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
manysort firstorder 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
prewindow technology.
They are found on essentially all unixbased 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 ExStudents 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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 Spring '08
 DONE
 Computer Science, Logic, Boolean Algebra, Type system, extra study

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