Download or read book Complex Arithmetic Patterns Behind Numbers written by and published by Nick Trif. This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Complex Numbers written by Walter Ledermann and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: THE purpose of this book is to prescnt a straightforward introduction to complex numbers and their properties. Complex numbers, like other kinds of numbers, are essen tially objects with which to perform calculations a:cording to certain rules, and when this principle is borne in mind, the nature of complex numbers is no more mysterious than that of the more familiar types of numbers. This formal approach has recently been recommended in a Reportt prepared for the Mathematical Association. We believe that it has distinct advantages in teaching and that it is more in line with modern algebraical ideas than the alternative geometrical or kinematical definitions of v -1 that used to be proposed. On the other hand, an elementary textbook is clearly not the place to enter into a full discussion of such questions as logical consistency, which would have to be included in a rigorous axiomatic treatment. However, the steps that had to be omitted (with due warning) can easily be filled in by the methods of abstract algebra, which do not conflict with the 'naive' attitude adopted here. I should like to thank my friend and colleague Dr. J. A. Green for a number of valuable suggestions, especially in connection with the chapter on convergence, which is a sequel to his volume Sequences and Series in this Library.
Download or read book Numbers Sequences and Series written by Keith Hirst and published by Elsevier. This book was released on 1994-12-08 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number and geometry are the foundations upon which mathematics has been built over some 3000 years. This book is concerned with the logical foundations of number systems from integers to complex numbers. The author has chosen to develop the ideas by illustrating the techniques used throughout mathematics rather than using a self-contained logical treatise. The idea of proof has been emphasised, as has the illustration of concepts from a graphical, numerical and algebraic point of view. Having laid the foundations of the number system, the author has then turned to the analysis of infinite processes involving sequences and series of numbers, including power series. The book also has worked examples throughout and includes some suggestions for self-study projects. In addition there are tutorial problems aimed at stimulating group work and discussion.
Download or read book Introduction To Analysis With Complex Numbers written by Irena Swanson and published by World Scientific. This book was released on 2021-02-18 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained book that covers the standard topics in introductory analysis and that in addition constructs the natural, rational, real and complex numbers, and also handles complex-valued functions, sequences, and series.The book teaches how to write proofs. Fundamental proof-writing logic is covered in Chapter 1 and is repeated and enhanced in two appendices. Many examples of proofs appear with words in a different font for what should be going on in the proof writer's head.The book contains many examples and exercises to solidify the understanding. The material is presented rigorously with proofs and with many worked-out examples. Exercises are varied, many involve proofs, and some provide additional learning materials.
Download or read book From Numbers To Analysis written by Inder K Rana and published by World Scientific Publishing Company. This book was released on 1998-10-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with the Zermelo-Fraenhel axiomatic set theory, this book gives a self-contained, step-by-step construction of real and complex numbers. The basic properties of real and complex numbers are developed, including a proof of the Fundamental Theorem of Algebra. Historical notes outline the evolution of the number systems and alert readers to the fact that polished mathematical concepts, as presented in lectures and books, are the culmination of the efforts of great minds over the years. The text also includes short life sketches of some of the contributing mathematicians. The book provides the logical foundation of Analysis and gives a basis to Abstract Algebra. It complements those books on real analysis which begin with axiomatic definitions of real numbers.The book can be used in various ways: as a textbook for a one semester course on the foundations of analysis for post-calculus students; for a seminar course; or self-study by school and college teachers.
Download or read book Number Systems written by Sergei Ovchinnikov and published by American Mathematical Soc.. This book was released on 2015-02-26 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a rigorous and coherent introduction to the five basic number systems of mathematics, namely natural numbers, integers, rational numbers, real numbers, and complex numbers. It is a subject that many mathematicians believe should be learned by any student of mathematics including future teachers. The book starts with the development of Peano arithmetic in the first chapter which includes mathematical induction and elements of recursion theory. It proceeds to an examination of integers that also covers rings and ordered integral domains. The presentation of rational numbers includes material on ordered fields and convergence of sequences in these fields. Cauchy and Dedekind completeness properties of the field of real numbers are established, together with some properties of real continuous functions. An elementary proof of the Fundamental Theorem of Algebra is the highest point of the chapter on complex numbers. The great merit of the book lies in its extensive list of exercises following each chapter. These exercises are designed to assist the instructor and to enhance the learning experience of the students.
Download or read book The Number Systems of Analysis written by Charles Huw Crawford Little and published by World Scientific. This book was released on 2003 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although students of analysis are familiar with real and complex numbers, few treatments of analysis deal with the development of such numbers in any depth. An understanding of number systems at a fundamental level is necessary for a deeper grasp of analysis. Beginning with elementary concepts from logic and set theory, this book develops in turn the natural numbers, the integers and the rational, real and complex numbers. The development is motivated by the need to solve polynomial equations, and the book concludes by proving that such equations have solutions in the complex number system.
Download or read book The Emergence Of Number written by John Newsome Crossley and published by World Scientific. This book was released on 1987-11-01 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents detailed studies of the development of three kinds of number. In the first part the development of the natural numbers from Stone-Age times right up to the present day is examined not only from the point of view of pure history but also taking into account archaeological, anthropological and linguistic evidence. The dramatic change caused by the introduction of logical theories of number in the 19th century is also treated and this part ends with a non-technical account of the very latest developments in the area of Gödel's theorem. The second part is concerned with the development of complex numbers and tries to answer the question as to why complex numbers were not introduced before the 16th century and then, by looking at the original materials, shows how they were introduced as a pragmatic device which was only subsequently shown to be theoretically justifiable. The third part concerns the real numbers and examines the distinction that the Greeks made between number and magnitude. It then traces the gradual development of a theory of real numbers up to the precise formulations in the nineteeth century. The importance of the Greek distinction between the number line and the geometric line is brought into sharp focus.This is an new edition of the book which first appeared privately published in 1980 and is now out of print. Substantial revisions have been made throughout the text, incorporating new material which has recently come to light and correcting a few relatively minor errors. The third part on real numbers has been very extensively revised and indeed the last chapter has been almost completely rewritten. Many revisions are the results of comments from earlier readers of the book.
Download or read book Journey from Natural Numbers to Complex Numbers written by Nita H. Shah and published by CRC Press. This book was released on 2020-12-02 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is for those interested in number systems, abstract algebra, and analysis. It provides an understanding of negative and fractional numbers with theoretical background and explains rationale of irrational and complex numbers in an easy to understand format. This book covers the fundamentals, proof of theorems, examples, definitions, and concepts. It explains the theory in an easy and understandable manner and offers problems for understanding and extensions of concept are included. The book provides concepts in other fields and includes an understanding of handling of numbers by computers. Research scholars and students working in the fields of engineering, science, and different branches of mathematics will find this book of interest, as it provides the subject in a clear and concise way.
Download or read book Fearless Symmetry written by Avner Ash and published by Princeton University Press. This book was released on 2008-08-24 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written in a friendly style for a general mathematically literate audience, 'Fearless Symmetry', starts with the basic properties of integers and permutations and reaches current research in number theory.
Download or read book Acquisition of Complex Arithmetic Skills and Higher Order Mathematics Concepts written by David C. Geary and published by Academic Press. This book was released on 2017-08-01 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts focuses on typical and atypical learning of complex arithmetic skills and higher-order math concepts. As part of the series Mathematical Cognition and Learning, this volume covers recent advances in the understanding of children’s developing competencies with whole-number arithmetic, fractions, and rational numbers. Each chapter covers these topics from multiple perspectives, including genetic disorders, cognition, instruction, and neural networks. Covers innovative measures and recent methodological advances in mathematical thinking and learning Contains contributions that improve instruction and education in these domains Informs policy aimed at increasing the level of mathematical proficiency in the general public
Download or read book The Story Of Numbers written by Asok Kumar Mallik and published by #N/A. This book was released on 2017-07-27 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: '… this could make an ideal end-of-year prize for a high-school student who is fascinated by all aspects of number. The subsections provide ideas and opportunities for mathematical exploration. This book might also be deemed a suitable resource for first-year undergraduates in that, via independent study, it would allow such students to broaden their knowledge of various number-theoretic ideas. I would recommend it for the purposes given above.'The Mathematical GazetteThis book is more than a mathematics textbook. It discusses various kinds of numbers and curious interconnections between them. Without getting into hardcore and difficult mathematical technicalities, the book lucidly introduces all kinds of numbers that mathematicians have created. Interesting anecdotes involving great mathematicians and their marvelous creations are included. The reader will get a glimpse of the thought process behind the invention of new mathematics. Starting from natural numbers, the book discusses integers, real numbers, imaginary and complex numbers and some special numbers like quaternions, dual numbers and p-adic numbers.Real numbers include rational, irrational and transcendental numbers. Iterations on real numbers are shown to throw up some unexpected behavior, which has given rise to the new science of 'Chaos'. Special numbers like e, pi, golden ratio, Euler's constant, Gauss's constant, amongst others, are discussed in great detail.The origin of imaginary numbers and the use of complex numbers constitute the next topic. It is shown why modern mathematics cannot even be imagined without imaginary numbers. Iterations on complex numbers are shown to generate a new mathematical object called 'Fractal', which is ubiquitous in nature. Finally, some very special numbers, not mentioned in the usual textbooks, and their applications, are introduced at an elementary level.The level of mathematics discussed in this book is easily accessible to young adults interested in mathematics, high school students, and adults having some interest in basic mathematics. The book concentrates more on the story than on rigorous mathematics.
Download or read book The Learning and Teaching of Number written by Rina Zazkis and published by Taylor & Francis. This book was released on 2021-05-23 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numbers are the backbones of mathematics. From 1 to infinity, numbers accompany and underlie the learning of mathematics and research. While perceived as familiar and understood, numbers present fascinating and often mysterious patterns, relationships and pedagogical issues. The Learning and Teaching of Number explores how mathematics education research has addressed issues related to the structure of numbers and number operations and provides a classroom context. It invites readers to explore less-travelled paths through a well-trodden terrain of number. This fascinating book combines mathematical content with pedagogical ideas and research results. Focusing on number, the book illustrates central ideas related to numbers via a variety of tasks at different levels of complexity. The Learning and Teaching of Number will allow the reader to examine and develop personal understanding of number sets and the relationships among them; enhance personal understanding of familiar topics associated with number operations; engage in a variety of tasks and strengthen personal problem-solving skills; enrich their repertoire of mathematical tasks and pedagogical actions; and consider research ideas and results related to teaching numbers, number operations and number relationships. This is a valuable resource for teacher education courses, graduate programs in mathematics education and professional development programs. Teacher trainers and maths teachers will find their personal understanding of numbers and relationships enriched and will draw connections between research and classroom pedagogy which will extend and enhance their teaching.
Download or read book The Book of Numbers written by John Horton Conway and published by . This book was released on 1996 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: In The Book of Numbers, two famous mathematicians fascinated by beautiful and intriguing number patterns share their insights and discoveries with each other and with readers. John Conway is the showman, master of mathematical games and flamboyant presentations; Richard Guy is the encyclopedist, always on top of problems waiting to be solved. Together they show us why patterns and properties of numbers have captivated mathematicians and non-mathematicians alike for centuries. The Book of Numbers features Conway and Guy's favorite stories about all the kinds of numbers any of us is likely to encounter, and many others besides. "Our aim," the authors write, "is to bring to the inquisitive reader ... an explanation of the many ways the word 'number' is used." They explore patterns that emerge in arithmetic, algebra, and geometry, describe these patterns' relevance both inside and outside mathematics, and introduce the strange worlds of complex, transcendental, and surreal numbers. This unique book brings together facts, pictures and stories about numbers in a way that no one but an extraordinarily talented pair of mathematicians and writers could do.
Download or read book A Mathematical Mosaic written by Ravi Vakil and published by Brendan Kelly Publishing Inc.. This book was released on 1996 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Powerful problem solving ideas that focus on the major branches of mathematics and their interconnections.
Download or read book Discovering Patterns in Mathematics and Poetry written by Marcia Birken and published by BRILL. This book was released on 2008-01-01 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: You are invited to join a fascinating journey of discovery, as Marcia Birken and Anne C. Coon explore the intersecting patterns of mathematics and poetry — bringing the two fields together in a new way. Setting the tone with humor and illustrating each chapter with countless examples, Birken and Coon begin with patterns we can see, hear, and feel and then move to more complex patterns. Number systems and nursery rhymes lead to the Golden Mean and sestinas. Simple patterns of shape introduce tessellations and concrete poetry. Fractal geometry makes fractal poetry possible. Ultimately, patterns for the mind lead to questions: How do mathematicians and poets conceive of proof, paradox, and infinity? What role does analogy play in mathematical discovery and poetic expression? The book will be of special interest to readers who enjoy looking for connections across traditional disciplinary boundaries. Discovering Patterns in Mathematics and Poetry features centuries of creative work by mathematicians, poets, and artists, including Fibonacci, Albrecht Dürer, M. C. Escher, David Hilbert, Benoit Mandelbrot, William Shakespeare, Edna St. Vincent Millay, Langston Hughes, E.E. Cummings, and many contemporary experimental poets. Original illustrations include digital photographs, mathematical and poetic models, and fractal imagery.
Download or read book The Pattern Book Fractals Art And Nature written by Clifford A Pickover and published by World Scientific. This book was released on 1995-06-09 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will allow you to travel through time and space. To facilitate your journey, the editor has scoured the four corners of the earth in a quest for unusual people and their fascinating patterns. From Mozambique, to Asia, to many European countries, the contributors to The Pattern Book include world-famous cancer researchers, little-known artists and eclectirc computer programmers. Some of the patterns are ultramodern, while others are centuries old. Many of the patterns are drawn from the universe of mathematics. Computer recipes are scattered throughout.Although the emphasis is on computer-generated patterns, the book is informal and the intended audience spans several fields. The emphasis is on the fun that the true pattern lover finds in doing, rather than in reading about the doing! The book is organized into three main parts: Representing Nature (for those patterns which describe or show real physical phenomena, e.g., visualizations of protein motion, sea lilies, etc.), Mathematics and Symmetry (for those patterns which describe or show mathematical behavior, e.g. fractals), and Human Art (for those patterns which are artistic works of humans and made without the aid of a computer, e.g. Moslem tiling patterns.)
