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A beginner’s guide to discrete mathematics

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Contents:

1 Properties of numbers
1.1 Numbers
1.2 Sums
1.3 Bases
1.4 Scientific notation
1.5 Aritmetic in computers

2 Sets and data structures
2.1 Propositions and logic
2.2 Elements of set theory
2.3 Proof methods in set operations
2.4 Some further set operations
2.5 Mathematical induction

3 Boolean algebras and circuits
3.1 Boolean algebra
3.2 Boolean forms
3.3 Finding minimal disjunctive forms
3.4 Digital circuits

4 Relations and functions
4.1 Relations
4.2 Some special kinds of relations
4.3 Functions

5 The theory of counting
5.1 Events
5.2 Unions of events
5.3 One-to-one correspondences and infinite sets
5.4 Arrangement problems
5.5 Selections
5.6 The binomial theorem and its applications
5.7 Some further counting results

6 Probability
6.1 Probability measures
6.2 Repeated experiments
6.3 Counting and probability
6.4 Bayes formula and applications

7 Graph theory
7.1 Introduction to graphs
7.2 The Konigsberg bridges; traversability
7.3 Walks, paths, and cycles
7.4 Distances and shortest paths
7.5 Trees
7.6 Hamiltonian cycles
7.7 The traveling salesman problem

8 Matrices
8.1 Vectors and matrices
8.2 Properties of the matrix product
8.3 Systems of linear aquations
8.4 More about linear systems and inverses
8.5 Adjacency matrices

9 Number theory and cryptography
9.1 Some elementary number theory
9.2 Modular arithmetic
9.3 An introduction to cryptography
9.4 Modern cryptography
9.5 Other cryptographic ideas
9.6 Attacks on the RSA system

10 The theory of voting
10.1 Simple elections
10.2 Multiple elections
10.3 Fair elections
10.4 Properties of electoral systems

Solutions to practice exercises
Answers to selected exercises
Index

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Availability

Detail Information

Series Title

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Call Number

511.1 WAL b

Publisher

New York : Springer., 2012

Collation

xiii, 427 hal.; ilus.; 24 cm

Language

English

ISBN/ISSN

9780817682859

Classification

511.1

Content Type

-

Media Type

-

Carrier Type

-

Edition

Second Edition

Subject(s)

Discrete mathematics

Specific Detail Info

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Statement of Responsibility

W.D. Wallis

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