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The Resource Amazing and Aesthetic Aspects of Analysis, by Paul Loya, (electronic resource)

Amazing and Aesthetic Aspects of Analysis, by Paul Loya, (electronic resource)

Creator
Summary
Lively prose and imaginative exercises draw the reader into this unique introductory real analysis textbook. Motivating the fundamental ideas and theorems that underpin real analysis with historical remarks and well-chosen quotes, the author shares his enthusiasm for the subject throughout. A student reading this book is invited not only to acquire proficiency in the fundamentals of analysis, but to develop an appreciation for abstraction and the language of its expression. In studying this book, students will encounter: the interconnections between set theory and mathematical statements and proofs; the fundamental axioms of the natural, integer, and real numbers; rigorous ε-N and ε-δ definitions; convergence and properties of an infinite series, product, or continued fraction; series, product, and continued fraction formulæ for the various elementary functions and constants. Instructors will appreciate this engaging perspective, showcasing the beauty of these fundamental results.--
Language
eng
Work
Publication
Extent
1 online resource (XV, 722 pages)
Contents
  • Preface
  • Some of the most beautiful formulæ in the world
  • Part 1. Some standard curriculum
  • 1. Very naive set theory, functions, and proofs
  • 2. Numbers, numbers, and more numbers
  • 3. Infinite sequences of real and complex numbers
  • 4. Limits, continuity, and elementary functions
  • 5. Some of the most beautiful formulæ in the world I-III
  • Part 2. Extracurricular activities
  • 6. Advanced theory of infinite series
  • 7. More on the infinite: Products and partial fractions
  • 8. Infinite continued fractions
  • Bibliography
  • Index
Isbn
9781493967957
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-1-4939-6795-7
Instance
Label
Amazing and Aesthetic Aspects of Analysis
Title
Amazing and Aesthetic Aspects of Analysis
Statement of responsibility
by Paul Loya
Creator
Author
Subject
Language
eng
Summary
Lively prose and imaginative exercises draw the reader into this unique introductory real analysis textbook. Motivating the fundamental ideas and theorems that underpin real analysis with historical remarks and well-chosen quotes, the author shares his enthusiasm for the subject throughout. A student reading this book is invited not only to acquire proficiency in the fundamentals of analysis, but to develop an appreciation for abstraction and the language of its expression. In studying this book, students will encounter: the interconnections between set theory and mathematical statements and proofs; the fundamental axioms of the natural, integer, and real numbers; rigorous ε-N and ε-δ definitions; convergence and properties of an infinite series, product, or continued fraction; series, product, and continued fraction formulæ for the various elementary functions and constants. Instructors will appreciate this engaging perspective, showcasing the beauty of these fundamental results.--
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Loya, Paul
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
ViFI723caNI
Image bit depth
0
Literary form
non fiction
Nature of contents
dictionaries
Series statement
  • Springer eBooks
  • Springer eBooks.
http://library.link/vocab/subjectName
  • Sequences (Mathematics)
  • Mathematics
Label
Amazing and Aesthetic Aspects of Analysis, by Paul Loya, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-1-4939-6795-7
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 -- Some of the most beautiful formulæ in the world -- Part 1. Some standard curriculum -- 1. Very naive set theory, functions, and proofs -- 2. Numbers, numbers, and more numbers -- 3. Infinite sequences of real and complex numbers -- 4. Limits, continuity, and elementary functions -- 5. Some of the most beautiful formulæ in the world I-III -- Part 2. Extracurricular activities -- 6. Advanced theory of infinite series -- 7. More on the infinite: Products and partial fractions -- 8. Infinite continued fractions -- Bibliography -- Index
Control code
978-1-4939-6795-7
Dimensions
unknown
Extent
1 online resource (XV, 722 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
9781493967957
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
122 illustrations
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1035557129
Label
Amazing and Aesthetic Aspects of Analysis, by Paul Loya, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-1-4939-6795-7
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 -- Some of the most beautiful formulæ in the world -- Part 1. Some standard curriculum -- 1. Very naive set theory, functions, and proofs -- 2. Numbers, numbers, and more numbers -- 3. Infinite sequences of real and complex numbers -- 4. Limits, continuity, and elementary functions -- 5. Some of the most beautiful formulæ in the world I-III -- Part 2. Extracurricular activities -- 6. Advanced theory of infinite series -- 7. More on the infinite: Products and partial fractions -- 8. Infinite continued fractions -- Bibliography -- Index
Control code
978-1-4939-6795-7
Dimensions
unknown
Extent
1 online resource (XV, 722 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
9781493967957
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
122 illustrations
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1035557129

Subject

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