Mathematics for digital science. Volume 1, Fundamentals / Gerard-Michel Cochard, Mhand Hifi.

Format:

Book

Author/Creator:

Cochard, Gérard-Michel, author.

Hifi, Mhand, author.

Contributor:

Wiley InterScience (Online service)

Series:

Sciences. Computer science; Operational research and decision

Language:

English

Subjects (All):

Computer science--Mathematics.

Computer science.

Physical Description:

1 online resource (368 pages)

Other Title:

Fundamentals

Place of Publication:

London : ISTE, Ltd. ; Hoboken, NJ : Wiley, 2025.

Contents:

Preface

Chapter 1. The Concept of Logic

1.1. Syllogisms

1.2. Elementary operations of propositional calculus

1.2.1. Negation

1.2.2. Conjunction

1.2.3. Disjunction

1.2.4. Conditional

1.2.5. Biconditional

1.2.6. Tautologies

1.3. Tools of deductive reasoning

1.4. Quantification

1.5. Prenex forms and pure forms

Chapter 2. Sets and Relationships

2.1. Generalities

2.2. Algebra of sets

2.3. Parts and partitions

2.4. Cartesian product

2.5. Binary relationships

2.6. Properties of relationships

2.7. Applications

Chapter 3. Counting and Combinatorial Analysis

3.1. Set cardinals

3.2. Permutations, arrangements, combinations

3.3. Properties of binomial coefficients

3.4. Stirling's formula

Chapter 4. Boolean Algebra and Boolean Functions

4.1. Special elements of an ordered set

4.2. Lattice

4.3. Boolean algebra

4.4. Boolean functions

Chapter 5. Logic Circuits

5.1. Canonical forms of a Boolean function

5.2. Reduction of a Boolean function

5.3. Karnaugh tables

5.4. Elementary logic circuits

5.5. A little on electronics

5.6. Construction of logical functions

5.7. A basic circuit: the binary adder

Chapter 6. Arithmetic

6.1. Reminder about integers

6.2. Euclidean division

6.3. Divisibility and prime numbers

6.4. GCD and LCM

6.5. Congruencies

6.6. Elliptic curves

6.7. Identity, theorem and Baezout algorithm

Chapter 7. Error Protection

7.1. General context

7.2. Linear codes

7.3. Polynomial codes

7.4. Convolutional codes

Chapter 8. Encryption Systems

8.1. Substitution and transposition

8.2. Substitution methods

8.2.1. Replacement of a symbol by a symbol

8.2.2. The code: replacement of a word by a word

8.3. Transposition methods

8.4. Asymmetric systems

8.5. DES

secret key system

8.6. RSA

public key system

8.7. Cryptography with elliptic curves

8.8. Quantum cryptography

8.9. Appendix: the Crow and the Fox

Chapter 9. Probabilities

9.1. Chance

9.2. Counting and probabilities

9.3. Events and probabilities

9.4. Statistics and probabilities

9.5. Compound probabilities

9.6. Graphs, states, transitions

9.7. Markov chains

9.7.1. Definition

9.7.2. Transition matrix

9.7.3. Evolution rules

9.7.4. Ergodicity

Chapter 10. Descriptive Statistics

10.1. Statistical description

10.1.1. A little vocabulary

10.1.2. Tabular presentation and frequency

10.1.3. Two-dimensional series

10.2. Graphical representations

10.2.1. Bar charts

10.2.2. Histograms

10.2.3. Cumulative diagrams

10.2.4. Polar diagrams

10.2.5. Pie charts

10.2.6. Figurative diagrams

10.2.7. Point clouds

10.3. Position parameters

10.3.1. Mode

10.3.2. Median

10.3.3. Averages

10.3.4. Comparison of position parameters

10.4. Dispersion parameters

10.4.1. Range, interquartile range, mean range

10.4.2. Variance and standard deviation

10.4.3. Coefficient of variation and concentration index

10.5. Linear adjustment

10.5.1. Principle of adjustment

10.5.2. Linear adjustment

10.6. Chronological series

10.6.1. Introduction

10.6.2. Study of the general trend

10.6.3. Study of seasonal variations

10.7. Covariance and correlation

10.7.1. Regression lines

10.7.2. Linear correlation

Chapter 11. Probability Laws and Simulation

11.1. Random variables

11.2. Mathematical expectation, variance and standard deviation

11.3. Distribution function

11.4. Usual probability laws

11.4.1. Uniform law

11.4.2. Binomial or Bernoulli's law

11.4.3. Poisson's law

11.4.4. Exponential law

11.4.5. Normal law

11.5. General information on simulation

11.5.1. Weak law of large numbers

11.5.2. Some simulations

11.5.3. Generation of random numbers

11.6. Generating programs

11.6.1. Usual laws

11.6.2. Any probability law

11.7. M/M/1 waiting system

11.7.1. Theoretical study

11.7.2. Simulation

11.8. Appendices

11.8.1. Appendix 1: Table for Poisson's law

11.8.2. Appendix 2: Table for normal law

11.8.3. Appendix 3: Buffon's needle

11.8.4. Appendix 4: Results for M/M/1

References

List of Authors

Index.

Notes:

Electronic reproduction. Hoboken, N.J. Available via World Wide Web.

Online resource; title from PDF title page (John Wiley, viewed February 18, 2025).

Other Format:

Print version:

ISBN:

9781394352050

1394352050

1394352042

9781394352043

1394352034

9781394352036

Publisher Number:

90103819573

CIPO000197634

Access Restriction:

Restricted for use by site license.