Jennifer Brooks

Exploring the Infinite (eBook, ePUB)

An Introduction to Proof and Analysis

• Format: ePub

Produktbeschreibung

This is a textbook for an introductory course in analysis, combining topics from a transition course. At some schools, a transition course is combined over one or two semesters to introduce topics from real analysis. This allows students a more gradual approach to the difficult topics of analysis. Beginning with logic and sets, this text gradually raises the sophistication level of students coming out of calculus and proceeds into analysis topics.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 300
• Erscheinungstermin: 30. November 2016
• Englisch
• ISBN-13: 9781498704526
• Artikelnr.: 59296241

Autorenporträt

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.

Inhaltsangabe

I Fundamentals of Abstract MathematicsBasic NotionsA First Look at Some
Familiar Number SystemsInequalitiesA First Look at Sets and
FunctionsProblemsMathematical InductionFirst ExamplesFirst ProgramsFirst
Proofs: The Principle of Mathematical InductionStrong InductionThe
Well-Ordering Principle and InductionProblemsBasic Logic and Proof
TechniquesLogical Statements and Truth TablesQuantified Statements and
Their NegationsProof TechniquesProblemsSets, Relations, and Functions
SetsRelationsFunctionsProblemsElementary Discrete MathematicsBasic
Principles of CombinatoricsLinear Recurrence RelationsAnalysis of
AlgorithmsProblemsNumber Systems and Algebraic StructuresRepresentations of
Natural NumbersIntegers and Divisibility Modular ArithmeticThe Rational
NumbersAlgebraic StructuresProblemsCardinalityThe Definition Finite Sets
RevistedCountably Infinite SetsUncountable SetsProblemsII Foundations of
AnalysisSequences of Real NumbersThe Limit of Real NumbersProperties of
LimitsCauchy SequencesProblemsA Closer Look at the Real Number SystemR as a
Complete Ordered FieldConstruction of RProblemsSeries, Part 1Basic
NotionsInfinite Geometric SeriesTests for Convergence of
SeriesRepresentations of Real NumbersProblemsThe Structure of the Real Line
Basic Notions from TopologyCompact SetsA First Glimpse at the Notion of
MeasureProblemsContinuous FunctionsSequential ContinuityRelated
NotionsImportant TheoremsProblemsDifferentiationDefinition and First
ExamplesProperties of Differential Functions and Rules for
DifferentiationApplications of the DerivativeProblemsSeries, Part 2
Absolutely and Conditionally Convergent SeriesRearrangementsProblemsA A
Very Short Course on PythonGetting StartedInstallation and
RequirementsPython BasicsFunctionsRecursion