Maryland Comprehensive Assessment Program (MCAP) Test Practice
Want to boost your child's Grade 8 math skills and Maryland MCAP readiness?Lumos' Maryland MCAP blended program (Workbook + Online Access) helps your child improve scores by 10% or more* in the 2025-26 MCAP assessment through realistic test simulations, targeted skills practice, and AI-powered intervention.This blended program includes: ✓ Practice questions covering 30+ Grade 8 Math skills in pen and paper format✓ Answer keys with detailed explanations in the workbook✓ 2 full-length online practice tests that simulate Maryland's MCAP✓ Personalized online study plan for targeted practice✓ AI Tutor for clear step-by-step explanations, hints, and instant feedback✓ Online program access codeTrusted by over 1.6 Million students and 200,000 teachers.Reduce your child's MCAP test anxiety using Lumos' Smart Test Prep MethodologyLumos' Smart Test Prep Methodology blends realistic Maryland test simulations, personalized guidance, and targeted practice to help students get ready for the state test.Students begin with a simulated MCAP test, follow an AI-personalized study plan, practice essential skills, and repeat the cycle-steadily building the skills and confidence they need for the Spring MCAP.Why is Lumos' MCAP Practice Workbook the Smart Choice for 2025-26?p✓ Realistic Practice Tests: Two full-length tests that simulate MCAP format, question types, rigor, standards, and pacing✓ Personalized Study Plan: Online Diagnostic Tests generate a personalized study plan for targeted skills practice using the workbook✓ Lumos AI Tutor: A built-in, on-demand AI coach that delivers real-time assistance just like a personal tutor✓ Online Program Access: Features guided practice questions, solved examples, a performance insights dashboard, videos, mind maps, flashcubes, and other engaging test prep resourcesWhy Parents Trust Lumos tedBook for Maryland MCAP Success?pLumos has a history of delivering measurable results. Its realistic test preparation builds confidence, and the performance reports offer clear insights into strengths and areas for improvement. With Lumos tedBook, families feel assured that their child is fully prepared to succeed on the Maryland state assessment."This book is awesome-I've bought it two years in a row. We used it to study for the MCAP Math in 7th grade and the MCAP Math in 8th grade, and my child aced both tests with a score of 4. The online resources that come with the book are amazing. Kids can practice online tests and individual lessons as many times as they want." - JesseniaHow Do Teachers Use Lumos tedBook in Their Classroom?pTeachers use Lumos tedBook to deliver personalized, standards-aligned practice that reinforces classroom learning. In addition to giving students the opportunity to experience a realistic MCAP simulation, Lumos Teacher Accounts provide access to insightful reports and guided classroom instructions to bridge learning gaps, track progress, and build student confidence for the MCAP assessment. It's ideal for classroom reinforcement, tutoring, or homeschooling.*10%+ improvement in state assessment scores is based on students who used the program consistently for about 45 minutes per week. Individual results may vary based on usage and completion of practice tests and the study plan.
Flatland
First published in 1884, Edwin A. Abbott's classic novella is many things: a biting social satire on Victorian society, an exhortation to literally think outside the box (or, if you're a privileged Spacelander, outside the cube), and above all a testament to the universal quest for knowledge and the inherent beauty and purity of mathematical truth. Flatland tells the story of "A SQUARE," a mathematician living in the Second dimension, known as Flatland, whose perceptions of his Universe are turned upside down when he is visited by a Sphere from the Third dimension, known as Spaceland. "A SQUARE" also muses on life in Lineland and Pointland. Flatland is one of the very few novels about math and philosophy that can appeal to almost any layperson. Published in 1880, this short fantasy takes us to a completely flat world of two physical dimensions where all the inhabitants are geometric shapes, and who think the planar world of length and width that they know is all there is. But one inhabitant discovers the existence of a third physical dimension, enabling him to finally grasp the concept of a fourth dimension. Watching our Flatland narrator, we begin to get an idea of the limitations of our own assumptions about reality, and we start to learn how to think about the confusing problem of higher dimensions. The book is also quite a funny satire on society and class distinctions of Victorian England.
A Nationwide Framework for Surveillance of Cardiovascular and Chronic Lung Diseases
A continuation of the authors' previous textbook, Second Semester Calculus for Students of Mathematics and Related Disciplines furthers students' learning and understanding of critical mathematical concepts.The text explores more advanced integration strategies, further limit techniques, improper integrals, infinite sequences and series, polar and parametric curves, conic sections, and two-dimensional vectors. It well prepares students to succeed in third-semester, multivariable calculus or other studies requiring knowledge of these topics.The book features a highly conversational yet detailed approach, as well as extensive examples with thorough explanations, often accompanied by alternative explanations and methods to solutions. Important points and common pitfalls are emphasized to keep students from making typical mistakes. The rich pedagogical material in the text makes it an exceptional resource for both traditional and flipped courses.Recognizing that second-semester calculus has historically been the hardest of a three-semester calculus sequence, Second Semester Calculus for Students of Mathematics and Related Disciplines provides students with a readable and straightforward approach designed to support their continued success.
The Logic of Entailment and Its History
What follows from what, and how do we make statements (whether true or false) about which inferences are correct? In this book, Edwin Mares provides a new philosophical, semantical and historical analysis of and justification for the relevant logic of entailment. In the first half of the book he examines some key ideas in the historical development of the logic of entailment, looking in particular at the notion 'is derivable from' and at how symbolic logic has attempted to capture this notion. In the second half of the book he develops his own theory connecting ideas from the traditions in mathematical logic with some ideas in the philosophy of science. The book's fresh and original perspective on the logic of entailment will be valuable for all who want to know more about the historical and philosophical origins of modern symbolic logic.
Ordinary Differential Equations and Applications
Differential equations can bring mathematics to life, describing phenomena originating in physics, chemistry, biology, economics, and more. Used by scientists and engineers alike, differential equations are also the starting point of much purely mathematical activity. They also play a role in the formulation and resolution of problems in harmonic analysis, differential geometry, and probability calculus. A large part of functional analysis has therefore been motivated by the need to solve questions in the analysis of differential systems, as with numerical analysis.Differential equations are doubly relevant, then: as significant in many areas of mathematics, and as important machinery for applying mathematics to real-world problems. This book therefore aims to provide a rigorous introduction to the theoretical study of differential equations, and to demonstrate their utility with applications in many fields.Ordinary Differential Equations and Applications originates from several courses given by the author for decades at the University of Seville. It aims to bring together rigorous mathematical theory and the rich variety of applications for differential equations. The book examines many aspects of differential equations: their existence, uniqueness, and regularity, alongside their continuous dependence on data and parameters. Delving into permanent interpretation of the laws of differential equations, we also look at the role of data and how their solutions behave. Each chapter finishes with a collection of exercises, many of which also contain useful hints.
A Brief History of Mathematics
This volume, originally published in China and translated into four other languages, presents a fascinating and unique account of the history of mathematics, divided into eight chronologically organized chapters. Tracing the development of mathematics across disparate regions and peoples, with particular emphasis on the relationship between mathematics and civilization, it examines mathematical sources and inspirations leading from Egypt, Babylon and ancient Greece and expanding to include Chinese, Indian and Arabic mathematics, the European Renaissance and the French revolution up through the Nineteenth and Twentieth Centuries. Each chapter explores connections among mathematics and cultural elements of the time and place treated, accompanying the reader in a varied and exciting journey through human civilizations. The book contemplates the intersections of mathematics with other disciplines, including the relationship between modern mathematics and modern art, and the resultingapplications, with the aid of images and photographs, often taken by the author, which further enhance the enjoyment for the reader. Written for a general audience, this book will be of interest to anyone who's studied mathematics in university or even high school, while also benefiting researchers in mathematics and the humanities.
Ordinary Differential Equations and Applications
Differential equations can bring mathematics to life, describing phenomena originating in physics, chemistry, biology, economics, and more. Used by scientists and engineers alike, differential equations are also the starting point of much purely mathematical activity. They also play a role in the formulation and resolution of problems in harmonic analysis, differential geometry, and probability calculus. A large part of functional analysis has therefore been motivated by the need to solve questions in the analysis of differential systems, as with numerical analysis.Differential equations are doubly relevant, then: as significant in many areas of mathematics, and as important machinery for applying mathematics to real-world problems. This book therefore aims to provide a rigorous introduction to the theoretical study of differential equations, and to demonstrate their utility with applications in many fields.Ordinary Differential Equations and Applications originates from several courses given by the author for decades at the University of Seville. It aims to bring together rigorous mathematical theory and the rich variety of applications for differential equations. The book examines many aspects of differential equations: their existence, uniqueness, and regularity, alongside their continuous dependence on data and parameters. Delving into permanent interpretation of the laws of differential equations, we also look at the role of data and how their solutions behave. Each chapter finishes with a collection of exercises, many of which also contain useful hints.
The Graphs Associated with Rings
A ring is an abstract structure with a commutative addition, and a multiplication which may or may not be commutative. This distinction yields two quite different theories: the theory of respectively commutative or non-commutative rings. These notes are mainly concerned about commutative rings. Non-commutative rings have been an object of systematic study only quite recently, during the 20th century. Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points does not matter. Each object in a graph is called a node. The subject of graph theory had its beginnings in recreational math problems (see number game), but it has grown into a significant area of mathematical research, with applications in chemistry, operations research, social sciences, and computer science. The study of algebraic structures using the properties of graphs becomes an exciting research topic in the past twenty years, leading to many fascinating results and questions. There are many papers on assigning a graph to a group or a ring. Also, investigation of algebraic properties of groups or rings using the associated graph becomes an exciting topic. In 1999, the zero-divisor graph of a commutative ring Γ(R) was defined by David F. Anderson and Paul S. Livingston as the undirected graph with vertex set Z(R)∗, in which there is an arc from x to y if and only if xy = 0. Through this book, we illustrate some results about the Graphs associated with Rings.
Love Triangle
AN INSTANT NEW YORK TIMES BESTSELLER! An ode to triangles, the shape that makes our lives possible Trigonometry is perhaps the most essential concept humans have ever devised. The simple yet versatile triangle allows us to record music, map the world, launch rockets into space, and be slightly less bad at pool. Triangles underpin our day-to-day lives and civilization as we know it. In Love Triangle, Matt Parker argues we should all show a lot more love for triangles, along with all the useful trigonometry and geometry they enable. To prove his point, he uses triangles to create his own digital avatar, survive a harrowing motorcycle ride, cut a sandwich, fall in love, measure tall buildings in a few awkward bounds, and make some unusual art. Along the way, he tells extraordinary and entertaining stories of the mathematicians, engineers, and philosophers--starting with Pythagoras--who dared to take triangles seriously. This is the guide you should have had in high school--a lively and definitive answer to "Why do I need to learn about trigonometry?" Parker reveals triangles as the hidden pattern beneath the surface of the contemporary world. Like love, triangles actually are all around. And in the air. And they're all you need.
Mathematics Phase 2
This book is part of 7 books which covers whole mathematics for the Board as well competitive exams. We have divided total mathematics syllabus in to 7 books each one will come in every phase. All of these books are designed to keep in mind the requirements of CBSE board as well IIT entrance exam syllabus. This Book consists of Nomoreclass concepts and previous IIT questions.
Syllogistic Logic and Mathematical Proof
Does syllogistic logic have the resources to capture mathematical proof? This volume provides the first unified account of the history of attempts to answer this question, the reasoning behind the different positions taken, and their far-reaching implications. Aristotle had claimed that scientific knowledge, which includes mathematics, is provided by syllogisms of a special sort: 'scientific' ('demonstrative') syllogisms. In ancient Greece and in the Middle Ages, the claim that Euclid's theorems could be recast syllogistically was accepted without further scrutiny. Nevertheless, as early as Galen, the importance of relational reasoning for mathematics had already been recognized. Further critical voices emerged in the Renaissance and the question of whether mathematical proofs could be recast syllogistically attracted more sustained attention over the following three centuries. Supported by more detailed analyses of Euclidean theorems, this led to attempts to extend logical theory to include relational reasoning, and to arguments purporting to reduce relational reasoning to a syllogistic form. Philosophical proposals to the effect that mathematical reasoning is heterogenous with respect to logical proofs were famously defended by Kant, and the implications of the debate about the adequacy of syllogistic logic for mathematics are at the very core of Kant's account of synthetic a priori judgments. While it is now widely accepted that syllogistic logic is not sufficient to account for the logic of mathematical proof, the history and the analysis of this debate, running from Aristotle to de Morgan and beyond, is a fascinating and crucial insight into the relationship between philosophy and mathematics.
Tropical Circuit Complexity
This book presents an enticing introduction to tropical circuits and their use as a rigorous mathematical model for dynamic programming (DP), which is one of the most fundamental algorithmic paradigms for solving combinatorial, discrete optimization problems. In DP, an optimization problem is broken up into smaller subproblems that are solved recursively. Many classical DP algorithms are pure in that they only use the basic (min, +) or (max, +) operations in their recursion equations. In tropical circuits, these operations are used as gates. Thanks to the rigorous combinatorial nature of tropical circuits, elements from the Boolean and arithmetic circuit complexity can be used to obtain lower bounds for tropical circuits, which play a crucial role in understanding the limitations and capabilities of these computational models. This book aims to offer a toolbox for proving lower bounds on the size of tropical circuits.In this work, the reader will find lower-bound ideas and methods that have emerged in the last few years, with detailed proofs. Largely self-contained, this book is meant to be approachable by graduate students in mathematics and computer science with a special interest in circuit complexity.
A First Course in Graph Theory and Combinatorics
This book discusses the origin of graph theory from its humble beginnings in recreational mathematics to its modern setting or modeling communication networks, as is evidenced by the World Wide Web graph used by many Internet search engines. The second edition of the book includes recent developments in the theory of signed adjacency matrices involving the proof of sensitivity conjecture and the theory of Ramanujan graphs. In addition, the book discusses topics such as Pick's theorem on areas of lattice polygons and Graham-Pollak's work on addressing of graphs. The concept of graph is fundamental in mathematics and engineering, as it conveniently encodes diverse relations and facilitates combinatorial analysis of many theoretical and practical problems. The text is ideal for a one-semester course at the advanced undergraduate level or beginning graduate level.
The Life and Work of James Bradley
The Life and Work of James Bradley: The New Foundations of 18th Century Astronomy is the first major work on the life and achievements of James Bradley for 190 years. This book offers a new perspective and new interpretations of previously published materials, together with various insights about recently researched sources. This book is a complete account of the life and work of Bradley as discerned from surviving documents of his working archive, as well as other documents and records. In addition, it offers a new interpretation of Bradley's work as an astronomer, not merely from his observations of Jupiter and Saturn and their satellites and annual aberration and the nutation of the Earth's axis, but also his corroborative work with pendulums and other horological work with George Graham. It also explores the little amount documented about his private life including a degree of speculation about his personal relationships. This work on 18th century astronomy is intended for students of the history of science, astronomy and 18th century English society, and for scholars seeking new lines of inquiry. It contains an extensive bibliography and a detailed chronology, both of which offer support for further reading and research.
Rediscovering L矇on Brunschvicg’s Critical Idealism
L矇on Brunschvicg's contribution to philosophical thought in fin-de-si癡cle France receives full explication in the first English-language study on his work. Arguing that Brunschvicg is crucial to understanding the philosophical schools which took root in 20th-century France, Pietro Terzi locates Brunschvicg alongside his contemporary Henri Bergson, as well as the range of thinkers he taught and influenced, including L矇vinas, Merleau-Ponty, de Beauvoir, and Sartre. Brunschvicg's deep engagement with debates concerning spiritualism and rationalism, neo-Kantian philosophy, and the role of mathematics in philosophy made him the perfect supervisor for a whole host of nascent philosophical ideas which were forming in the work of his students. Terzi outlines Brunchvicg's defence of neo-Kantian judgement, historical analysis and the inextricability of the natural and humanist sciences to any rigorous system of philosophy, with wide-ranging implications for contemporary scholarship.
Uncomplicated Calculus
Embark on a guided journey with Uncomplicated Calculus!Starting with the very basics of functions and limits, you'll explore the landscape of derivatives and integrals, and journey into the realms of sequences, series, and differential equations. Advanced topics such as multivariable calculus, vectors, and line and surface integrals, once daunting, become comprehensible under clear explanations and practical examples.Interwoven throughout are real-world applications demonstrating the relevance of calculus in fields as diverse as physics, economics, and computer science. The book also offers ample exercises and problem-solving techniques to strengthen your understanding, allowing you to master calculus concepts at your own pace.Whether you're a student, a teacher, or a lifelong learner, this book illuminates the elegance of calculus, propelling your mathematical journey forward.
The Calabi Problem for Fano Threefolds
Algebraic varieties are shapes defined by polynomial equations. Smooth Fano threefolds are a fundamental subclass that can be thought of as higher-dimensional generalizations of ordinary spheres. They belong to 105 irreducible deformation families. This book determines whether the general element of each family admits a K瓣hler-Einstein metric (and for many families, for all elements), addressing a question going back to Calabi 70 years ago. The book's solution exploits the relation between these metrics and the algebraic notion of K-stability. Moreover, the book presents many different techniques to prove the existence of a K瓣hler-Einstein metric, containing many additional relevant results such as the classification of all K瓣hler-Einstein smooth Fano threefolds with infinite automorphism groups and computations of delta-invariants of all smooth del Pezzo surfaces. This book will be essential reading for researchers and graduate students working on algebraic geometry and complex geometry.
Optimal Control
This book may serve as a basis for students and teachers. The text should provide the reader with a quick overview of the basics for Optimal Control and the link with some important conceptes of applied mathematical, where an agent controls underlying dynamics to find the strategy optimizing some quantity. There are broad applications for optimal control across the natural and social sciences, and the finale to this text is an invitation to read current research on one such application. The balance of the text will prepare the reader to gain a solid understanding of the current research they read.
Oxford's Sedleian Professors of Natural Philosophy
Established in the early seventeenth century following a bequest to the university by Sir William Sedley, Oxford's Sedleian Professorship of Natural Philosophy is one of the university's oldest professorships. In common with other such positions established around this time, such as the Savilian Professorships of Geometry and Astronomy, for example, its purpose was to provide centrally organised lectures on a specific subject. While the Professorship is now a high-profile research post in applied mathematics, it has previously been held by physicians, an astronomer, and several people in the eighteenth century whose credentials in natural philosophy are much less clear. This edited volume traces the varied history of the chair through the first four centuries of its existence, combining specialised contributions from historians of medicine, of science, of mathematics, and of universities, together with personal reminiscences of some of the more recent holders of the post.
Advances in Image Enhancement
In the era of the Internet of Things, images have played important roles in human-computer interactions, and with the arrival of big data technology, people have higher requirements regarding image quality, especially for images collected in dark light. This can be addressed through the development of camera hardware quality, i.e., the resolution and exposure time of cameras, which may require high computational costs. As an alternative, image enhancement techniques can exact salient features to improve the quality of captured images according to the differences in diverse features, although they suffer from some challenges, i.e., a low contrast, artifacts, and overexposure, thus making it decidedly necessary to determine how to use advanced image enhancement techniques. The topic of advances in the image enhancement of electronics is presented in this reprint, which brings together the research accomplishments of researchers from academia and industry. The secondary goal of this reprint is to display the latest research results of advances in image enhancement.
Beyond the Learned Academy
The tremendous growth of the mathematical sciences in the early modern world was reflected contemporaneously in an increasingly sophisticated level of practical mathematics in fields such as merchants' accounts, instrument making, teaching, navigation, and gauging. In many ways, mathematics shaped the knowledge culture of the age, infiltrating workshops, dockyards, and warehouses, before extending through the factories of the Industrial Revolution to the trading companies and banks of the nineteenth century. While theoretical developments in the history of mathematics have been made the topic of numerous scholarly investigations, in many cases based around the work of key figures such as Descartes, Huygens, Leibniz, or Newton, practical mathematics, especially from the seventeenth century onwards, has been largely neglected. The present volume, comprising fifteen essays by leading authorities in the history of mathematics, seeks to fill this gap by exemplifying the richness, diversity, and breadth of mathematical practice from the seventeenth century through to the middle of the nineteenth century.
Basic Topology 1
This first of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It studies metric spaces and general topology. It starts with the concept of the metric which is an abstraction of distance in the Euclidean space. The special structure of a metric space induces a topology that leads to many applications of topology in modern analysis and modern algebra, as shown in this volume. This volume also studies topological properties such as compactness and connectedness. Considering the importance of compactness in mathematics, this study covers the Stone-Cech compactification and Alexandroff one-point compactification. This volume also includes the Urysohn lemma, Urysohn metrization theorem, Tietz extension theorem, and Gelfand-Kolmogoroff theorem. The content of this volume is spread into eight chapters of which the last chapter conveys the history of metric spaces and the history of the emergence of the conceptsleading to the development of topology as a subject with their motivations with an emphasis on general topology. It includes more material than is comfortably covered by beginner students in a one-semester course. Students of advanced courses will also find the book useful. This book will promote the scope, power, and active learning of the subject, all the while covering a wide range of theories and applications in a balanced unified way.
The Mathematical Papers of Sir William Rowan Hamilton: Volume 4
Lectures on Lagrangian Torus Fibrations
Symington's almost toric fibrations have played a central role in symplectic geometry over the past decade, from Vianna's discovery of exotic Lagrangian tori to recent work on Fibonacci staircases. Four-dimensional spaces are of relevance in Hamiltonian dynamics, algebraic geometry, and mathematical string theory, and these fibrations encode the geometry of a symplectic 4-manifold in a simple 2-dimensional diagram. This text is a guide to interpreting these diagrams, aimed at graduate students and researchers in geometry and topology. First the theory is developed, and then studied in many examples, including fillings of lens spaces, resolutions of cusp singularities, non-toric blow-ups, and Vianna tori. In addition to the many examples, students will appreciate the exercises with full solutions throughout the text. The appendices explore select topics in more depth, including tropical Lagrangians and Markov triples, with a final appendix listing open problems. Prerequisites include familiarity with algebraic topology and differential geometry.
Linear Algebra for Data Science
This book serves as an introduction to linear algebra for undergraduate students in data science, statistics, computer science, economics, and engineering. The book presents all the essentials in rigorous (proof-based) manner, describes the intuition behind the results, while discussing some applications to data science along the way.The book comes with two parts, one on vectors, the other on matrices. The former consists of four chapters: vector algebra, linear independence and linear subspaces, orthonormal bases and the Gram-Schmidt process, linear functions. The latter comes with eight chapters: matrices and matrix operations, invertible matrices and matrix inversion, projections and regression, determinants, eigensystems and diagonalizability, symmetric matrices, singular value decomposition, and stochastic matrices. The book ends with the solution of exercises which appear throughout its twelve chapters.
Lectures on Lagrangian Torus Fibrations
Symington's almost toric fibrations have played a central role in symplectic geometry over the past decade, from Vianna's discovery of exotic Lagrangian tori to recent work on Fibonacci staircases. Four-dimensional spaces are of relevance in Hamiltonian dynamics, algebraic geometry, and mathematical string theory, and these fibrations encode the geometry of a symplectic 4-manifold in a simple 2-dimensional diagram. This text is a guide to interpreting these diagrams, aimed at graduate students and researchers in geometry and topology. First the theory is developed, and then studied in many examples, including fillings of lens spaces, resolutions of cusp singularities, non-toric blow-ups, and Vianna tori. In addition to the many examples, students will appreciate the exercises with full solutions throughout the text. The appendices explore select topics in more depth, including tropical Lagrangians and Markov triples, with a final appendix listing open problems. Prerequisites include familiarity with algebraic topology and differential geometry.
Partial Differential Equations
Quite a number of phenomena in science and technology, industrial and/or agricultural production and transport, medical and/or biological flows and movements, social and/or economical developments, etc., depend on many variables, and are very much complicated. Although the detailed knowledge is accumulated in respective fields, it is meaningful to model and analyze the essential part of the phenomena in terms of smaller number of variables, which falls into partial differential equations. This book aims at providing students and researchers the basic ideas and the methods to solve problems in various fields. Particular attention is paid to bridge the gap between mathematics and the real world. To do this, we start from a simple system with intuitively understandable physical background, extract the essential part, formulate into mathematical tools, and then generalize for further application. Here logical thinking in depth and wide linking to various fields are sought to construct intellectual network.
Partial Differential Equations
Quite a number of phenomena in science and technology, industrial and/or agricultural production and transport, medical and/or biological flows and movements, social and/or economical developments, etc., depend on many variables, and are very much complicated. Although the detailed knowledge is accumulated in respective fields, it is meaningful to model and analyze the essential part of the phenomena in terms of smaller number of variables, which falls into partial differential equations. This book aims at providing students and researchers the basic ideas and the methods to solve problems in various fields. Particular attention is paid to bridge the gap between mathematics and the real world. To do this, we start from a simple system with intuitively understandable physical background, extract the essential part, formulate into mathematical tools, and then generalize for further application. Here logical thinking in depth and wide linking to various fields are sought to construct intellectual network.
Mental Multiplication Volume 2
My goal in the educational arena is to cause students to realize their potential in this mathematical criteria. The free- thinking in this incredible journey that multiplication can take you to, will show the student how to find treasures in understanding. The higher and deeper depths that I have reached is so miraculous that I can achieve wonders without the use of a calculator except to confirm my answers. It is my desire that the student can reach such depths also! Prayer has caused such a methodology that I have never encountered in all my study of this mystery. In my many past years of hours and days and months of looking into this treasure of knowledge, many other areas of mathematics has increased. I invite you to try Mental Multiplication Volume 2, you will love it!
Pi
In this delightful layperson's introduction to one of math's most interesting phenomena, Drs. Posamentier and Lehmann review pi's history from prebiblical times to the 21st century, the many amusing and mind-boggling ways of estimating pi over the centuries, quirky examples of obsessing about pi, and useful applications of pi in everyday life, including statistics.
Fair Share
Kofi Annan, former Secretary General of the United Nations, argued that "We need to create a world that is equitable, that is stable and a world where we bear in mind the needs of others, and not only what we need immediately. We are all in the same boat."American businessman, John Landgraf stated: "I hope that most of us believe that we actually would all benefit from living in a more equitable society. If that's not happening, we're squandering human potential." For the world to be fair, one needs to know how to divide. Without the mathematics of division, humankind cannot function...Marie Antoinette, Queen of France (infamously) said "If people have no bread, let them eat cake," and while Ahmes ― the scribe of the Rhind Mathematical Papyrus ― dealt with loaves of bread, prosperous people in the twentieth century dealt with cake division, although bread is also uniformly available. You'll be surprised, but there are at least four books and over 200 scientific (not gastronomical!) papers on cake division. Those authors were not overly concerned with obesity, one can guess, but whether distributing loaves, cakes, chores, or dividends, one needs to master division.This book deals with a wide spectrum of division problems, and provides the historical background, giving a sense of how pervasive division is in our lives. In particular, the second part focuses on a problem that remained open until 1985, when Professor Robert John Aumann (Nobel laureate in Economics, 2005) and Professor Michael Maschler solved it using game-theoretic techniques. Simple alternative solutions are given, which are suitable for high schools and other educational institutions.
Tree successor algebra
Tree successor algebra: A new branch in mathematics is a book about a formal theory of tree generation with an axiomatic basis for a new object called collection space. The elements of this space, in other words collections, have a clear connection to rooted trees and are treated as variables in sum form equations, the application area of tree successor algebra. With connections to different branches of mathematics such as number theory, linear algebra and algebra, tree successor algebra shows a fundamental link between rooted tree generation and partition generation, establishing a well-defined order in which rooted trees are generated. This in turn makes it possible to define a successor operator, the unit of least action in tree generation, and generalize it in order to create a concept of tree sequences. Due to this, the concept of the infinite sequence of all rooted trees can be formed, and the notion of a rooted tree line, and thus the need for tools to solve sum form equations rises. The axiomatic system answers to this need.
Logic for Kids
Getting started in logic at the earliest opportunity is the answer. While other books adopt a formal approach, using abstractions and arcane jargon, this book explains logical reasoning in simple and intuitive ways through its breezy writing style and with clipart lightening the mood.
Recent Advances in Mathematical Aspect in Engineering
The present text is an edited Special Issue in reprint form. This Special Issue took the opportunity to invite researchers to contribute their latest original research findings, which were either advances in the state-of-the-art of mathematical methods, theoretical studies, or experimental studies that extend the bounds of existing methodologies to new contributions, addressing current challenges and engineering problems on "Recent Advances in Mathematical Aspect in Engineering". Although this reprint is not a formal textbook, it will definitely be useful for university teachers, research students and industrial researchers, and will assist in overcoming difficulties while dealing with the nonlinear governing equations of fluid mechanics, energy, heat transfer, steady and unsteady flow problems, nanofluids, thermodynamics, magnetohydrodynamics, peristaltic and blood flow. For nonlinear and coupled differential equations, it is often more difficult to achieve an analytic solution or even a numerical one. This reprint has successfully handled this challenging task with the techniques reported within. In addition, the findings of the simulations are logically realistic and meet the standard of sufficient scientific value.
Topics in Graph Theory
The interplay between graph theory and a wide variety of models and applications in mathematics, computer science, operations research, and the natural and social sciences continues to grow.
Numerical Methods for Scientists and Engineers
The present shape of the book is based on my experience, extending over a long period of teaching Mathematics to under-graduate and post-graduate students of different colleges and universities. It is a self-contained textbook, designed for undergraduate students, who have mathematics as one of their subsidiary subjects. This book covers the different numerical methods, which are useful to solve algebraic and transcendental equations, systems of linear algebraic equations, and ordinary differential equations (initial value problems), and also covers the different strategies of numerical integration. This book contains various solved examples and a large number of standard unsolved questions that are given as exercise at the end of each chapter. In this book, each chapter contains the different MCQs, which are helpful for various competitive examinations of central and state services.
Math in Drag
A 2025 Los Angeles Times Book Prizes finalist. Unleash your inner math diva.Finalist for the LA Times Book PrizeJoin sensational drag queen Kyne Santos on an extraordinary journey through the glamorous world of . . . math? This sassy book is your VIP pass, taking you behind the scenes with a TikTok superstar who shatters stereotypes and proves that math can be fascinating and fun, even for people who think they aren't good at it.With her irreverent style and unique perspective, Kyne investigates mathematical mysteries while educating us about the art of drag. She explores surprising connections, such as the elegance of ballroom culture and the nature of infinity, the rebellious joys of Pride and dividing by zero, and the role of statistics in her own experience on Drag Race. Kyne gets personal while sharing her experiences as a queer person forging a path in STEM, overcoming obstacles to stay fierce, stay real, and thrive! She empowers readers of all skill levels to break school rules, question everything, and embrace math's beauty. In Math in Drag, numbers glitter, equations sashay through history, and inclusivity is a celebration. Read it to fire your excitement and unleash your inner math diva!
EZ Math Workbook
I HATE MATH.....There I said it! I bet thousands of students and parents have said it. When I was really having problems with Algebra in the 9th grade, my Grandmother ( who was a teacher) told me "math isn't hard if you understand it". When I started my career in teaching math in Jacksonville Florida I soon learned that all the math books we had were lacking really good easy to understand instructions on explaining specific areas. Most of the math books did have good parts i.e. one might have a really good section or chapter on fractions but lacked in explaining decimals etc. I taught 7 years plus both sessions of summer school for 5 years at several junior and senior high schools. Each school had "adopted" different math books to teach from. This is where the idea of creating my own math book self guide stated. Over several years I started writing and explaining the different areas of math. It is my hope that this workbook helps students and parents who my be frustrated with "new" math and "common core" principles. In this workbook you will find every area that is covered in math for secondary students. The chapter problems are specially designed to address several levels of a students skill sets. I found that most students would fall into various levels....advanced; standard; basic and remedial. Each chapter problems and chapter tests are designed with levels of "difficult", "moderate" and " easy" problems. As a former math teacher and a parent of three adult children I really hope this book helps.
Quantum Hydrodynamic Equation and Its Mathematical Theory
Quantum hydrodynamics comes from superfluid, superconductivity, semiconductor and so on. Quantum hydrodynamic model describes Helium II superfluid, Bose-Einstein condensation in inert gas, dissipative perturbation of Hamilton-Jacobi system, amplitude and dissipative perturbation of Eikonal quantum wave and so on. Owing to the broad application of quantum hydrodynamic equations, the study of the quantum hydrodynamic equations has aroused the concern of more and more scholars. Based on the above facts, we collected and collated the data of quantum hydrodynamic equations, and studied the concerning mathematical problems.The main contents of this book are: the derivation and mathematical models of quantum hydrodynamic equations, global existence of weak solutions to the compressible quantum hydrodynamic equations, existence of finite energy weak solutions of inviscid quantum hydrodynamic equations, non-isentropic quantum Navier-Stokes equations with cold pressure, boundary problem of compressible quantum Euler-Poisson equations, asymptotic limit to the bipolar quantum hydrodynamic equations.
Mathfatuated
Mathfatuated includes unique poems representing math topics associated with the lovable subject, making it the perfect gift for the math lover. Creating a poetry book about math can be a unique way of exploring mathematical concepts that may seem boringly challenging to some. Poetry can give a fresh perspective and bring an imaginative approach to learning about math. It can also help people remember mathematical concepts better. Moreover, it can bridge the gap between math and art and appeal to a larger audience. Overall, a poetry book about math can be an appealing and creative way to engage with the subject.
A new perspective on the determination of the prime numbers
Academic Paper from the year 2023 in the subject Mathematics - Number Theory, grade: 2.00, language: English, abstract: A procedure is developed for determining the primality of a number, N, but does not examine the number, rather a function of that number. The function has several properties, by means of which many of the non-primes may be identified and discarded without further investigation. Using the concept of cage numbers (defined in the text) a matrix of all of the counting numbers is produced, where, with the exception of the prime numbers 2 and 3, all of the prime numbers are embedded in one column of the matrix. Strings of consecutive numbers are extracted from the matrix, and it is seen that the only places within the whole of the range of the counting numbers where prime numbers can exist is at the positions of the second and penultimate numbers within a string By means of the function of N, all of the odd numbers may be generated and examined for primality.
The Geometry of Cubic Hypersurfaces
Cubic hypersurfaces are described by almost the simplest possible polynomial equations, yet their behaviour is rich enough to demonstrate many of the central challenges in algebraic geometry. With exercises and detailed references to the wider literature, this thorough text introduces cubic hypersurfaces and all the techniques needed to study them. The book starts by laying the foundations for the study of cubic hypersurfaces and of many other algebraic varieties, covering cohomology and Hodge theory of hypersurfaces, moduli spaces of those and Fano varieties of linear subspaces contained in hypersurfaces. The next three chapters examine the general machinery applied to cubic hypersurfaces of dimension two, three, and four. Finally, the author looks at cubic hypersurfaces from a categorical point of view and describes motivic features. Based on the author's lecture courses, this is an ideal text for graduate students as well as an invaluable reference for researchers in algebraic geometry.
The Navier-Stokes Problem in the 21st Century
This book provides a self-contained guide to the role of harmonic analysis in the PDEs of fluid mechanics, now revised to include fresh examples, theorems, results, and references that have become relevant since the first edition published in 2016.
Outlier Detection Using Power Mean
Outliers have been regarded as the noisy data in statistics which have now turned out to be an important problem and are now been researched in diverse fields and application domains. Outlier detection has been in core interest of not only the statisticians but all the professionals who are working on a particular data set. Many outlier detection techniques have been developed specific to certain application domains, while some techniques are more generic. This work has added one more technique to the bucket list of all those professionals. Power mean which has been used as a general method to calculate various means like arithmetic mean (power mean with power 1), geometric mean (power mean with power 0), Lorentz mean (power mean with power 1/3) etc. can also be used to detect the sensitivity of the data towards being the outlier. This work studies various powers of power mean for outlier detection. It contains two different data sets, one containing fractions and the other integers. The results have been verified by the existing standard techniques of outlier detection. Thus this book contains description of detecting outliers using power mean with different types of data sets, graphs and figures for better understanding. The idea is to check the efficacy of the method using a data set in which the outlier or the anomaly is already known and then testing the same method for a data set in which the outliers are not known to us. The open research issues and challenges at the end will provide researchers a clear path for the future of outlier detection methods. The book would be useful for practitioners of applied statistics and data analysts.
Introduction to Proofs and Proof Strategies
Emphasizing the creative nature of mathematics, this conversational textbook guides students through the process of discovering a proof. The material revolves around possible strategies to approaching a problem without classifying 'types of proofs' or providing proof templates. Instead, it helps students develop the thinking skills needed to tackle mathematics when there is no clear algorithm or recipe to follow. Beginning by discussing familiar and fundamental topics from a more theoretical perspective, the book moves on to inequalities, induction, relations, cardinality, and elementary number theory. The final supplementary chapters allow students to apply these strategies to the topics they will learn in future courses. With its focus on 'doing mathematics' through 200 worked examples, over 370 problems, illustrations, discussions, and minimal prerequisites, this course will be indispensable to first- and second-year students in mathematics, statistics, and computer science. Instructor resources include solutions to select problems.
Four-Dimensional Manifolds and Projective Structure
This book may be considered first as an introduction to differential geometry and, in particular, to 4-dimensional manifolds, and secondly as an introduction to the study of projective structure and projective relatedness in manifolds.
