ISBN 9780367349943
July 19, 2020 Forthcoming by Chapman and Hall/CRC
338 Pages - 30 B/W Illustrations
Modern computer-intensive statistical methods play a key role in solving many problems across a wide range of scientific
disciplines. Like its bestselling predecessors, the fourth edition of Randomization, Bootstrap and Monte Carlo Methods in
Biology illustrates a large number of statistical methods with an emphasis on biological applications. The focus is now on
the use of randomization, bootstrapping, and Monte Carlo methods in constructing confidence intervals and doing tests of
significance. The text provides comprehensive coverage of computer-intensive applications, with data sets available online.
Presents an overview of computer-intensive statistical methods and applications in biology
Covers a wide range of methods including bootstrap, Monte Carlo, ANOVA, regression, and Bayesian methods
Makes it easy for biologists, researchers, and students to understand the methods used
Provides information about computer programs and packages to implement calculations, particularly using R code
Includes a large number of real examples from a range of biological disciplines
Written in an accessible style, with minimal coverage of theoretical details, this book provides an excellent introduction to
computer-intensive statistical methods for biological researchers. It can be used as a course text for graduate students, as
well as a reference for researchers from a range of disciplines. The detailed, worked examples of real applications will
enable practitioners to apply the methods to their own biological data.
1.Randomization
2.The Bootstrap
3.Monte Carlo Methods
4.Some General Considerations
5.One and Two Sample Tests
6.Analysis of Variance
7.Regression Analysis
8.Distance Matrices and Spatial Data
9.Other Analyses on Spatial Data
10.Time series
11.Survival and Growth Data
12.Non-standard Situations
13.Bayesian Methods
14.Conclusion and Final Comments
15.Appendix
ISBN 9780367334727
August 12, 2020 Forthcoming by Chapman and Hall/CRC
364 Pages - 82 B/W Illustrations
Differential Equations are very important tools in Mathematical Analysis. They are widely found in mathematics itself and in
its applications to statistics, computing, electrical circuit analysis, dynamical systems, economics, biology, and so on.
Recently there has been an increasing interest in and widely-extended use of differential equations and systems of fractional
order (that is, of arbitrary order) as better models of phenomena in various physics, engineering, automatization, biology
and biomedicine, chemistry, earth science, economics, nature, and so on. Now, new unified presentation and extensive
development of special functions associated with fractional calculus are necessary tools, being related to the theory of
differentiation and integration of arbitrary order (i.e., fractional calculus) and to the fractional order (or multi-order)
differential and integral equations.
This book provides learners with the opportunity to develop an understanding of advancements of special functions and the
skills needed to apply advanced mathematical techniques to solve complex differential equations and Partial Differential
Equations (PDEs). Subject matters should be strongly related to special functions involving mathematical analysis and its
numerous applications. The main objective of this book is to highlight the importance of fundamental results and techniques
of the theory of complex analysis for differential equations and PDEs and emphasizes articles devoted to the mathematical
treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical
aspects and novel problems and their solutions.
Specific topics include but are not limited to
Partial differential equations
Least squares on first-order system
Sequence and series in functional analysis
Special functions related to fractional (non-integer) order control systems and equations
Various special functions related to generalized fractional calculus
Operational method in fractional calculus
Functional analysis and operator theory
Mathematical physics
Applications of numerical analysis and applied mathematics
Computational mathematics
Mathematical modeling
This book provides the recent developments in special functions and differential equations and publishes high-quality,
peer-reviewed book chapters in the area of nonlinear analysis, ordinary differential equations, partial differential
equations, and related applications.
ISBN 9781138052734
August 21, 2020 Forthcoming by Chapman and Hall/CRC
512 Pages - 28 B/W Illustrations
Like the prize-winning first edition, this second edition of Principles of Uncertainty is an accessible, comprehensive guide
to the theory of Bayesian Statistics written in an appealing, inviting style, and packed with interesting examples. It
presents a comprehensive guide to the subjective Bayesian approach which has played a pivotal role in game theory, economics,
and the recent boom in Markov Chain Monte Carlo methods. This new edition has been updated throughout and features a new
material on Nonparametric Bayesian Methods, the Dirichlet distribution, a simple proof of the central limit theorem, and new
problems.
First edition won the 2011 DeGroot Prize
Well-written and comprehensive introduction to theory of Bayesian statistics
Each of the introductory chapters begins by introducing one new concept or assumption
Uses "just-in-time mathematics The introduction to mathematical ideas just before they are applied
Probability. Conditional Probability and Bayes Theorem. Discrete Random Variables. Probability generating functions.
Continuous Random Variables. Transformations. Normal Distribution. Making Decisions. Conjugate Analysis. Hierarchical
Structuring of a Model. Markov Chain Monte Carlo. Multiparty Problems. Exploration of Old Ideas. Nonparametric Bayesian
Methods. Epilogue: Applications'
Available for pre-order. Item will ship after November 16, 2020
ISBN 9780367468644
November 15, 2020 Forthcoming by Chapman and Hall/CRC
368 Pages - 94 B/W Illustrations
Lorentz Geometry is a very important intersection between Mathematics and Physics, being the mathematical language of General
Relativity.
Learning this type of geometry is the first step in properly understanding questions regarding the structure of the universe,
such as: What is the shape of the universe? What is a spacetime? What is the relation between gravity and curvature? Why
exactly is time treated in a different manner than other spatial dimensions?
Introduction to Lorentz Geometry: Curves and Surfaces intends to provide the reader with the minimum mathematical background
needed to pursue these very interesting questions, by presenting the classical theory of curves and surfaces in both
Euclidean and Lorentzian ambient spaces simultaneously.
Over 300 exercises
Suitable for senior undergraduates and graduates studying Mathematics and Physics
Written in an accessible style without loss of precision or mathematical rigour
Solution manual available on www.routledge.com/9780367468644
1. Welcome to Lorentz-Minkowski Space. 1.1. Pseudo?Euclidean Spaces. 1.2. Subspaces of R??. 1.3. Contextualization in Special
Relativity. 1.4. Isometries in R??. 1.5. Investigating O1(2, R) And O1(3, R). 1.6 Cross Product in R??. 2. Local Theory of
Curves. 2.1. Parametrized Curves in R??. 2.2. Curves in the Plane. 2.3. Curves in Space. 3. Surfaces in Space. 3.1. Basic
Topology of Surfaces. 3.2. Casual type of Surfaces, First Fundamental Form. 3.3. Second Fundamental Form and Curvatures. 3.4.
The Diagonalization Problem. 3.5. Curves in Surface. 3.6. Geodesics, Variational Methods and Energy. 3.7. The Fundamental
Theorem of Surfaces. 4. Abstract Surfaces and Further Topics. 4.1. Pseudo-Riemannian Metrics. 4.2. Riemannfs Classification
Theorem. 4.3. Split-Complex Numbers and Critical Surfaces. 4.4 Digression: Completeness and Causality
Available for pre-order. Item will ship after December 11, 2020
Hardback ISBN 9780367536930
Paperback ISBN 9780367536817
200 Pages - 18 B/W Illustrations
Proofs 101: An Introduction to Formal Mathematics serves as an introduction to proofs for mathematics majors who have
completed the calculus sequence (at least Calculus I and II) and Linear Algebra.
It prepares students for the proofs they will need to analyse and write, the axiomatic nature of mathematics, and the rigors
of upper-level mathematics courses. Basic number theory, relations, functions, cardinality, and set theory will provide the
material for the proofs and lay the foundation for a deeper understanding of mathematics, which students will need to carry
with them throughout their future studies
? Designed to be teachable across a single semester
? Suitable as an undergraduate textbook for Introduction to Proofs or Transition to Advanced Mathematics courses
? A balanced variety of easy, moderate, and difficult exercises.
1. Logic. 1.1 Introduction. 1.2. Statements and Logical Connectives. 1.3 Logical Equivalence. 1.4. Predicates and
Quantifiers. 1.5. Negation. 2. Proof Techniques. 2.1. Introduction. 2.2. The Axiomatic and Rigorous Nature of Mathematics.
2.3. Foundations. 2.4. Direct Proof. 2.5. Proof by Contrapositive. 2.5. Proof by Cases. 2.6. Proof by Contradiction. 3. Sets.
3.1. The Concept of a Set. 3.2. Subset of Set Equality. 3.3. Operations on Sets. 3.4. Indexed Sets. 3.5. Russelfs Paradox.
4. Proof by Mathematical Induction. 4.1. Introduction. 4.2. The Principle of Mathematical Induction. 4.3. Proof by strong
Induction. 5. Relations. 5.1. Introduction. 5.2. Properties of Relations. 5.3. Equivalence Relations. 6. Introduction. 6.1.
Definition of a Function. 6.2. One-To-One and Onto Functions. 6.3. Composition of Functions. 6.4. Inverse of a Function. 7.
Cardinality of Sets. 7.1. Introduction. 7.2. Sets with the same Cardinality. 7.3. Finite and Infinite Sets. 7.4. Countably
Infinite Sets. 7.5. Uncountable Sets. 7.6 Comparing Cardinalities.