The technology of mechanized program verification can play a supporting role in many kinds of research projects in computer science, and related tools for formal proof-checking are seeing increasing adoption in mathematics and engineering. This book provides an introduction to the Coq software for writing and checking mathematical proofs. It takes ...
This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability...
In problem solving, as in street fighting, rules are for fools: do whatever works - don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only...
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...
This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its overall importance and use? It provides overviews of critical mathematics education, and the most relevant mode...
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...
This open access textbook takes the reader step-by-step through the concepts of mechanics in a clear and detailed manner. Mechanics is considered to be the core of physics, where a deep understanding of the concepts is essential in understanding all branches of physics. Many proofs and examples are included to help the reader grasp the fundamentals...
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 ...
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 ...
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, includin...
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...
Cryptography is an indispensable tool used to protect information in computing systems. It is used everywhere and by billions of people worldwide on a daily basis. It is used to protect data at rest and data in motion. Cryptographic systems are an integral part of standard protocols, most notably the Transport Layer Security (TLS) protocol, making ...
SAT/SMT solvers can be viewed as solvers of huge systems of equations. The difference is that SMT solvers takes systems in arbitrary format, while SAT solvers are limited to boolean equations in CNF 1 form. A lot of real world problems can be represented as problems of solving system of equations....
This collection of essays from world-renowned scholar Hans Walter Gabler contains writings from a decade and a half of retirement spent exploring textual criticism, genetic criticism, and literary criticism. In these sixteen stimulating contributions, he develops theories of textual criticism and editing that are inflected by our advance into the d...
This open book features a selection of articles written by Erich Ch. Wittmann between 1984 to 2019, which shows how the "design science conception" has been continuously developed over a number of decades. The articles not only describe this conception in general terms, but also demonstrate various substantial learning environments that s...
In this open book, our goal is to study the fundamental concepts in programming languages, as opposed to learning a range of specific languages. Languages are easy to learn, it is the concepts behind them that are difficult. The basic features we study in turn include higher-order functions, data structures in the form of records and variants, muta...
The purpose of the 3rd edition of this book is to give a sound and self-contained (in the sense that the necessary probability theory is included) introduction to classical or mainstream statistical theory. It is not a statistical-methods-cookbook, nor a compendium of statistical theories, nor is it a mathematics book. The book is intended to be a ...
A new edition of a graduate-level machine learning textbook that focuses on the analysis and theory of algorithms.
This book is a general introduction to machine learning that can serve as a textbook for graduate students and a reference for researchers. It covers fundamental modern topics in machine learning while providing the theoretical basi...
This book is a comprehensive, formal treatment of anonymous point collection. The proposed definition does not only provide a strong notion of security and privacy, but also covers features which are important for practical use. An efficient realization is presented and proven to fulfill the proposed definition. The resulting building block is the ...