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Chaitin, the inventor of algorithmic information theory, presents in this book the strongest possible version of Gdel's incompleteness theorem, using an information theoretic approach based on the size of computer programs. One half of the book is concerned with studying the halting probability of a universal computer if its program is chosen by tossing a coin. The other half is concerned with encoding the halting probability as an algebraic equation in integers, a so-called exponential diophantine equation....

Advanced Data Structures presents a comprehensive look at the ideas, analysis, and implementation details of data structures as a specialized topic in applied algorithms. Data structures are how data is stored within a computer, and how one can go about searching for data within. This text examines efficient ways to search and update sets of numbers, intervals, or strings by various data structures, such as search trees, structures for sets of intervals or piece-wise constant functions, orthogonal range search structures, heaps, union-find structures, dynamization and persistence of structures, structures for strings, and hash tables. This is the first volume to show data structures as a crucial algorithmic topic, rather than relegating them as trivi...

This introduction to 3D computer graphics emphasizes fundamentals and the mathematics underlying computer graphics, while also covering programming techniques using OpenGL, a platform-independent graphics programming environment. The minimal prerequisites make it suitable for self-study or for use as an advanced undergraduate or introductory graduate text as the author leads step-by-step from the basics of transformations to advanced topics such as animations and kinematics. Accompanying software, including source code for a ray tracing software package, is available freely from the book's web site....