The Calculus of Computation

Prepare for Advanced Computer Science Courses. Learn how to program and think like a Computer Scientist.

A wide-ranging history of the algorithm.

Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear programming, and nonlinear optimization are closely linked. This book offers a comprehensive introduction to the whole subject and leads the reader to the frontiers of current research.

Konrad Zuse is one of the great pioneers of the computerage. He created thefirst fully automated, programcontrolled, freely programmable computer using binaryfloating-point calculation. It was operational in 1941. Hebuilt his first machines in Berlin during the Second WorldWar, with bombs falling all around, and after the war hebuilt up a company that was taken over by Siemens in 1967.Zuse was an inventor in the traditional style, full ofphantastic ideas, but also gifted with a powerful analyticalmind. Single-handedly, he developed one of the firstprogramming languages, the Plan Calculus, including featurescopied only decades later in other languages. He wrotenumerousbooks and articles and won many honors and awards.This is his autobiography, written in an engagingly livelyand pleasant style, full of anecdotes, reminiscences, andphilosophical asides. It traces his life from his childhoodin East Prussia, through tense wartime experiences and hardtimes building up his business after the war, to a ripe oldage andwell-earned celebrity.

This book provides an in-depth and accessible description of special relativity and quantum mechanics which together form the foundation of 21st century physics. A novel aspect is that symmetry is given its rightful prominence as an integral part of this foundation. The book offers not only a conceptual understanding of symmetry, but also the mathematical tools necessary for quantitative analysis. As such, it provides a valuable precursor to more focused, advanced books on special relativity or quantum mechanics.

Towards and through the vector fields, part 2 of 2. Integrals and vector calculus.

An understanding of emergent computation requires a profound revision of the most fundamental ideas. A noticeable attempt of such a rethinking is a world view in which natural systems are seen not as separate entities but as integrated parts of a unified whole. The book for the first time presents such a mathematical structure, which remarkably is based on integers as the single concept. As integers are considered to be the most fundamental entities irreducible to something simpler, this makes the mathematical structure a final theory, and thus we do not have to look for its explanation in terms of deeper concepts. The book is not only applicable to models of computation and optimization but also has scientific consequences, as it contributes to a rethinking of the most fundamental ideas about nature.

How THIS BOOK DIFFERS This book is about the calculus. What distinguishes it, however, from other books is that it uses the pocket calculator to illustrate the theory. A computation that requires hours of labor when done by hand with tables is quite inappropriate as an example or exercise in a beginning calculus course. But that same computation can become a delicate illustration of the theory when the student does it in seconds on his calculator.