The Arithmetic Of The Real Numbers

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College Algebra

Author : Jay Abramson
Publisher :
ISBN 13 : 9789888407439
Total Pages : 892 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis College Algebra by : Jay Abramson

Download or read book College Algebra written by Jay Abramson and published by . This book was released on 2018-01-07 with total page 892 pages. Available in PDF, EPUB and Kindle. Book excerpt: College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they've learned. Coverage and Scope In determining the concepts, skills, and topics to cover, we engaged dozens of highly experienced instructors with a range of student audiences. The resulting scope and sequence proceeds logically while allowing for a significant amount of flexibility in instruction. Chapters 1 and 2 provide both a review and foundation for study of Functions that begins in Chapter 3. The authors recognize that while some institutions may find this material a prerequisite, other institutions have told us that they have a cohort that need the prerequisite skills built into the course. Chapter 1: Prerequisites Chapter 2: Equations and Inequalities Chapters 3-6: The Algebraic Functions Chapter 3: Functions Chapter 4: Linear Functions Chapter 5: Polynomial and Rational Functions Chapter 6: Exponential and Logarithm Functions Chapters 7-9: Further Study in College Algebra Chapter 7: Systems of Equations and Inequalities Chapter 8: Analytic Geometry Chapter 9: Sequences, Probability and Counting Theory

The Real Numbers

Author : John Stillwell
Publisher : Springer Science & Business Media
ISBN 13 : 331901577X
Total Pages : 253 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis The Real Numbers by : John Stillwell

Download or read book The Real Numbers written by John Stillwell and published by Springer Science & Business Media. This book was released on 2013-10-16 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The arithmetic of the real numbers

Author : University of Illinois (Urbana-Champaign campus). Committee on School Mathematics
Publisher :
ISBN 13 :
Total Pages : 176 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis The arithmetic of the real numbers by : University of Illinois (Urbana-Champaign campus). Committee on School Mathematics

Download or read book The arithmetic of the real numbers written by University of Illinois (Urbana-Champaign campus). Committee on School Mathematics and published by . This book was released on 1960 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Real Numbers, Generalizations of the Reals, and Theories of Continua

Author : P. Ehrlich
Publisher : Springer Science & Business Media
ISBN 13 : 9401582483
Total Pages : 313 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Real Numbers, Generalizations of the Reals, and Theories of Continua by : P. Ehrlich

Download or read book Real Numbers, Generalizations of the Reals, and Theories of Continua written by P. Ehrlich and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their appearance in the late 19th century, the Cantor--Dedekind theory of real numbers and philosophy of the continuum have emerged as pillars of standard mathematical philosophy. On the other hand, this period also witnessed the emergence of a variety of alternative theories of real numbers and corresponding theories of continua, as well as non-Archimedean geometry, non-standard analysis, and a number of important generalizations of the system of real numbers, some of which have been described as arithmetic continua of one type or another. With the exception of E.W. Hobson's essay, which is concerned with the ideas of Cantor and Dedekind and their reception at the turn of the century, the papers in the present collection are either concerned with or are contributions to, the latter groups of studies. All the contributors are outstanding authorities in their respective fields, and the essays, which are directed to historians and philosophers of mathematics as well as to mathematicians who are concerned with the foundations of their subject, are preceded by a lengthy historical introduction.

Exploring the Real Numbers

Author : Frederick W. Stevenson
Publisher :
ISBN 13 :
Total Pages : 392 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Exploring the Real Numbers by : Frederick W. Stevenson

Download or read book Exploring the Real Numbers written by Frederick W. Stevenson and published by . This book was released on 2000 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploring the Real Numbers helps readers understand the real number system. Stevenson brings readers up to date with the study of the nature of real numbers, and provides a sense of the historical journey that has led to our current knowledge of the subject. Presents many interesting topics that arise during study of the real numbers. Offers 21 exploratory projects, encouraging readers to pursue concepts beyond the book. Includes over 100 carefully worked examples. Features abundant exercises throughout. For anyone interested in learning more about some of the very different and often beautiful aspects of mathematics.

Introduction to Real Analysis

Author : William F. Trench
Publisher : Prentice Hall
ISBN 13 : 9780130457868
Total Pages : 0 pages
Book Rating : 4.4/5 (578 download)

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Book Synopsis Introduction to Real Analysis by : William F. Trench

Download or read book Introduction to Real Analysis written by William F. Trench and published by Prentice Hall. This book was released on 2003 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using an extremely clear and informal approach, this book introduces readers to a rigorous understanding of mathematical analysis and presents challenging math concepts as clearly as possible. The real number system. Differential calculus of functions of one variable. Riemann integral functions of one variable. Integral calculus of real-valued functions. Metric Spaces. For those who want to gain an understanding of mathematical analysis and challenging mathematical concepts.

Elements of Set Theory

Author : Herbert B. Enderton
Publisher : Academic Press
ISBN 13 : 0080570429
Total Pages : 294 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Elements of Set Theory by : Herbert B. Enderton

Download or read book Elements of Set Theory written by Herbert B. Enderton and published by Academic Press. This book was released on 1977-05-23 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.

The Arithmetic of Real Numbers

Author : University of Illinois. Committee on School Mathematics
Publisher :
ISBN 13 :
Total Pages : 350 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis The Arithmetic of Real Numbers by : University of Illinois. Committee on School Mathematics

Download or read book The Arithmetic of Real Numbers written by University of Illinois. Committee on School Mathematics and published by . This book was released on 1963 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Intermediate Algebra 2e

Author : Lynn Marecek
Publisher :
ISBN 13 : 9781951693848
Total Pages : pages
Book Rating : 4.6/5 (938 download)

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Book Synopsis Intermediate Algebra 2e by : Lynn Marecek

Download or read book Intermediate Algebra 2e written by Lynn Marecek and published by . This book was released on 2020-05-06 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Arithmetic of Real Numbers

Author : University of Illinois. Committee on School Mathematics
Publisher :
ISBN 13 :
Total Pages : 336 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis The Arithmetic of Real Numbers by : University of Illinois. Committee on School Mathematics

Download or read book The Arithmetic of Real Numbers written by University of Illinois. Committee on School Mathematics and published by . This book was released on 1963 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Structure of the Real Number System

Author : Leon Warren Cohen
Publisher :
ISBN 13 :
Total Pages : 136 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis The Structure of the Real Number System by : Leon Warren Cohen

Download or read book The Structure of the Real Number System written by Leon Warren Cohen and published by . This book was released on 1977 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Theorem Proving with the Real Numbers

Author : John Harrison
Publisher : Springer Science & Business Media
ISBN 13 : 1447115910
Total Pages : 193 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Theorem Proving with the Real Numbers by : John Harrison

Download or read book Theorem Proving with the Real Numbers written by John Harrison and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the use of the real numbers in theorem proving. Typ ically, theorem provers only support a few 'discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification of float ing point hardware and hybrid systems. It also allows the formalization of many more branches of classical mathematics, which is particularly relevant for attempts to inject more rigour into computer algebra systems. Our work is conducted in a version of the HOL theorem prover. We de scribe the rigorous definitional construction of the real numbers, using a new version of Cantor's method, and the formalization of a significant portion of real analysis. We also describe an advanced derived decision procedure for the 'Tarski subset' of real algebra as well as some more modest but practically useful tools for automating explicit calculations and routine linear arithmetic reasoning. Finally, we consider in more detail two interesting application areas. We discuss the desirability of combining the rigour of theorem provers with the power and convenience of computer algebra systems, and explain a method we have used in practice to achieve this. We then move on to the verification of floating point hardware. After a careful discussion of possible correctness specifications, we report on two case studies, one involving a transcendental function.

The Theory of Functions of Real Variables

Author : Lawrence M Graves
Publisher : Courier Corporation
ISBN 13 : 0486158136
Total Pages : 361 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis The Theory of Functions of Real Variables by : Lawrence M Graves

Download or read book The Theory of Functions of Real Variables written by Lawrence M Graves and published by Courier Corporation. This book was released on 2012-01-27 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This balanced introduction covers all fundamentals, from the real number system and point sets to set theory and metric spaces. Useful references to the literature conclude each chapter. 1956 edition.

A Readable Introduction to Real Mathematics

Author : Daniel Rosenthal
Publisher : Springer
ISBN 13 : 3319056549
Total Pages : 171 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis A Readable Introduction to Real Mathematics by : Daniel Rosenthal

Download or read book A Readable Introduction to Real Mathematics written by Daniel Rosenthal and published by Springer. This book was released on 2014-07-03 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for an undergraduate course or for independent study, this text presents sophisticated mathematical ideas in an elementary and friendly fashion. The fundamental purpose of this book is to engage the reader and to teach a real understanding of mathematical thinking while conveying the beauty and elegance of mathematics. The text focuses on teaching the understanding of mathematical proofs. The material covered has applications both to mathematics and to other subjects. The book contains a large number of exercises of varying difficulty, designed to help reinforce basic concepts and to motivate and challenge the reader. The sole prerequisite for understanding the text is basic high school algebra; some trigonometry is needed for Chapters 9 and 12. Topics covered include: mathematical induction - modular arithmetic - the fundamental theorem of arithmetic - Fermat's little theorem - RSA encryption - the Euclidean algorithm -rational and irrational numbers - complex numbers - cardinality - Euclidean plane geometry - constructability (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass). This textbook is suitable for a wide variety of courses and for a broad range of students in the fields of education, liberal arts, physical sciences and mathematics. Students at the senior high school level who like mathematics will also be able to further their understanding of mathematical thinking by reading this book.

Set Theory: The Structure of Arithmetic

Author : Norman T. Hamilton
Publisher : Courier Dover Publications
ISBN 13 : 0486830470
Total Pages : 289 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Set Theory: The Structure of Arithmetic by : Norman T. Hamilton

Download or read book Set Theory: The Structure of Arithmetic written by Norman T. Hamilton and published by Courier Dover Publications. This book was released on 2018-05-16 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is formulated on the fundamental idea that much of mathematics, including the classical number systems, can best be based on set theory. 1961 edition.

Numbers: Rational and Irrational

Author : Ivan Niven
Publisher :
ISBN 13 :
Total Pages : 148 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Numbers: Rational and Irrational by : Ivan Niven

Download or read book Numbers: Rational and Irrational written by Ivan Niven and published by . This book was released on 1961 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-study guide on the classification of numbers and the standards used to determine whether a number is rational or irrational.

Real Numbers: Algebra Basics

Author : Contemporary
Publisher : McGraw-Hill Education
ISBN 13 : 9780809242092
Total Pages : 0 pages
Book Rating : 4.2/5 (42 download)

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Book Synopsis Real Numbers: Algebra Basics by : Contemporary

Download or read book Real Numbers: Algebra Basics written by Contemporary and published by McGraw-Hill Education. This book was released on 1991-04-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contemporary's Real Numbers six book series builds real-life math, test-taking, and problem-solving skills.