Science & Mathematics
September 2020
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Science & MathematicsGuide to the Research on Mathematical education II
by Dianzhou Zhang
This book is a mathematical discipline education research method books written by Zhang Dianzhou, academician of International Academy of Sciences for Europe and Asia(IASEA). Its publication is designed to help people understand math education for the forefront of progress in the study of mathematics education, raising the level of scientific research in mathematics education research, guidance for mathematics education research method of strategy.
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MathematicsSeptember 2015Mathematics for economists
An introductory textbook (new edition)
by Malcolm Pemberton, Nicholas Rau
This book is a self-contained treatment of all the mathematics needed by undergraduate and masters-level students of economics. Building up gently from a very low level, the authors provide a clear, systematic coverage of calculus and matrix algebra. The second half of the book gives a thorough account of probability, optimisation and dynamics. The final two chapters are an introduction to the rigorous mathematical analysis used in graduate-level economics. The emphasis throughout is on intuitive argument and problem-solving. All methods are illustrated by examples, exercises and problems selected from central areas of modern economic analysis. The book's careful arrangement in short chapters enables it to be used in a variety of course formats for students with or without prior knowledge of calculus, for reference and for self-study. This new fourth edition includes two chapters on probability theory, providing the essential mathematical background for upper-level courses on economic theory, econometrics and finance. Answers to all exercises and complete solutions to all problems are available online from a regularly updated website.
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Science & MathematicsSeptember 2023Mathematics for economists
An introductory textbook, fifth edition
by Malcolm Pemberton, Nicholas Rau
This book is a self-contained treatment of all the mathematics needed by undergraduate and masters-level students of economics, econometrics and finance. Building up gently from a very low level, the authors provide a clear, systematic coverage of calculus and matrix algebra. The second half of the book gives a thorough account of probability, dynamics and static and dynamic optimisation. The last three chapters are an accessible introduction to the rigorous mathematical analysis used in graduate-level economics. The emphasis throughout is on intuitive argument and problem-solving. All methods are illustrated by examples, exercises and problems selected from central areas of modern economic analysis. The book's careful arrangement in short chapters enables it to be used in a variety of course formats for students with or without prior knowledge of calculus, for reference and for self-study.
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Science & MathematicsSeptember 2023Mathematics for economists
An introductory textbook, fifth edition
by Malcolm Pemberton, Nicholas Rau
This book is a self-contained treatment of all the mathematics needed by undergraduate and masters-level students of economics, econometrics and finance. Building up gently from a very low level, the authors provide a clear, systematic coverage of calculus and matrix algebra. The second half of the book gives a thorough account of probability, dynamics and static and dynamic optimisation. The last three chapters are an accessible introduction to the rigorous mathematical analysis used in graduate-level economics. The emphasis throughout is on intuitive argument and problem-solving. All methods are illustrated by examples, exercises and problems selected from central areas of modern economic analysis. The book's careful arrangement in short chapters enables it to be used in a variety of course formats for students with or without prior knowledge of calculus, for reference and for self-study.
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Trusted Partner
Science & MathematicsSeptember 2023Mathematics for economists
An introductory textbook, fifth edition
by Malcolm Pemberton, Nicholas Rau
This book is a self-contained treatment of all the mathematics needed by undergraduate and masters-level students of economics, econometrics and finance. Building up gently from a very low level, the authors provide a clear, systematic coverage of calculus and matrix algebra. The second half of the book gives a thorough account of probability, dynamics and static and dynamic optimisation. The last three chapters are an accessible introduction to the rigorous mathematical analysis used in graduate-level economics. The emphasis throughout is on intuitive argument and problem-solving. All methods are illustrated by examples, exercises and problems selected from central areas of modern economic analysis. The book's careful arrangement in short chapters enables it to be used in a variety of course formats for students with or without prior knowledge of calculus, for reference and for self-study.
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Science & MathematicsJuly 2012Gayatri’s Maths Mantra
by Gayatri Lodha
Generally school going children find it difficult to understand mathematics. This book explains simple techniques of basic mathematical calculations such as multiplication and division. With the help of these techniques one can improve the speed of calculation as well as accuracy.
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Science & MathematicsFebruary 2020Cambridge International AS & A Level Mathematics
Revision Guide for Pure Mathematics 3
by Yong Yau, Lee Lip Seong, Amy Khoo
Cambridge International AS & A Level Mathematics: Revision Guide for Pure Mathematics 3 is a study guide that aims to support students preparing for the Cambridge International AS & A Level Mathematics (9709) examination. Written by seasoned lecturers, this book provides in-depth coverage of the latest 2020–2022 syllabus for the Pure Mathematics 3 component of the examination. This book is filled with step-by-step worked examples, clear and concise explanations, insightful study tips, and questions from actual past examination papers for self-assessment. This book is suitable for students taking Paper 3 of the Cambridge International AS & A Level Mathematics (9709) examination.
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Science & MathematicsJuly 2020Time-Varying Stochastic Systems: Stability and Adaptive Theory (Second Edition)
by GUO Lei
Time-varying Stochastic Systems widely exist in reality and many random recursive algorithms can also be studied as such systems. The stability, adaptive estimation and adaptive control of such systems are discussed in this book. The book consists of eight chapters, which not only include the classical results of stability and stabilization commonly used, but also focus on the introduction of basic adaptive estimation, filtering and control problems and the theoretical basis of corresponding algorithms, most of which belong to the author’s research results.
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Science & MathematicsApril 2021Cosmic Zoom
Scale, Knowledge, and Mediation
by Horton, Zachary
Many of us have encountered a version of what Zachary Horton calls the “cosmic zoom”—a visual journey through the many scales of the universe, from the microscopic to the cosmic. Most of our daily perception operates at a level of scale somewhere between that of quarks and galaxies, and it is this comfort with the immediately visible everyday world that the cosmic zoom unsettles. Horton uses the history of the cosmic zoom to explore how that scale itself has been constructed over the past seventy years. How has cosmic zoom media influenced scientific and popular understanding of the unseen world and how it may be known, accessed, and exploited? Horton insists that scale is the key to understanding and addressing major contemporary issues including climate change and big data, but people working on issues of scale in various disciplines often talk past each other. Horton starts by sketching four common ways of thinking about scale derived from cartography, physics, engineering/biology, and mathematics. He then shows how these concepts operate in various disciplines, explains why they don’t fit together, and puts forth a new, transdisciplinary theory and vocabulary of scale, one that links the natural sciences, humanities, and social sciences. In this ambitious work, scale becomes a foundation for rethinking the relationships between knowledge, mediation, and environment.
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Humanities & Social SciencesAugust 2022Greens Drive SUVs and Jogging Makes You Immortal
On “Unstatistics” and Their Perils
by Thomas Bauer, Gerd Gigerenzer, Walter Krämer, Katharina Schüller
Why Forecasts Are Always Wrong—the Power of Statistics Understanding how figures relate to reality poses a challenge in an age when we are confronted at every turn with fake news and clickbait telling us to be very afraid. Each day brings headlines to outdo those of the day before, yet often they are based on a false interpretation of the data. Gerd Gigerenzer (a psychologist), Katharina Schuller (an expert on data analysis), Thomas Bauer (an economist), and Walter Krämer (a statistician) have for some years now presented an “Unstatistic of the Month” as an indictment of a deficient understanding of figures, risk, and probability. Drawing on new and shocking examples, the four authors explain how we can recognize nonsense, contextualize forecasts, tell correlation from causation, and generally make sense of an increasingly complex world. It’s not just fun—it’s more important than ever. • More relevant than ever: the power of statistics in the age of fake news • An entertaining exploration of and remedy for statistical illiteracy
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AlgebraLINEAR ALGEBRA
A GEOMETRIC APPROACH
by KUMARESAN, S.
This clear, concise and highly readable text is designed for a first course in linear algebra and is intended for undergraduate courses in mathematics. It focusses throughout on geometric explanations to make the student perceive that linear algebra is nothing but analytic geometry of n dimensions. From the very start, linear algebra is presented as an extension of the theory of simultaneous linear equations and their geometric interpretation is shown to be a recurring theme of the subject. The integration of abstract algebraic concepts with the underlying geometric notions is one of the most distinguishing features of this book — designed to help students in the pursuit of multivariable calculus and differential geometry in subsequent courses. Explanations and concepts are logically presented in a conversational tone and well-constructed writing style so that students at a variety of levels can understand the material and acquire a solid foundation in the basic skills of linear algebra. Key FeaturesEntices students to geometric way of thinking about linear algebra.Includes about 100 solved examples for consolidation of the important concepts introduced.Gives about 400 exercises of various levels of difficulty to prepare students for original thinking. Google Preview: https://bit.ly/3AYZXKb
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MathematicsDecember 2016Euclidean Geometry in Mathematical Olympiads
by Evan Chen
This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains a selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions. This book is especially suitable for students preparing for national or international mathematical olympiads or for teachers looking for a text for an honor class.
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Science & MathematicsNonlinear Wave Equations
by Li Tatsien, Zhou Yi
Nonlinear wave equations belong to a typical category of nonlinear evolutionary equations that is of great theoretical significance and practical value. The whole book has got fifteen chapters in all. The first seven serve as a prelude for later discussions, but still have their own meanings and values. Among the later eight chapters, five discuss the global existence and the lower bound estimates of life-span for classical solutions in all possible situations by adopting the global iteration method, including the proof of global existence of classical solutions under the hypothesis of the null condition; two focus on demonstrating the sharpness of the obtained lower bound estimates of life-span; and the last chapter entails relevant applications and extensions.
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Science & MathematicsA Discrete Transition to Advanced Mathematics, Second Edition
by Bettina Richmond and Thomas Richmond
Pure and Applied Undergraduate Texts Volume: 63; 2023; 523 pp MSC: Primary 00; This textbook bridges the gap between lower-division mathematics courses and advanced mathematical thinking. Featuring clear writing and appealing topics, the book introduces techniques for writing proofs in the context of discrete mathematics. By illuminating the concepts behind techniques, the authors create opportunities for readers to sharpen critical thinking skills and develop mathematical maturity. Beginning with an introduction to sets and logic, the book goes on to establish the basics of proof techniques. From here, chapters explore proofs in the context of number theory, combinatorics, functions and cardinality, and graph theory. A selection of extension topics concludes the book, including continued fractions, infinite arithmetic, and the interplay among Fibonacci numbers, Pascal's triangle, and the golden ratio. A Discrete Transition to Advanced Mathematics is suitable for an introduction to proof course or a course in discrete mathematics. Abundant examples and exercises invite readers to get involved, and the wealth of topics allows for course customization and further reading. This new edition has been expanded and modernized throughout, featuring: A new chapter on combinatorial geometry; An expanded treatment of the combinatorics of indistinguishable objects; New sections on the inclusion-exclusion principle and circular permutations; Over 365 new exercises. Ancillaries: Student Solutions Manual (Selected Problems) Instructor's Manual Readership Undergraduate students who need a strong conceptual foundation for higher mathematical thinking.
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Science & MathematicsThe Tiling Book
An Introduction to the Mathematical Theory of Tilings
by Colin Adams
2022; 298 pp MSC: Primary 05; 52; Tiling theory provides a wonderful opportunity to illustrate both the beauty and utility of mathematics. It has all the relevant ingredients: there are stunning pictures; open problems can be stated without having to spend months providing the necessary background; and there are both deep mathematics and applications. Furthermore, tiling theory happens to be an area where many of the sub-fields of mathematics overlap. Tools can be applied from linear algebra, algebra, analysis, geometry, topology, and combinatorics. As such, it makes for an ideal capstone course for undergraduates or an introductory course for graduate students. This material can also be used for a lower-level course by skipping the more technical sections. In addition, readers from a variety of disciplines can read the book on their own to find out more about this intriguing subject. This book covers the necessary background on tilings and then delves into a variety of fascinating topics in the field, including symmetry groups, random tilings, aperiodic tilings, and quasicrystals. Although primarily focused on tilings of the Euclidean plane, the book also covers tilings of the sphere, hyperbolic plane, and Euclidean 3-space, including knotted tilings. Throughout, the book includes open problems and possible projects for students. Readers will come away with the background necessary to pursue further work in the subject. Preview some of these beautiful and intricate patterns here. Readership Undergraduate and graduate students and researchers interested in tilings and tessellations.
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MathematicsIt All Adds Up
How Numerology Change Your Life
by Margaret Neylon
A simple guide to the science of numbers and how it can change your life. It All Adds Up shows us how to work out the special numbers in our live, using simple addition. When you know what you should do and the right time to do it then you are on the road to success.
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MathematicsSimply Gödel
by Richard Tieszen
Kurt Gödel (1906–1978) was born in Austria-Hungary (now the Czech Republic) and grew up in an ethnic German family. As a student, he excelled in languages and mathematics, mastering university-level math while still in high school. He received his doctorate from the University of Vienna at the age of 24 and, a year later, published the pioneering theorems on which his fame rests. In 1939, with the rise of Nazism, Gödel and his wife settled in the U.S., where he continued his groundbreaking work at the Institute for Advanced Study (IAS) in Princeton and became a close friend of Albert Einstein’s. In Simply Gödel, Richard Tieszen traces Gödel’s life and career, from his early years in tumultuous, culturally rich Vienna to his many brilliant achievements as a member of IAS, as well as his repeated battles with mental illness. In discussing Gödel’s ideas, Tieszen not only provides an accessible explanation of the incompleteness theorems, but explores some of his lesser known writings, including his thoughts on time travel and his proof of the existence of God. With clarity and sympathy, Simply Gödel brings to life Gödel’s fascinating personal and intellectual journey and conveys the lasting impact of his work on our modern world.
