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Mathematics 2 - Discrete Mathematics (Spring 2011) |
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| Course code : | IDISM2-U1 | ||
| ECTS Credits : | 5 | Status : | Compulsory |
| Revised : | 12/01 2011 | Written : | 13/01 2009 |
| Placement : | 2. semester | Hours per week : | 4 |
| Length : | 1 semester | Teaching Language : | Danish if no English students are present |
| Objective : | 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. |
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| Principal Content : | 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. |
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| Teaching method : | 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. |
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| Required prequisites : | Documented knowledge corresponding to Mathematics 1 and Programming 1. | ||
| Recommended prerequisites : | - | ||
| Relations : | - | ||
| Type of examination : | Oral examination based on assignments | ||
| External examiner : | Internal | ||
| Marking : | 7 step scale | ||
| Remarks : | 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. |
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| Teaching material : | W W Chen, “Discrete Mathematics” web version 2008 www.maths.mq.edu.au/~wchen/lndmfolder/lndm.html and supplementary material. |
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| Responsible teacher : | John Aasted Sørensen
, jaas@dtu.dk |
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