Finite Difference Computing with PDEs
This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algo...
Finite Difference Computing with Exponential Decay Models
This text provides a very simple, initial introduction to the complete scientific computing pipeline: models, discretization, algorithms, programming, verification, and visualization. The pedagogical strategy is to use one case study – an ordinary differential equation describing exponential decay processes – to illustrate fundamental concepts ...
Solving PDEs in Python
This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier - Stokes equations, and systems of nonlinear advection - diffusion - reaction equations, it...
Introduction to Digital Systems Design
This book has been designed for a first course on digital design for engineering and computer science students. It offers an extensive introduction on fundamental theories, from Boolean algebra and binary arithmetic to sequential networks and finite state machines, together with the essential tools to design and simulate systems composed of a contr...
Abstract Algebra
This carefully written textbook offers a thorough introduction to abstract algebra, covering the fundamentals of groups, rings and fields. The first two chapters present preliminary topics such as properties of the integers and equivalence relations. The author then explores the first major algebraic structure, the group, progressing as far as the ...
Physical (A)Causality
This book addresses the physical phenomenon of events that seem to occur spontaneously and without any known cause. These are to be contrasted with events that happen in a (pre-)determined, predictable, lawful, and causal way. All our knowledge is based on self-reflexive theorizing, as well as on operational means of empirical perception. Some of ...
Planar Maps, Random Walks and Circle Packing
This free book focuses on the interplay between random walks on planar maps and Koebe's circle packing theorem. Further topics covered include electric networks, the He–Schramm theorem on infinite circle packings, uniform spanning trees of planar maps, local limits of finite planar maps and the almost sure recurrence of simple random walks on the...
Statistical Learning and Sequential Prediction
This free book will focus on theoretical aspects of Statistical Learning and Sequential Prediction. Until recently, these two subjects have been treated separately within the learning community. The course will follow a unified approach to analyzing learning in both scenarios. To make this happen, we shall bring together ideas from probability and ...
Structural Dynamics
The 6th edition of Structural Dynamics: Theory and Computation is the complete and comprehensive text in the field. It presents modern methods of analysis and techniques adaptable to computer programming clearly and easily. The book is ideal as a text for advanced undergraduates or graduate students taking a first course in structural dynamics. It ...
Philosophical and Mathematical Logic
This book was written to serve as an introduction to logic, with in each chapter – if applicable – special emphasis on the interplay between logic and philosophy, mathematics, language and (theoretical) computer science. The reader will not only be provided with an introduction to classical logic, but to philosophical (modal, epistemic, deontic...
Demystifying Climate Models
This book demystifies the models we use to simulate present and future climates, allowing readers to better understand how to use climate model results. In order to predict the future trajectory of the Earth's climate, climate-system simulation models are necessary. When and how do we trust climate model predictions? The book offers a framework for...
Programming for Computations - MATLAB/Octave
This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs o...
Programming for Computations - Python
This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs o...
Forecasting and Assessing Risk of Individual Electricity Peaks
The overarching aim of this book is to present self-contained theory and algorithms for investigation and prediction of electric demand peaks. A cross-section of popular demand forecasting algorithms from statistics, machine learning and mathematics is presented, followed by extreme value theory techniques with examples.In order to achieve carbon t...
Programming for Computations - Python
This book presents computer programming as a key method for solving mathematical problems. This second edition of the well-received book has been extensively revised: All code is now written in Python version 3.6 (no longer version 2.7). In addition, the two first chapters of the previous edition have been extended and split up into five new chapte...
Tensor Network Contractions
Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important a...
An Invitation to Statistics in Wasserstein Space
This open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also provides an accessible introduction to the fundamentals of this current topic, as well as an overvie...
Measure, Integration & Real Analysis
This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a v...
Linear Algebra with Applications
Linear Algebra with Applications by W. Keith Nicholson, traditionally published for many years is now being released as an open educational resource. Overall, the aim of the book is to achieve a balance among computational skills, theory, and applications of linear algebra. It is a relatively advanced introduction to the ideas and techniques of ...
Theory of Statistics
This book is directed toward students for whom mathematical statistics is or will become an important part of their lives. Obviously, such students should be able to work through the details of 'hard' proofs and derivations. In addition, students at this level should acquire, or begin acquiring, a deep appreciation for the field, including its hist...
Stability and Control of Linear Systems
This advanced textbook introduces the main concepts and advances in systems and control theory, and highlights the importance of geometric ideas in the context of possible extensions to the more recent developments in nonlinear systems theory. Although inspired by engineering applications, the content is presented within a strong theoretical framew...
Energy and the Wealth of Nations
In this updated edition of a groundbreaking text, concepts such as energy return on investment (EROI) provide powerful insights into the real balance sheets that drive our "petroleum economy." Hall and Klitgaard explore the relation between energy and the wealth explosion of the 20th century, and the interaction of internal limits to grow...
Cosmology for the Curious
This book is an introductory text for all those wishing to learn about modern views of the cosmos. Our universe originated in a great explosion – the big bang. For nearly a century cosmologists have studied the aftermath of this explosion: how the universe expanded and cooled down, and how galaxies were gradually assembled by gravity. The nature ...
Reinforcement Learning
Reinforcement learning, one of the most active research areas in artificial intelligence, is a computational approach to learning whereby an agent tries to maximize the total amount of reward it receives while interacting with a complex, uncertain environment. In Reinforcement Learning, Richard Sutton and Andrew Barto provide a clear and simple acc...
Understanding Machine Learning
The subject of this book is automated learning, or, as we will more often call it, Machine Learning (ML). That is, we wish to program computers so that they can "learn" from input available to them. Roughly speaking, learning is the process of converting experience into expertise or knowledge. The input to a learning algorithm is training...