Book Review:
Book Description
This is a book about algorithms for computing with modular forms. It was written for a graduate course at Harvard University. This book is meant to answer the question "How do you compute spaces of modular forms", which theoretical mathematicians often asked, and to provide a rigorous foundation for the specific algorithms used by the author, some of which have until now never been formally stated or proven to be correct.
The book tries to find the best ways to compute with classical modular forms for congruence subgroups of SL2(Z), and how to implement most of these algorithms. Much of this work has involved turning formulas and constructions burried in books and papers into precise computable recipes, then testing these in many cases and eliminating subtle inaccuracies (published theorems often contain very small mistakes that are greatly magnified when implemented and run on a computer). The goal of this book is to explain the results, and also describe unsolved problems whose solution would move the theory forward.
At the time this book was written, there were no other books on computing with modular forms, the closest work being Cremona's book, which is about computing with elliptic curves, and Cohen's book about algebraic number theory. This field is not mature, and there are some missing details and potential improvements to many of the algorithms, which the reader might fill in, and which would be greatly appreciated by other mathematicians. Also, it seems that nobody has tried to analyze the formal complexity of any of the algorithms in this book (the author intends to do this as he writes the book) again this is somewhere the reader might contribute.
add to del.icio.us
Digg Freebookzone.com!
You may use anyone of the download options
Missing Link?, Report It and you may wish to find Similar Books from amazon.
Similar Book titles in Mathematics section: GraphTheoretic Algorithms Numerical Computing with MATLAB Algorithms for Modular Elliptic Curves, Second Edition Combinatorial Algorithms for Computers and Calculators, Second Edition Discrete Mathematics with Algorithms
Similar Book titles in Other sections:
Section: BioChemistry Algorithms for Molecular Biology EMBnet Biocomputing Tutorials BioComputing
Section: Data Structures and Algorithms Handbook of Algorithms and Data Structures Problems on Algorithms, 2nd Edition Algorithms and Complexity Introduction to Algorithms Design and Analysis of Computer Algorithms Show all..
Section: Parallel Computing Fundamentals of Grid Computing
Section: CS > Theory Fundamentals of Computing Fundamentals of Grid Computing Information Theory, Inference and Learning Algorithms An Introduction to Computing Global Optimization Algorithms  Theory and Application Show all..
Section: Device Drivers Writing Solaris PCI Device Drivers for Sun SPARC Platforms
Section: Microprocessor Extensible Firmware Interface: booting the new generation of Intel Architecture platforms
Section: Java Networking Java Thin Client for Network Computing
Section: Miscellaneous Applied Cryptography: Protocols, Algorithms, and Source Code in C, 2nd Edition Discreteevent Control of Stochastic Networks: Multimodularity and Regularity Parallel Computing Works! Digraphs Theory, Algorithms and Applications
Section: Microsoft C Sharp (C#) Data Structures and Algorithms with ObjectOriented Design Patterns in C#
Section: Networking PVM: Parallel Virtual Machine: A Users' Guide and Tutorial for Network Parallel Computing
Section: C++ Language Algorithms And Data Structures in C++ Data Structures and Algorithms with ObjectOriented Design Patterns in C++
Section: Other Programming Modular Programming with Fortran 90
Section: Smalltalk Squeak: Open Personal Computing and Multimedia
Section: Redbooks Draft IBM Workplace Forms 2.6 Inmemory Computing with SAP HANA on IBM eX5 Systems, 2nd Edition IBM Platform Computing Big Data for Analytics Workloads Implementing an IBM High Performance Computing (HPC) Solution on IBM POWER8
Section: Redbooks DB2 Performance Expert for Multiplatforms V2.2 IBM Workplace Forms: Guide to Building and Integrating a Sample Workplace Forms Application Introduction to the New Mainframe: LargeScale Commercial Computing IBM Workplace Forms 2.6: Guide to Building and Integrating a Sample Workplace Forms Application Infoprint Server for z/OS Infoprint Transforms Show all..
Section: Redpapers Amsterdam Density Functional (ADF) Benchmarking on IBM Platforms Porting and tuning the Amsterdam Density Functional package on IBM p575+ Linux Platforms Clustering Solutions Overview: Parallel Sysplex and Other Platforms IBM System Blue Gene Solution: High Performance Computing Toolkit for Blue Gene/P High Throughput Computing Validation for Drug Discovery Using the DOCK Program on a Massively Parallel System Show all..
Section: Redpapers Draft IBM System Blue Gene Solution: High Performance Computing Toolkit IBM Platform Computing Cloud Service
Section: Software Engineering How to Design Programs: An Introduction to Programming and Computing
Section: XML, XSL & UML XForms Essentials XForms: XML Powered Web Forms Introduction to XForms
Similar Books from Amazon :

