\section{Course Overview}


\subsection{Course Goals and Content}

This course is actually a combination of three ``miniature'' courses:
thinking (9 lectures), counting (8), and gambling (9).  We aim to
cover:

\begin{description}
\item[Basic discrete math concepts.]
  Basic data types and structures used in programming and in reasoning
  about computer systems\.
  Numbers, Booleans, strings; sets, functions, relations; digraphs, graphs,
  trees; state machines\.
  Their properties.

\item[Proofs.]
  How to do them, how to read them, how to recognize correct/incorrect ones\.
  Reasoning about propositions, about predicates (with quantifiers)\.
  Common proof strategies:  Direct proof, proof by contradiction, by cases\.
  Induction (very important in this course and elsewhere in CS)\.  We'll
  be working on this topic throughout the term.

\item[Mathematical foundations for programming.]
  Basic concepts and methods underlying formal specification and verification
  of software systems\.
  Developing models for programs and their required behavior\.
  Proving that a program model satisfies its correctness requirements (6.170).

\item[Analytic Tools.]  The quantitative part of discrete math\.
  Methods for handling series, sums, recurrences, asymptotic analysis,
  counting\.  More than calculus, The kind of math that tends to arise
  in computer science problems\.
  Much used in analysis of algorithms (6.046).

\item[Discrete probability.]  
  How to analyze random events\.
  Probability provides good ways of modeling the unpredictability of the
  real world\.
  Critical in the study of real computer systems (6.033).
\end{description}

Overall, we want you to learn how to use mathematics to help you think
about concepts in computer science:
\begin{itemize}
\item Define abstract models for computer science objects like programs,
  computers, networks...
\item Think about these models carefully, correctly.
\item Use the conclusions to help understand the real-world objects.
\end{itemize}

\forlecture{

\subsection{Administrivia}

  {\large \bf SIGN UP} {\tt http://theory.lcs.mit.edu/classes/6.042/}

  \noindent
  See Handout 1\.
  Faculty, TAs, secy
  Prerequisites: First year calculus\.
  Books\.
  Handouts\.
  Lectures, tutorials\.
  Exams\.
  Problem sets\.
  Collaboration policy\.
  Grading
  }
