Mathematics

Taeyoung Lee, Melvin Leok, N. Harris McClamroch, “Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds: A Geometric Approach to Modeling and Analysis”

Mathematical Statistics: Essays on History and Methodology By Johann Pfanzagl

The Musical-Mathematical Mind: Patterns and Transformations By Gabriel Pareyon, Silvia Pina-Romero, Octavio A. Agustín-Aquino, Emilio Lluis-Puebla

Computer Mathematics: 9th Asian Symposium (ASCM2009), Fukuoka, December 2009, 10th Asian Symposium (ASCM2012), Beijing, October 2012, Contributed Papers and Invited Talks By Ruyong Feng, Wen-shin Lee, Yosuke Sato

An Introduction to Modeling Neuronal Dynamics (Texts in Applied Mathematics) by Christoph Börgers

Taeyoung Lee, Melvin Leok, N. Harris McClamroch, “Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds: A Geometric Approach to Modeling and Analysis”

English | EPUB | 2017 (2018 Edition) | 561 Pages | ISBN : 3319569511 | 7 MB

This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce a general methodology for obtaining globally valid equations of motion on configuration manifolds that are Lie groups, homogeneous spaces, and embedded manifolds, thereby avoiding the difficulties associated with coordinate singularities.

The material is presented in an approachable fashion by considering concrete configuration manifolds of increasing complexity, which then motivates and naturally leads to the more general formulation that follows. Understanding of the material is enhanced by numerous in-depth examples throughout the book, culminating in non-trivial applications involving multi-body systems.

This book is written for a general audience of mathematicians, engineers, and physicists with a basic knowledge of mechanics. Some basic background in differential geometry is helpful, but not essential, as the relevant concepts are introduced in the book, thereby making the material accessible to a broad audience, and suitable for either self-study or as the basis for a graduate course in applied mathematics, engineering, or physics.

Mathematical Statistics: Essays on History and Methodology By Johann Pfanzagl

English | PDF,EPUB | 2017 | 321 Pages | ISBN : 3642310834 | 10.58 MB

This book presents a detailed description of the development of statistical theory. In the mid twentieth century, the development of mathematical statistics underwent an enduring change, due to the advent of more refined mathematical tools. New concepts like sufficiency, superefficiency, adaptivity etc. motivated scholars to reflect upon the interpretation of mathematical concepts in terms of their real-world relevance.

Questions concerning the optimality of estimators, for instance, had remained unanswered for decades, because a meaningful concept of optimality (based on the regularity of the estimators, the representation of their limit distribution and assertions about their concentration by means of Anderson’s Theorem) was not yet available. The rapidly developing asymptotic theory provided approximate answers to questions for which non-asymptotic theory had found no satisfying solutions. In four engaging essays, this book presents a detailed description of how the use of mathematical methods stimulated the development of a statistical theory. Primarily focused on methodology, questionable proofs and neglected questions of priority, the book offers an intriguing resource for researchers in theoretical statistics, and can also serve as a textbook for advanced courses in statisticc.

The Musical-Mathematical Mind: Patterns and Transformations By Gabriel Pareyon, Silvia Pina-Romero, Octavio A. Agustín-Aquino, Emilio Lluis-Puebla

English | PDF,EPUB | 2017 | 352 Pages | ISBN : 3319473360 | 18.35 MB

This book presents a deep spectrum of musical, mathematical, physical, and philosophical perspectives that have emerged in this field at the intersection of music and mathematics. In particular the contributed chapters introduce advanced techniques and concepts from modern mathematics and physics, deriving from successes in domains such as Topos theory and physical string theory.

The authors include many of the leading researchers in this domain, and the book will be of value to researchers working in computational music, particularly in the areas of counterpoint, gesture, and Topos theory.

Computer Mathematics: 9th Asian Symposium (ASCM2009), Fukuoka, December 2009, 10th Asian Symposium (ASCM2012), Beijing, October 2012, Contributed Papers and Invited Talks By Ruyong Feng, Wen-shin Lee, Yosuke Sato

English | PDF,EPUB | 2014 | 498 Pages | ISBN : 3662437988 | 18.82 MB

This book covers original research and the latest advances in symbolic, algebraic and geometric computation; computational methods for differential and difference equations, symbolic-numerical computation; mathematics software design and implementation; and scientific and engineering applications based on features, invited talks, special sessions and contributed papers presented at the 9th (in Fukuoka, Japan in 2009) and 10th (in Beijing China in 2012) Asian Symposium on Computer Mathematics (ASCM).

Thirty selected and refereed articles in the book present the conference participants’ ideas and views on researching mathematics using computers.

An Introduction to Modeling Neuronal Dynamics (Texts in Applied Mathematics) by Christoph Börgers

English | 25 Apr. 2017 | ISBN: 331951170X | 457 Pages | EPUB | 6.74 MB

This book is intended as a text for a one-semester course on Mathematical and Computational Neuroscience for upper-level undergraduate and beginning graduate students of mathematics, the natural sciences, engineering, or computer science. An undergraduate introduction to differential equations is more than enough mathematical background. Only a slim, high school-level background in physics is assumed, and none in biology.

Topics include models of individual nerve cells and their dynamics, models of networks of neurons coupled by synapses and gap junctions, origins and functions of population rhythms in neuronal networks, and models of synaptic plasticity.