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.
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.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
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
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
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