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**: 16,527

**Type**: N/A

**Publisher**:
n/a

**License**:
n/a

**Post time**: 09 Dec 2007 06:51:39

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
40
Introduction to Computer Science
41
Algorithms and Data Structures
19
Object Oriented Programming
21
Theory of Computation
18
Formal Methods
17
Functional Programming
10
Logic Programming
23
Artificial Intelligence
21
Computer Vision
9
Big Data
3
Neural Networks
18
Compiler Design and Construction
16
Computer Organization and Architecture
9
Parallel Computing
3
Concurrent Programming
22
Operating Systems
22
Data Communication and Networks
29
Information Security
6
Information Theory
23
Digital Libraries
14
Information Systems
61
Software Engineering
17
Game Development and Multimedia
9
Data Mining
20
Machine Learning

Mathematics
65
Mathematics
1
Precalculus
9
Algebra
6
Calculus
5
Category Theory
24
Linear Algebra
16
Computer Aided Mathematics
5
Proofs
15
Discrete Mathematics
6
Numerical Methods
3
Number Theory
10
Graph Theory
11
Operations Research
1
Complex Analysis
5
Queueing Theory
29
Statistics
9
Probability

Supporting Fields
Operating System
Programming/Scripting
6
Ada
12
Assembly
33
C / C++
8
Common Lisp
2
Forth
34
Java
8
JavaScript
1
Lua
14
Microsoft .NET
12
Perl
5
PHP
54
Python
1
Rebol
10
Ruby
1
Scheme
3
Tcl/Tk

Miscellaneous