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Exploring the Infinite: An Introduction to Proof and Analysis (Textbooks in Mathematics) - Softcover
Synopsis
Exploring the Infinite addresses the trend toward
a combined transition course and introduction to analysis course. It
guides the reader through the processes of abstraction and log-
ical argumentation, to make the transition from student of mathematics to
practitioner of mathematics.
This requires more than knowledge of the definitions of mathematical structures,
elementary logic, and standard proof techniques. The student focused on only these
will develop little more than the ability to identify a number of proof templates and
to apply them in predictable ways to standard problems.
This book aims to do something more; it aims to help readers learn to explore
mathematical situations, to make conjectures, and only then to apply methods
of proof. Practitioners of mathematics must do all of these things.
The chapters of this text are divided into two parts. Part I serves as an introduction
to proof and abstract mathematics and aims to prepare the reader for advanced
course work in all areas of mathematics. It thus includes all the standard material
from a transition to proof" course.
Part II constitutes an introduction to the basic concepts of analysis, including limits
of sequences of real numbers and of functions, infinite series, the structure of the
real line, and continuous functions.
Features
- Two part text for the combined transition and analysis course
- New approach focuses on exploration and creative thought
- Emphasizes the limit and sequences
- Introduces programming skills to explore concepts in analysis
- Emphasis in on developing mathematical thought
- Exploration problems expand more traditional exercise sets
"synopsis" may belong to another edition of this title.
About the Author
Jennifer Halfpap is an Associate Professor in the Department of Mathematical Sciences at the University of Montana, Missoula, USA. She is also the Associate Chair of the department, directing the Graduate Program.
"About this title" may belong to another edition of this title.
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Exploring the Infinite: An Introduction to Proof and Analysis
Published by
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ISBN 10: 1032477040
ISBN 13: 9781032477046
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Exploring the Infinite
Published by
Taylor & Francis, Chapman And Hall/CRC, 2023
ISBN 10: 1032477040
ISBN 13: 9781032477046
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Exploring the Infinite addresses the trend toward a combined transition course and introduction to analysis course. Itguides the reader through the processes of abstraction and log-ical argumentation, to make the transition from student of mathematics topractitioner of mathematics. This requires more than knowledge of the definitions of mathematical structures, elementary logic, and standard proof techniques. The student focused on only these will develop little more than the ability to identify a number of proof templates and to apply them in predictable ways to standard problems. This book aims to do something more; it aims to help readers learn to explore mathematical situations, to make conjectures, and only then to apply methods of proof. Practitioners of mathematics must do all of these things.The chapters of this text are divided into two parts. Part I serves as an introduction to proof and abstract mathematics and aims to prepare the reader for advanced course work in all areas of mathematics. It thus includes all the standard material from a transition to proof' course. Part II constitutes an introduction to the basic concepts of analysis, including limitsof sequences of real numbers and of functions, infinite series, the structure of the real line, and continuous functions. FeaturesTwo part text for the combined transition and analysis courseNew approach focuses on exploration and creative thoughtEmphasizes the limit and sequences Introduces programming skills to explore concepts in analysisEmphasis in on developing mathematical thoughtExploration problems expand more traditional exercise sets 300 pp. Englisch. Seller Inventory # 9781032477046
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Exploring the Infinite: An Introduction to Proof and Analysis
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Exploring the Infinite : An Introduction to Proof and Analysis
Published by
Taylor & Francis, Chapman And Hall/CRC, 2023
ISBN 10: 1032477040
ISBN 13: 9781032477046
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Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Exploring the Infinite addresses the trend toward a combined transition course and introduction to analysis course. Itguides the reader through the processes of abstraction and log-ical argumentation, to make the transition from student of mathematics topractitioner of mathematics. This requires more than knowledge of the definitions of mathematical structures, elementary logic, and standard proof techniques. The student focused on only these will develop little more than the ability to identify a number of proof templates and to apply them in predictable ways to standard problems. This book aims to do something more; it aims to help readers learn to explore mathematical situations, to make conjectures, and only then to apply methods of proof. Practitioners of mathematics must do all of these things.The chapters of this text are divided into two parts. Part I serves as an introduction to proof and abstract mathematics and aims to prepare the reader for advanced course work in all areas of mathematics. It thus includes all the standard material from a transition to proof' course. Part II constitutes an introduction to the basic concepts of analysis, including limitsof sequences of real numbers and of functions, infinite series, the structure of the real line, and continuous functions. FeaturesTwo part text for the combined transition and analysis courseNew approach focuses on exploration and creative thoughtEmphasizes the limit and sequences Introduces programming skills to explore concepts in analysisEmphasis in on developing mathematical thoughtExploration problems expand more traditional exercise sets. Seller Inventory # 9781032477046
Quantity: 2 available
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Exploring the Infinite : An Introduction to Proof and Analysis
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