Explorations in Mathematics

Author: A.A. Hattangadi

Publisher: Universities Press


Category: Mathematical recreations

Page: 240

View: 368

A Primer of Analytic Number Theory

From Pythagoras to Riemann

Author: Jeffrey Stopple

Publisher: Cambridge University Press


Category: Mathematics

Page: 383

View: 686

An undergraduate-level 2003 introduction whose only prerequisite is a standard calculus course.

Riordan Arrays: A Primer

Author: Paul Barry

Publisher: Lulu.com




View: 456

The aim of this text is to introduce the beginner to the theory of Riordan arrays. Starting in a simple and constructive manner, the basic structure of these arrays is explained with clear examples, before a more theoretical grounding is provided. Ordinary Riordan arrays and exponential Riordan arrays are examined, with many explicit examples, and their applications to combinatorics and other areas are explored. The production matrix of a Riordan array is shown to play a key role, along with various sequence characterizations. Formal prerequisites are kept to a minimum, in order to provide a gentle introduction to this exciting area, that involves linear algebra, group theory and combinatorics. The reader will be well positioned to further explore Riordan arrays and their applications, and to undertake their own projects. They will join a community of interested mathematicians that now spans all continents, in a growing area of research and application.

A Primer on Radial Basis Functions with Applications to the Geosciences

Author: Bengt Fornberg

Publisher: SIAM


Category: Science

Page: 221

View: 704

Adapted from a series of lectures given by the authors, this monograph focuses on radial basis functions (RBFs), a powerful numerical methodology for solving PDEs to high accuracy in any number of dimensions. This method applies to problems across a wide range of PDEs arising in fluid mechanics, wave motions, astro- and geosciences, mathematical biology, and other areas and has lately been shown to compete successfully against the very best previous approaches on some large benchmark problems. Using examples and heuristic explanations to create a practical and intuitive perspective, the authors address how, when, and why RBF-based methods work. The authors trace the algorithmic evolution of RBFs, starting with brief introductions to finite difference (FD) and pseudospectral (PS) methods and following a logical progression to global RBFs and then to RBF-generated FD (RBF-FD) methods. The RBF-FD method, conceived in 2000, has proven to be a leading candidate for numerical simulations in an increasingly wide range of applications, including seismic exploration for oil and gas, weather and climate modeling, and electromagnetics, among others. This is the first survey in book format of the RBF-FD methodology and is suitable as the text for a one-semester first-year graduate class.

A Primer in Biological Data Analysis and Visualization Using R

Author: Gregg Hartvigsen

Publisher: Columbia University Press


Category: Science

Page: 160

View: 736

R is the most widely used open-source statistical and programming environment for the analysis and visualization of biological data. Drawing on Gregg Hartvigsen's extensive experience teaching biostatistics and modeling biological systems, this text is an engaging, practical, and lab-oriented introduction to R for students in the life sciences. Underscoring the importance of R and RStudio in organizing, computing, and visualizing biological statistics and data, Hartvigsen guides readers through the processes of entering data into R, working with data in R, and using R to visualize data using histograms, boxplots, barplots, scatterplots, and other common graph types. He covers testing data for normality, defining and identifying outliers, and working with non-normal data. Students are introduced to common one- and two-sample tests as well as one- and two-way analysis of variance (ANOVA), correlation, and linear and nonlinear regression analyses. This volume also includes a section on advanced procedures and a chapter introducing algorithms and the art of programming using R.

PCR Primer Design

Author: Anton Yuryev

Publisher: Springer Science & Business Media


Category: Science

Page: 431

View: 769

In the past decade, molecular biology has been transformed from the art of cloning a single gene to a statistical science measuring and calculating properties of entire genomes. New high-throughput methods have been developed for genome sequencing and studying the cell at different systematic levels such as transcriptome, proteome, metabolome and other -omes. At the heart of most high-throughput methods is the technique of polymerase chain reaction (PCR). PCR Primer Design focuses on primer design, which is critical to both the efficiency and the accuracy of the PCR. With intricate descriptions of basic approaches as well as specialized methods, this volume is an exceptional reference for all those involved in studying the genome. In PCR Primer Design, authors describe basic approaches for PCR primer design in addition to specialized methods. These state-of-the-art methods can be used for both genome-scale experiments and for small-scale individual PCR amplifications. This volume will be useful for organizations performing whole genome studies, companies designing instruments that utilize PCR, and individual scientists ??? geneticists, molecular biologists, molecular geneticists, and more ??? who routinely use PCR in their research.

First Steps in Number Theory

A Primer on Divisibility

Author: S. Shirali

Publisher: Universities Press


Category: Number theory

Page: 170

View: 159

Drosophila melanogaster, Drosophila simulans: So Similar, So Different

Author: Pierre Capy

Publisher: Springer Science & Business Media


Category: Science

Page: 293

View: 185

This book brings together most of the information available concerning two species that diverged 2-3 million years ago. The objective was to try to understand why two sibling species so similar in several characteristics can be so different in others. To this end, it was crucial to confront all data from their ecology and biogeography with their behavior and DNA polymorphism. Drosophila melanogaster and Drosophila simulans are among the two sibling species for which a large set of data is available. In this book, ecologists, physiologists, geneticists, behaviorists share their data on the two sibling species, and several scenarios of evolution are put forward to explain their similarities and divergences. This is the first collection of essays of its kind. It is not the final point of the analyses of these two species since several areas remain obscure. However, the recent publication of the complete genome of D. melanogaster opens new fields for research. This will probably help us explain why D. melanogaster and D. simulans are sibling species but false friends.

Trends in Intelligent Systems and Computer Engineering

Author: Oscar Castillo

Publisher: Springer Science & Business Media


Category: Computers

Page: 670

View: 281

This volume contains contributions from participants in the 2007 International Multiconference of Engineers and Computer Scientists. It covers a variety of subjects in the frontiers of intelligent systems and computer engineering and their industrial applications. The book offers up-to-date information on advances in intelligent systems and computer engineering and also serves as an excellent reference work for researchers and graduate students working in the field.