are numbers real

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Are Numbers Real

Author : Brian Clegg
ISBN : 9781472139771
Genre : Science
File Size : 28. 42 MB
Format : PDF, ePub, Docs

Have you ever wondered what humans did before numbers existed? How they organized their lives, traded goods, or kept track of their treasures? What would your life be like without them? Numbers began as simple representations of everyday things, but mathematics rapidly took on a life of its own, occupying a parallel virtual world. In Are Numbers Real? Brian Clegg explores the way that maths has become more and more detached from reality, yet despite this is driving the development of modern physics. From devising a new counting system based on goats, through the weird and wonderful mathematics of imaginary numbers and infinity to the debate over whether mathematics has too much influence on the direction of science, this fascinating and accessible book opens the reader's eyes to the hidden reality of the strange yet familiar world of numbers.

Which Numbers Are Real

Author : Michael Henle
ISBN : 9780883857779
Genre : Mathematics
File Size : 21. 79 MB
Format : PDF, Kindle

Everyone knows the real numbers, those fundamental quantities that make possible all of mathematics from high school algebra and Euclidean geometry through the Calculus and beyond; and also serve as the basis for measurement in science, industry, and ordinary life. This book surveys alternative real number systems: systems that generalize and extend the real numbers yet stay close to these properties that make the reals central to mathematics.Alternative real numbers include many different kinds of numbers, for example multidimensional numbers (the complex numbers, the quaternions and others), infinitely small and infinitely large numbers (the hyperreal numbers and the surreal numbers), and numbers that represent positions in games (the surreal numbers). Each system has a well-developed theory, including applications to other areas of mathematics and science, such as physics, the theory of games, multi-dimensional geometry, and formal logic. They are all active areas of current mathematical research and each has unique features, in particular, characteristic methods of proof and implications for the philosophy of mathematics, both highlighted in this book.Alternative real number systems illuminate the central, unifying role of the real numbers and include some exciting and eccentric parts of mathematics. Which Numbers Are Real? Will be of interest to anyone with an interest in numbers, but specifically to upper-level undergraduates, graduate students, and professional mathematicians, particularly college mathematics teachers.

What Are Numbers

Author : Louis Auslander
ISBN : STANFORD:36105033141560
Genre : Number theory
File Size : 52. 69 MB
Format : PDF

Precalculus With Calculus Previews

Author : Dennis G. Zill
ISBN : 9781449645151
Genre : Mathematics
File Size : 75. 38 MB
Format : PDF, ePub, Docs

Incorporating Zill's student-friendly writing style and modern examples, Precalculus with Calculus Previews, Fifth Edition includes all of the outstanding features and learning tools found in the original text, Essentials of Precalculus with Calculus Previews, while incorporating additional coverage that some courses may require. With a continued aim to keep the text complete, yet concise, the authors added four additional chapters making the text a clear choice for many mainstream courses. This student-friendly, four-color text offers numerous exercise sets and examples to aid in students' learning and understanding, and graphs and figures throughout serve to better illuminate key concepts. The exercise sets include engaging problems that focus on algebra, graphing, and function theory, the sub-text of so many calculus problems. The authors are careful to use the terminology of calculus in an informal and comprehensible way to facilitate the student's successful transition into future calculus courses. - Includes a new chapter, - Provides a "no nonsense" approach to precalculus with an informal, intuitive, and straightforward writing style. - Incorporates the terminology used in calculus in an informal way to acclimate students to these new terms. - Includes over 1600 figures to help illuminate key concepts. - Notes from the Classroom sections address a variety of student/textbook/classroom/calculus issues such as alternative terminology, reinforcement of important concepts, tips on memorization, misinterpretations, common errors, solution procedures, calculators, and advice on the importance of neatness and organization. - Calculus Previews conclude each chapter and highlight a single calculus concept with a focus on the algebraic, logarithmic, and trigonometric manipulations necessary for successfully completing the problem. Translating Words into Functions illustrates how to translate a verbal description into a symbolic representation of a function.

Essentials Of Precalculus With Calculus Previews

Author : Dennis G. Zill
ISBN : 9781449614973
Genre : Mathematics
File Size : 77. 66 MB
Format : PDF, ePub, Docs

Perfect for the one-term course, Essentials of Precalculus with Calculus Previews, Fifth Edition provides a complete, yet concise, introduction to precalculus concepts, focusing on important topics that will be of direct and immediate use in most calculus courses. Consistent with Professor Zill's eloquent writing style , this full-color text offers numerous exercise sets and examples to aid in student comprehension, while graphs and figures throughout serve to illuminate key concepts. The exercise sets include engaging problems that focus on algebra, graphing, and function theory, the sub-text of many calculus problems. The authors are careful to use calculus terminology in an informal and accessible way to facilitate the students successful transition into future calculus courses. With an outstanding collection of student and instructor resources, Essentials of Precalculus with Calculus Previews offers a complete teaching and learning package. Key Features: • Available with WebAssign Online Homework and Grading System • Vibrant four-color design illuminates key concepts and improves students' comprehension of graphs and figures. • Translating Words into Functions section illustrates how to translate a verbal description into a symbolic representation of a function and demonstrates these translations with actual calculus problems. • Chapter Review Exercises include problems that focus on the algebra, graphing, and function theory, the sub-text of so many calculus problems. Review questions include conceptual fill--in-the-blank and true/false, as well as numerous thought-provoking exercises. • The Calculus Preview found at the end of each chapter offers students a glimpse of a single calculus concept along with the algebraic, logarithmic, and trigonometric manipulations that are necessary for the successful completion on typical problems related to that concept. • Provides a complete teaching and learning program with numerous student and instructor resources, including the Student Resource Manual, WebAssign Access, Complete eLearning Center, and • Complete Instructor Solutions Manual. • Includes a new section on simple harmonic motion in Chapter 4. • A new section of parametric equations, as well as a new calculus preview of 3-space, has been added to Chapter 6. • Rotation of polar graphs is now discussed in Section 6.6 • The discussion of the hyperbolic functions in Section 5.4 has been expanded. • Numerous new problems have been added throughout the text. • The final exam at the end of the text has been expanded.

Precalculus With Calculus Previews

Author : Dennis G. Zill
ISBN : 9781449644253
Genre : Mathematics
File Size : 58. 58 MB
Format : PDF, Mobi

Instructors are always faced with the dilemma of too much material and too little time. Perfect for the one-term course, Precalculus with Calculus Previews, Fourth Edition provides a complete, yet manageable, introduction to precalculus concepts while focusing on important topics that will be of direct and immediate use in most calculus courses. Consistent with Professor Zill's eloquent writing style, this four-color text offers numerous exercise sets and examples to aid in students' learning and understanding, while graphs and figures throughout serve to illuminate key concepts. The exercise sets include engaging problems that focus on algebra, graphing, and function theory, the sub-text of so many calculus problems. The authors are careful to use the terminology of calculus in an informal and comprehensible way to facilitate the student's successful transition into future calculus courses. With an extensive Student Study Guide and a full Solutions Manual for instructors, Precalculus with Calculus Previews offers a complete teaching and learning package!

Crash Course Jee Main Aieee Mathematics

Author : V&S EDITORIAL BOARD
ISBN : 9789352150601
Genre : Education
File Size : 43. 17 MB
Format : PDF, Kindle

This book is meant to be a quick refresher for JEE (MAIN)/AIEEE aspirants. With the aim and scope of providing a comprehensive study package for aspirants of JEE (MAIN)/AIEEE, this crash course focuses less on theory and more on concepts, formulae and tips. This is supported by plenty of practice problems based on the latest formats, structure and syllabus of JEE (MAIN)/AIEEE. This is further supplemented by a CD given along with this study kit with fully solved 2012 JEE (MAIN)/AIEEE question paper.Salient features: A Based on the latest pattern and syllabus of JEE (MAIN)/AIEEE A Solved examples, practice problems in each chapter A Previous years question papers fully solved A Less theory and more concepts, formulae and tips A Practice CD with fully solved JEE (MAIN)/AIEEE 2012 question paper A Plenty of problems for practice A Comprehensive, holistic revision of the complete syllabus of JEE (MAIN)/AIEEE A In-depth analysis of the recent trends of JEE (MAIN)/AIEEE A A quick and efficient study kit for JEE (MAIN)/AIEEE aspirants A Facilitates self-study. A Low priced, handy book for quick and efficient revision

The Real Numbers

Author : John Stillwell
ISBN : 9783319015774
Genre : Mathematics
File Size : 53. 87 MB
Format : PDF, ePub, Docs

While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory—uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself. By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis—the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to "assume" the real numbers. Its prerequisites are calculus and basic mathematics. Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor–Schröder–Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions.

Algebra In Ancient And Modern Times

ISBN : 082180989X
Genre : Mathematics
File Size : 55. 62 MB
Format : PDF, ePub, Docs

From the reviews: This is a fine book on two counts. First ... there is the singularly excellent treatment of the solution of biquadratic equations. Second, it paints a strong picture of mathematics as a very long sequence of accomplishments, each building on the ones before, in a way that beginning mathematicians can understand and appreciate it. It paints the picture in a concise and economical style, the style that mathematicians find elegant. I would particularly recommend Algebra in Ancient and Modern Times to strong high school students, to high school algebra teachers, to people who want a history of mathematics with a lot of mathematics in the history, and to anyone who needs to know how to find an analytic solution to a nasty fourth degree polynomial. -- MAA Online Varadarajan spins a captivating tale, and the mathematics is first-rate. The book belongs on the shelf of any teacher of algebra ... The great treasure of this book is the discussion of the work of the great Hindu mathematicians Aryabhata (c.476-550), Brahmagupta (c.598-665), and Bhaskara (c.1114-1185). Teachers of mathematics history will be especially interested in Varadarajan's exposition of the remarkable cakravala, an algorithm for solving $X^2 - NY^2= \pm 1$. The book contains many exercises that enhance and supplement the text and that also include historical information. Many of the exercises ask readers to apply the historical techniques. Some of the exercises are quite difficult and will challenge any student. --Mathematics Teacher This text offers a special account of Indian work in diophantine equations during the 6th through 12th centuries and Italian work on solutions of cubic and biquadratic equations from the 11th through 16th centuries. The volume traces the historical development of algebra and the theory of equations from ancient times to the beginning of modern algebra, outlining some modern themes such as the fundamental theorem of algebra, Clifford algebras, and quaternions. It is geared toward undergraduates who have no background in calculus. V. S. Varadarajan is a professor of mathematics at the University of California, Los Angeles.

Aristotelian Logic

Author : William T. Parry
ISBN : 0791406903
Genre : Philosophy
File Size : 76. 51 MB
Format : PDF, Kindle