Algorithmic Mathematics

Introduces the basic algorithms for computing and provides a constructive approach to abstract mathematics.

**Tag(s):**
Mathematics

**Publication date**: 01 Jan 2004

**ISBN-10**:
n/a

**ISBN-13**:
n/a

**Paperback**:
n/a

**Views**: 19,490

**Type**: N/A

**Publisher**:
n/a

**License**:
n/a

**Post time**: 09 Dec 2007 05:51:39

Algorithmic Mathematics

Introduces the basic algorithms for computing and provides a constructive approach to abstract mathematics.

Excerpts from the Preface:

This text contains sufficient material for a one-semester course in mathematical algorithms, for second year mathematics students. The course requires some exposure to the basic concepts of discrete mathematics, but no computing experience.

The aim of this course is twofold. Firstly, to introduce the basic algorithms for computing exactly with integers, polynomials and vector spaces. In doing so, the student is expected to learn how to think algorithmically and how to design and analyze algorithms.

Secondly, to provide a constructive approach to abstract mathematics, algebra in particular. When introducing the elements of ring and field theory, algorithms offer concrete tools, constructive proofs, and a crisp environment where the benefits of rigour and abstraction become tangible.

We shall write algorithms in a straightforward language, which incorporates freely standard mathematical notation. The specialized constructs are limited to the if-structure and the while-loop, which are universal.

Exercises are provided. They have a degree of difficulty comparable to that of examination questions. Some of the exercises consist of short essays; in this context, the notation [ ] indicates that mathematical symbols are not permitted in the essay. Starred sections contain optional material, which is not examinable.

This text contains sufficient material for a one-semester course in mathematical algorithms, for second year mathematics students. The course requires some exposure to the basic concepts of discrete mathematics, but no computing experience.

The aim of this course is twofold. Firstly, to introduce the basic algorithms for computing exactly with integers, polynomials and vector spaces. In doing so, the student is expected to learn how to think algorithmically and how to design and analyze algorithms.

Secondly, to provide a constructive approach to abstract mathematics, algebra in particular. When introducing the elements of ring and field theory, algorithms offer concrete tools, constructive proofs, and a crisp environment where the benefits of rigour and abstraction become tangible.

We shall write algorithms in a straightforward language, which incorporates freely standard mathematical notation. The specialized constructs are limited to the if-structure and the while-loop, which are universal.

Exercises are provided. They have a degree of difficulty comparable to that of examination questions. Some of the exercises consist of short essays; in this context, the notation [ ] indicates that mathematical symbols are not permitted in the essay. Starred sections contain optional material, which is not examinable.

Tweet

About The Author(s)

No information is available for this author.

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