Format: Paperback / softback, 89 pages, height x width: 235x155 mm, 30 Illustrations, color; 5 Illustrations, black and white; VI, 94 p. 34 illus., 30 illus. in color., 1 Paperback / softback
Series: SpringerBriefs in Statistics
Pub. Date: 09-Oct-2024
ISBN-13: 9783031688614
This book provides a concise discussion of fundamental functional data analysis (FDA) techniques for analysing biomechanical data, along with an up-to-date review of their applications. The core of the book covers smoothing, registration, visualisation, functional principal components analysis and functional regression, framed in the context of the challenges posed by biomechanical data and accompanied by an extensive case study and reproducible examples using R. This book proposes future directions based on recently published methodological advancements in FDA and emerging sources of data in biomechanics. This is a vibrant research area, at the intersection of applied statistics, or more generally, data science, and biomechanics and human movement research. This book serves as both a contextual literature review of FDA applications in biomechanics and as an introduction to FDA techniques for applied researchers. In particular, it provides a valuable resource for biomechanics researchers seeking to broaden or deepen their FDA knowledge.
1. Introduction.-
2. Preparing Biomechanical Data for Functional Data Analysis.-
3. Exploring Variation in Biomechanical Data.-
4. Functional Regression Models in Biomechanics.-
5. Case Study: The GaitRec Data.-
6. Future Directions of FDA in Biomechanics.
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Format: Paperback / softback, 193 pages, height x width: 235x155 mm, 11 Illustrations, color; 36 Illustrations, black and white; Approx. 220 p. 34 illus., 13 illus. in color., 1 Paperback / softback
Series: Springer Undergraduate Mathematics Series
Pub. Date: 01-Nov-2024
ISBN-13: 9783031661815
This textbook provides an undergraduate introduction to Galois theory and its most notable applications.
Galois theory was born in the 19th century to study polynomial equations. Both powerful and elegant, this theory was at the origin of a substantial part of modern algebra and has since undergone considerable development. It remains an extremely active research subject and has found numerous applications beyond pure mathematics. In this book, the authors introduce Galois theory from a contemporary point of view. In particular, modern methods such as reduction modulo prime numbers and finite fields are introduced and put to use. Beyond the usual applications of ruler and compass constructions and solvability by radicals, the book also includes topics such as the transcendence of e and , the inverse Galois problem, and infinite Galois theory.
Based on courses of the authors at the Ecole Polytechnique, the book is aimed at students with a standard undergraduate background in (mostly linear) algebra. It includes a collection of exam questions in the form of review exercises, with detailed solutions.
1 Invitation to Galois Theory.- 2 Basic Concepts of Group Theory.- 3
Basic Concepts of Ring Theory.- 4 Basic Concepts of Algebras Over a Field.- 5
Finite Fields, Perfect Fields.- 6 The Galois Correspondence.- 7 Addendum:
Infinite Galois Correspondence.- 8 Cyclotomy and Constructibility.- 9
Solvability by Radicals.- 10 Reduction Modulo p.- 11 Complements.- 12 Review
Exercises.- 13 Solutions to Exercises.
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Format: Hardback, 214 pages, height x width: 240x168 mm, 11 Illustrations, color; 14 Illustrations, black and white; X, 120 p., 1 Hardback
Series: Synthesis Lectures on Mathematics & Statistics
Pub. Date: 23-Oct-2024
ISBN-13: 9783031679537
This book focuses on the theoretical aspects of calculus. The book begins with a chapter on set theory before thoroughly discussing real numbers, then moves onto sequences, series, and their convergence. The author explains why an understanding of real numbers is essential in order to create a foundation for studying analysis. Since the Cantor set is elusive to many, a section is devoted to binary/ternary numbers and the Cantor set. The book then moves on to continuous functions, differentiations, integrations, and uniform convergence of sequences of functions. An example of a nontrivial uniformly Cauchy sequence of functions is given. The author defines each topic, identifies important theorems, and includes many examples throughout each chapter. The book also provides introductory instruction on proof writing, with an emphasis on how to execute a precise writing style.
Set Theory.- Real Numbers.- Sequences and Series.- Continuous Functions.- Differentiations.- Integrations.- Sequences and Series of Functions.
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Format: Hardback, 716 pages, height x width: 235x155 mm, 13 Illustrations, color; 151 Illustrations, black and white; X, 705 p. 164 illus., 1 Hardback
Series: Texts and Readings in Physical Sciences 22
Pub. Date: 26-Oct-2024
ISBN-13: 9789819744756
This well-rounded and self-contained treatment of classical mechanics strikes a balance between examples, concepts, phenomena and formalism. While addressed to graduate students and their teachers, the minimal prerequisites and ground covered should make it useful also to undergraduates and researchers. Starting with conceptual context, physical principles guide the development. Chapters are modular and the presentation is precise yet accessible, with numerous remarks, footnotes and problems enriching the learning experience. Essentials such as Galilean and Newtonian mechanics, the Kepler problem, Lagrangian and Hamiltonian mechanics, oscillations, rigid bodies and motion in noninertial frames lead up to discussions of canonical transformations, angle-action variables, Hamilton-Jacobi and linear stability theory. Bifurcations, nonlinear and chaotic dynamics as well as the wave, heat and fluid equations receive substantial coverage. Techniques from linear algebra, differential equations, manifolds, vector and tensor calculus, groups, Lie and Poisson algebras and symplectic and Riemannian geometry are gently introduced. A dynamical systems viewpoint pervades the presentation. A salient feature is that classical mechanics is viewed as part of the wider fabric of physics with connections to quantum, thermal, electromagnetic, optical and relativistic physics highlighted. Thus, this book will also be useful in allied areas and serve as a stepping stone for embarking on research.
Mechanical systems with one degree of freedom.- Keplers gravitational
two-body problem.- Newtonian to Lagrangian and Hamiltonian mechanics.-
Introduction to special relativistic mechanics.- Dynamics viewed as a vector
eld on state space.- Small oscillations for one degree of freedom.-
Nonlinear oscillations: pendulum and anharmonic oscillator.- Rigid body
mechanics.- Motion in noninertial frames of reference.- Canonical
transformations.- Angle-action variables.- Hamilton-Jacobi equation.- Normal
modes of oscillation and linear stability.- Bifurcations: qualitative changes
in dynamics.- From regular to chaotic motion.- Dynamics of continuous
deformable media.- Vibrations of a stretched string and the wave equation.-
Heat diffusion equation and Brownian motion.- Introduction to uid mechanics.
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Format: Hardback, 585 pages, height x width: 235x155 mm, 1 Illustrations, color; 17 Illustrations, black and white; X, 590 p. 17 illus., 1 Hardback
Series: Springer Texts in Statistics
Pub. Date: 04-Dec-2024
ISBN-13: 9781071641712
Applied Probability presents a unique blend of theory and applications, with special emphasis on mathematical modeling, computational techniques, and examples from the biological sciences. Chapter 1 reviews elementary probability and provides a brief survey of relevant results from measure theory. Chapter 2 is an extended essay on calculating expectations. Chapter 3 deals with probabilistic applications of convexity, inequalities, and optimization theory. Chapters 4 and 5 touch on combinatorics and combinatorial optimization. Chapters 6 through 11 present core material on stochastic processes.
If supplemented with appropriate sections from Chapters 1 and 2, there is sufficient material for a traditional semester-long course in stochastic processes covering the basics of Poisson processes, Markov chains, branching processes, martingales, and diffusion processes. This third edition includes new topics and many worked exercises. The new chapter on entropy stresses Shannon entropy and its mathematical applications. New sections in existing chapters explain the Chinese restaurant problem, the infinite alleles model, saddlepoint approximations, and recurrence relations. The extensive list of new problems pursues topics such as random graph theory omitted in the previous editions. Computational probability receives even greater emphasis than earlier. Some of the solved problems are coding exercises, and Julia code is provided.
Mathematical scientists from a variety of backgrounds will find Applied Probability appealing as a reference. This updated edition can serve as a textbook for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics. Readers should have a working knowledge of multivariate calculus, linear algebra, ordinary differential equations, and elementary probability theory.
Basic Notions of Probability Theory.- Calculation of Expectations.- Convexity, Optimization, and Inequalities.- Combinatorics.- Combinatorial Optimization.- Poisson Processes.- Discrete-Time Markov Chains.- Continuous-Time Markov Chains.- Branching Processes.- Martingales.- Diffusion Processes.- Asymptotic Methods.- Numerical Methods.- Poisson Approximation.- Number Theory.- Entropy.- Appendix: Mathematical Review.
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Format: Paperback / softback, 340 pages, height x width: 235x155 mm, 30 Illustrations, color;
2 Illustrations, black and white; XII, 206 p. 31 illus., 30 illus. in color., 1 Paperback / softback
Series: Universitext
Pub. Date: 16-Oct-2024
ISBN-13: 9783031668777
This textbook presents the spectral theory of self-adjoint operators on Hilbert space and its applications in quantum mechanics. Based on a course taught by the author in Paris, the book not only covers the mathematical theory but also provides its physical interpretation, offering an accessible introduction to quantum mechanics for students with a background in mathematics. The presentation incorporates numerous physical examples to illustrate the abstract theory. The final two chapters present recent findings on Schrodingers equation for systems of particles.
While primarily designed for graduate courses, the book can also serve as a valuable introduction to the subject for more advanced readers. It requires no prior knowledge of physics, assuming only a graduate-level understanding of mathematical analysis from the reader.
1 Introduction to quantum mechanics: the hydrogen atom.- 2
Self-adjointness.- 3 Self-adjointness criteria: Rellich, Kato & Friedrichs.-
4 Spectral theorem and functional calculus.- 5 Spectrum of self-adjoint
operators.- 6 N-particle systems, atoms, molecules.- 7 Periodic Schrodinger
operators, electronic properties of materials.- Appendix A: Sobolev spaces.-
Appendix B: Problems.
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Format: Hardback, 173 pages, height x width: 235x155 mm, 50 Illustrations, color;
82 Illustrations, black and white; X, 190 p. 60 illus., 50 illus. in color., 1 Hardback
Pub. Date: 06-Nov-2024
ISBN-13: 9783031701405
This book offers a gentle yet rigorous introduction to probability theory, with a special focus on finite probability spaces. Drawing inspiration from card games, casino games, mahjong, and two-up, it also delves into real-world applications such as weather forecasting, lotteries, hereditary diseases, and PCR virus testing. Discover which casino game gives you the best chance of winning and which one offers the worst odds.
Assuming only a high school mathematics background, this book is an excellent resource for both students and teachers, providing clear explanations and engaging examples. The technical material is lightened with entertaining stories, such as how someone became a millionaire by spotting a flaw in a national lottery and how another person helped fund a war using winnings from a well-known card game he invented.
Engaging and informative, this book is perfect for anyone looking to deepen their understanding of probability theory while enjoying some fascinating anecdotes along the way.
Finite Probability Spaces and Examples.- Permutations and Combinations.-
Conditional Probability.- Stirlings Approximation Formula and Improvements.
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