Format: Hardback, 271 pages, height x width: 235x155 mm, 12 Illustrations, color; 12 Illustrations, black and white; X, 290 p., 1 Hardback
Series: University Texts in the Mathematical Sciences
Pub. Date: 18-Nov-2024
ISBN-13: 9789819766468
Targeted at undergraduate mathematics students, this book aims to cover courses in group theory. Based on lectures in group theory, it includes many illustrations and examples, numerous solved exercises and detailed proofs of theorems. The book acts as a guide to teachers and is also useful to graduate students. The book discusses major topics in group theory such as groups and subgroups, binary operations, fundamental algebraic structure of groups, symmetric groups, cyclic groups, normal subgroups, quotient groups, homomorphisms, isomorphisms, direct product of groups, simple groups, set on a group, Sylow's theorem, finite group, Abelian groups and non-isomorphic Abelian groups.
GROUPS AND SUBGROUPS.- NORMAL SUBGROUPS.- FINITE GROUPS.- SERIES GROUPS.
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Format: Paperback / softback, 444 pages, height x width: 235x155 mm, 89 Illustrations, color; 34 Illustrations, black and white; Approx. 450 p. 33 illus., 1 Paperback / softback
Series: Springer Undergraduate Mathematics Series
Pub. Date: 15-Nov-2024
ISBN-13: 9783031654909
This textbook provides an introduction to the mathematical methods used to analyse deterministic models in life sciences, including population dynamics, epidemiology and ecology. The book covers both discrete and continuous models.
The presentation emphasises the solvability of the equations appearing in the mathematical modelling of natural phenomena and, in the absence of solutions, the analysis of their relevant properties. Of particular interest are methods that allow for determining the long-term behaviour of solutions. Thus, the book covers a range of techniques, from the classical Lyapunov theorems and positivity methods based on the Perron?Frobenius theorem, to the more modern monotone dynamical system approach. The book offers a comprehensive presentation of the Lyapunov theory, including the inverse Lyapunov theorems with applications to perturbed equations and Vidyasagar theorem. Furthermore, it provides a coherent presentation of the foundations of the theory of monotone dynamical systems with its applications to epidemiological models. Another feature of the book is the derivation of the McKendrick?von Foerster equation from the discrete Leslie model and the analysis of the long-term behaviour of its solutions.
Designed for upper undergraduate courses and beyond, this textbook is written for students and researchers looking to master the mathematics of the tools commonly used to analyse life science models. It therefore goes somewhat deeper into mathematics than typical books at this level but should be accessible to anyone with a good command of calculus with elements of real and complex analysis and linear algebra; the necessary concepts are collected in the appendices.
1 Mathematical modelling.- Part I Unstructured Models.- 2 Models with
discrete time.- 3 Models with continuous time.- 4 Qualitative theory for a
single equation.- Part II Models with discrete structure.- 5 Linear models
with discrete structure.- 6 Continuous time non-linear models for interacting
species and age-structured populations.- 7 Discrete time non-linear models
for interacting species and structured populations.- 8 Positivity in natural
science models.- Part III Models with continuous age structure.- 9
McKendrickvon Foerster model.- 10 Basic nonlinear models. Part IV
Appendices.- A Spaces, norms and order.- B Differential equations and
systems.- C Linear algebra tools.- D First order partial differential
equations and the method of characteristics.
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Format: Hardback, 112 pages, height x width: 235x155 mm, 19 Illustrations, black and white; Approx. 150 p., 1 Hardback
Series: Quantitative Methods in the Humanities and Social Sciences
Pub. Date: 16-Nov-2024
ISBN-13: 9783031700507
This book is about the interplay between chance and order, but limited to mostly binary events, such as success/failure as they occur in a diversity of interesting applications. The goal is to entertain and instruct with topics that range from unexpected encounters with chance in everyday experiences, to significant “must know” insights regarding human health and other concerns in the social sciences.
The first section provides the tools for being able to discuss random sequences with hints at what is to follow. This is followed by another surprising and, to some extent, bizarre result known as Stein’s Paradox, which is applied to baseball.
The troublesome topic of disease clusters, namely to decide whether the clumping of events is due to chance or some environmental cause, is treated using both the Poisson and normal approximations to the binomial distribution and this leads naturally into a discussion of the base rate fallacy and a case study of hospital performance. Next, another medical case study this time concerning some tricky questions about the effectiveness of colonoscopy and other medical interventions. A brief discussion of the mathematics of clinical trials, follows.
Then, the book examines the error in random sampling, when polling for candidate preference with specific current examples. The essential tool here is covariance of random variables. The author follows this with a treatment of the spooky quality of coincidence using appropriate mathematical tools. After this, code breaking at Bletchley Park using Baye’s theorem. It returns to Poisson events to discuss another unexpected result, followed by the use of spatial Poisson events in the delivery of emergency response services.
Finally, an account of fluctuations that occur in a run of Bernoulli trials as a bookend to the very first section of the book. The probability theory involved is elementary using the binomial theorem and its extensions to Poisson and normal events in addition to conditional probability and covariance. The author provides an optional brief tutorial at the end, that covers the basic ideas in probability and statistics needed in the main text. Besides a list of references, several codes written in Matlab that were used to illustrate various topics in the text, as well as to support several figures that appear throughout, are provided.
Success Runs in Bernoulli Trials.
Chapter 2. The Remarkable Streak of Joe Di Maggio.
Chapter 3. Inherited, Not Acquired.
Chapter 4. A Subtle Bias.
Chapter 5. Addendum : Conditional Expectation.
Chapter 6. Hot Hands in Basketball.
Chapter 7. Restricted Choice.
Chapter 8. Another Conundrum : What Does Crowd Size at Wimbledons Tennis Match Tell us About Baseball Batting Averages?
Chapter 9. Cancer Clusters.
Chapter 10. Medical Mis-Readings.
Chapter 11. The Wrong Conclusion.
Chapter 12. Clinical Trials.
Chapter 13. Margin of Error.
Chapter 14. What Are the Odds of That?
Chapter 15. Turings Evidence.
Chapter 16. Bells Inequality.-
Chapter 17. The Paradox of Random Arrivals.
Chapter 18. The Inverse Square Root Law.
Chapter 19. Runs, Again.
Chapter 20. Addendum : Tutorial on Elementary Probability.
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Format: Hardback, 240 pages, height x width: 235x155 mm, 1 Illustrations, color; 1 Illustrations, black and white; Approx. 250 p., 1 Hardback
Series: Latin American Mathematics Series UFSCar subseries
Pub. Date: 18-Nov-2024
ISBN-13: 9783031697012
This volume convenes selected, peer-reviewed papers presented at the international workshop dedicated to Dr. Jorge Hounie on the occasion of his 75th birthday, held in Serra Negra, Brazil, from July 31 to August 4, 2023. The papers in this volume cover areas that include several complex variables, Cauchy-Riemann geometry, and partial differential equations.
An Emeritus at the Federal University of S?o Carlos (UFScar), Brazil, Dr. Hounie has made significant contributions to partial differential equations, complex variables, harmonic analysis, and involutive structures. He has also been a kind and great mentor to numerous graduate students and postdocs who have gone on to pursue successful academic careers. Born in Bahia Blanca, Argentina, he completed his PhD studies at Rutgers University in 1974 and joined UFSCar as a Full Professor in 1995. He is a Full Member of the Brazilian Academy of Sciences.
Within this book, readers will encounter a collection of cutting-edge research papers reflecting Dr. Hounie's research interests, valuable for both experienced researchers and graduate students alike.
On Some Of The Works Of Jorge Hounie.- On The Research Of J. Hounie: A
Personal Statement.- The Taylor Expansion Of Cr Germs On A Class Of Levi
Degenerate Models.- On A Model Sum Of Squares Operator.- On The Local
Regularity Of The Gevrey Vectors For Hormanders Operators.- Bergman
Logarithmically Flat And Obstruction Flat Hypersurfaces And Their Cr
Structures.- Analyticity In A Dispersive Camassa-Holm Equation With Cubic
Nonlinearities.- Distributions With Decay And Restriction Problems.- Equality
Of Commutator Type And Levi Form Type For An (N 2)-Dimensional Bundle.-
Characterization Of Real-Analytic Infinitesimal Cr Automorphisms For A Class
Of Hypersurfaces In C4.- On Some Singular Integrals Linked To Solvability And
Signal Theory.- Report on the Paper on Spectral Properties Of Certain
Semiregular Systems of Pdes with Polynomial Coefficients.- Friedrichs' Lemma
For Besov And Triebel-Lizorkin Spaces.- On The Solvability Of
Pseudodifferential Equations In Microdistributions.- Contribution to the
study of closed 1-forms and its applications.
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Format: Hardback, 417 pages, height x width: 235x155 mm, 1 Illustrations, color; V, 409 p. 1 illus. in color., 1 Hardback
Series: Forum for Interdisciplinary Mathematics
Pub. Date: 03-Nov-2024
ISBN-13: 9789819765195
This book is a comprehensive and advanced exploration of trace inequalities in the context of matrices and operators acting on Hilbert spaces. Its goal is to present elegant inequalities with innovative proofs. Instead of presenting generalized versions that can be complicated and lack clarity, the book focuses on beautiful and original inequalities. Divided into eight chapters, this book is designed for researchers and graduate students in mathematics, physics, and engineering. It provides detailed explanations for most of the results and includes a variety of exercises and problems to help readers understand the content and inspire further research into advanced topics.
Chapter 1 Fundamentals of Matrices and Operators.
Chapter 2 Unitarily Invariant Norms and Inequalities.
Chapter 3 Trace Inequalities for Positive Semidefinite Matrices.
Chapter 4 Norm Inequalities for Positive Semidefinite Matrices.
Chapter 5 Positive Maps and Operator Means.
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Format: Hardback, 309 pages, height x width: 235x155 mm, 8 Illustrations, black and white; VIII, 292 p. 20 illus., 10 illus. in color., 1 Hardback
Series: Coimbra Mathematical Texts 3
Pub. Date: 28-Nov-2024
ISBN-13: 9783031696459
The aim of this book is to honor the memory of Professor Jose Carlos Petronilho and hence focuses on his main research areas (Special Functions, Orthogonal Polynomials, Approximation Theory). It is a collaborative book and among the contributing authors are outstanding leaders in the field. The book addresses different topics exploring the connection between the areas already mentioned and their applications, from different perspectives and using several tools, both analytical and algebraic. Beside the researches working in these topics, the book potentially interests the readers working in areas of Mathematics, Science and Technology where Approximation Theory, Special Functions and Orthogonality are potentially useful tools.
1. Aleksandrov measures.-
2. Matrix Orthogonal Polynomials: A RiemannHilbert approach.-
3. The computation of ?? (2?? ), ?? (2?? + 1) and beyond by using telescoping series.-
4. Sobolev orthogonal polynomials for solving the Schrodinger equation with potentials ?? (??) = ??2?? , ?? 1.-
5. Charting the ??-Askey scheme. III. Verde-Star scheme for ?? = 1.
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Format: Hardback, 497 pages, height x width: 235x155 mm, Approx. 480 p., 1 Hardback
Series: Springer Texts in Statistics
Pub. Date: 22-Nov-2024
ISBN-13: 9781071641316
This book, Statistical Modeling and Computation, provides a unique introduction to modern statistics from both classical and Bayesian perspectives. It also offers an integrated treatment of mathematical statistics and modern statistical computation, emphasizing statistical modeling, computational techniques, and applications.
The 2nd edition changes the programming language used in the text from MATLAB to Julia. For all examples with computing components, the authors provide data sets and their own Julia codes. The new edition features numerous full color graphics to illustrate the concepts discussed in the text, and adds three entirely new chapters on a variety of popular topics, including:
Regularization and the Lasso regression
Bayesian shrinkage methods
Nonparametric statistical tests
Splines and the Gaussian process regression
??Probability Models.- Random Variables and Probability Distributions.- Joint Distributions.- Common Statistical Models.- Statistical Inference.- Likelihood.- Monte Carlo Sampling.- Bayesian Inference.- Generalized Linear Models.- Dependent Data Models.- State Space Models.- References.- Solutions.- MATLAB Primer.- Mathematical Supplement.- Index.