This volume gathers contributions from theoretical, experimental and computational researchers who are working on various topics in theoretical/computational/mathematical neuroscience. The focus is on mathematical modeling, analytical and numerical topics, and statistical analysis in neuroscience with applications. The following subjects are considered: mathematical modelling in Neuroscience, analytical and numerical topics; statistical analysis in Neuroscience; Neural Networks; Theoretical Neuroscience. The book is addressed to researchers involved in mathematical models applied to neuroscience.

In recent years, Artificial Intelligence researchers have largely focused their efforts on solving specific problems, with less emphasis on 'the big picture' - automating large scale tasks which require human-level intelligence to undertake. The subject of this book, automated theory formation in mathematics, is such a large scale task. Automated theory formation requires the invention of new concepts, the calculating of examples, the making of conjectures and the proving of theorems. This book, representing four years of PhD work by Dr. Simon Colton demonstrates how theory formation can be automated. Building on over 20 years of research into constructing an automated mathematician carried out in Professor Alan Bundy's mathematical reasoning group in Edinburgh, Dr. Colton has implemented the HR system as a solution to the problem of forming theories by computer. HR uses various pieces of mathematical software, including automated theorem provers, model generators and databases, to build a theory from the bare minimum of information - the axioms of a domain. The main application of this work has been mathematical discovery, and HR has had many successes. In particular, it has invented 20 new types of number of sufficient interest to be accepted into the Encyclopaedia of Integer Sequences, a repository of over 60,000 sequences contributed by many (human) mathematicians.

Didactics of Mathematics as a Scientific Discipline describes the state of the art in a new branch of science. Starting from a general perspective on the didactics of mathematics, the 30 original contributions to the book, drawn from 10 different countries, go on to identify certain subdisciplines and suggest an overall structure or `topology' of the field. The book is divided into eight sections: (1) Preparing Mathematics for Students; (2) Teacher Education and Research on Teaching; (3) Interaction in the Classroom; (4) Technology and Mathematics Education; (5) Psychology of Mathematical Thinking; (6) Differential Didactics; (7) History and Epistemology of Mathematics and Mathematics Education; (8) Cultural Framing of Teaching and Learning Mathematics. Didactics of Mathematics as a Scientific Discipline is required reading for all researchers into the didactics of mathematics, and contains surveys and a variety of stimulating reflections which make it extremely useful for mathematics educators and teacher trainers interested in the theory of their practice. Future and practising teachers of mathematics will find much to interest them in relation to their daily work, especially as it relates to the teaching of different age groups and ability ranges. The book is also recommended to researchers in neighbouring disciplines, such as mathematics itself, general education, educational psychology and cognitive science.

Epitaxy is a very active area of theoretical research since several years. It is experimentally well-explored and technologically relevant for thin film growth. Recently powerful numerical techniques in combination with a deep understanding of the physical and chemical phenomena during the growth process offer the possibility to link atomistic effects at the surface to the macroscopic morphology of the film. The goal of this book is to summarize recent developments in this field, with emphasis on multiscale approaches and numerical methods. It covers atomistic, step-flow, and continuum models and provides a compact overview of these approaches. It also serves as an introduction into this highly active interdisciplinary field of research for applied mathematicians, theoretical physicists and computational materials scientists.

This book presents a simple and original theory of distributions, both real and vector, adapted to the study of partial differential equations. It deals with value distributions in a Neumann space, that is, in which any Cauchy suite converges, which encompasses the Banach and Frechet spaces and the same "weak" spaces. Alongside the usual operations - derivation, product, variable change, variable separation, restriction, extension and regularization - Distributions presents a new operation: weighting. This operation produces properties similar to those of convolution for distributions defined in any open space. Emphasis is placed on the extraction of convergent sub-sequences, the existence and study of primitives and the representation by gradient or by derivatives of continuous functions. Constructive methods are used to make these tools accessible to students and engineers.

This volume is based on lectures presented at the N.A.T.O. Advanced Studies Institute on Data Base Management Theory and Applications. The meeting took place in Estoril Portugal for a two week periQd in June 1981. The lecturers represented distinguished research centers in industry, gvvernment and academia. Lectures presented basic material in data base management, as well as sharing recent developments in the field. The participants were drawn from data processing groups in government, industry and academia, located in N.A.T.O. countries. All participants had a common goal of learning about the exciting new developments in the field of data base management with the potential for application to their fields of interest. In addition to formal lectures and the informal discussions among participants, which are characteristic of N.A.T.O. AS! gatherings, participants had the opportunity for hands-on experience in building application systems with a data base management system. Participants were organized into groups that designed and implemented application systems using data base technology on micro computers. The collection of papers is organized into four major sections. The first section deals with various aspects of data modeling from the conceptual and logical perspectives. These issues are crucial in the initial design of application systems.

The book outlines two separate processes for working with groups and discusses their separate applications as well as how they work together for a holistic approach to institutional transformation; it emphasizes group level processes, including academic departments, an area which currently lacks development. The text integrates across a wide range of disciplines and interdisciplinary fields, thus it brings institutional transformation concepts into conversations across many boundaries highlighting how insights from one field can address issues in another. The book is timely in topic, focusing on solutions for institutional racism and sexism and a pathway to collectively address calls for racial justice and equity by blending theory and practice into a praxis for how to implement and sustain socially just institutions; it includes outcomes documenting the positive impacts of the practices described in the text.

Ten years from now, what do you want or expect your students to remember from your course? We realized that in ten years what matters will be how students approach a problem using the tools they carry with them- common sense and common knowledge- not the particular mathematics we chose for the curriculum. Using our text, students work regularly with real data in moderately complex everyday contexts, using mathematics as a tool and common sense as a guide. The focus is on problems suggested by the news of the day and topics that matter to students, like inflation, credit card debt, and loans. We use search engines, calculators, and spreadsheet programs as tools to reduce drudgery, explore patterns, and get information. Technology is an integral part of today's world- this text helps students use it thoughtfully and wisely. This second edition contains revised chapters and additional sections, updated examples and exercises, and complete rewrites of critical material based on feedback from students and teachers who have used this text. Our focus remains the same: to help students to think carefully- and critically- about numerical information in everyday contexts.

Posthuman Community Psychology is an exploration of mainstream psychology through a critical posthumanity perspective, examining psychology’s place in the world and its relationship with marginalised people, with a focus on people with disabilities. The book argues that the history of modern psychology is underpinned by reductionism and individualism, which is embedded within the contemporary psychology that we know today despite the challenges from critical and community psychologists who seek a more empowering, inclusive, and activist psychology. The posthuman community psychology ideas that emerge in this book examine and intersect with mainstream psychology, critical and community psychologies, critical posthumanities and disability studies to propose an imaginative, reflective, and relational new psychology that represents a collection of possibilities that do not remain entrenched in older ways of thinking about humans and human connections. Richards proposes that psychology has the potential to evolve and make a powerful and profound difference for marginalised people, but a genuine desire for change from psychologists is essential for this to happen. Illustrating the important considerations needed when examining the relationship between the discipline of psychology and marginalised people, this book is fascinating reading for community psychology students and academics, aspiring professional psychologists, community workers, and policy makers.

Posthuman Community Psychology is an exploration of mainstream psychology through a critical posthumanity perspective, examining psychology’s place in the world and its relationship with marginalised people, with a focus on people with disabilities. The book argues that the history of modern psychology is underpinned by reductionism and individualism, which is embedded within the contemporary psychology that we know today despite the challenges from critical and community psychologists who seek a more empowering, inclusive, and activist psychology. The posthuman community psychology ideas that emerge in this book examine and intersect with mainstream psychology, critical and community psychologies, critical posthumanities and disability studies to propose an imaginative, reflective, and relational new psychology that represents a collection of possibilities that do not remain entrenched in older ways of thinking about humans and human connections. Richards proposes that psychology has the potential to evolve and make a powerful and profound difference for marginalised people, but a genuine desire for change from psychologists is essential for this to happen. Illustrating the important considerations needed when examining the relationship between the discipline of psychology and marginalised people, this book is fascinating reading for community psychology students and academics, aspiring professional psychologists, community workers, and policy makers.

This monograph gives the reader an up-to-date account of the fine properties of real-valued functions and measures. The unifying theme of the book is the notion of nonmeasurability, from which one gets a full understanding of the structure of the subsets of the real line and the maps between them. The material covered in this book will be of interest to a wide audience of mathematicians, particularly to those working in the realm of real analysis, general topology, and probability theory. Set theorists interested in the foundations of real analysis will find a detailed discussion about the relationship between certain properties of the real numbers and the ZFC axioms, Martin's axiom, and the continuum hypothesis.

Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. Bowever, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programmi ng profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "completely integrable systems," "chaos, synergetics and large-s.cale order," which are almost impossible to fit into the existing classifica tion schemes. They draw upon widely different sections of mathe matics."

Updated classic statistics text, with new problems and examples Probability and Statistical Inference, Third Edition helps students grasp essential concepts of statistics and its probabilistic foundations. This book focuses on the development of intuition and understanding in the subject through a wealth of examples illustrating concepts, theorems, and methods. The reader will recognize and fully understand the why and not just the how behind the introduced material. In this Third Edition, the reader will find a new chapter on Bayesian statistics, 70 new problems and an appendix with the supporting R code. This book is suitable for upper-level undergraduates or first-year graduate students studying statistics or related disciplines, such as mathematics or engineering. This Third Edition Introduces an all-new chapter on Bayesian statistics and offers thorough explanations of advanced statistics and probability topics Includes 650 problems and over 400 examples - an excellent resource for the mathematical statistics class sequence in the increasingly popular "flipped classroom" format Offers students in statistics, mathematics, engineering and related fields a user-friendly resource Provides practicing professionals valuable insight into statistical tools Probability and Statistical Inference offers a unique approach to problems that allows the reader to fully integrate the knowledge gained from the text, thus, enhancing a more complete and honest understanding of the topic.

Alexander Reznikov (1960-2003) was a brilliant and highly original mathematician. This book presents 18 articles by prominent mathematicians and is dedicated to his memory. In addition it contains an influential, so far unpublished manuscript by Reznikov of book length. The book further provides an extensive survey on Kleinian groups in higher dimensions and some articles centering on Reznikov as a person.

Modern finite element analysis has grown into a basic mathematical tool for almost every field of engineering and the applied sciences. This introductory textbook fills a gap in the literature, offering a concise, integrated presentation of methods, applications, software tools, and hands-on projects. Included are numerous exercises, problems, and Mathematica/Matlab-based programming projects. The emphasis is on interdisciplinary applications to serve a broad audience of advanced undergraduate/graduate students with different backgrounds in applied mathematics, engineering, physics/geophysics. The work may also serve as a self-study reference for researchers and practitioners seeking a quick introduction to the subject for their research.

Proven and practical strategies for success on the Math Skills section of the SAT-completely revised and updated for the latest version of the exam There are many comprehensive SAT prep books out there, but if you're looking to master specific skills and increase your score, Top 50 SAT Math Skills, Third Edition offers most effective study strategy available. The first book of its kind to present the heart of each of the 50 most important SAT concepts, this essential guide provides exercises that show you exactly how each math concept is tested on the SAT. Written by a renowned educational counselor, this book was created specifically for visual learners, with small bits of information to aid in quick, concentrated study. Within each topic, solved problems of gradually increasing difficulty help you build your problem-solving skills. Features: 50 essential skills, each presented clearly on a two-page spread, offer quick targeted review; the content was created specifically for the visual learner A pre-test designed to identify weaknesses in the critical math concepts on the SAT that students often struggle with Visually appealing, two- to four-page spreads with lessons that boost knowledge in the 50 essential skills, with step-by-step sample exercises A post-test designed to track your progress in each specific skill A full answer key with helpful explanations 2 extra tests online

• Utilizes case studies from different disciplines and sectors within engineering and other related technical areas to demonstrate how to go from data, to insight, and to decision making • Introduces various approaches to build models that exploits different algorithms • Discusses predictive models that can be built through machine learning and used to mine patterns from large datasets • Explores the augmentation of technical and mathematical materials with explanatory worked examples • Includes a glossary, lecture notes, self-assessments, and worked-out practice exercises

The theory of Memory Evolutive Systems represents a mathematical model for natural open self-organizing systems, such as biological, sociological or neural systems. In these systems, the dynamics are modulated by the cooperative and/or competitive interactions between the global system and a net of internal Centers of Regulation (CR) wich a differential access to a central heirarchical Memory.
The MES proposes a mathematical model for autonomous evolutionary systems and is based on the Category Theory of mathematics. It provides a framework to study and possibly simulate the structre of "living systems" and their dynamic behavior. MES explores what characterizes a complex evolutionary system, what distinguishes it from inanimate physical systems, its functioning and evolution in time, from its birth to its death.
The behavior of this type of system depends heavily on its former experiences, and a model representing the system over a period of time, could anticipate later behavior and perhaps even predict some evolutionary alternatives.
The role of the MES model will be two-fold: theoretical, for a comprehension of a fundamental nature and practical, for applications in biology, medicine, sociology, ecology, economy, meteorology, and other sciences.
Key Features:
*Comprehensive and comprehensible coverage of Memory Evolutive System
*Written by the developers of the Memory Evolutive Systems
*Designed to explore the common language between sciences

The aim of this book is to reflect the current cutting-edge thinking and established practices in the investigation of queueing systems and networks. This first volume includes ten chapters written by experts well-known in their areas. The book studies the analysis of queues with interdependent arrival and service times, characteristics of fluid queues, modifications of retrial queueing systems and finite-source retrial queues with random breakdowns, repairs and customers' collisions. Some recent tendencies in the asymptotic analysis include the average and diffusion approximation of Markov queueing systems and networks, the diffusion and Gaussian limits of multi-channel queueing networks with rather general input flow, and the analysis of two-time-scale nonhomogenous Markov chains using the large deviations principle. The book also analyzes transient behavior of infinite-server queueing models with a mixed arrival process, the strong stability of queueing systems and networks, and applications of fast simulation methods for solving high-dimension combinatorial problems.

-Explores the development of elementary students’ understanding of the mathematics of measure, demonstrating how measurement can serve as an anchor for supporting a deeper understanding of future mathematics learning, as well as learning in other STEM disciplines. -Describes a learning progression built on benchmarks of student learning about measure in length, angle, area, volume, and rational number, exploring related concepts, classroom experiences, and instructional practices at each stage—an approach relevant for scholars, teacher educators, and specialists in math education. -Written by two leading researchers in math and science education, who draw from decades of experience in K-5 classroom research. -Accompanied by online resources developed for practitioners, including instructional guides, examples of student thinking, and other teacher-focused materials, helping clarify how to bring concepts of measure and rational number to life in classrooms.

-Explores the development of elementary students’ understanding of the mathematics of measure, demonstrating how measurement can serve as an anchor for supporting a deeper understanding of future mathematics learning, as well as learning in other STEM disciplines. -Describes a learning progression built on benchmarks of student learning about measure in length, angle, area, volume, and rational number, exploring related concepts, classroom experiences, and instructional practices at each stage—an approach relevant for scholars, teacher educators, and specialists in math education. -Written by two leading researchers in math and science education, who draw from decades of experience in K-5 classroom research. -Accompanied by online resources developed for practitioners, including instructional guides, examples of student thinking, and other teacher-focused materials, helping clarify how to bring concepts of measure and rational number to life in classrooms.

This book engages with contemporary, and often polarizing, debates surrounding the risks of adolescent use of digital media and internet technologies. By drawing on multiple research studies, the text synthesizes current understandings of the impacts of social network use, online gaming, pornography, and phenomena, including cyberbullying, cyberstalking, and internet addiction, to develop recommendations for the effective identification of at-risk youth, as well as strategies for informed communication about online risks and opportunities. It shows how media discussion of risks to children and teenagers from new technology is highly emotive and often exaggerated, rooted in the “moral panic” surrounding new cultural practices that young people engage in, but which adults do not understand. Online risks are thus conceptualized as centering on three areas, specific to adolescence, which have undergone radical changes due to new internet technology. These include young people’s identity, the types of content that are accessed, and social relationships. The author shows how these matters stem from the potential of new technology to establish new interpersonal connections, emphasizing how it brings opportunities, as much as risks. As such, he provides a uniquely balanced discussion of potential dangers, while also emphasizing the opportunities for social, academic, and personal growth which new technologies afford young people. It will be indispensable for researchers and clinicians interested in assessing levels of online risk, as well as scholars and educators with interests in cyberpsychology, social psychology, cyber culture, social aspects of computing and media, and adolescent development.