Discrete Mathematics

This book discusses a number of selected results and methods on discrete mathematics, mostly from the areas of combinatorics, graph theory, and combinatorial geometry, with a little elementary number theory.

**Tag(s):**
Discrete Mathematics

**Publication date**: 30 Nov -0001

**ISBN-10**:
n/a

**ISBN-13**:
n/a

**Paperback**:
n/a

**Views**: 45,350

**Type**: N/A

**Publisher**:
n/a

**License**:
n/a

**Post time**: 09 Dec 2006 10:40:19

Discrete Mathematics

This book discusses a number of selected results and methods on discrete mathematics, mostly from the areas of combinatorics, graph theory, and combinatorial geometry, with a little elementary number theory.

Document Excerpts:

There are many success stories of applied mathematics outside calculus. A recent hot topic is mathematical cryptography, which is based on number theory (the study of positive integers 1,2,3,...), and is widely applied, among others, in computer security and electronic banking. Other important areas in applied mathematics include linear programming, coding theory, theory of computing. The mathematics in these applications is collectively called discrete mathematics. ("Discrete" here is used as the opposite of "continuous"; it is also often used in the more restrictive sense of "finite".)

The aim of this book is not to cover "discrete mathematics" in depth (it should be clear from the description above that such a task would he ill-defined and impossible anyway). Rather, this book discusses a number of selected results and methods, mostly from the areas of combinatorics, graph theory, and combinatorial geometry, with a little elementary number theory.

At the same time, it is important to realize that mathematics cannot be done without proofs. Merely stating the facts, without, saying something about why these facts are valid, would be terribly far from the spirit of mathematics and would make it impossible to give any idea about how it works. Thus, wherever possible, this book will give the proofs of the theorems stated. Sometimes this is not possible; quite simple, elementary facts can be extremely difficult to prove, and some such proofs may take advanced courses to go through. In these cases, this book will state at least that the proof is highly technical and goes beyond the scope of this book.

Another important, ingredient of mathematics is problem solving. One won't be able to learn any mathematics without dirtying his hands and trying out the ideas he learn about in the solution of problems. To some, this may sound frightening, but in fact most people pursue this type of activity almost, every day: everybody who plays a game of chess, or solves a puzzle, is solving discrete mathematical problems. The reader is strongly advised to answer the questions posed in the text and to go through the problems at the end of each chapter of this book.

There are many success stories of applied mathematics outside calculus. A recent hot topic is mathematical cryptography, which is based on number theory (the study of positive integers 1,2,3,...), and is widely applied, among others, in computer security and electronic banking. Other important areas in applied mathematics include linear programming, coding theory, theory of computing. The mathematics in these applications is collectively called discrete mathematics. ("Discrete" here is used as the opposite of "continuous"; it is also often used in the more restrictive sense of "finite".)

The aim of this book is not to cover "discrete mathematics" in depth (it should be clear from the description above that such a task would he ill-defined and impossible anyway). Rather, this book discusses a number of selected results and methods, mostly from the areas of combinatorics, graph theory, and combinatorial geometry, with a little elementary number theory.

At the same time, it is important to realize that mathematics cannot be done without proofs. Merely stating the facts, without, saying something about why these facts are valid, would be terribly far from the spirit of mathematics and would make it impossible to give any idea about how it works. Thus, wherever possible, this book will give the proofs of the theorems stated. Sometimes this is not possible; quite simple, elementary facts can be extremely difficult to prove, and some such proofs may take advanced courses to go through. In these cases, this book will state at least that the proof is highly technical and goes beyond the scope of this book.

Another important, ingredient of mathematics is problem solving. One won't be able to learn any mathematics without dirtying his hands and trying out the ideas he learn about in the solution of problems. To some, this may sound frightening, but in fact most people pursue this type of activity almost, every day: everybody who plays a game of chess, or solves a puzzle, is solving discrete mathematical problems. The reader is strongly advised to answer the questions posed in the text and to go through the problems at the end of each chapter of this book.

Tweet

About The Author(s)

László Lovász is a Professor in the Department of Computer Science of the Eötvös Loránd University in Budapest, Hungary. His research topics cover combinatorial optimization, algorithms, complexity, graph theory, and random walks.

No information is available for this author.

Book Categories

Computer Science
Introduction to Computer Science
Introduction to Computer Programming
Algorithms and Data Structures
Artificial Intelligence
Computer Vision
Machine Learning
Neural Networks
Game Development and Multimedia
Data Communication and Networks
Coding Theory
Computer Security
Information Security
Cryptography
Information Theory
Computer Organization and Architecture
Operating Systems
Image Processing
Parallel Computing
Concurrent Programming
Relational Database
Document-oriented Database
Data Mining
Big Data
Data Science
Digital Libraries
Compiler Design and Construction
Functional Programming
Logic Programming
Object Oriented Programming
Formal Methods
Software Engineering
Agile Software Development
Information Systems
Geographic Information System (GIS)

Mathematics
Mathematics
Algebra
Abstract Algebra
Linear Algebra
Number Theory
Numerical Methods
Precalculus
Calculus
Differential Equations
Category Theory
Proofs
Discrete Mathematics
Theory of Computation
Graph Theory
Real Analysis
Complex Analysis
Probability
Statistics
Game Theory
Queueing Theory
Operations Research
Computer Aided Mathematics

Supporting Fields
Web Design and Development
Mobile App Design and Development
System Administration
Cloud Computing
Electric Circuits
Embedded System
Signal Processing
Integration and Automation
Network Science
Project Management

Operating System
Programming/Scripting
Ada
Assembly
C / C++
Common Lisp
Forth
Java
JavaScript
Lua
Microsoft .NET
Rexx
Perl
PHP
Python
R
Rebol
Ruby
Scheme
Tcl/Tk

Miscellaneous
Sponsors