1st Edition
Exploring the Infinite An Introduction to Proof and Analysis
By Jennifer Brooks
Copyright 2017
300 Pages
25 B/W Illustrations
by
Chapman & Hall
300 Pages
25 B/W Illustrations
by
Chapman & Hall
300 Pages
25 B/W Illustrations
by
Chapman & Hall
Also available as eBook on:
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,... Read more
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 FunctionsSetsRelationsFunctionsProblemsElementary 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 LineBasic 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 2Absolutely and Conditionally Convergent SeriesRearrangementsProblemsA A Very Short Course on PythonGetting StartedInstallation and RequirementsPython BasicsFunctionsRecursion
Biography
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.
