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A History of Folding in Mathematics: Mathematizing The Margins (Science Networks. Historical Studies #59)
by Michael FriedmanWhile it is well known that the Delian problems are impossible to solve with a straightedge and compass – for example, it is impossible to construct a segment whose length is the cube root of 2 with these instruments – the discovery of the Italian mathematician Margherita Beloch Piazzolla in 1934 that one can in fact construct a segment of length the cube root of 2 with a single paper fold was completely ignored (till the end of the 1980s). This comes as no surprise, since with few exceptions paper folding was seldom considered as a mathematical practice, let alone as a mathematical procedure of inference or proof that could prompt novel mathematical discoveries. A few questions immediately arise: Why did paper folding become a non-instrument? What caused the marginalisation of this technique? And how was the mathematical knowledge, which was nevertheless transmitted and prompted by paper folding, later treated and conceptualised? Aiming to answer these questions, this volume provides, for the first time, an extensive historical study on the history of folding in mathematics, spanning from the 16th century to the 20th century, and offers a general study on the ways mathematical knowledge is marginalised, disappears, is ignored or becomes obsolete. In doing so, it makes a valuable contribution to the field of history and philosophy of science, particularly the history and philosophy of mathematics and is highly recommended for anyone interested in these topics.
A History of Geometrical Methods (Dover Books on Mathematics)
by Julian Lowell CoolidgeFull and authoritative, this history of the techniques for dealing with geometric questions begins with synthetic geometry and its origins in Babylonian and Egyptian mathematics; reviews the contributions of China, Japan, India, and Greece; and discusses the non-Euclidean geometries. Subsequent sections cover algebraic geometry, starting with the precursors and advancing to the great awakening with Descartes; and differential geometry, from the early work of Huygens and Newton to projective and absolute differential geometry. The author's emphasis on proofs and notations, his comparisons between older and newer methods, and his references to over 600 primary and secondary sources make this book an invaluable reference. 1940 edition.
A History of Greek Mathematics, Volume I: From Thales to Euclid
by Thomas Heath"As it is, the book is indispensable; it has, indeed, no serious English rival." — Times Literary Supplement. "Sir Thomas Heath, foremost English historian of the ancient exact sciences in the twentieth century." — Professor W. H. Stahl"Indeed, seeing that so much of Greek is mathematics, it is arguable that, if one would understand the Greek genius fully, it would be a good plan to begin with their geometry." The perspective that enabled Sir Thomas Heath to understand the Greek genius — deep intimacy with languages, literatures, philosophy, and all the sciences — brought him perhaps closer to his beloved subjects and to their own ideal of educated men, than is common or even possible today. Heath read the original texts with a critical, scrupulous eye, and brought to this definitive two-volume history the insights of a mathematician communicated with the clarity of classically taught English. "Of all the manifestations of the Greek genius none is more impressive and even awe-inspiring than that which is revealed by the history of Greek mathematics." Heath records that history with the scholarly comprehension and comprehensiveness that marks this work as obviously classic now as when it first appeared in 1921. The linkage and unity of mathematics and philosophy suggest the outline for the entire history. Heath covers in sequence Greek numerical notation, Pythagorean arithmetic, Thales and Pythagorean geometry, Zeno, Plato, Euclid, Aristarchus, Archimedes, Apollonius, Hipparchus and trigonometry, Ptolemy, Heron, Pappus, Diophantus of Alexandria and the algebra. Interspersed are sections devoted to the history and analysis of famous problems: squaring the circle, angle trisection, duplication of the cube, and an appendix on Archimedes' proof of the subtangent property of a spiral. The coverage is everywhere thorough and judicious; but Heath is not content with plain exposition: It is a defect in the existing histories that, while they state generally the contents of, and the main propositions proved in, the great treatises of Archimedes and Apollonius, they make little attempt to describe the procedure by which the results are obtained. I have therefore taken pains, in the most significant cases, to show the course of the argument in sufficient detail to enable a competent mathematician to grasp the method used and to apply it, if he will, to other similar investigations. Mathematicians, then, will rejoice to find Heath back in print and accessible after many years. Historians of Greek culture and science can renew acquaintance with a standard reference; readers in general will find, particularly in the energetic discourses on Euclid and Archimedes, exactly what Heath means by impressive and awe-inspiring.
A History of Greek Mathematics, Volume II: From Aristarchus to Diophantus
by Thomas HeathThe perspective that enabled Sir Thomas Heath to understand the Greek genius — deep intimacy with languages, literatures, philosophy, and all the sciences — brought him perhaps closer to his beloved subjects, and to their own ideal of educated men than is common or even possible today. Heath read the original texts with a critical, scrupulous eye and brought to this definitive two-volume history the insights of a mathematician communicated with the clarity of classically taught English."Of all the manifestations of the Greek genius none is more impressive and even awe-inspiring than that which is revealed by the history of Greek mathematics." Heath records that history with the scholarly comprehension and comprehensiveness that marks this work as obviously classic now as when it first appeared in 1921. The linkage and unity of mathematics and philosophy suggest the outline for the entire history. Heath covers in sequence Greek numerical notation, Pythagorean arithmetic, Thales and Pythagorean geometry, Zeno, Plato, Euclid, Aristarchus, Archimedes, Apollonius, Hipparchus and trigonometry, Ptolemy, Heron, Pappus, Diophantus of Alexandria and the algebra. Interspersed are sections devoted to the history and analysis of famous problems: squaring the circle, angle trisection, duplication of the cube, and an appendix on Archimedes's proof of the subtangent property of a spiral. The coverage is everywhere thorough and judicious; but Heath is not content with plain exposition: It is a defect in the existing histories that, while they state generally the contents of, and the main propositions proved in, the great treatises of Archimedes and Apollonius, they make little attempt to describe the procedure by which the results are obtained. I have therefore taken pains, in the most significant cases, to show the course of the argument in sufficient detail to enable a competent mathematician to grasp the method used and to apply it, if he will, to other similar investigations.Mathematicians, then, will rejoice to find Heath back in print and accessible after many years. Historians of Greek culture and science can renew acquaintance with a standard reference; readers in general will find, particularly in the energetic discourses on Euclid and Archimedes, exactly what Heath means by impressive and awe-inspiring.
A History of Japanese Mathematics (Dover Books on Mathematics)
by David E. Smith Yoshio MikamiOne of the first books to show Westerners the nature of Japanese mathematics, this survey highlights the leading features in the development of the wasan, the Japanese system of mathematics. Topics include the use of the soroban, or abacus; the application of sangi, or counting rods, to algebra; the discoveries of the 17th-century sage Seki Kowa; the yenri, or circle principle; the work of 18th-century geometer Ajima Chokuyen; and Wada Nei's contributions to the understanding of hypotrochoids. Unabridged republication of the classic 1914 edition. 74 figures. Index.
A History of Kinematics from Zeno to Einstein: On the Role of Motion in the Development of Mathematics (History of Mechanism and Machine Science #46)
by Teun KoetsierThis book covers the history of kinematics from the Greeks to the 20th century. It shows that the subject has its roots in geometry, mechanics and mechanical engineering and how it became in the 19th century a coherent field of research, for which Ampère coined the name kinematics. The story starts with the important Greek tradition of solving construction problems by means of kinematically defined curves and the use of kinematical models in Greek astronomy. As a result in 17th century mathematics motion played a crucial role as well, and the book pays ample attention to it. It is also discussed how the concept of instantaneous velocity, unknown to the Greeks, etc was introduced in the late Middle Ages and how in the 18th century, when classical mechanics was formed, kinematical theorems concerning the distribution of velocity in a solid body moving in space were proved. The book shows that in the 19th century, against the background of the industrial revolution, the theory of machines and thus the kinematics of mechanisms received a great deal of attention. In the final analysis, this led to the birth of the discipline.
A History of Mathematical Notations: Two Volumes Bound as One
by Florian CajoriThis classic study notes the first appearance of a mathematical symbol and its origin, the competition it encountered, its spread among writers in different countries, its rise to popularity, its eventual decline or ultimate survival. The author's coverage of obsolete notations -- and what we can learn from them -- is as comprehensive as those which have survived and still enjoy favor. Originally published in 1929 in a two-volume edition, this monumental work is presented here in one volume.
A History of Mathematics (History Of Mathematics Ser. #Vol. 2)
by Carl B. Boyer Uta C. MerzbachThe updated new edition of the classic and comprehensive guide to the history of mathematics For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of humankind’s relationship with numbers, shapes, and patterns. This revised edition features up-to-date coverage of topics such as Fermat’s Last Theorem and the Poincaré Conjecture, in addition to recent advances in areas such as finite group theory and computer-aided proofs. Distills thousands of years of mathematics into a single, approachable volume Covers mathematical discoveries, concepts, and thinkers, from Ancient Egypt to the present Includes up-to-date references and an extensive chronological table of mathematical and general historical developments. Whether you're interested in the age of Plato and Aristotle or Poincaré and Hilbert, whether you want to know more about the Pythagorean theorem or the golden mean, A History of Mathematics is an essential reference that will help you explore the incredible history of mathematics and the men and women who created it.
The History of Mathematics
by Roger L. CookeThis Third Edition of The History of Mathematics examines the elementary arithmetic, geometry, and algebra of numerous cultures, tracing their usage from Mesopotamia, Egypt, Greece, India, China, and Japan all the way to Europe during the Medieval and Renaissance periods where calculus was developed. Aimed primarily at undergraduate students studying the history of mathematics for science, engineering, and secondary education, the book focuses on three main ideas: the facts of who, what, when, and where major advances in mathematics took place; the type of mathematics involved at the time; and the integration of this information into a coherent picture of the development of mathematics. In addition, the book features carefully designed problems that guide readers to a fuller understanding of the relevant mathematics and its social and historical context. Chapter-end exercises, numerous photographs, and a listing of related websites are also included for readers who wish to pursue a specialized topic in more depth. Additional features of The History of Mathematics, Third Edition include:Material arranged in a chronological and cultural context. Specific parts of the history of mathematics presented as individual lessons. New and revised exercises ranging between technical, factual, and integrative. Individual PowerPoint presentations for each chapter and a bank of homework and test questions (in addition to the exercises in the book) An emphasis on geography, culture, and mathematics. In addition to being an ideal coursebook for undergraduate students, the book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the history of mathematics.
History of Mathematics and Its Contexts: Essays in Honor of Gert Schubring (Trends in the History of Science)
by Andrea Verdugo Rohrer Joerg ZenderThis book celebrates Gert Schubring's 80th birthday and honors his impactful contributions to the field of history of mathematics and its education. Recognized with the prestigious Hans Freudenthal Award in 2019, Schubring's academic work sets the tone for this volume. The thoughtfully curated articles in this collection offer insightful studies on textbooks and biographies of key figures in mathematics and mathematics education, contextualizing their significance within the broader historical landscape, and providing the readers with a deeper understanding of the development of the history of mathematics and its education. Researchers as well as curious readers and students will find this collection to be a valuable resource in the field.
History of Mathematics Teaching and Learning
by Alexander Karp Fulvia FuringhettiThis work examines the main directions of research conducted on the history of mathematics education. It devotes substantial attention to research methodologies and the connections between this field and other scholarly fields. The results of a survey about academic literature on this subject are accompanied by a discussion of what has yet to be done and problems that remain unsolved. The main topics you will find in ICME-13 Topical Survey include: Discussions of methodological issues in the history of mathematics education and of the relation between this field and other scholarly fields. The history of the formation and transformation of curricula and textbooks as a reflection of trends in social-economic, cultural and scientific-technological development. The influence of politics, ideology and economics on the development of mathematics education, from a historical perspective. The history of the preeminent mathematics education organizations and the work of leading figures in mathematics education. Mathematics education practices and tools and the preparation of mathematics teachers, from a historical perspective. "
The History Of Modern Mathematical Statistics: From Laplace To More Recent Times
by Prakash Gorroochurn"There is nothing like it on the market. . . no others are as encyclopedic. . . the writing is exemplary: simple, direct, and competent. " -George Cobb, Professor Emeritus of Mathematics and Statistics, Mount Holyoke College Written in a direct and clear manner, Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times presents a comprehensive guide to the history of mathematical statistics and details the major results and crucial developments over a 200 year period. Presented in chronological order, the book features an account of the classical and modern works that are essential to understanding the applications of mathematical statistics. Divided into three parts, the book begins with extensive coverage of the probabilistic works of Laplace, who laid much of the foundations of later developments in statistical theory. Subsequently, the second part introduces 20th century statistical developments including work from Karl Pearson, Student, Fisher, and Neyman. Lastly, the author deals with post-Fisherian developments. Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times also features: A detailed account of Galton's discovery of regression and correlation as well as the subsequent development of Karl Pearson's X2 and Student's t A comprehensive treatment of the permeating influence of Fisher in all aspects of modern statistics beginning with his work in 1912 Significant coverage of Neyman-Pearson theory, which includes a discussion of the differences to Fisher's works Discussions on key historical developments as well as the various disagreements, contrasting information, and alternative theories in the history of modern mathematical statistics in an effort to provide a thorough historical treatment Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times is an excellent reference for academicians with a mathematical background who are teaching or studying the history or philosophical controversies of mathematics and statistics. The book is also a useful guide for readers with a general interest in statistical inference.
The History Of New York City: Understand Properties Of Multiplication (Rosen Common Core Math Readers Ser.)
by Katie WhiteIn this book, readers will take a tour of major New York City historical attractions while learning how to use properties of operations for multiplication and division. This volume meets CCSS Math Standard 3.OA.B.5.
A History of Pi
by Petr BeckmannThe history of pi, says the author, though a small part of the history of mathematics, is nevertheless a mirror of the history of man. Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.
The History of Statistics: The Measurement of Uncertainty before 1900
by Stephen M. StiglerThis magnificent book is the first comprehensive history of statistics from its beginnings around 1700 to its emergence as a distinct and mature discipline around 1900. Stephen M. Stigler shows how statistics arose from the interplay of mathematical concepts and the needs of several applied sciences including astronomy, geodesy, experimental psychology, genetics, and sociology. He addresses many intriguing questions: How did scientists learn to combine measurements made under different conditions? And how were they led to use probability theory to measure the accuracy of the result? Why were statistical methods used successfully in astronomy long before they began to play a significant role in the social sciences? How could the introduction of least squares predate the discovery of regression by more than eighty years? On what grounds can the major works of men such as Bernoulli, De Moivre, Bayes, Quetelet, and Lexis be considered partial failures, while those of Laplace, Galton, Edgeworth, Pearson, and Yule are counted as successes? How did Galton’s probability machine (the quincunx) provide him with the key to the major advance of the last half of the nineteenth century? Stigler’s emphasis is upon how, when, and where the methods of probability theory were developed for measuring uncertainty in experimental and observational science, for reducing uncertainty, and as a conceptual framework for quantitative studies in the social sciences. He describes with care the scientific context in which the different methods evolved and identifies the problems (conceptual or mathematical) that retarded the growth of mathematical statistics and the conceptual developments that permitted major breakthroughs. Statisticians, historians of science, and social and behavioral scientists will gain from this book a deeper understanding of the use of statistical methods and a better grasp of the promise and limitations of such techniques. The product of ten years of research, The History of Statistics will appeal to all who are interested in the humanistic study of science.
The History of the Calculus and Its Conceptual Development
by Carl B. BoyerThis book, for the first time, provides laymen and mathematicians alike with a detailed picture of the historical development of one of the most momentous achievements of the human intellect - the calculus. It describes with accuracy and perspective the long development of both the integral and the differential calculus from their early beginnings in antiquity to their final emancipation in the 19th century from both physical and metaphysical ideas alike and their final elaboration as mathematical abstractions, as we know them today, defined in terms of formal logic by means of the idea of a limit of an infinite sequence.But while the importance of the calculus and mathematical analysis - the core of modern mathematics - cannot be overemphasized, the value of this first comprehensive critical history of the calculus goes far beyond the subject matter. This book will fully counteract the impression of laymen, and of many mathematicians, that the great achievements of mathematics were formulated from the beginning in final form. It will give readers a sense of mathematics not as a technique, but as a habit of mind, and serve to bridge the gap between the sciences and the humanities. It will also make abundantly clear the modern understanding of mathematics by showing in detail how the concepts of the calculus gradually changed from the Greek view of the reality and immanence of mathematics to the revised concept of mathematical rigor developed by the great 19th century mathematicians, which held that any premises were valid so long as they were consistent with one another. It will make clear the ideas contributed by Zeno, Plato, Pythagoras, Eudoxus, the Arabic and Scholastic mathematicians, Newton, Leibnitz, Taylor, Descartes, Euler, Lagrange, Cantor, Weierstrass, and many others in the long passage from the Greek "method of exhaustion" and Zeno's paradoxes to the modern concept of the limit independent of sense experience; and illuminate not only the methods of mathematical discovery, but the foundations of mathematical thought as well.
History of the Calcutta School of Physical Sciences
by Purabi Mukherji Atri MukhopadhyayThis book highlights the role of Sir Asutosh Mookerjee, founder of the Calcutta school of physics and the Calcutta Mathematical Society, and his talented scholars – Sir C.V. Raman, D.M. Bose, S.N. Bose, M.N. Saha, Sir K.S. Krishnan and S.K. Mitra – all of whom played a significant role in fulfilling their goal of creating an outstanding school of physical sciences in the city of Calcutta. The main objective of the book is to bring to the fore the combined contributions of the greatest physicists of India, who in the colonial period worked with practically no modern amenities and limited financial resources, but nonetheless with total dedication and self-confidence, which is unmatched in today’s world. The book presents the golden age of the physical sciences in India in compact form; in addition, small anecdotes, mostly unknown to many, have been brought the forefront. The book consists of 10 chapters, which include papers by these distinguished scientists along with detailed accounts of their academic lives and main research contributions, particularly during their time in Calcutta. A synopsis of the contents is provided in the introductory chapter. In the following chapters, detailed discussions are presented in straightforward language. The complete bibliographies of the great scientists have been added at the end. This book will be of interest to historians, philosophers of science, linguists, anthropologists, students, research scholars and general readers with a love for the history of science.
The History of the International Biometric Society
by Lynne BillardThe International Biometric Society (IBS) was formed at the First International Biometric Conference at Woods Hole on September 6, 1947. The History of the International Biometric Society presents a deep dive into the voluminous archival records, with primary focus on IBS’s first fifty years. It contains numerous photos and extracts from the archival materials, and features many photos of important leaders who served IBS across the decades. Features: Describes events leading up to and at Woods Hole on September 6, 1947 that led to the formation of IBS Outlines key markers that shaped IBS after the 1947 formation through to the modern day Describes the regional and national group structure, and the formation of regions and national groups Describes events surrounding the key scientific journal of IBS, Biometrics, including the transfer of ownership to IBS, content, editors, policies, management, and importance Describes the other key IBS publications – Biometric Bulletin, Journal of Agricultural Biological and Environmental Statistics, and regional publications Provides details of International Biometric Conferences and key early symposia Describes IBS constitution and by-laws processes, and the evolution of business arrangements Provides a record of international officers, including regional presidents, national group secretaries, journal editors, and the locations of meetings Includes a gallery of international Presidents, and a gallery of Secretaries and Treasurers The History of the International Biometric Society will appeal to anyone interested in the activities of our statistical and biometrical forebearers. The focus is on issues and events that engaged the attention of the officers of IBS. Some of these records are riveting, some entertaining, some intriguing, and some colorful. Some of the issues covered were difficult to handle, but even these often resulted in changes that benefited IBS.
History of the Theory of Numbers, Volume II: Diophantine Analysis
by Leonard Eugene DicksonThe three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This second volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to the subject of diophantine analysis. It can be read independently of the preceding volume, which explores divisibility and primality, and volume III, which examines quadratic and higher forms.Featured topics include polygonal, pyramidal, and figurate numbers; linear diophantine equations and congruences; partitions; rational right triangles; triangles, quadrilaterals, and tetrahedra; the sums of two, three, four, and n squares; the number of solutions of quadratic congruences in n unknowns; Liouville's series of eighteen articles; the Pell equation; squares in arithmetical or geometrical progression; equations of degrees three, four, and n; sets of integers with equal sums of like powers; Waring's problem and related results; Fermat's last theorem; and many other related subjects. Indexes of authors cited and subjects appear at the end of the book.
A History of the Work Concept: From Physics to Economics (History of Mechanism and Machine Science #24)
by Agamenon R. E. OliveiraThis book traces the history of the concept of work from its earliest stages and shows that its further formalization leads to equilibrium principle and to the principle of virtual works, and so pointing the way ahead for future research and applications. The idea that something remains constant in a machine operation is very old and has been expressed by many mathematicians and philosophers such as, for instance, Aristotle. Thus, a concept of energy developed. Another important idea in machine operation is Archimedes' lever principle. In modern times the concept of work is analyzed in the context of applied mechanics mainly in Lazare Carnot mechanics and the mechanics of the new generation of polytechnical engineers like Navier, Coriolis and Poncelet. In this context the word "work" is finally adopted. These engineers are also responsible for the incorporation of the concept of work into the discipline of economics when they endeavoured to combine the study of the work of machines and men together.
History of Virtual Work Laws
by Danilo CapecchiThe book presents a history of classical mechanics by focusing on issues of equilibrium. The historical point of view adopted here restricts attention to cases where the effectiveness of forces is assessed on the basis of the virtual motion of their points of application. For completeness, hints of the alternative approach are also referred, the Archimedean for ancient mechanics and the Newtonian for modern mechanics. The laws resulting from consideration of virtual motions are named laws of virtual work. The modern formulations of the principle of virtual work are only a particular form of them. The book begins with the first documented formulations of laws of virtual work in the IV century BC in Greece and proceeds to the end of the XIX century AD in Europe. A significant space is devoted to Arabic and Latin mechanics of Middle Ages. With the Renaissance it began to appear slightly different wordings of the laws, which were often proposed as unique principles of statics. The process reached its apex with Bernoulli and Lagrange in the XVIII century. The book ends with some chapters dealing with the discussions that took place in the French school on the role of the Lagrangian version of the law of virtual work and its applications to continuum mechanics.
HIV/AIDS in South Africa 25 Years On
by Seth C. Kalichman Poul Rohleder E. Cameron Leslie Swartz Leickness Chisamu SimbayiMuch has happened since the first appearance of AIDS in 1981: it has been identified, studied, and occasionally denied. The virus has shifted host populations and spread globally. Medicine, the social sciences, and world governments have joined forces to combat and prevent the disease. And South Africa has emerged as ground zero for the pandemic. The editors of HIV/AIDS in South Africa 25 Years On present the South African crisis as a template for addressing the myriad issues surrounding the epidemic worldwide, as the book brings together a widely scattered body of literature, analyzes psychosocial and sexual aspects contributing to HIV transmission and prevention, and delves into complex intersections of race, gender, class, and politics. Including largely overlooked populations and issues (e.g., prisoners, persons with disabilities, stigma), as well as challenges shaping future research and policy, the contributors approach their topics with rare depth, meticulous research, carefully drawn conclusions, and profound compassion. Among the topics covered: The relationship between HIV and poverty, starting from the question, "Which is the determinant and which is the consequence?"Epidemiology of HIV among women and men: concepts of femininity and masculinity, and gender inequities as they affect HIV risk; gender-specific prevention and intervention strategies. The impact of AIDS on infants and young children: risk and protective factors; care of children by HIV-positive mothers; HIV-infected children.Current prevention and treatment projects, including local-level responses, community-based work, and VCT (voluntary counseling and testing) programs.New directions: promoting circumcision, vaccine trials, "positive prevention."South Africa's history of AIDS denialism.The urgent lessons in this book apply both globally and locally, making HIV/AIDS in South Africa 25 Years On uniquely instructive and useful for professionals working in HIV/AIDS and global public health.
HMH GoMath!: Student Edition (StA) Volume 1 Grade 4 2016
by Houghton Mifflin Harcourt*This textbook has been transcribed in UEB, formatted according to Braille textbook formats, proofread and corrected. <P><P>
HMH GoMath!: Student Edition (StA) Volume 2 Grade 4 2016
by Houghton Mifflin Harcourt*This textbook has been transcribed in UEB, formatted according to Braille textbook formats, proofread and corrected. <P><P>
HMH: Modules 10 - 20
by Dixon Juli K. Kanold TimothyWelcome to Into Math, Grade 5! In this program, you will develop skills and make sense of mathematics by solving real-world problems, using hands-on tools and strategies, and collaborating with your classmates. With the support of your teacher and by engaging with meaningful practice, you will learn to persevere when solving problems. Into Math will not only help you deepen your understanding of mathematics, but also build your confidence as a learner of mathematics. Even more exciting, you will write all your ideas and solutions right in your book. In your Into Math book, writing and drawing on the pages will help you think deeply about what you are learning, help you truly understand math, and most important, you will become a confident user of mathematics!