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 o...

What does it mean to be a scientist working today; specifically, a scientist whose subject matter is human life? Scientists often overstate their claim to certainty, sorting the world into categorical distinctions that obstruct rather than clarify its complexities. In this book Daniel Nettle urges the reader to unpick such distinctions - biological...

This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discre...

Rethinking the Internet of Things was a 2014 Jolt Award Finalist, the highest honor for a programming book. And the amazing part is that there is no code in the book.
Over the next decade, most devices connected to the Internet will not be used by people in the familiar way that personal computers, tablets and smart phones are. Billions of inter...

Complexity science uses computation to explore the physical and social sciences. In Think Complexity, you'll use graphs, cellular automata, and agent-based models to study topics in physics, biology, and economics.
Whether you're an intermediate-level Python programmer or a student of computational modeling, you'll delve into exam...

This book has brought together leading investigators who work in the new arena of brain connectomics. This includes 'macro-connectome' efforts to comprehensively chart long-distance pathways and functional networks; 'micro-connectome' efforts to identify every neuron, axon, dendrite, synapse, and glial process within restricted ...

Applied Combinatorics is an open-source book for a course covering the fundamental enumeration techniques (permutations, combinations, subsets, pigeon hole principle), recursion and mathematical induction, more advanced enumeration techniques (inclusion-exclusion, generating functions, recurrence relations, Polyá theory), discrete structures (grap...

Algorithms are the lifeblood of computer science. They are the machines that proofs build and the music that programs play. Their history is as old as mathematics itself. This book is a wide-ranging, idiosyncratic treatise on the design and analysis of algorithms, covering several fundamental techniques, with an emphasis on intuition and the proble...

The Algorithms Notes for Professionals book is compiled from Stack Overflow Documentation, the content is written by the beautiful people at Stack Overflow....

This is an introductory book on algorithmic graph theory. Theory and algorithms are illustrated using the Sage open source mathematics software....

The goals of this textbook are to help students acquire the technical skills of using software and managing a database, and develop research skills of collecting data, analyzing information and presenting results. We emphasize that the need to investigate the potential and practicality of GIS technologies in a typical planning setting and evaluate ...

A unified treatment of the most important results in the study of fractional graph concepts, this volume explores the various ways in which integer-valued concepts can be modified to derive nonintegral values. It begins with the general fractional theory of hypergraphs and presents in-depth coverage of fundamental and advanced topics. Subjects incl...

Discrete Mathematics: An Open Introduction is a free, open source textbook appropriate for a first or second year undergraduate course for math majors, especially those who will go on to teach. Since Spring 2013, the book has been used as the primary textbook or a supplemental resource at more than 75 colleges and universities around the world (see...

Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways. Many real-worl...

Applied Discrete Structures, is a two semester undergraduate text in discrete mathematics, focusing on the structural properties of mathematical objects. These include matrices, functions, graphs, trees, lattices and algebraic structures. The algebraic structures that are discussed are monoids, groups, rings, fields and vector spaces.
Applied D...

This open access book explores the amazing similarity between paths taken by people and many other things in life, and its impact on the way we live, teach and learn.
Offering insights into the new scientific field of paths as part of the science of networks, it entertainingly describes the universal nature of paths in large networked structures. ...

The growth of social media over the last decade has revolutionized the way individuals interact and industries conduct business. Individuals produce data at an unprecedented rate by interacting, sharing, and consuming content through social media. Understanding and processing this new type of data to glean actionable patterns presents challenges an...

Each chapter comprises a separate study on some optimization problem giving both an introductory look into the theory the problem comes from and some new developments invented by author(s). Usually some elementary knowledge is assumed, yet all the required facts are quoted mostly in examples, remarks or theorems....

Lecture notes for the Yale Computer Science course CPSC 469/569 Randomized Algorithms. Suitable for use as a supplementary text for an introductory graduate or advanced undergraduate course on randomized algorithms. Discusses tools from probability theory, including random variables and expectations, union bound arguments, concentration bounds, app...

It is increasingly clear that the shapes of reality - whether of the natural world, or of the built environment - are in some profound sense mathematical. Therefore it would benefit students and educated adults to understand what makes mathematics itself 'tick', and to appreciate why its shapes, patterns and formulae provide us with preci...

The purpose of this book is to give you a thorough introduction to competitive programming. It is assumed that you already know the basics of programming, but no previous background in competitive programming is needed.
The book is especially intended for students who want to learn algorithms and possibly participate in the International Olympi...

Geometry with an Introduction to Cosmic Topology approaches geometry through the lens of questions that have ignited the imagination of stargazers since antiquity. What is the shape of the universe? Does the universe have an edge? Is it infinitely big?
This text develops non-Euclidean geometry and geometry on surfaces at a level appropriate for ...

Contemporary Mathematics is designed to meet the scope and sequence requirements for a liberal arts mathematics course. This resource provides stand-alone sections with a focus on showing relevance in the features as well as the examples, exercises, and exposition. Contemporary Mathematics integrates technology applications, projects, and highlight...