Mathematical Foundations of Neuroscience

This book is motivated by a perceived need for an overview of how dynamical systems and computational analysis have been used in understanding the types of models that come out of neuroscience.

The study of mathematical cognition and the ways in which the ideas of space, time and number are encoded in brain circuitry has become a fundamental issue for neuroscience. How such encoding differs across cultures and educational level is of further interest in education and neuropsychology. This rapidly expanding field of research is overdue for an interdisciplinary volume such as this, which deals with the neurological and psychological foundations of human numeric capacity. A uniquely integrative work, this volume provides a much needed compilation of primary source material to researchers from basic neuroscience, psychology, developmental science, neuroimaging, neuropsychology and theoretical biology.

Some investigators have argued that emotions, especially animal emotions, are illusory concepts outside the realm of scientific inquiry. However, with advances in neurobiology and neuroscience, researchers are demonstrating that this position is wrong as they move closer to a lasting understanding of the biology and psychology of emotion. In Affective Neuroscience

This book provides a comprehensive introduction to the mathematical foundations of economics, from basic set theory to fixed point theorems and constrained optimization. Rather than simply offer a collection of problem-solving techniques, the book emphasizes the unifying mathematical principles that underlie economics.

0387955267"In From Computer to Brain: Foundations of Computational Neuroscience, William W. Lytton provides a gentle but rigorous introduction to the art of modeling neurons and neural systems. It is an accessible entry to the methods and approaches used to model the brain at many different levels, ranging from synapses and dendrites to neurons and neural circuits. This book gives a balanced view of the wide range of modeling techniques that are available in a way that is accessible to a wide audience. This is a book that will bring a smile to your face as well as inspire your imagination." - Terrence J. Sejnowski Howard Hughes Medical Institute, Salk Institute, University of California at San Diego ...

Comprehensive account of constructive theory of first-order predicate calculus. Covers formal methods including algorithms and epi-theory, brief treatment of Markov's approach to algorithms, elementary facts about lattices and similar algebraic systems, more. Philosophical and reflective as well as mathematical. Graduate-level course. 1963 edition. Exercises.

Foundations of Analysis covers a variety of issues that will interest undergraduates and first-year graduate students studying pure mathematics and philosophy. It covers the development of different number systems and how their consideration leads to specific branches of mathematics. ...

This book reports on the development of a mathematical theory of general systems, initiated ten years ago. The theory is based on a broad and ambitious program aimed at formalizing all major systems concepts and the development of an axiomatic and general theory of systems. The present book provides the foundations for, and the initial steps toward, the fulfillment of that program. The interest in the present volume is strictly in the mathematical aspects of the theory. Applications and philosophical implications will be considered elsewhere. ...

Theoretical physicists tend to discuss their theories in the language of mathematics. However, the adequate mathematical formulation may not yet be available when the physical law is first discovered. Mathematical physicists trying to develop the relevant mathematics for these theories, may obtain new insights into old mathematical structures or may even disclose entirely new structures. Gauge Theory is such a gift from physics to mathematics. This volume presents a self-contained development of a differential geometric formulation of gauge theories, in particular, the theory of Yang-Mills fields....

The author's intent in writing this book is to cover in descriptive terms a good part of the mathematics that bears upon computer programming and, in some cases, upon computer design. We are not concerned with the substantial body of mathematics relevant to the uses of the computer but restrict the discussion to those subjects that have implications to the fundamental nature of the computing process. ...