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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
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Exploring the Infinite - An Introduction to Proof and Analysis (Paperback)
Loot Price: R1,447
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Exploring the Infinite - An Introduction to Proof and Analysis (Paperback)
Series: Textbooks in Mathematics
Expected to ship within 10 - 15 working days
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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
General
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