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Mathematics 2 - Discrete Mathematics (Spring 2010 ) (Forår 2010)

Kursuskode : IDISM2-U1
ECTS Point : 7,5 Status : Obligatorisk
Revideret : 22/01 2010 Oprettet : 13/01 2009
Placering : 2. semester Timer pr. uge : 4
Længde : 1 semester Undervisningssprog : Dansk hvis der ikke er engelsksprogede studerende tilstede
Målsætning : The objectives of Discrete Mathematics are: The introduction of the mathematics
needed for analysis and design of discrete systems, including the application of
programming languages for computer systems.
Having completed the Discrete Mathematics the student is able to carry out the
following:
Expressions and sets:
Define a set; define a logic expression; negate a logic expression; combine logic
expressions; construct a truth table for a logic expression; apply reduction rules
for logic expressions.
Relations and functions:
Define a product set; define and apply equivalence relations; construct and apply
functions.
Natural numbers and induction:
Define the natural numbers; apply the principle of induction to verify a selection
of properties of natural numbers.
Division and factorizing:
Define a prime number and use Euclid´s algorithm for factorizing an integer.
Regular languages:
Define a language from the elements of a set; define a regular language; form
strings from a regular language; construct examples on regular languages.
Finite state machines:
Define a finite state machine as a 6-tuple; describe simple finite state machines
by tables and graphs; pattern recognition by finite state machines; minimizing
the number of states in a finite state machine; construct a finite state machine for
a given application.
Data exploration and pattern recognition:
Define a data clustering method and exemplify the application of the method in a
pattern recognition problem of relevance to the understanding of basic principles
in proactive computer systems.
Hovedindhold : Discrete Mathematics Part:
Expressions and sets; reduction rules for logic expressions; relations and functions;
define and apply equivalence relations; construct and apply functions;
natural numbers; apply induction to verify properties of natural numbers; define
a prime number and use Euclid´s algorithm for factorizing an integer; define a
language from the elements of a set; define a regular language; form strings from
a regular language; construct examples on regular languages; define a finite state
machine as a 6-tuble; describe simple finite state machines by tables and graphs;
pattern recognition by finite state machines; minimizing the number of states in a
finite state machine; construct a finite state machine for a given application;
apply a simple clustering method for exploration of data; apply the clustering in
a simple pattern recognition system.
Undervisningsform : The teaching in Discrete Mathematics is a combination of sessions with lectures
and students solving problems, either manually or by using Matlab.
Furthermore a selection of problems must be solved and handed in during the
course.
Krævede forudsætninger : Documented knowledge corresponding to Mathematics 1 and Programming 1.
Anbefalede forudsætninger : -
Relationer : -
Prøveform : Mundtlig evaluering på grundlag af kursusopgaver
Censur : Intern
Bedømmelse : 7-trinsskala
Bemærkninger : 7 step scale
3 steps of this marking scale are described as follows:
12 is given for the excellent presentation, which completely fulfills the course
goals, with no or very few errors of marginal importance.
7 is given for the average presentation, which fulfills the course goals, with some
errors in the presentation.
02 is given for the minimum acceptable presentation, which fulfills the course
goals.
Undervisningsmateriale : W W Chen, “Discrete Mathematics” web version 2008
www.maths.mq.edu.au/~wchen/lndmfolder/lndm.html
and supplementary material.
Ansvarlig underviser : John Aasted Sørensen , jaas@dtu.dk