Exploring the infinite : an introduction to proof and analysis / Jennifer Brooks

By:

Brooks, Jennifer [author]

Material type: Text

TextSeries: Textbooks in mathematics (Boca Raton, Fla.)Publication details: Boca Raton : CRC Press, Taylor & Francis Group, 2017.Description: xv, 283 pages ; 25 cmISBN:

9781498704496

Subject(s):

Mathematical analysis -- Textbooks

DDC classification:

23 515 B791E

Contents:

Pt. I. Fundamentals of abstract mathematics. Basic notions -- Mathematical induction -- Basic logic and proof techniques -- Sets, relations, and functions -- Elementary discrete mathematics -- Number systems : algebraic structures -- Cardinality -- pt. II. Foundations of analysis. Sequences of real numbers -- A closer look at the real number system -- Series, part 1 -- The structure of the real line -- Continuous functions -- Differentiation -- Series, part 2 -- A very short course of Python.

Summary: "This text introduces proof and analysis by describing the processes of abstraction and logical argumentation and help students transition to practitioners of mathematics. It aims to help students move beyond knowledge of the definitions of mathematical structures, elementary logic, and standard proof techniques and learn to explore mathematical situations, make conjectures, and apply methods of proof. Chapters describe proof and abstract mathematics, including induction, basic logic, elementary set theory, functions and relations, and basic number theory and combinatorics, then the basic concepts of analysis, including limits of sequences of real numbers and functions, infinite series, the structure of the real line, and continuous functions."--Provided by publisher.

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Holdings
Item type	Current library	Call number	Status	Date due	Barcode
Books	Library and Documentation Division	515 B791E (Browse shelf(Opens below))	Available		107529

Pt. I. Fundamentals of abstract mathematics. Basic notions --
Mathematical induction --
Basic logic and proof techniques --
Sets, relations, and functions --
Elementary discrete mathematics --
Number systems : algebraic structures --
Cardinality --
pt. II. Foundations of analysis. Sequences of real numbers --
A closer look at the real number system --
Series, part 1 --
The structure of the real line --
Continuous functions --
Differentiation --
Series, part 2 --
A very short course of Python.

"This text introduces proof and analysis by describing the processes of abstraction and logical argumentation and help students transition to practitioners of mathematics. It aims to help students move beyond knowledge of the definitions of mathematical structures, elementary logic, and standard proof techniques and learn to explore mathematical situations, make conjectures, and apply methods of proof. Chapters describe proof and abstract mathematics, including induction, basic logic, elementary set theory, functions and relations, and basic number theory and combinatorics, then the basic concepts of analysis, including limits of sequences of real numbers and functions, infinite series, the structure of the real line, and continuous functions."--Provided by publisher.

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