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extra-study-topics

# extra-study-topics - Extra Study Topics ENGINEER 1D04 Dr...

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Extra Study Topics ENGINEER 1D04 Dr. William M. Farmer and Dr. Spencer Smith McMaster University, Fall 2010 Revised: 2 November 2010 Topics for extra study will be presented in the lectures. These topics are intended for students who want to broaden their background in computing. This document briefly describes each topic. We hope these descriptions will whet the reader’s appetite. Further information about these topics is easily found on the Web. Extra Study 1: The use of types in computing and logic. The notion of a data type is a fundamental idea in computing, particularly in programming languages. Almost all programming languages employ a type system of some kind. However, type systems vary widely from one programming language to another. The purpose of a type system is to catch type errors. A major part of learning a programming language is usually learning how its type system works. Types are also a fundamental idea in logic. Types are used in many logics and most software specification languages. A simple logic with types is many-sort first-order logic . A more expressive logic with types is simple type theory , which is often viewed as an alternative reasoning system to the set theory mathematicians use. Extra Study 2: The text editors Emacs and Vi. Emacs and Vi are two families of sophisticated text editors that were de- veloped in the unix world in the 1970s. Both are very powerful but use pre-window technology. They are found on essentially all unix-based sys- tems (including Macs and Linux boxes). Most Emacs users are strongly committed to never give up using Emacs and to never use Vi, while most Vi users are just as committed to never give up using Vi and to never use Emacs. Extra Study 3: The surreal numbers. The surreal numbers is a number system that includes the real numbers as well as infinite and infinitesimal numbers and that satisfies the same algebraic properties as the real numbers. The surreals were first defined by the British mathematicians John Horton Conway (1937– ). Their definition is surprisingly simple—but that doesn’t mean it is easy to understand. In his 1974 little novel Surreal Numbers: How Two Ex-Students Turned on 1

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to Pure Mathematics and Found Total Happiness , the American computer scientist Donald Knuth (1938– ) presented Conway’s numbers and named them surreal numbers . The name stuck, for these numbers really do seem “surreal”.
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extra-study-topics - Extra Study Topics ENGINEER 1D04 Dr...

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