Paperback ISBN: 9780128140666
Published Date: 1st August 2018
Page Count: 300
Algebraic and Combinatorial Computational Biology introduces students and researchers to a panorama of powerful and current methods for mathematical problem-solving in modern computational biology. Presented in a modular format, each topic introduces the biological foundations of the field, covers specialized mathematical theory, and concludes by highlighting connections with ongoing research, particularly open questions. The work addresses problems from signaling, gene regulation, genomics, RNA folding, infectious disease dynamics, drug resistance modeling, phylogenetics, neuroscience, and ecological networks. Supporting online supplements are provided to aid instruction and provide practical experience with the material.
Integrates a comprehensive selection of tools from computational biology into education or research programs
Emphasizes practical problem-solving through multiple exercises, projects and spinoff computational simulations
Contains scalable material for graduate classes and project use
Supported by illustrative datasets and adaptable MATLAB computer code
Upper division undergraduate and graduate students. Early career researchers in biology or mathematics, particularly those transitioning into the field of mathematical and computational biology. Some practitioners seeking a methods-based primer for the field
1. DNA nanostructures: Mathematical design and problem encoding
2. Understanding DNA rearrangements: Graphs and polynomials
3. Multi-scale graph-theoretic modeling of bimolecular structures
4. Toward revealing protein function: Identifying biologically relevant clusters with graph spectral methods
5. Multistationarity in biochemical networks: Results, analysis, and examples
6. Regulation of gene expression by operons: Boolean, logical, and local models
7. Modeling the stochastic nature of gene regulation: probabilistic Boolean networks
8. Inferring interactions in molecular networks via primary decompositions of monomial ideals
9. Analysis of combinatorial neural codes: an algebraic approach
10. Predicting neural network dynamics: insights from graph theory
11. Clustering via self-organizing maps on biology and medicine
12. Optimization problems in phylogenetics: Polytopes, programming and interpretation
13. The relative accuracy of SVDquartets on simulated data with varying model conditions: connecting algebraic statistics to data analysis
Publication planned for: June 2018
format: Hardback
isbn: 9781108423915
format: Paperback
isbn: 9781108439138
This book surveys the mathematical and computational properties of finite sets of points in the plane, covering recent breakthroughs on important problems in discrete geometry, and listing many open problems. It unifies these mathematical and computational views using forbidden configurations, which are patterns that cannot appear in sets with a given property, and explores the implications of this unified view. Written with minimal prerequisites and featuring plenty of figures, this engaging book will be of interest to undergraduate students and researchers in mathematics and computer science. Most topics are introduced with a related puzzle or brain-teaser. The topics range from abstract issues of collinearity, convexity, and general position to more applied areas including robust statistical estimation and network visualization, with connections to related areas of mathematics including number theory, graph theory, and the theory of permutation patterns. Pseudocode is included for many algorithms that compute properties of point sets.
1. A happy ending
2. Overview
3. Configurations
4. Subconfigurations
5. Properties, parameters, and obstacles
6. Computing with configurations
7. Complexity theory
8. Collinearity
9. General position
10. General-position partitions
11. Convexity
12. More on convexity
13. Integer realizations
14. Stretched permutations
15. Configurations from graphs
16. Universality
17. Stabbing
18. The big picture.
Date Published: February 2018
availability: Available
format: Paperback
isbn: 9780980232783
This second edition has two parts. The first part is the complete classic by Gilbert Strang and George Fix, first published in 1973. The original book demonstrates the solid mathematical foundation of the finite element idea, and the reasons for its success. The second part is a new textbook by Strang. It provides examples, codes, and exercises to connect the theory of the Finite Element Method directly to the applications. The reader will learn how to assemble the stiffness matrix K and solve the finite element equations KU=F. Discontinuous Galerkin methods with a numerical flux function are now included. Strang's approach is direct and focuses on learning finite elements by using them.
Introduction to the second edition
Foreword to the 1997 edition
Preface
Part I:
1. An introduction to the theory
A summary of the theory
3. Approximation
4. Variational crimes, 5. Stability
6. Eigenvalue problems
7. Initial-value problems
8. Singularities
Bibliography
Index of notations
Index
Part II:
9. Finite elements in one dimension
10. The finite element method in 2D and 3D
11. Errors in projections and eigenvalues
12. Mixed finite elements: velocity and pressure
Appendix A. Discontinuous Galerkin methods
Appendix B. Fast Poisson solvers
Index for chapters 9-12 and appendices A and B.
Publication planned for: June 2018
format: Hardback
isbn: 9781107059825
format: Paperback
isbn: 9781107640481
Why study infinite series? Not all mathematical problems can be solved exactly or have a solution that can be expressed in terms of a known function. In such cases, it is common practice to use an infinite series expansion to approximate or represent a solution. This informal introduction for undergraduate students explores the numerous uses of infinite series and sequences in engineering and the physical sciences. The material has been carefully selected to help the reader develop the techniques needed to confidently utilize infinite series. The book begins with infinite series and sequences before moving onto power series, complex infinite series and finally onto Fourier, Legendre, and Fourier-Bessel series. With a focus on practical applications, the book demonstrates that infinite series are more than an academic exercise and helps students to conceptualize the theory with real world examples and to build their skill set in this area.
Preface
1. Infinite sequences
2. Infinite series
3. Power series
4. Complex infinite series
5. Series solutions for differential equations
6. Fourier, Legendre, and Fourier-Bessel series
References
Index.