My Wish Lists Login / Join

Algebraic Complexity Theory

By: T. Lickteig, Peter BÃ¼rgisser, Michael Clausen

Write A Review

Hardcover | 1 December 1996

At a Glance

Hardcover
652 Pages

Dimensions(cm)
23.39 x 15.6 x 3.51

Hardcover

$343.75

or 4 interest-free payments of $85.94 with

Ships in 10 to 15 business days

The algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search for a precise and sufficiently general formalization of the notions of computability and algorithm. In the 1930s, a number of quite different concepts for this purpose were pro posed, such as Turing machines, WHILE-programs, recursive functions, Markov algorithms, and Thue systems. All these concepts turned out to be equivalent, a fact summarized in Church's thesis, which says that the resulting definitions form an adequate formalization of the intuitive notion of computability. This had and continues to have an enormous effect. First of all, with these notions it has been possible to prove that various problems are algorithmically unsolvable. Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem. Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under standing of the intrinsic computational difficulty of problems.

Industry Reviews

P. B¼rgisser, M. Clausen, M.A. Shokrollahi, and T. Lickteig

Algebraic Complexity Theory

"The book contains interesting exercises and useful bibliographical notes. In short, this is a nice book."-MATHEMATICAL REVIEWS

From the reviews:

"This book is certainly the most complete reference on algebraic complexity theory that is available hitherto. ... superb bibliographical and historical notes are given at the end of each chapter. ... this book would most certainly make a great textbook for a graduate course on algebraic complexity theory. ... In conclusion, any researchers already working in the area should own a copy of this book. ... beginners at the graduate level who have been exposed to undergraduate pure mathematics would find this book accessible." (Anthony Widjaja, SIGACT News, Vol. 37 (2), 2006)

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Computing & I.T.Computer Science Mathematical Theory of Computation Mathematics Mathematical Foundation Mathematical Logic Algebra Combinatorics & Graph Theory Groups & Group Theory Geometry Algebraic Geometry

Computer Programming & Software Development Algorithms & Data Structures Applied Mathematics

Other Editions and Formats

Paperback

Published: 5th December 2010

View Product

Introduction
Efficient Polynomial Arithmetic
Efficient Algorithms with Branching
Models of Computation
Preconditioning and Transcendence Degree
The Substitution Method
Differential Methods
The Degree Bound
Specific Polynomials which Are Hard to Compute
Branching and Degree
Branching and Connectivity
Additive Complexity
Linear Complexity
Multiplicative and Bilinear Complexity
Asymptotic Complexity of Matrix Multiplication
Problems Related to Matrix Multiplication
Lower Bounds for the Complexity of Algebras
Rank over Finite Fields and Codes
Rank of 2-Slice and 3-Slice Tensors
Typical Tensorial Rank
P Versus NP: A Nonuniform Algebraic Analogue
Bibliography
List of Notation
Index
Table of Contents provided by Blackwell. All Rights Reserved.

Algebraic Complexity Theory

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

More in Mathematics

Numeracy in Early Childhood

Shared Contexts For Teaching And Learning

How to Win At Chess

The Ultimate Guide for Beginners and Beyond

A Little History of Mathematics

Little Histories

Humble Pi

A Comedy of Maths Errors

The Golden Ratio

Divine Beauty of Mathematics

Primary Mathematics

4th Edition - Integrating Theory with Practice

Statistics and Data Handling for Biologists

A Student's Guide

Statistics and Data Handling for Biologists

A Student's Guide

The Score

How to Stop Playing Someone Else's Game

Modal Semirings and Applications

Trends in Logic

Mathematics of Uncertainty Applied to Global Issues

Sustainability, Mistreatment of Women, Nuclear Power, Smart Cities, Digitalization

Stochastic Control in Energy, Environmental and Resource Management Applications

Emerging Methodologies and Applications in Modelling, Identification and Control

Dynamics of Marine Structures

Data Science and Social Research III

Epistemology, Methods, Technology, Applications, and Relation to Artificial Intelligence

Recent Advances in Information Systems

Proceedings of the ICRAIS, Pointe aux Piments, Mauritius, 10-12 September 2025

Calculus

9th edition - Early Transcendentals, Metric

Second Grade Math with Confidence Bundle (Math with Confidence)

Math with Confidence

Discrete Mathematics with Applications, Metric Edition

5th edition

Antifragile

Things That Gain from Disorder

Oxford Maths for Australian Schools Year 6 Practice and Mastery Book

3rd Edition

Oxford Maths for Australian Schools Year 4 Value Pack

3rd Edition

Fooled By Randomness

The Hidden Role of Chance in Life and in the Markets

The Infinite Game

From the bestselling author of Start With Why

Precalculus

8th Edition - Mathematics for Calculus, International Metric Edition

This product is categorised by