[PDF] Are Numbers Real

Are Numbers Real  PDF
Author: Brian Clegg
Publisher: Hachette UK
ISBN: 1472139771
Size: 49.83 MB
Format: PDF, ePub, Docs
Category : Science
Languages : en
Pages : 304
View: 6810

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Are Numbers Real

by Brian Clegg, release date 2017-02-02, Are Numbers Real Books available in PDF, EPUB, Mobi Format. Download Are Numbers Real books, 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.




[PDF] Which Numbers Are Real

Which Numbers Are Real  PDF
Author: Michael Henle
Publisher: MAA
ISBN: 0883857774
Size: 52.66 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 219
View: 4002

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Which Numbers Are Real

by Michael Henle, release date 2012-09-27, Which Numbers Are Real Books available in PDF, EPUB, Mobi Format. Download Which Numbers Are Real books, 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.




[PDF] The Real Numbers

The Real Numbers PDF
Author: John Stillwell
Publisher: Springer Science & Business Media
ISBN: 331901577X
Size: 58.70 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 244
View: 6780

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The Real Numbers

by John Stillwell, release date 2013-10-16, The Real Numbers Books available in PDF, EPUB, Mobi Format. Download The Real Numbers books, 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.




[PDF] The Real Numbers And Real Analysis

The Real Numbers and Real Analysis PDF
Author: Ethan D. Bloch
Publisher: Springer Science & Business Media
ISBN: 0387721762
Size: 33.25 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 554
View: 6017

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The Real Numbers And Real Analysis

by Ethan D. Bloch, release date 2011-05-27, The Real Numbers And Real Analysis Books available in PDF, EPUB, Mobi Format. Download The Real Numbers And Real Analysis books, This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a distinctive, flexible way that would make it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus. The Real Numbers and Real Analysis will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus.




[PDF] Precalculus With Calculus Previews

Precalculus with Calculus Previews PDF
Author: Dennis G. Zill
Publisher: Jones & Bartlett Publishers
ISBN: 1449645151
Size: 76.35 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 549
View: 1580

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Precalculus With Calculus Previews

by Dennis G. Zill, release date 2013, Precalculus With Calculus Previews Books available in PDF, EPUB, Mobi Format. Download Precalculus With Calculus Previews books, 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.




[PDF] Study Package For Cat Online

Study Package for CAT Online PDF
Author: SHARMA
Publisher: Tata McGraw-Hill Education
ISBN: 1259027031
Size: 70.42 MB
Format: PDF, ePub, Docs
Category :
Languages : en
Pages :
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Study Package For Cat Online

by SHARMA, release date , Study Package For Cat Online Books available in PDF, EPUB, Mobi Format. Download Study Package For Cat Online books,




[PDF] Essentials Of Precalculus With Calculus Previews

Essentials of Precalculus with Calculus Previews PDF
Author: Dennis G. Zill
Publisher: Jones & Bartlett Publishers
ISBN: 1449614973
Size: 31.36 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 440
View: 5399

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Essentials Of Precalculus With Calculus Previews

by Dennis G. Zill, release date 2010-12-15, Essentials Of Precalculus With Calculus Previews Books available in PDF, EPUB, Mobi Format. Download Essentials Of Precalculus With Calculus Previews books, 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.




[PDF] Comprehensive Algebra Vol 1

Comprehensive Algebra Vol  1 PDF
Author: KUMAR
Publisher: Tata McGraw-Hill Education
ISBN: 1259064220
Size: 70.81 MB
Format: PDF, ePub, Mobi
Category :
Languages : en
Pages : 752
View: 3571

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Comprehensive Algebra Vol 1

by KUMAR, release date , Comprehensive Algebra Vol 1 Books available in PDF, EPUB, Mobi Format. Download Comprehensive Algebra Vol 1 books, Algebra is a key topic of mathematics. A significant ?number of questions are asked from this segment in various engineering entrance examinations. This book aims to provide a thorough understanding of the topic starting from the basics. In the process, it sharpens problem solving skill.?