Advanced Mathematics: A Transitional Reference

ISBN-13: 9781119563518 / Angielski / Twarda / 2019 / 480 str.

Stanley J. Farlow

Opis

"This book provides a "crash course" in beginning pure mathematics"--

Spis treści

Preface viiPossible Beneficial Audiences ixWow Factors of the Book xChapter by Chapter (the nitty-gritty) xiNote to the Reader xiiiAbout the Companion Website xivChapter 1 Logic and Proofs 11.1 Sentential Logic 31.2 Conditional and Biconditional Connectives 241.3 Predicate Logic 381.4 Mathematical Proofs 511.5 Proofs in Predicate Logic 711.6 Proof by Mathematical Induction 83Chapter 2 Sets and Counting 952.1 Basic Operations of Sets 972.2 Families of Sets 1152.3 Counting: The Art of Enumeration 1252.4 Cardinality of Sets 1432.5 Uncountable Sets 1562.6 Larger Infinities and the ZFC Axioms 167Chapter 3 Relations 1793.1 Relations 1813.2 Order Relations 1953.3 Equivalence Relations 2123.4 The Function Relation 2243.5 Image of a Set 242Chapter 4 The Real and Complex Number Systems 2554.1 Construction of the Real Numbers 2574.2 The Complete Ordered Field: The Real Numbers 2694.3 Complex Numbers 281Chapter 5 Topology 2995.1 Introduction to Graph Theory 3015.2 Directed Graphs 3215.3 Geometric Topology 3345.4 Point-Set Topology on the Real Line 349Chapter 6 Algebra 3676.1 Symmetries and Algebraic Systems 3696.2 Introduction to the Algebraic Group 3856.3 Permutation Groups 4036.4 Subgroups: Groups Inside a Group 4196.5 Rings and Fields 433Index 443

O autorze

STANLEY J. FARLOW, PHD, is Professor Emeritus of Mathematics, University of Maine, USA. He was a Professor of Mathematics at the University of Maine for 47 years from 1968 to 2016, doing research in control theory, PDEs, and neural networks (GMDH algorithm) as well as teaching graduate and undergraduate courses in real and complex analysis, topology, differential equations, statistics, and a transition to higher math course.