Download or read book Mathematical Explorations written by Alan F. Beardon and published by Cambridge University Press. This book was released on 2016-10-13 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides readers with experience of working on difficult unsolved problems. No deep mathematical background is required.
Download or read book Explorations in Mathematical Physics written by Don Koks and published by Springer Science & Business Media. This book was released on 2006-09-15 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You will see how the accelerated frames of special relativity tell us about gravity. On the journey, you will discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis built solely on the metric and vectors, with no need for one-forms. This gives a much more geometrical and intuitive insight into vector and tensor calculus, together with general relativity, than do traditional, more abstract methods. Don Koks is a physicist at the Defence Science and Technology Organisation in Adelaide, Australia. His doctorate in quantum cosmology was obtained from the Department of Physics and Mathematical Physics at Adelaide University. Prior work at the University of Auckland specialised in applied accelerator physics, along with pure and applied mathematics.
Download or read book Mathematical Expeditions written by Frank J. Swetz and published by JHU Press. This book was released on 2012-07-16 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A collection of over 500 culturally and historically diverse mathematical problems carefully chosen to enrich mathematics teaching from middle school through the college level."--Provided by publisher.
Download or read book Early Mathematical Explorations written by Nicola Yelland and published by Cambridge University Press. This book was released on 2014-01-20 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents teachers with a sound theoretical framework for encouraging children to explore mathematical concepts and become numerate in the 21st century. It shows that mathematical learning can occur in a variety of ways, including when children explore ideas through play, problem solving and problem posing, engage in a rich variety of multimodal learning experiences, pursue self-directed activities and cooperate with others, and make connections between ideas and experiences in their everyday worlds. - Back cover
Download or read book Mathematical Expeditions written by Reinhard Laubenbacher and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: The stories of five mathematical journeys into new realms, pieced together from the writings of the explorers themselves. Some were guided by mere curiosity and the thrill of adventure, others by more practical motives. In each case the outcome was a vast expansion of the known mathematical world and the realisation that still greater vistas remain to be explored. The authors tell these stories by guiding readers through the very words of the mathematicians at the heart of these events, providing an insightinto the art of approaching mathematical problems. The five chapters are completely independent, with varying levels of mathematical sophistication, and will attract students, instructors, and the intellectually curious reader. By working through some of the original sources and supplementary exercises, which discuss and solve -- or attempt to solve -- a great problem, this book helps readers discover the roots of modern problems, ideas, and concepts, even whole subjects. Students will also see the obstacles that earlier thinkers had to clear in order to make their respective contributions to five central themes in the evolution of mathematics.
Download or read book Mathematical Explorations written by Alan F. Beardon and published by Cambridge University Press. This book was released on 2016-10-13 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Explorations follows on from the author's previous book, Creative Mathematics, in the same series, and gives the reader experience in working on problems requiring a little more mathematical maturity. The author's main aim is to show that problems are often solved by using mathematics that is not obviously connected to the problem, and readers are encouraged to consider as wide a variety of mathematical ideas as possible. In each case, the emphasis is placed on the important underlying ideas rather than on the solutions for their own sake. To enhance understanding of how mathematical research is conducted, each problem has been chosen not for its mathematical importance, but because it provides a good illustration of how arguments can be developed. While the reader does not require a deep mathematical background to tackle these problems, they will find their mathematical understanding is enriched by attempting to solve them.
Download or read book Mathematical Explorations for the Christian Thinker written by Jason Vanbilliard and published by CreateSpace. This book was released on 2014-08-15 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: What does it mean to learn math from a Christian perspective? This book is ideally suited for a Christian audience who wishes to significantly extend his or her knowledge of mathematics while developing biblical perspectives on the mathematical-philosophical questions posed in each section. Among other compelling issues, readers will wrestle with questions as to the relationships between God, nature, mathematics, and humans. The integration of Christian thought is weaved throughout the text.[**Note: there are two versions of this book. Read below for more details.]Through the mathematics content presented in this book, you will broaden your understanding of geometry by investigating dimensions, fractals, topological equivalence, and other geometries. You will develop your reasoning skills through identifying deception in statistics, discriminating between cause and correlation, evaluating various voting methods, and exploring chaos theory. Finally, you will refine your understanding of numbers and systems through studying prime, figurate, vampire, narcissistic, powerful, abundant, and transcendental numbers.After studying each mathematical topic, you will consider how the topic informs your answers to questions like: Who are we? What is the nature of reality? How do we know if something is true? What is good? What is beautiful? These questions and their related sub-questions have been part of the human experience from the dawn of human history. Considering how mathematics helps to inform these questions provides for a deeper, more meaningful understanding of mathematics and our world.This book is ideal for:- An undergraduate “Mathematics for Liberal Arts” course at a Christian college- A half-year senior mathematics elective as part of a focus on worldview at a Christian high school - A Christian homeschool family that wishes to extend their children's learning beyond the standard curriculum in a Christian centered context- Anyone interested in extending his or her own understanding of the scope and depth of mathematicsEach section features:- Introductory exercises that prompt the reader to recall relevant information or skills- Concept development sections that explain the mathematics for even the math-phobic student- Content sections that connect the mathematics to literature, art, music, science, and other subjects- A “Something to Consider” section that asks the reader to think about related enduring questions from a Christian perspective- “Covering the Reading” questions that help to process the text- “Problems” that require the reader to research and consider the topic more thoroughly[** There is another version of this book titled "The Mathematical Expanse: Excursions into the Enduring Questions." That version asks many similar questions but is appropriate for a public school setting.]
Download or read book Strange Curves Counting Rabbits Other Mathematical Explorations written by Keith Ball and published by Princeton University Press. This book was released on 2003 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: How does mathematics enable us to send pictures from space back to Earth? Where does the bell-shaped curve come from? Why do you need only 23 people in a room for a 50/50 chance of two of them sharing the same birthday? In Strange Curves, Counting Rabbits, and Other Mathematical Explorations, Keith Ball highlights how ideas, mostly from pure math, can answer these questions and many more. Drawing on areas of mathematics from probability theory, number theory, and geometry, he explores a wide range of concepts, some more light-hearted, others central to the development of the field and used daily by mathematicians, physicists, and engineers. Each of the book's ten chapters begins by outlining key concepts and goes on to discuss, with the minimum of technical detail, the principles that underlie them. Each includes puzzles and problems of varying difficulty. While the chapters are self-contained, they also reveal the links between seemingly unrelated topics. For example, the problem of how to design codes for satellite communication gives rise to the same idea of uncertainty as the problem of screening blood samples for disease. Accessible to anyone familiar with basic calculus, this book is a treasure trove of ideas that will entertain, amuse, and bemuse students, teachers, and math lovers of all ages.
Download or read book Playing with Infinity written by Rozsa Peter and published by . This book was released on 1986-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Popular account ranges from counting to mathematical logic and covers many concepts related to infinity: graphic representation of functions; pairings, other combinations; prime numbers; logarithms, circular functions; more. 216 illustrations.
Download or read book Mathematical Explorations for Young Minds written by Bálint Hujter and published by Springer Nature. This book was released on with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Origamics written by Kazuo Haga and published by World Scientific. This book was released on 2008 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: The art of origami, or paper folding, is carried out using a square piece of paper to obtain attractive figures of animals, flowers or other familiar figures. It is easy to see that origami has links with geometry. Creases and edges represent lines, intersecting creases and edges make angles, while the intersections themselves represent points. Because of its manipulative and experiential nature, origami could become an effective context for the learning and teaching of geometry.In this unique and original book, origami is an object of mathematical exploration. The activities in this book differ from ordinary origami in that no figures of objects result. Rather, they lead the reader to study the effects of the folding and seek patterns. The experimental approach that characterizes much of science activity can be recognized throughout the book, as the manipulative nature of origami allows much experimenting, comparing, visualizing, discovering and conjecturing. The reader is encouraged to fill in all the proofs, for his/her own satisfaction and for the sake of mathematical completeness. Thus, this book provides a useful, alternative approach for reinforcing and applying the theorems of high school mathematics.
Download or read book Cows in the Maze written by Ian Stewart and published by OUP Oxford. This book was released on 2010-04-22 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the mathematics of mazes, to cones with a twist, and the amazing sphericon - and how to make one - Ian Stewart is back with more mathematical stories and puzzles that are as quirky as they are fascinating, and each from the cutting edge of the world of mathematics. We find out about the mathematics of time travel, explore the shape of teardrops (which are not tear-drop shaped, but something much, much more strange!), dance with dodecahedra, and play the game of Hex, amongst many more strange and delightful mathematical diversions.
Download or read book Explorations in Mathematical Anthropology written by Paul Kay and published by Mit Press. This book was released on 1974-10-01 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an excellent sampling of mathematical, statistical, and computer techniques used by anthropologists to tackle a wide range of substantive problems.The scope of topics considered in this volume is so wide and various as to be an impressive indication of a strong future for mathematics in anthropology. Briefly, such topics include interinformant reliability, cultural distinctiveness in conceptual areas, cultural systems as mental systems of identification, classification, evaluation and action, diffusional versus functional explanations, general interaction theory, kinship terminologies as logical systems, folklore, cultural systems as systems of knowledge and belief, systemic culture patterns, endogamy/exogamy, genealogy, relation of social structure to relational terminology, cultural continuity, and cultural change.
Download or read book Mathematical Explorations with MATLAB written by Ke Chen and published by Cambridge University Press. This book was released on 1999-04-15 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the kind of mathematics usually encountered in first year university courses. A key feature of the book is that this mathematics is explored in depth using the popular and powerful package Matlab. The emphasis is on understanding and investigating the mathematics, and putting it into practice in a wide variety of modelling situations. In the process, the reader will gain some fluency with Matlab, no starting knowledge of the package being assumed.
Download or read book Explorations in Monte Carlo Methods written by Ronald W. Shonkwiler and published by Springer Science & Business Media. This book was released on 2009-08-11 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods are among the most used and useful computational tools available today, providing efficient and practical algorithims to solve a wide range of scientific and engineering problems. Applications covered in this book include optimization, finance, statistical mechanics, birth and death processes, and gambling systems. Explorations in Monte Carlo Methods provides a hands-on approach to learning this subject. Each new idea is carefully motivated by a realistic problem, thus leading from questions to theory via examples and numerical simulations. Programming exercises are integrated throughout the text as the primary vehicle for learning the material. Each chapter ends with a large collection of problems illustrating and directing the material. This book is suitable as a textbook for students of engineering and the sciences, as well as mathematics.
Download or read book Math Explorations with a Geoboard written by Charles Lund and published by . This book was released on 2001 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reproducible resource book presents activities for students to gain hands-on experience with polygons and their properties, problem-solving puzzles and games, investigations, graphing, fractions, ratios, percents, and logical reasoning. Includes masters and selected answers and comments.
Download or read book The Heart of Calculus written by Philip M. Anselone and published by American Mathematical Soc.. This book was released on 2015-12-31 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains enrichment material for courses in first and second year calculus, differential equations, modeling, and introductory real analysis. It targets talented students who seek a deeper understanding of calculus and its applications. The book can be used in honors courses, undergraduate seminars, independent study, capstone courses taking a fresh look at calculus, and summer enrichment programs. The book develops topics from novel and/or unifying perspectives. Hence, it is also a valuable resource for graduate teaching assistants developing their academic and pedagogical skills and for seasoned veterans who appreciate fresh perspectives. The explorations, problems, and projects in the book impart a deeper understanding of and facility with the mathematical reasoning that lies at the heart of calculus and conveys something of its beauty and depth. A high level of rigor is maintained. However, with few exceptions, proofs depend only on tools from calculus and earlier. Analytical arguments are carefully structured to avoid epsilons and deltas. Geometric and/or physical reasoning motivates challenging analytical discussions. Consequently, the presentation is friendly and accessible to students at various levels of mathematical maturity. Logical reasoning skills at the level of proof in Euclidean geometry suffice for a productive use of the book.
