Course Objectives and Outcomes
Objectives
On completion of 6.042, students will be able to explain and apply
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.
In particular, students will be able to
 reason
mathematically about basic data types and structures (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.

model and analyze computational processes
using analytic and combinatorial methods.
 apply principles of discrete
probability to calculate probabilities and expectations of simple
random processes.

work in small teams to accomplish all the objectives above.
Learning Outcomes
Students will be able to:

use logical notation to define and reason
about fundamental mathematical concepts such as sets, relations,
functions, and integers.

evaluate elementary mathematical
arguments and identify fallacious reasoning (not just fallacious
conclusions).

synthesize induction hypotheses and simple
induction proofs.
 prove elementary properties of modular
arithmetic and explain their applications in Computer Science,
for example, in cryptography and hashing algorithms.

apply graphtheoretic models of data structures
and state machines to solve problems of connectivity and constraint
satisfaction (e.g. scheduling).

apply the method of invariants and wellfounded
ordering to prove correctness and termination of processes and
state machines.

derive closedform and asymptotic
expressions from series and recurrences for growth rates of processes.

calculate numbers of possible outcomes of
elementary combinatorial processes such as permutations and combinations.
 calculate probabilities and
discrete distributions for simple combinatorial processes; calculate
expectations.

problem solve and study in a small
team with fellow students.
See also the 6.042 Curricular
Goals Map giving a dynamic graphical display connecting the class
outcomes with the outcomes of other subjects in the Course 6
curriculum.

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