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Mathematical thinking provides a clear, crisp way of defining problems. Our whole technology is based on it. What is less appreciated is that mathematical thinking can also be applied to problems in the social and behavioral sciences. This book illustrates how mathematics can be used to understand human and animal behavior, using examples in psychology, sociology, economics, ecology, and even marriage counseling.
This book illustrates how mathematics can be used to understand human and animal behavior, using examples in psychology, sociology, economics, ecology, and even marriage counseling. It is intended as an introduction to the use of mathematical thinking in the social and behavioral sciences.
Using examples from finance and modern warfare to the flocking of birds and the swarming of bacteria, the collected research in this volume demonstrates the common methodological approaches and tools for modeling and simulating collective behavior. The topics presented point toward new and challenging frontiers of applied mathematics, making the volume a useful reference text for applied mathematicians, physicists, biologists, and economists involved in the modeling of socio-economic systems.
Using the behavioural approach to mathematical modelling, this book views a system as a dynamical relation between manifest and latent variables. The emphasis is on dynamical systems that are represented by systems of linear constant coefficients. The first part analyses the structure of the set of trajectories generated by such dynamical systems, and derives the conditions for two systems of differential equations to be equivalent in the sense that they define the same behaviour. In addition the memory structure of the system is analysed through state space models. The second part of the book is devoted to a number of important system properties, notably controllability, observability, and stability. In the third part, control problems are considered, in particular stabilisation and pole placement questions. Suitable for advanced undergraduate or beginning graduate students in mathematics and engineering, this text contains numerous exercises, including simulation problems, and examples, notably of mechanical systems and electrical circuits.
“Tell the administration what they want to hear, then do what is best for your students.” That’s advice Barry Garelick tries to follow in the process of becoming a fully credentialed teacher which entails being monitored by two mentors. As the Mark Twain of education writing, Garelick presents this collection of essays which chronicle his experiences at two schools, teaching math. With essays such as, “Not Making Sense, and a Conversation I Never Had; “Math Talk”, Stalin’s Hemorrhoids and Murder of Crows”, Garelick gives the reader a verité-style glimpse into the daily routines of math teaching and exposes a lot of the nonsense that teachers are advised to follow, and which they feel guilty about when they don’t.
The aim of the book is to present side-by-side representative and cutting-edge samples of work in mathematical psychology and the analytic philosophy with prominent use of mathematical formalisms.
Behavior Analysis with Machine Learning Using R introduces machine learning and deep learning concepts and algorithms applied to a diverse set of behavior analysis problems. It focuses on the practical aspects of solving such problems based on data collected from sensors or stored in electronic records. The included examples demonstrate how to perform common data analysis tasks such as: data exploration, visualization, preprocessing, data representation, model training and evaluation. All of this, using the R programming language and real-life behavioral data. Even though the examples focus on behavior analysis tasks, the covered underlying concepts and methods can be applied in any other domain. No prior knowledge in machine learning is assumed. Basic experience with R and basic knowledge in statistics and high school level mathematics are beneficial. Features: Build supervised machine learning models to predict indoor locations based on WiFi signals, recognize physical activities from smartphone sensors and 3D skeleton data, detect hand gestures from accelerometer signals, and so on. Program your own ensemble learning methods and use Multi-View Stacking to fuse signals from heterogeneous data sources. Use unsupervised learning algorithms to discover criminal behavioral patterns. Build deep learning neural networks with TensorFlow and Keras to classify muscle activity from electromyography signals and Convolutional Neural Networks to detect smiles in images. Evaluate the performance of your models in traditional and multi-user settings. Build anomaly detection models such as Isolation Forests and autoencoders to detect abnormal fish behaviors. This book is intended for undergraduate/graduate students and researchers from ubiquitous computing, behavioral ecology, psychology, e-health, and other disciplines who want to learn the basics of machine learning and deep learning and for the more experienced individuals who want to apply machine learning to analyze behavioral data.
Shows instructors what mathematics is used at the undergraduate level in various parts of economics. Separate sections provide students with opportunities to apply their mathematics in relevant economics contexts. Brings together many different mathematics applications to such varied economics topics.
A comprehensive introduction to the mathematical foundations of movement and actuation that apply equally to animals and machines. This textbook offers a computational framework for the sensorimotor stage of development as applied to robotics. Much work in developmental robotics is based on ad hoc examples, without a full computational basis. This book's comprehensive and complete treatment fills the gap, drawing on the principal mechanisms of development in the first year of life to introduce what is essentially an operating system for developing robots. The goal is to apply principles of development to robot systems that not only achieve new levels of performance but also provide evidence for scientific theories of human development.
This book is the second edition of Behavioral Decision Theory, published in 2014. The main approach and structure of this book have been retained in the new edition. However, this second edition provides a fresh overview of the idea of behavioral decision theory and related research findings such as theoretical and empirical discoveries of preference formation, time discounting, social interaction, and social decision making. The book covers a wide range from classical to relatively recent major studies concerning behavioral decision theory, which, in brief, is a general term for descriptive theories to explain the psychological knowledge related to people’s decision-making behavior. It is called a theory but is actually a combination of various psychological theories, for which no axiomatic systems—such as those associated with the utility theory widely used in economics—have been established. The utility theory is often limited to qualitative knowledge; however, as the studies of Nobel laureates H. A. Simon, D. Kahneman, and R. Thaler have suggested, the psychological methodology and knowledge of behavioral decision theory have been applied widely in such fields as economics, business administration, and engineering and are expected to become even more useful in the future. Research into people’s decision making represents an important part in those fields, various aspects of which overlap with the scope of behavioral decision theory. This theory is closely related to behavioral economics and behavioral finance, which have come into greater use in recent years. This book will appeal especially to graduate students, advanced undergraduate students, and researchers who are interested in decision-making phenomena.