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The Resource A Readable Introduction to Real Mathematics, by Daniel Rosenthal, David Rosenthal, Peter Rosenthal, (electronic resource)

A Readable Introduction to Real Mathematics, by Daniel Rosenthal, David Rosenthal, Peter Rosenthal, (electronic resource)

Creator
Author
Contributor
Summary
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 teach mathematical thinking while conveying the beauty and elegance of mathematics. The book contains a large number of exercises of varying difficulty, some of which are designed to help reinforce basic concepts and others of which will challenge virtually all readers. The sole prerequisite for reading this text is high school algebra. 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 * constructibility (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass)* infinite series * higher dimensional spaces. This textbook is suitable for a wide variety of courses and for a broad range of students of mathematics and other subjects. Mathematically inclined senior high school students will also be able to read this book. From the reviews of the first edition: “It is carefully written in a precise but readable and engaging style... I thoroughly enjoyed reading this recent addition to the Springer Undergraduate Texts in Mathematics series and commend this clear, well-organised, unfussy text to its target audiences.” (Nick Lord, The Mathematical Gazette, Vol. 100 (547), 2016) “The book is an introduction to real mathematics and is very readable. ... The book is indeed a joy to read, and would be an excellent text for an ‘appreciation of mathematics’ course, among other possibilities.” (G.A. Heuer, Mathematical Reviews, February, 2015) “Many a benighted book misguidedly addresses the need [to teach mathematical thinking] by framing reasoning, or narrowly, proof, not as pervasive modality but somehow as itself an autonomous mathematical subject. Fortunately, the present book gets it right.... [presenting] well-chosen, basic, conceptual mathematics, suitably accessible after a K-12 education, in a detailed, self-conscious way that emphasizes methodology alongside content and crucially leads to an ultimate clear payoff. ... Summing Up: Recommended. Lower-division undergraduates and two-year technical program students; general readers.” (D.V. Feldman, Choice, Vol. 52 (6), February, 2015).--
Language
eng
Work
Publication
Edition
2nd ed. 2018.
Extent
1 online resource (XVIII, 218 pages)
Contents
  • Preface to the Second Edition
  • Preface for Readers
  • Preface for Instructors
  • 1. Introduction to the Natural Numbers
  • 2. Mathematical Induction
  • 3. Modular Arithmetic
  • 4. The Fundamental Theorem of Arithmetic
  • 5. Fermat's Theorem and Wilson's Theorem
  • 6. Sending and Receiving Coded Messages
  • 7. The Euclidean Algorithm and Applications
  • 8. Rational Numbers and Irrational Numbers
  • 9. The Complex Numbers
  • 10. Sizes of Infinite Sets
  • 11. Fundamentals of Euclidean Plane Geometry
  • 12. Constructability
  • 13. An Introduction to Infinite Series
  • 14. Some Higher Dimensional Spaces
  • Index
Isbn
9783030006327
Link
https://link-springer-com.eui.idm.oclc.org/book/10.1007/978-3-030-00632-7
Instance
Label
A Readable Introduction to Real Mathematics
Title
A Readable Introduction to Real Mathematics
Statement of responsibility
by Daniel Rosenthal, David Rosenthal, Peter Rosenthal
Creator
Contributor
Author
Author
Subject
Language
eng
Summary
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 teach mathematical thinking while conveying the beauty and elegance of mathematics. The book contains a large number of exercises of varying difficulty, some of which are designed to help reinforce basic concepts and others of which will challenge virtually all readers. The sole prerequisite for reading this text is high school algebra. 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 * constructibility (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass)* infinite series * higher dimensional spaces. This textbook is suitable for a wide variety of courses and for a broad range of students of mathematics and other subjects. Mathematically inclined senior high school students will also be able to read this book. From the reviews of the first edition: “It is carefully written in a precise but readable and engaging style... I thoroughly enjoyed reading this recent addition to the Springer Undergraduate Texts in Mathematics series and commend this clear, well-organised, unfussy text to its target audiences.” (Nick Lord, The Mathematical Gazette, Vol. 100 (547), 2016) “The book is an introduction to real mathematics and is very readable. ... The book is indeed a joy to read, and would be an excellent text for an ‘appreciation of mathematics’ course, among other possibilities.” (G.A. Heuer, Mathematical Reviews, February, 2015) “Many a benighted book misguidedly addresses the need [to teach mathematical thinking] by framing reasoning, or narrowly, proof, not as pervasive modality but somehow as itself an autonomous mathematical subject. Fortunately, the present book gets it right.... [presenting] well-chosen, basic, conceptual mathematics, suitably accessible after a K-12 education, in a detailed, self-conscious way that emphasizes methodology alongside content and crucially leads to an ultimate clear payoff. ... Summing Up: Recommended. Lower-division undergraduates and two-year technical program students; general readers.” (D.V. Feldman, Choice, Vol. 52 (6), February, 2015).--
Member of
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Provided by publisher
http://library.link/vocab/creatorName
Rosenthal, Daniel
Image bit depth
0
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
  • Rosenthal, David
  • Rosenthal, Peter
Series statement
  • Undergraduate Texts in Mathematics,
  • Springer eBooks
  • Springer eBooks.
http://library.link/vocab/subjectName
  • Mathematics
  • Number theory
  • Geometry
Label
A Readable Introduction to Real Mathematics, by Daniel Rosenthal, David Rosenthal, Peter Rosenthal, (electronic resource)
Link
https://link-springer-com.eui.idm.oclc.org/book/10.1007/978-3-030-00632-7
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preface to the Second Edition -- Preface for Readers -- Preface for Instructors -- 1. Introduction to the Natural Numbers -- 2. Mathematical Induction -- 3. Modular Arithmetic -- 4. The Fundamental Theorem of Arithmetic -- 5. Fermat's Theorem and Wilson's Theorem -- 6. Sending and Receiving Coded Messages -- 7. The Euclidean Algorithm and Applications -- 8. Rational Numbers and Irrational Numbers -- 9. The Complex Numbers -- 10. Sizes of Infinite Sets -- 11. Fundamentals of Euclidean Plane Geometry -- 12. Constructability -- 13. An Introduction to Infinite Series -- 14. Some Higher Dimensional Spaces -- Index
Control code
978-3-030-00632-7
Dimensions
unknown
Edition
2nd ed. 2018.
Extent
1 online resource (XVIII, 218 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783030006327
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
63 illustrations
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1096326816
Label
A Readable Introduction to Real Mathematics, by Daniel Rosenthal, David Rosenthal, Peter Rosenthal, (electronic resource)
Link
https://link-springer-com.eui.idm.oclc.org/book/10.1007/978-3-030-00632-7
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preface to the Second Edition -- Preface for Readers -- Preface for Instructors -- 1. Introduction to the Natural Numbers -- 2. Mathematical Induction -- 3. Modular Arithmetic -- 4. The Fundamental Theorem of Arithmetic -- 5. Fermat's Theorem and Wilson's Theorem -- 6. Sending and Receiving Coded Messages -- 7. The Euclidean Algorithm and Applications -- 8. Rational Numbers and Irrational Numbers -- 9. The Complex Numbers -- 10. Sizes of Infinite Sets -- 11. Fundamentals of Euclidean Plane Geometry -- 12. Constructability -- 13. An Introduction to Infinite Series -- 14. Some Higher Dimensional Spaces -- Index
Control code
978-3-030-00632-7
Dimensions
unknown
Edition
2nd ed. 2018.
Extent
1 online resource (XVIII, 218 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783030006327
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
63 illustrations
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1096326816

Subject

Member of

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