Introduction to Discrete Mathematics via Logic and Proof

Description

This textbook introduces discrete mathematics by emphasizing the importance of reading and writing proofs. Because it begins by carefully establishing a familiarity with mathematical logic and proof, this approach suits not only a discrete mathematics course, but can also function as a transition to proof. Its unique, deductive perspective on mathematical logic provides students with the tools to more deeply understand mathematical methodology—an approach that the author has successfully classroom tested for decades. Chapters are helpfully organized so that, as they escalate in complexity, their underlying connections are easily identifiable. Mathematical logic and proofs are first introduced before moving onto more complex topics in discrete mathematics. Some of these topics include: Mathematical and structural inductionSet theoryCombinatoricsFunctions, relations, and ordered setsBoolean algebra and Boolean functionsGraph theory Introduction to Discrete Mathematics via Logic and Proof will suit intermediate undergraduates majoring in mathematics, computer science, engineering, and related subjects with no formal prerequisites beyond a background in secondary mathematics. Front Matter ....Pages i-xx Propositional Logic (Calvin Jongsma)....Pages 1-99 First-Order Logic (Calvin Jongsma)....Pages 101-147 Mathematical Induction and Arithmetic (Calvin Jongsma)....Pages 149-204 Basic Set Theory and Combinatorics (Calvin Jongsma)....Pages 205-253 Set Theory and Infinity (Calvin Jongsma)....Pages 255-296 Functions and Equivalence Relations (Calvin Jongsma)....Pages 297-342 Posets, Lattices, and Boolean Algebra (Calvin Jongsma)....Pages 343-417 Topics in Graph Theory (Calvin Jongsma)....Pages 419-466 Back Matter ....Pages 467-482