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Prime Numbers In Dynamic Geometry
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Book Synopsis Exploring Numbers Beyond Primes by : N.B. Singh
Download or read book Exploring Numbers Beyond Primes written by N.B. Singh and published by N.B.Singh. This book was released on with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Exploring Numbers Beyond Primes" is a comprehensive and accessible introduction to the fascinating world of number theory, designed specifically for absolute beginners. This book takes readers on a captivating journey through the mysteries of prime numbers and Diophantine equations, offering clear explanations and engaging examples along the way. From the historical origins of number theory to modern approaches and future directions, each chapter provides a step-by-step exploration of key concepts, supported by vivid descriptions and relatable analogies. Whether you're a curious novice or an aspiring mathematician, "Exploring Numbers Beyond Primes" invites you to discover the beauty and wonder of numbers, inspiring a lifelong passion for mathematical inquiry.
Download or read book Beyond Primes written by N.B. Singh and published by N.B. Singh. This book was released on with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Beyond Primes" delves into the fascinating world of number theory beyond the realm of prime numbers. From exploring topics like composite numbers, perfect numbers, and cryptographically significant numbers, to investigating unsolved problems and conjectures in number theory, this book offers readers a captivating journey into the depths of mathematical exploration. With clear explanations and intriguing examples, "Beyond Primes" is an essential read for anyone interested in the beauty and complexity of number theory, offering insights into the mysteries that lie beyond the realm of primes.
Book Synopsis Elementary Number Theory: Primes, Congruences, and Secrets by : William Stein
Download or read book Elementary Number Theory: Primes, Congruences, and Secrets written by William Stein and published by Springer Science & Business Media. This book was released on 2008-10-28 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di?e and Hellman introduced the ?rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predetermined secret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles’ resolution of Fermat’s Last Theorem.
Book Synopsis Developing Thinking in Geometry by : Sue Johnston-Wilder
Download or read book Developing Thinking in Geometry written by Sue Johnston-Wilder and published by SAGE. This book was released on 2005-08-18 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Geometry is often given less time in the teaching timetable than other aspects of mathematics. This book encourages practitioners to think about and raise its profile, indeed achieving what its title suggest' - Primary Practice `This creative, innovative and fascinating book/CD package is one you "MUST BUY". All prospective, new and experienced teachers of mathematics can use it to transform their teaching. All readers can use it to reignite their fascination with mathematics' - Professor Sylvia Johnson, Sheffield Hallam University 'This book exudes activity and interactivity. Moreover, it provides challenge in the context of a significant pedagogy, one that is not just present but actually made explicit. It is undoubtedly a book to learn geometry with, but also one to learn to think more deeply about geometry, about its nature and essence, and also about its teaching and learning' - David Pimm Developing Thinking in Geometry enables teachers and their support staff to experience and teach geometric thinking. As well as discussing key teaching principles, the book and accompanying interactive CD include many activities that encourage readers to extend their own learning, and consequently their teaching practices. The book is constructed around the following key themes: - invariance; - language and points of view; - reasoning using invariance; - visualising and representing. These themes draw on teaching principles developed by the team at the Open University's Centre for Mathematics Education which has a 20-year track record of innovative approaches to teaching and learning geometry. This is a 'must have' text for all primary mathematics specialists, secondary and Further Education mathematics teachers and their support staff. Anyone who wishes to create an understanding and enthusiasm for geometry based upon firm research and effective practice, will enjoy this book. This is the course reader for the Open University Course ME627 Developing Geometric Thinking
Book Synopsis The Cinderella.2 Manual by : Jürgen Richter-Gebert
Download or read book The Cinderella.2 Manual written by Jürgen Richter-Gebert and published by Springer Science & Business Media. This book was released on 2012-01-13 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cinderella.2, the new version of the well-known interactive geometry software, has become an even more versatile tool than its predecessor. The geometry component extends the functionality to such spectacular objects as dynamic fractals, and the software includes two major new components: physical simulation such as of mechanical objects, virtual electronic devices, and electromagnetic properties. Cinderella.2 Documentation offers complete instruction and techniques for using Cinderella.2.
Book Synopsis Explanation and Proof in Mathematics by : Gila Hanna
Download or read book Explanation and Proof in Mathematics written by Gila Hanna and published by Springer Science & Business Media. This book was released on 2009-12-04 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the four decades since Imre Lakatos declared mathematics a "quasi-empirical science," increasing attention has been paid to the process of proof and argumentation in the field -- a development paralleled by the rise of computer technology and the mounting interest in the logical underpinnings of mathematics. Explanantion and Proof in Mathematics assembles perspectives from mathematics education and from the philosophy and history of mathematics to strengthen mutual awareness and share recent findings and advances in their interrelated fields. With examples ranging from the geometrists of the 17th century and ancient Chinese algorithms to cognitive psychology and current educational practice, contributors explore the role of refutation in generating proofs, the varied links between experiment and deduction, the use of diagrammatic thinking in addition to pure logic, and the uses of proof in mathematics education (including a critique of "authoritative" versus "authoritarian" teaching styles). A sampling of the coverage: The conjoint origins of proof and theoretical physics in ancient Greece. Proof as bearers of mathematical knowledge. Bridging knowing and proving in mathematical reasoning. The role of mathematics in long-term cognitive development of reasoning. Proof as experiment in the work of Wittgenstein. Relationships between mathematical proof, problem-solving, and explanation. Explanation and Proof in Mathematics is certain to attract a wide range of readers, including mathematicians, mathematics education professionals, researchers, students, and philosophers and historians of mathematics.
Book Synopsis Nanobrain by : Anirban Bandyopadhyay
Download or read book Nanobrain written by Anirban Bandyopadhyay and published by CRC Press. This book was released on 2020-04-03 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Making an artificial brain is not a part of artificial intelligence. It will be a revolutionary journey of mankind exploring a science where one cannot write an equation, a material will vibrate like geometric shape, and then those shapes will change to make decisions. Geometry of silence plays like a musical instrument to mimic a human brain; our thoughts, imagination, everything would be a 3D shape playing as music; composing music would be the brain’s singular job. For a century, the Turing machine ruled human civilization; it was believed that irrespective of complexity all events add up linearly. This book is a thesis to explore the science of decision-making where events are 3D-geometric shapes, events grow within and above, never side by side. The book documents inventions and discoveries in neuroscience, computer science, materials science, mathematics and chemistry that explore the possibility of brain or universe as a time crystal. The philosophy of Turing, the philosophy of membrane-based neuroscience and the philosophy of linear, sequential thought process are challenged here by considering that a nested time crystal encompasses the entire conscious universe. Instead of an algorithm, the pattern of maximum free will is generated mathematically and that very pattern is encoded in materials such that its natural vibration integrates random events exactly similar to the way nature does it in every remote corner of our universe. Find how an artificial brain avoids any necessity for algorithm or programming using the pattern of free will.
Book Synopsis Brain-like Super Intelligence from Bio-electromagnetism by : Anirban Bandyopadhyay
Download or read book Brain-like Super Intelligence from Bio-electromagnetism written by Anirban Bandyopadhyay and published by Springer Nature. This book was released on with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Roads to Geometry by : Edward C. Wallace
Download or read book Roads to Geometry written by Edward C. Wallace and published by Waveland Press. This book was released on 2015-10-23 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now available from Waveland Press, the Third Edition of Roads to Geometry is appropriate for several kinds of students. Pre-service teachers of geometry are provided with a thorough yet accessible treatment of plane geometry in a historical context. Mathematics majors will find its axiomatic development sufficiently rigorous to provide a foundation for further study in the areas of Euclidean and non-Euclidean geometry. By using the SMSG postulate set as a basis for the development of plane geometry, the authors avoid the pitfalls of many “foundations of geometry” texts that encumber the reader with such a detailed development of preliminary results that many other substantive and elegant results are inaccessible in a one-semester course. At the end of each section is an ample collection of exercises of varying difficulty that provides problems that both extend and clarify results of that section, as well as problems that apply those results. At the end of chapters 3–7, a summary list of the new definitions and theorems of each chapter is included.
Book Synopsis Intelligent Computer Mathematics by : Florian Rabe
Download or read book Intelligent Computer Mathematics written by Florian Rabe and published by Springer. This book was released on 2018-08-02 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 11th International Conference on Intelligent Computer Mathematics, CICM 2018, held in Hagenberg, Austria, in August 2018. The 23 full papers presented were carefully reviewed and selected from a total of 36 submissions. The papers focos on the Calculemus, Digital Mathematics Libraries, and Mathematical Knowledge Management tracks which also correspond to the subject areas of the predecessor meetings. Orthogonally, the Systems and Projects track called for descriptions of digital resources, such as data and systems, and of projects, whether old, current, or new, and survey papers covering any topics of relevance to the CICM community.
Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Book Synopsis Mathematics & Mathematics Education: Searching for Common Ground by : Michael N. Fried
Download or read book Mathematics & Mathematics Education: Searching for Common Ground written by Michael N. Fried and published by Springer Science & Business Media. This book was released on 2013-11-29 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the fruit of a symposium in honor of Ted Eisenberg concerning the growing divide between the mathematics community and the mathematics education community, a divide that is clearly unhealthy for both. The work confronts this disturbing gap by considering the nature of the relationship between mathematics education and mathematics, and by examining areas of commonality as well as disagreement. It seeks to provide insight into the mutual benefit both stand to gain by building bridges based on the natural bonds between them.
Book Synopsis Exemplary Practices for Secondary Math Teachers by : Alfred S. Posamentier
Download or read book Exemplary Practices for Secondary Math Teachers written by Alfred S. Posamentier and published by ASCD. This book was released on 2007-03-15 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every year new secondary mathematics teachers take up positions in middle and high schools. The luckiest novices receive assistance from a coach or mentor: a master mathematics teacher who makes constructive comments, models effective approaches, and illuminates other practical aspects of teaching secondary math. But many new teachers don't have this advantage and must further their development on their own. If you are one of these teachers, this is the book you need. In these pages, veteran mathematics educators Alfred S. Posamentier, Daniel Jaye, and Stephen Krulik present a treasure chest of ideas to guide new secondary math teachers through the challenging first few months and also provide more experienced teachers with interesting alternatives to familiar methods. The topics covered include * The most effective instructional practices * The best uses of the textbook * Designing successful lessons * Creating homework that promotes learning * Incorporating challenge * Teaching reasoning and problem solving * Strategies for assessment and grading * Specific innovative ideas for teaching key concepts * Options for extracurricular activities * Long-term professional enrichment and growth. It's during the first few years of a teacher's experience that he or she develops the habits, methods, procedures, and techniques that tend to define a career. Exemplary Practices for Secondary Math Teachers provides both a foundation for excellence and a touchstone for years to come. Note: This product listing is for the Adobe Acrobat (PDF) version of the book.
Book Synopsis Algorithm Design Practice for Collegiate Programming Contests and Education by : Yonghui Wu
Download or read book Algorithm Design Practice for Collegiate Programming Contests and Education written by Yonghui Wu and published by CRC Press. This book was released on 2018-11-15 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book can be used as an experiment and reference book for algorithm design courses, as well as a training manual for programming contests. It contains 247 problems selected from ACM-ICPC programming contests and other programming contests. There's detailed analysis for each problem. All problems, and test datum for most of problems will be provided online. The content will follow usual algorithms syllabus, and problem-solving strategies will be introduced in analyses and solutions to problem cases. For students in computer-related majors, contestants and programmers, this book can polish their programming and problem-solving skills with familarity of algorithms and mathematics.
Book Synopsis Fundamentals of Dynamic Geometry by : Paul Haralyi Fejér
Download or read book Fundamentals of Dynamic Geometry written by Paul Haralyi Fejér and published by . This book was released on 1981 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Practical Guide to Teaching Mathematics in the Secondary School by : Clare S. Lee
Download or read book A Practical Guide to Teaching Mathematics in the Secondary School written by Clare S. Lee and published by Routledge. This book was released on 2013 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers straightforward advice, inspiration and support for mathematics teachers whether in training or newly qualified. Based on the best research and practice available, it offers a wide range of tried and tested approaches that succeed in secondary classrooms.
Book Synopsis The New Revolution in Psychology and the Neurosciences by : Mario Manto
Download or read book The New Revolution in Psychology and the Neurosciences written by Mario Manto and published by Springer Nature. This book was released on 2022-06-23 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: Historically researchers of neuroscience and psychology have believed that the cerebral cortex produces the unique mental capacities of human beings. However, a prevalence of brain-imaging evidence now shows that the cerebral cortex, while the seat of our everyday experience (notably in working memory), is not predominant in actually formulating our amazing capabilities. Rather, the achievements that mark humans as “Homo sapiens” originate in the cerebellum which increased three- to fourfold in size and acquired massive cognitive and social optimization capabilities over the last million years. Thus, through its optimization of experience and skill of the cerebral cortex, it was the cerebellum that was and is predominant in producing culture, language, mathematics, creativity, and extreme levels of skill in all areas from sports to computer science and art. These optimizing functions of the cerebellum are shown in the cases of Albert Einstein, Wolfgang Amadeus Mozart, Maryam Mirzakhani, and the predictive powers of Stonehenge. This book fills a critical role in bringing courses up-to-date with the profound, basic changes this newly understood predominant role of the cerebellum provides for understanding the mechanisms related to all topics in psychology and neuroscience. It is critical that this “new revolution in psychology and the neurosciences” be introduced and reviewed in courses that are part of both undergraduate and graduate studies in psychology and neuroscience. This text might also be of use to courses in anthropology and cross-disciplinary studies as the cerebellum was critically involved in the evolution of cognitive and social behaviour.
