Program Proofs

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 a practical engineering focus throughout, emphasizing techniques that will help users to build, understand, and maintain large Coq developments and minimize the cost of code change over time.

Learn the theoretical concepts of linear programming to solve optimization tasks.

This must-read text presents the pioneering work of the late Professor Jacob (Jack) T. Schwartz on computational logic and set theory and its application to proof verification techniques, culminating in the ÆtnaNova system, a prototype computer program designed to verify the correctness of mathematical proofs presented in the language of set theory.

BreezeBrowser Pro is the powerful and versatile browser based tool for viewing and manipulating digital images. Do you need a fast and simple way to browse and select from your growing collection of digital photos or to create sophisticated web page image galleries without needing to learn HTML? Perhaps you need to rotate, crop and save your JPEG’s without any loss of quality or work with images in their RAW format.

In this monograph, leading researchers in the world of numerical analysis, partial differential equations, and hard computational problems study the properties of solutions of the Navier–Stokes partial differential equations on (x, y, z, t) ∈ ℝ3 × [0, T]. Initially converting the PDE to a system of integral equations, the authors then describe spaces A of analytic functions that house solutions of this equation, and show that these spaces of analytic functions are dense in the spaces S of rapidly decreasing and infinitely differentiable functions.

BreezeBrowser Pro is the powerful and versatile browser based tool for viewing and manipulating digital images. Do you need a fast and simple way to browse and select from your growing collection of digital photos or to create sophisticated web page image galleries without needing to learn HTML? Perhaps you need to rotate, crop and save your JPEG’s without any loss of quality or work with images in their RAW format.