Advanced mathematics : a transitional reference /: a transitional reference. (2019)

• Record Type: Book
• Further Information: Note: Stanley J. Farlow.
• Authors: Farlow, Stanley J, 1937-
• Contents: Preface vii Possible Beneficial Audiences ix Wow Factors of the Book x Chapter by Chapter (the nitty-gritty) xi Note to the Reader xiii About the Companion Website xiv Chapter 1 Logic and Proofs 1 1.1 Sentential Logic 3 1.2 Conditional and Biconditional Connectives 24 1.3 Predicate Logic 38 1.4 Mathematical Proofs 51 1.5 Proofs in Predicate Logic 71 1.6 Proof by Mathematical Induction 83 Chapter 2 Sets and Counting 95 2.1 Basic Operations of Sets 97 2.2 Families of Sets 115 2.3 Counting: The Art of Enumeration 125 2.4 Cardinality of Sets 143 2.5 Uncountable Sets 156 2.6 Larger Infinities and the ZFC Axioms 167 Chapter 3 Relations 179 3.1 Relations 181 3.2 Order Relations 195 3.3 Equivalence Relations 212 3.4 The Function Relation 224 3.5 Image of a Set 242 Chapter 4 The Real and Complex Number Systems 255 4.1 Construction of the Real Numbers 257 4.2 The Complete Ordered Field: The Real Numbers 269 4.3 Complex Numbers 281 Chapter 5 Topology 299 5.1 Introduction to Graph Theory 301 5.2 Directed Graphs 321 5.3 Geometric Topology 334 5.4 Point-Set Topology on the Real Line 349 Chapter 6 Algebra 367 6.1 Symmetries and Algebraic Systems 369 6.2 Introduction to the Algebraic Group 385 6.3 Permutation Groups 403 6.4 Subgroups: Groups Inside a Group 419 6.5 Rings and Fields 433 Index 443
• Edition: 1st
• Publisher Details: Hoboken, New Jersey : John Wiley & Sons, Inc
• Publication Date: 2019
• Extent: 1 online resource
• Subjects: 515.353; Differential equations, Partial
• Languages: English
• ISBNs: 9781119563532; 9781119563488
• Notes: Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.