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  <title>6.042 Course Objectives and Outcomes, Spring 2004</title>
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  <a href="">6.042/18.062J<br>
   Spring 2007</a>
  

  
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<h1>Course Objectives and Outcomes</h1>

<p>

<h2>Objectives</h2>


<p> On completion of 6.042, students will be able to explain and apply
the basic methods of discrete (noncontinuous) mathematics in Computer
Science.  They will be able to use these methods in subsequent courses
in the design and analysis of algorithms, computability theory,
software engineering, and computer systems.

<p>
In particular, students will be able to

<ol type="1">
<li><a name="Basic Discrete Mathematics Concepts"> </a><b>reason
mathematically about basic data types and structures</b> (such as numbers, sets,
graphs, and trees) used in computer algorithms and systems; distinguish
rigorous definitions and conclusions from merely plausible ones;
synthesize elementary proofs, especially proofs by induction.<p></li>

<li>
<a name="Computational Processes">
</a> 
<b>model and analyze computational processes</b>
using analytic and combinatorial methods.<p></li>

<li> <a name="Discrete Probability"> </a> <b>apply principles of discrete
probability</b> to calculate probabilities and expectations of simple
random processes.<p></li>

<li> 
<a name="Teams Objective">
</a> 
<b>work in small teams</b> to accomplish all the objectives above.<p></li>
</ol>

<p>

<h2>Learning Outcomes</h2>

<p>

<p>
Students will be able to:

<ol type="1">
<li> <a name="basic">
</a> use <b>logical notation</b> to define and reason
about <b>fundamental mathematical concepts</b> such as sets, relations,
functions, and integers.<p></li>

<li> <a name="soundness">
</a> <b>evaluate elementary mathematical
arguments</b> and identify fallacious <em>reasoning</em> (not just fallacious
conclusions).<p></li>

<li> <a name="proofs">
</a> <b>synthesize induction hypotheses and simple
induction proofs</b>.<p></li>

<li> <a name="arithmetic"> </a> prove <b>elementary properties of modular
arithmetic</b> and explain their applications in Computer Science,
for example, in cryptography and hashing algorithms.<p></li>

<li> <a name="graphs">
</a> <b>apply graph theory models</b> of data structures
and state machines to solve problems of connectivity and constraint
satisfaction, for example, scheduling.<p></li>

<li> <a name="invariants">
</a> apply the method of invariants and well-founded
ordering to <b>prove correctness and termination of processes</b> and
state machines.<p></li>

<li> <a name="closed-forms">
</a> <b>derive closed-form and asymptotic
expressions</b> from series and recurrences for growth rates of processes.<p></li>

<li> <a name="counting">
</a> <b>calculate numbers of possible outcomes</b> of
elementary combinatorial processes such as permutations and combinations.<p></li>

<li> <a name="probability"> </a> <b>calculate probabilities</b> and
discrete distributions for simple combinatorial processes; calculate
expectations.<p></li>


<li> <a name="teams outcome">
</a> problem solve and <b>study in a small
team</b> with fellow students.<p></li>
</ol>

<p class="timestamp">
This document last modified Wednesday, 29-Mar-2006 11:25:50 EST
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