This book covers four-digit numbers, division, measurement, geometry, and fractions. The worktext contains both the necessary instruction and the problems & exercises (the 'text' & and the 'work'; thus a "worktext"), and is fairly self-teaching. The curriculum meets and exceeds the Common Core standards. Please note this is a student worktext and does not contain the answers. The answer key book is available separately.FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the math, not just learn "HOW" to do it.Concepts are often explained with visual models, followed by exercises using those models. These visual models can take the place of manipulatives for many children; however, it is very easy to add corresponding manipulatives to the lessons if so desired.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.There is a strong emphasis on mental math and number sense.It requires very little teacher preparation, which is a big help to most parents.The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material.After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice.For multiplication tables and division facts, you can use our online practice program (free).The curriculum is essentially the same as the U.S. version of Math Mammoth Grade 3, only customized for the Canadian audience in these aspects: The curriculum teaches the metric measurement units. Imperial units, such as inches and pounds, are not used.The spelling conforms mostly to American English, taking into account a few key differences where Canadian English follows British English.Numbers are formatted with a space as a thousands separator, and a point as a decimal separator.Page (paper) size is Letter.
Math Mammoth Grade 3-A Worktext, Canadian Version
Math Mammoth Grade 3-A Worktext (2024 edition) is the student book for the first half of grade 3, and part of the Math Mammoth Grade 3 complete curriculum. This book covers addition, subtraction, rounding, word problems, the concept of multiplication, multiplication tables, time, and money. The worktext contains both the necessary instruction and the problems & exercises (the 'text' & and the 'work'; thus a "worktext"), and is fairly self-teaching.The curriculum meets and exceeds the Common Core standards. Please note this is a student worktext and does not contain the answers. The answer key book is available separately.FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the math, not just learn "HOW" to do it.Concepts are often explained with visual models, followed by exercises using those models. These visual models can take the place of manipulatives for many children; however, it is very easy to add corresponding manipulatives to the lessons if so desired.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.There is a strong emphasis on mental math and number sense.It requires very little teacher preparation, which is a big help to most parents.The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material.After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice.This curriculum is essentially the same as the U.S. version of Math Mammoth Grade 3, only customized for the Canadian audience in these aspects: The curriculum teaches the metric measurement units. Imperial units, such as inches and pounds, are not used.The spelling conforms mostly to American English, taking into account a few key differences where Canadian English follows British English.Numbers are formatted with a space as a thousands separator, and a point as a decimal separator.The currency used in the chapter on money is the Canadian dollar.Page (paper) size is Letter.
The First 500 Primes Written Out in Alphabetical Order
This book came to Mario one night in a dream. The cover, format, and content (except for the essay and index) is presented here exactly as he dreamed it. Page through the first five hundred primes to attain a meditative state of number appreciation. Then read Mario's wide-ranging essay in which he offers a personal account of primes and the beauty of mathematics.
Introduction to Mathematical Modeling and Computer Simulations
Introduction to Mathematical Modeling and Computer Simulations, Second Edition continues to serve as an engaging and accessible textbook for undergraduates studying mathematical modeling and computer simulations. The book is heavily focussed on applications, and so may have a particular appeal to applied mathematicians, engineers, and others working in applied quantitative disciplines. The book may also be useful as a reference text for reference text for early-career stage practitioners. New to this Edition: A new chapter on Machine Learning and Data Analysis in order to account for recent developments in the field. Chapter 9, 'Asymptotic Methods in Composites', has been entirely re-written to make it more consistent with industry and scientific standards. Includes an elementary introduction to programming in Python language. The Jupyter notebooks with examples for Chapter 10 and Appendix A are available for a download from www.Routledge.com/9781032661513.
The largest known prime number
A prime number is a natural number greater than 1 with no divisors other than 1 and itself. According to Euclid's theorem, there are infinitely many prime numbers, so there is no largest prime.On October 12, 2024, the GIMPS (Great internet Mersenne Prime Search) discovered 52nd Mersenne prime, the number 2136279841 - 1, which has 41,024,320 digits and is now the largest known prime number.Here we present that number printed, in all its digits, in a single volume.Note: due to the number of digits in the number and the limitations of the physical book, the print is in a very small font.
Computational Mathematics
Computational Mathematics: Models, Methods, and Analysis with MATLAB(R) and MPI is a unique book covering the concepts and techniques at the core of computational science. The author delivers a hands-on introduction to nonlinear, 2D, and 3D models; nonrectangular domains; systems of partial differential equations; and large algebraic problems requiring high-performance computing. The book shows how to apply a model, select a numerical method, implement computer simulations, and assess the ensuing results.Providing a wealth of MATLAB, Fortran, and C++ code online for download, the Second Edition of this very popular text: Includes a new chapter with two sections on the finite element method, two sections on shallow water waves, and two sections on the driven cavity problem Introduces multiprocessor/multicore computers, parallel MATLAB, and message passing interface (MPI) in the chapter on high-performance computing Updates and adds code and documentation Computational Mathematics: Models, Methods, and Analysis with MATLAB(R) and MPI, Second Edition is an ideal textbook for an undergraduate course taught to mathematics, computer science, and engineering students. By using code in practical ways, students take their first steps toward more sophisticated numerical modeling.
Fields and Galois Theory
Unleashing the Badassery of Mathematics: Galois Theory and Its Applications is a revolutionary and engaging book that challenges traditional textbooks, making math cool and relevant again. With a humorous and irreverent tone, this book explores the beauty of mathematics, introduces fundamental concepts like fields and polynomials, and dives deep into Galois Theory. From the life of the rebellious ?variste Galois to the application of Galois Theory in solving equations and real-world problems like constructing numbers and cryptography, this book will leave you awestruck by the power and awesomeness of mathematics.
Math Mammoth Grade 8 Answer Keys, International Version
This book includes answers for the Math Mammoth Grade 8-A and 8-B student worktexts (international version), for all the chapter tests, the end-of-year test, and for the cumulative revisions.
Math Mammoth Grade 8-A Worktext, International Version
Math Mammoth Grade 8-A Worktext (International Version) is the first student book for eighth grade mathematics, and part of the Math Mammoth Grade 8 complete curriculum.This book starts with a study of exponent laws, using both numerical and algebraic expressions. The first chapter also covers scientific notation (both with large and small numbers), significant digits, and calculations with numbers given in scientific notations.In chapter 2, students learn about geometric transformations (translations, reflections, rotations, dilations), common angle relationships, and volume of prisms, cylinders, spheres, and cones. Next, in chapter 3, our focus is on linear equations.Students both review and learn more about solving linear equations, including equations whose solutions require the usage of the distributive property and equations where the variable is on both sides.Chapter 4 presents an introduction to functions. Students construct functions to model linear relationships, learn to use the rate of change and initial value of the function, and they describe functions qualitatively based on their graphs.
Introduction to Ring Theory
Discover the captivating world of Ring Theory in this comprehensive guide, covering everything from the basics to advanced topics and real-world applications in coding theory, cryptography, algebraic geometry, physics, engineering, and computer science. Whether youre a math enthusiast, a student, or a professional in any of these fields, this book will take you on a journey into the fascinating realm of rings. Dive into the powerful concepts of ring operations, ideals, homomorphisms, and non-commutative rings, while exploring their practical applications in diverse disciplines. With clear explanations, insightful examples, and engaging discussions, this book offers a wealth of knowledge and inspiring insights for anyone interested in the rich and diverse world of Ring Theory.
Analytic Number Theory
Get ready to dive into the captivating world of number theory in 'The Beauty of Fucking Numbers.' Explore the enigma of prime numbers, unlock the secrets of the Riemann Hypothesis, meet historical legends in the field, unravel the mysteries of Diophantine equations, and discover how cryptography keeps your secrets secure. With engaging storytelling and a digital-age perspective, this book challenges the myth that number theory is useless, providing a compelling exploration of the challenges and rewards of studying analytic number theory.
Polyadic Transcendental Number Theory
The existence of transcendental numbers was first proved in 1844, by Joseph Liouville. Advances were made by Charles Hermite, proving the transcendence of the number e, and Ferdinand von Lindemann, proving the transcendence of the number π. The consequence of these discoveries was the negative solution to the problem of squaring the circle, which has stood for many years. In the 20th century, the theory of transcendental numbers developed further, with general methods of investigating the arithmetic nature of various classes of numbers. One of these methods is the Siegel-Shidlovskii method, previously used for the so-called E- and G-functions.Polyadic Transcendental Number Theory outlines the extension of the Siegel-Shidlovskii method to a new class of F-series (also called Euler-type series). Analogues of Shidlovskii's famous theorems on E-functions are obtained. Arithmetic properties of infinite-dimensional vectors are studied, and therefore elements of direct products of rings of integer p-adic numbers are considered. Hermite-Pad矇 approximations are used to investigate the values of hypergeometric series with algebraic irrational parameters. Moreover, the book describes how to use Hermite-Pad矇 approximations to obtain results on the values of hypergeometric series with certain transcendental (polyadic Liouville) parameters. Based on recent results, this book contains indications of promising areas in a new field of research. The methods described will allow readers to obtain many new results.
Sequences, Series, and Convergence
In The Ultimate Guide to Sequences, Series, and Convergence, delve into the mind-blowing world of mathematical patterns and learn how to calculate, prove, and conquer sequences and series like a true badass. Discover unexpected applications in real life, explore the mysteries of infinite series, and unleash the power of convergence. With captivating examples, clear explanations, and practical techniques, this book will revolutionize your understanding of mathematics.
An Introduction To Chaotic Dynamical Systems
This widely used graduate text introduces modern topics in dynamical systems. The author includes new material on complex dynamics leading to key revisions. Striking color photos illustrating both Julia and Mandelbrot sets are included. This book assumes no prior acquaintance with advanced mathematical topics.
Vedic Tricks Made Mathematics Easy
Unveiling the Power of Vedic Mathematics: Essential InsightsEfficiency in Calculation: Vedic Mathematics provides highly efficient techniques for mental calculations, enabling individuals to perform complex computations quickly. This efficiency is particularly valuable in situations where rapid calculation is crucial.Versatility Across Mathematical Operations: The techniques in Vedic Mathematics are versatile and applicable across various mathematical operations, including addition, subtraction, multiplication, division, algebraic equations, and even advanced mathematical concepts.Promote Skills of Mental Calculations: Vedic Mathematics strongly emphasizes mental calculations, fostering the development of strong mental calculation skills. It not only enhances cognitive abilities but also makes mathematical tasks more accessible without the reliance on external tools.Applicability to Competitive Exams: Many of the Vedic Mathematics techniques are designed to streamline calculations in competitive exams where time is a critical factor. As a result, students find these methods beneficial for solving problems quickly and accurately in exam settings.Mental Calculation: Vedic Mathematics emphasizes mental calculation, promoting the development of mental agility and mathematical intuition.Universality and Speed: The techniques are not limited to specific types of problems; they can be applied universally, making them adaptable to various mathematical scenarios. The methods are designed to be straightforward and can often lead to faster calculations compared to conventional methods.Educational Applications: Vedic Mathematics is often used as an educational tool to make learning mathematics more engaging, accessible, and enjoyable for students.Connection to Profound Wisdom: Vedic Mathematics is sometimes considered a part of the broader Vedic tradition, with enthusiasts believing it embodies a profound approach to mathematics.
Math Mammoth Grade 8 Answer Keys, Canadian Version
This book includes answers for Math Mammoth Grade 8-A and 8-B student worktexts (Canadian version), for all of the chapter tests, and for the cumulative reviews. The other parts of the curriculum may be purchased separately.
Techniques for Designing and Analyzing Algorithms
This text presents the main techniques of algorithm design, namely, divide-and-conquer algorithms, greedy algorithms, dynamic programming algorithms, and backtracking. Graph algorithms are studied in detail, and a careful treatment of the theory of NP-completeness is presented.
Math Mammoth Grade 8-A Worktext, Canadian Version
Math Mammoth Grade 8-A Worktext, Canadian version is the student book for the first half of grade 8, and part of the Math Mammoth Grade 8 complete curriculum. The curriculum is essentially the same as the U.S. version of Math Mammoth Grade 8, only customized for the Canadian audience in these aspects: - The curriculum uses the metric measurement units. Since Canadians do use some imperial units (e.g. miles, pounds) in some contexts, the curriculum does infrequently use them.- The spelling conforms mostly to American English, taking into account a few key differences where Canadian English follows British English.- Numbers are formatted with a space as a thousands separator, and a point as a decimal separator.- Page (paper) size is Letter.The US version of the curriculum is aligned to the Common Core Standards, which means this curriculum may not be properly aligned to the eighth grade standards in your province. However, you can probably find material for any missing topics in neighbouring grades.This book starts with a study of exponent laws, using both numerical and algebraic expressions. The first chapter also covers scientific notation (both with large and small numbers), significant digits, and calculations with numbers given in scientific notations.In chapter 2, students learn about geometric transformations (translations, reflections, rotations, dilations), common angle relationships, and volume of prisms, cylinders, spheres, and cones. Next, in chapter 3, our focus is on linear equations.Students both review and learn more about solving linear equations, including equations whose solutions require the usage of the distributive property and equations where the variable is on both sides.Chapter 4 presents an introduction to functions. Students construct functions to model linear relationships, learn to use the rate of change and initial value of the function, and they describe functions qualitatively based on their graphs.FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so students can understand the math, not just learn "HOW" to do it.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.It requires very little teacher preparation.The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext.After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice.
Math Mammoth Grade 8-B Worktext, Canadian Version
Math Mammoth Grade 8-B Worktext, Canadian version is the student book for the second half of grade 8, and part of the Math Mammoth Grade 8 complete curriculum. The curriculum is essentially the same as the U.S. version of Math Mammoth Grade 8, only customized for the Canadian audience in these aspects: - The curriculum uses the metric measurement units. Since Canadians do use some imperial units (e.g. miles, pounds) in some contexts, the curriculum does infrequently use them.- The spelling conforms mostly to American English, taking into account a few key differences where Canadian English follows British English.- Numbers are formatted with a space as a thousands separator, and a point as a decimal separator.- Page (paper) size is Letter.The US version of the curriculum is aligned to the Common Core Standards, which means this curriculum may not be properly aligned to the eighth grade standards in your province. However, you can probably find material for any missing topics in neighbouring grades.The book starts with chapter 5, graphing linear equations. Students study slope, and graph and write linear equations in slope-intercept and standard forms. They also learn about parallel and perpendicular lines.In chapter 6, students delve into square roots, cube roots, and irrational numbers and solve equations involving square and cube roots. The rest of the chapter is spent studying the Pythagorean Theorem and its applications.Next, in chapter 7, we focus on systems of linear equations. Students learn the three basic techniques for solving these and also solve a variety of problems that are solved with a pair of linear equations. The last chapter covers statistical topics: scatter plots and two-way tables.FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so students can understand the math, not just learn "HOW" to do it.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.It requires very little teacher preparation.: )The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext.Each chapter introduction also includes a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice.
Math Mammoth Grade 8 Tests and Cumulative Reviews, Canadian Version
Math Mammoth Grade 8 Tests & Cumulative Reviews (Canadian version) contains the chapter tests, end-of-year test and cumulative reviews for Math Mammoth Grade 8 complete curriculum (Canadian version).
Discovering Dynamical Systems Through Experiment and Inquiry
The book differs from most texts on the topic by blending the use of computer simulations with inquiry-based learning (IBL). Students can discover examples and counterexamples through manipulations built into the software though a link to the website.
Handbook of the Tutte Polynomial and Related Topics
The Tutte Polynomial touches on nearly every area of combinatorics as well as many other fields, including statistical mechanics, coding theory, and DNA sequencing. It is one of the most studied graph polynomials.Handbook of the Tutte Polynomial and Related Topics is the first handbook published on the Tutte Polynomial. It consists of thirty-four chapters written by experts in the field, which collectively offer a concise overview of the polynomial's many properties and applications. Each chapter covers a different aspect of the Tutte polynomial and contains the central results and references for its topic. The chapters are organized into six parts. Part I describes the fundamental properties of the Tutte polynomial, providing an overview of the Tutte polynomial and the necessary background for the rest of the handbook. Part II is concerned with questions of computation, complexity, and approximation for the Tutte polynomial; Part III covers a selection of related graph polynomials; Part IV discusses a range of applications of the Tutte polynomial to mathematics, physics, and biology; Part V includes various extensions and generalizations of the Tutte polynomial; and Part VI provides a history of the development of the Tutte polynomial.Features Written in an accessible style for non-experts, yet extensive enough for experts Serves as a comprehensive and accessible introduction to the theory of graph polynomials for researchers in mathematics, physics, and computer science Provides an extensive reference volume for the evaluations, theorems, and properties of the Tutte polynomial and related graph, matroid, and knot invariants Offers broad coverage, touching on the wide range of applications of the Tutte polynomial and its various specializations
Calling Carlos
English: James gives details of what he does during the day. The main thing he does is, he calls his friend, Carlos. At bedtime, since he was unable to contact Carlos, he thinks about the many things they both did that day. Before going to sleep, James decides to reset his alarm clock for 7:00 a.m., and he can't wait until tomorrow to call Carlos, again! This book helps children learn how to tell time to the hour and to the half hour with the use of analogue and digital clock illustrations on every page. The digital clocks include "AM" or "PM" to help with this concept. The story is bilingual (English and Spanish), so it can help with teaching about time in both languages. The back pages include learning activities. Espanol: James da detalles de lo que hizo durante el d穩a. Lo que hace principalmente es, llamar a su amigo, Carlos. A la hora de dormir, como no pudo comunicarse con Carlos, piensa en las muchas cosas que los dos hicieron ese d穩a. Antes de dormirse, James decide volver a poner su despertador para las 7:00 a.m., y no puede esperar hasta ma簽ana para llamar a Carlos, 癒otra vez! Este libro ayuda para que los ni簽os y ni簽as aprendan a leer el reloj a la hora y a la media hora con el uso de ilustraciones de un reloj anal籀gico y otro digital en cada p獺gina. El reloj digital incluye "AM" o "PM" para ayudar con ese concepto. El libro es biling羹e (ingl矇s y espa簽ol), as穩 que puede ayudar con la ense簽anza del reloj en los dos lenguajes. Las p獺ginas de atr獺s incluyen actividades de aprendizaje.
Math Mammoth Grade 3-B Worktext
Math Mammoth Grade 3-B Worktext (2024 edition) is the student book for the latter half of grade 3, and part of the Math Mammoth Grade 3 complete curriculum. This book covers four-digit numbers, division, measurement, geometry, and fractions. The worktext contains both the necessary instruction and the problems & exercises (the 'text' & and the 'work'; thus a "worktext"), and is fairly self-teaching. The curriculum meets and exceeds the Common Core standards. Please note this is a student worktext and does not contain the answers. The answer key book is available separately.FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the math, not just learn "HOW" to do it.Concepts are often explained with visual models, followed by exercises using those models. These visual models can take the place of manipulatives for many children; however, it is very easy to add corresponding manipulatives to the lessons if so desired.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.There is a strong emphasis on mental math and number sense.It requires very little teacher preparation, which is a big help to most parents.The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material.After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice.For multiplication tables and division facts, you can use our online practice program (free).
Math Mammoth Grade 3-A Worktext
Math Mammoth Grade 3-A Worktext (2024 edition) is the student book for the first half of grade 3, and part of the Math Mammoth Grade 3 complete curriculum. This book covers addition, subtraction, rounding, word problems, the concept of multiplication, multiplication tables, time, and money. The worktext contains both the necessary instruction and the problems & exercises (the 'text' & and the 'work'; thus a "worktext"), and is fairly self-teaching.The curriculum meets and exceeds the Common Core standards. Please note this is a student worktext and does not contain the answers. The answer key book is available separately.FeaturesMath Mammoth focuses on conceptual understanding. It explains the "WHY", so your children can understand the math, not just learn "HOW" to do it.Concepts are often explained with visual models, followed by exercises using those models. These visual models can take the place of manipulatives for many children; however, it is very easy to add corresponding manipulatives to the lessons if so desired.The curriculum is mastery-oriented. This means it concentrates fairly long on a topic, delving into its various aspects. This promotes conceptual understanding, as opposed to spiral curricula that often tend to jump from topic to topic too much.There is a strong emphasis on mental math and number sense.It requires very little teacher preparation, which is a big help to most parents.The curriculum has no separate teacher's manual nor is it scripted. The introduction to each chapter has some notes for the teacher concerning the material in the chapter. All the instruction is written directly to the student in the worktext, and there also exist accompanying videos where you can see Maria herself teach the material.After each chapter introduction, you will find a list of Internet links and resources (games, quizzes, animations, etc.) that can be used for fun, illustrations, and further practice.
Math Mammoth Grade 3 Tests and Cumulative Reviews
Math Mammoth Grade 3 Tests and Cumulative Reviews (2024 edition) includes consumable student copies of end-of-chapter tests, the end-of-year test, and additional cumulative review lessons that match the Math Mammoth Grade 3 curriculum.
Math Mammoth Grade 6 Tests and Cumulative Revisions, International Version
Math Mammoth Grade 6 Tests and Cumulative Revisions (international version) contains the chapter tests, end-of-year test, and cumulative revision worksheets for Math Mammoth Grade 6 curriculum (international version). It does not contain answers; the answer key book may be purchased separately. This is the 2022 edition.
Math Mammoth Grade 6-B Worktext, International Version
Math Mammoth Grade 6-B worktext (International Version; 2022 edition) is the second part of a complete math curriculum for sixth grade, and part of the Math Mammoth Grade 6 complete curriculum. This book covers a revision of the four operations with whole numbers, beginning algebra concepts, decimal arithmetic, ratios, and percent.In this book, the main areas of focus are: prime factorization, GCF, and LCM;a revision of fraction arithmetic, plus division of fractions;the concept of integers, coordinate grid, addition & subtraction of integers;geometry: revision of quadrilaterals & drawing problems; area of triangles & polygons; volume of rectangular prisms with fractional edge lengths; surface area; statistics: concept of distribution, measures of centre, measures of variation, boxplots, histograms.A companion to this book, Math Mammoth Grade 6-A worktext covers the first half of 6th grade math (available separately). Also available are the answer keys and a book containing cumulative revisions and chapter tests.
