عنوان

Introduction to discrete mathematics via logic and proof /

(Number (ISBN

3030253589

(Number (ISBN

9783030253585

Erroneous ISBN

9783030253578

Title Proper

Introduction to discrete mathematics via logic and proof /

General Material Designation

[Book]

First Statement of Responsibility

Calvin Jongsma.

Place of Publication, Distribution, etc.

Cham, Switzerland :

Name of Publisher, Distributor, etc.

Springer,

Date of Publication, Distribution, etc.

2019.

Specific Material Designation and Extent of Item

1 online resource (xx, 482 pages) :

Other Physical Details

illustrations (some color)

Series Title

Undergraduate texts in mathematics,

ISSN of Series

0172-6056

Text of Note

Includes index.

Text of Note

Intro; Preface; Topics Selected; Intended Audiences; Goals and Approach; Prerequisites and Course Emphases; For Students: Reading a Mathematics Text; Acknowledgements; List of Notations; Logical Acronyms; Contents; 1 Propositional Logic; 1.1 A Gentle Introduction to Logic and Proof; 1.2 Conjunction, Disjunction, and Negation; 1.3 Argument Semantics for Propositional Logic; 1.4 Conditional and Biconditional Sentences; 1.5 Introduction to Deduction; Rules for AND; 1.6 Elimination Rules for CONDITIONALS; 1.7 Introduction Rules for CONDITIONALS; 1.8 Proof by Contradiction: Rules for NOT

Text of Note

1.9 Inference Rules for OR2 First-Order Logic; 2.1 Symbolizing Sentences; 2.2 First-Order Logic: Syntax and Semantics; 2.3 Rules for Identity and Universal Quantifiers; 2.4 Rules for Existential Quantifiers; 3 Mathematical Induction and Arithmetic; 3.1 Mathematical Induction and Recursion; 3.2 Variations on Mathematical Induction and Recursion; 3.3 Recurrence Relations; Structural Induction; 3.4 Peano Arithmetic; 3.5 Divisibility; 4 Basic Set Theory and Combinatorics; 4.1 Relations and Operations on Sets; 4.2 Collections of Sets and the Power Set; 4.3 Multiplicative Counting Principles

Text of Note

4.4 Combinations4.5 Additive Counting Principles; 5 Set Theory and Infinity; 5.1 Countably Infinite Sets; 5.2 Uncountably Infinite Sets; 5.3 Formal Set Theory and the Halting Problem; 6 Functions and Equivalence Relations; 6.1 Functions and Their Properties; 6.2 Composite Functions and Inverse Functions; 6.3 Equivalence Relations and Partitions; 6.4 The Integers and Modular Arithmetic; 7 Posets, Lattices, and Boolean Algebra; 7.1 Partially Ordered Sets; 7.2 Lattices; 7.3 From Boolean Lattices to Boolean Algebra; 7.4 Boolean Functions and Logic Circuits; 7.5 Representing Boolean Functions

Text of Note

7.6 Simplifying Boolean Functions8 Topics in Graph Theory; 8.1 Eulerian Trails; 8.2 Hamiltonian Paths; 8.3 Planar Graphs; 8.4 Coloring Graphs; Image Credits; A Inference Rules for PL and FOL; Index

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8

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Text of Note

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 induction Set theory Combinatorics Functions, relations, and ordered sets Boolean algebra and Boolean functions Graph 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.

Discrete mathematics.

Discrete mathematics.

Number

Edition

Class number

Jongsma, Calvin

Date of Transaction

20200823093353.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y