Discrete Mathematics - Proof Techniques And Mathematical Structures - R. C. Penner

Instant online reading.
Don't wait for delivery!
Go digital and save!

Discrete Mathematics - Proof Techniques And Mathematical Structures

By: R. C. Penner

Write A Review

Hardcover | 20 October 1999

At a Glance

Hardcover
488 Pages

Dimensions(cm)
26.04 x 17.15 x 3.18

Hardcover

RRP $156.99

$141.75

10%OFF

or 4 interest-free payments of $35.44 with

or

Ships in 15 to 25 business days

This book offers an introduction to mathematical proofs and to the fundamentals of modern mathematics. No real prerequisites are needed other than a suitable level of mathematical maturity. The text is divided into two parts, the first of which constitutes the core of a one-semester course covering proofs, predicate calculus, set theory, elementary number theory, relations, and functions, and the second of which applies this material to a more advanced study of selected topics in pure mathematics, applied mathematics, and computer science, specifically cardinality, combinatorics, finite-state automata, and graphs. In both parts, deeper and more interesting material is treated in optional sections, and the text has been kept flexible by allowing many different possible courses or emphases based upon different paths through the volume.

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

More in Computer Science

The Tech Coup

How to Save Democracy from Silicon Valley

Paperback

RRP $29.99

$26.75

11%
OFF

Python Crash Course

3rd Edition - A Hands-On, Project-Based Introduction to Programming

Paperback

RRP $89.99

$64.99

28%
OFF

Microsoft 365 Excel For Dummies

For Dummies (Computer/Tech)

Paperback

RRP $49.95

$38.75

22%
OFF

The New Age of Sexism

How the AI Revolution is Reinventing Misogyny

Paperback

RRP $36.99

$29.75

20%
OFF

Nexus

A Brief History of Information Networks from the Stone Age to AI

Paperback

RRP $29.99

$24.99

17%
OFF

If Anyone Builds It, Everyone Dies

The Case Against Superintelligent AI

Paperback

RRP $36.99

$29.75

20%
OFF

The AI Con

How To Fight Big Tech's Hype and Create the Future We Want

Paperback

RRP $36.99

$29.75

20%
OFF

Microsoft 365 Excel All-in-One For Dummies

Excel for Dummies

Paperback

RRP $74.95

$55.75

26%
OFF

Creative Machines

AI, Art & Us

Hardcover

RRP $57.95

$44.75

23%
OFF

The AI-Driven Leader : Harnessing AI to Make Faster, Smarter Decisions - Geoff Woods

$21.75

13%
OFF

Empire of AI

Inside the reckless race for total domination

Hardcover

RRP $55.00

$40.75

26%
OFF

Python All-in-One For Dummies

3rd Edition

Paperback

RRP $74.95

$55.75

26%
OFF

Explainable Artificial Intelligence-based Industrial Internet of Things : Technologies and Applications - Aditya Khamparia

$22.75

19%
OFF

Autonomous Cyber Resilience - Alexander Kott

$85.75

10%
OFF

Cognitive Cloud Computing

Building Intelligent Systems for Tomorrow

Hardcover

RRP $273.00

$255.99

General Preface	p. xi
Preface for Instructors	p. xii

Proof Techniques	p. 1
Elements of Logic and Induction	p. 2
Definitions	p. 2
Propositions and Predicates	p. 3
Conjunction and Negation	p. 7
Implication	p. 9
Proofs by Induction for Natural Numbers	p. 12
Methods of Proof	p. 24
Chains of Implications	p. 24
Proof by Contradiction	p. 32
Instantiation	p. 38
Constructive and Non-Constructive Proofs	p. 40
Disproofs	p. 43
Predicate Calculus	p. 45
Logical Operators	p. 46
Propositional Forms	p. 48
Parentheses	p. 50
Standard Logical Identities	p. 53
Standard Rules of Inference	p. 55
Aristotelean Logic	p. 57
Logical Equivalence	p. 62
Commutativity and Associativity	p. 68
Proving Propositional Forms	p. 72
Predicate Forms and Quantification	p. 74
Standard Valid Predicate Forms	p. 80
Proving Predicate Forms	p. 83
Disproofs	p. 86
Set Theory	p. 93
Axioms and the Primitives of Set Theory	p. 94
The Basics of Set Theory	p. 98
ZFC Set Theory	p. 107
Binary Operations on Sets	p. 114
Cartesian Products	p. 122
Absolute Complements and DeMorgan's Laws	p. 127
The Set of Non-Negative Integers	p. 134
Inductive Definitions	p. 141
Sets of Numbers	p. 150
Elementary Number Theory	p. 151
Common Multiples	p. 152
The Division Algorithm	p. 154
Common Divisors	p. 156
Relatively Prime Pairs	p. 157
Linear Diophantine Equations	p. 159
The Fundamental Theorem of Arithmetic	p. 164
The Euclidean Algorithm	p. 168
Continued Fractions	p. 172
Relations	p. 179
N-ary Relations	p. 180
Binary Relations and Digraphs	p. 184
Properties of Relations	p. 189
Set-Theoretic Operations	p. 194
Inversion	p. 196
Composition	p. 198
Iterations	p. 203
Posets	p. 208
Linear and Well Orders	p. 214
Bounds in Posets	p. 222
Axiom of Choice Revisited	p. 225
Equivalence Relations	p. 227
Partitions	p. 234
Closure Operations	p. 241
Meets and Joins of Partitions	p. 249
Lattices	p. 252
Functions	p. 259
Definitions and Examples	p. 260
Composition	p. 269
Restriction and Extension	p. 275
Injectivity, Surjectivity, and Bijectivity	p. 278
Inverses	p. 285
Images and Pre-Images	p. 292
Elements of Dynamical Systems	p. 301
Permutations	p. 307

Cardinality	p. 313
Finite Sets	p. 314
Infinite Sets	p. 319
Countable Sets	p. 322
Uncountable Sets	p. 328
Comparing Cardinalities	p. 332
Elements of Combinatorics	p. 341
Finite Cardinalities	p. 342
Combinatorial Proofs	p. 345
Recursively Defined Sequences	p. 353
Inductive Proofs and Solving Recursions	p. 361
Characteristic Equations	p. 368
Generating Functions	p. 374
Languages and Finite State Automata	p. 383
Alphabets, Words, and Concatenation	p. 384
Languages	p. 388
Regular Expressions	p. 396
Finite State Automata	p. 399
Kleene's Theorem	p. 408
Semigroups and Monoids	p. 417
Graphs	p. 425
Definitions and Examples	p. 426
Trees	p. 432
Hamiltonian and Eulerian Paths	p. 438
Planarity	p. 441
Connectivity, Matching, and Coloring	p. 446
Suggestions for Further Reading	p. 455
Index of Notation	p. 456
Index	p. 459
Table of Contents provided by Syndetics. All Rights Reserved.

Discrete Mathematics - Proof Techniques And Mathematical Structures

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Computer Science

The Tech Coup

How to Save Democracy from Silicon Valley

Python Crash Course

3rd Edition - A Hands-On, Project-Based Introduction to Programming

Microsoft 365 Excel For Dummies

For Dummies (Computer/Tech)

The New Age of Sexism

How the AI Revolution is Reinventing Misogyny

Nexus

A Brief History of Information Networks from the Stone Age to AI

If Anyone Builds It, Everyone Dies

The Case Against Superintelligent AI

The AI Con

How To Fight Big Tech's Hype and Create the Future We Want

Microsoft 365 Excel All-in-One For Dummies

Excel for Dummies

Creative Machines

AI, Art & Us

The AI-Driven Leader

Harnessing AI to Make Faster, Smarter Decisions

Genesis

Artificial Intelligence, Hope, and the Human Spirit

Empire of AI

Inside the reckless race for total domination

Python All-in-One For Dummies

3rd Edition

Explainable Artificial Intelligence-based Industrial Internet of Things

Technologies and Applications

Unleashing User Innovation

Multidisciplinary Perspectives on End-User Development and Generative AI

Causal Inference and Machine Learning

In Economics, Social, and Health Sciences

The Shortest History of AI

Autonomous Cyber Resilience

Data Science and Machine Learning for Non-Programmers

Using SAS Enterprise Miner

Cognitive Cloud Computing

Building Intelligent Systems for Tomorrow

Hands-On Machine Learning with Scikit-Learn and PyTorch

Concepts, Tools, and Techniques to Build Intelligent Systems

AI for Cybersecurity

Research and Practice

Scary Smart

The Future of Artificial Intelligence and How You Can Save Our World

Computer Architecture

A Quantitative Approach

This product is categorised by