Artificial Intelligence Engines. A Tutorial Introduction to the Mathematics of Deep Learning

James V Stone

This book is a comprehensive guide to the mathematics behind artificial intelligence engines, taking readers from foundational concepts to advanced applications. It begins with an introduction to artificial neural networks, exploring topics like perceptrons, linear associative networks, and gradient descent. Practical examples accompany each chapter, making complex mathematical principles accessible, even for those with limited prior knowledge.The book's detailed structure covers key algorithms like backpropagation, Hopfield networks, and Boltzmann machines, advancing to deep restricted Boltzmann machines, variational autoencoders, and convolutional neural networks. Modern topics such as generative adversarial networks, reinforcement learning, and capsule networks are explored in depth. Each section connects theory to real-world AI applications, helping readers understand how these techniques are used in practice.Ideal for students, researchers, and AI enthusiasts, the book balances theoretical depth with practical insights. Basic mathematical knowledge or foundation is recommended, allowing readers to fully engage with the content. This book serves as an accessible yet thorough resource for anyone eager to dive deeper into artificial intelligence and machine learning.

Information Theory. A Tutorial Introduction to the Principles and Applications of Information Theory

James V Stone

This book offers a comprehensive journey through the fascinating world of information theory, beginning with the fundamental question: what is information? Early chapters introduce key concepts like entropy, binary representation, and data compression, providing a clear and accessible foundation. Readers explore Shannon's source coding theorem and practical tools like Huffman coding to understand how information is quantified and optimized.Building on these basics, the book delves into advanced topics such as the noisy channel coding theorem, mutual information, and error correction techniques. It examines entropy in continuous systems, channel capacity, and rate-distortion theory, making complex ideas accessible through real-world examples. Connections between information and thermodynamics are also explored, including Maxwell’s Demon, the Landauer Limit, and the second law of thermodynamics.The final chapters tie information theory to biology and artificial intelligence, investigating its role in evolution, the human genome, and brain computation. With practical examples throughout, this book balances theoretical depth with hands-on learning, making it an essential resource for mastering information theory. A basic mathematical foundation will be beneficial but is not required to engage with the material.

Linear Regression With Python. A Tutorial Introduction to the Mathematics of Regression Analysis

James V Stone

This book offers a detailed yet approachable introduction to linear regression, blending mathematical theory with Python-based practical applications. Beginning with fundamentals, it explains the best-fitting line, regression and causation, and statistical measures like variance, correlation, and the coefficient of determination. Clear examples and Python code ensure readers can connect theory to implementation.As the journey continues, readers explore statistical significance through concepts like t-tests, z-tests, and p-values, understanding how to assess slopes, intercepts, and overall model fit. Advanced chapters cover multivariate regression, introducing matrix formulations, the best-fitting plane, and methods to handle multiple variables. Topics such as Bayesian regression, nonlinear models, and weighted regression are explored in depth, with step-by-step coding guides for hands-on practice.The final sections tie together these techniques with maximum likelihood estimation and practical summaries. Appendices provide resources such as matrix tutorials, key equations, and mathematical symbols. Designed for both beginners and professionals, this book ensures a structured learning experience. Basic mathematical knowledge or foundation is recommended.