Logic, Mathematics, and Computer Science - Modern Foundations with Practical Applications.pdf

Logic, Mathematics, and Computer Science - Modern Foundations with Practical Applications PDF

Yves Nievergelt

This text for the first or second year undergraduate in mathematics, logic, computer science, or social sciences, introduces the reader to logic, proofs, sets, and number theory. It also serves as an excellent independent study reference and resource for instructors. Adapted from Foundations of Logic and Mathematics : Applications to Science and Cryptography 2002 Birkhäuser, this second edition provides a modern introduction to the foundations of logic, mathematics, and computers science, developing the theory that demonstrates construction of all mathematics and theoretical computer science from logic and set theory. The focus is on foundations, with specific statements of all the associated axioms and rules of logic and set theory, and provides complete details and derivations of formal proofs. Copious references to literature that document historical development is also provided. Answers are found to many questions that usually remain unanswered : Why is the truth table for logical implication so unintuitive ? Why are there no recipes to design proofs ? Where do these numerous mathematical rules come from ? What issues in logic, mathematics, and computer science still remain unresolved ? And the perennial question : In what ways are we going to use this material ? Additionally, the selection of topics presented reflects many major accomplishments from the twentieth century and includes applications in game theory and Nashs equilibrium, Gale and Shapleÿ s match making algorithms, Arrows Impossibility Theorem in voting, to name a few.

Computer Science (CS) 1 COMPUTER SCIENCE (CS) CS 100A. Problem-solving Lab for CS106A. 1 Unit. Computer Vision: Foundations and Applications. 3-4 Units. Robots that can navigate space and perform duties, search engines that can index billions of images and videos, algorithms that can diagnose medical images for diseases, or smart cars that can see and drive safely: Lying in the heart of Computational logic: its origins and applications ...

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Logic, Mathematics, and Computer Science - Modern Foundations with Practical Applications.pdf


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