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Mathematics 2 - Discrete Mathematics (Fall 2011) |
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| Course code : | IDISM2-U1 | ||
| ECTS Credits : | 5 | Status : | Compulsory |
| Revised : | 13/07 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 (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able to accomplish the fol¬lowing: - Understand and apply formal representations in discrete mathema¬tics. - Understand and apply formal representations in pro¬blems within discrete mathematics. - Understand methods for solving problems in discrete mathe¬matics. - Apply methods for solving problems in discrete mathematics. Having completed this, 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. Apply these concepts to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties of natural numbers. Apply these concepts to new problems. Division, factorizing, coding and cryptography: Define a prime number and apply Euclid´s algorithm for factorizing an integer. Basic number theory, Hamming codes and public key cryptography. 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. Apply these concepts to new problems. Finite state machines: 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 these concepts to new problems. |
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| Principal Content : | Discrete Mathematics (IDISM2): Expressions and sets; reduction rules for logic expressions; relations and func¬tions; define and apply equivalence relations; construct and apply functions; natural numbers; apply induction to verify properties of natural numbers; defi¬ne a prime number and use Euclid´s algorithm for factorizing an integer; Hamming codes; public key cryptography; 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-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. . |
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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 projects 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 : | Not applied. | ||
| Relations : | Not applied. | ||
| Type of examination : | Look under remarks | ||
| External examiner : | External | ||
| Marking : | 7 step scale | ||
| Remarks : | The oral examination is carried out by letting each student select by random one of the projects solved during the course. This project and elements from the course curriculum are then presented and discussed during the examination. 7 point grading scale. Three of the grading scale markings are described below. 12 is given for the excellent performance, with no or very few errors of marginal importance, which completely fulfills the additional course goals of applying me¬th¬o¬ds for solving problems in discrete mathematics. 7 is given for the average performance, with some errors, which fulfills the addi¬tional course goals of understanding methods for solving problems in discrete ma¬the¬matics. 02 is given for the minimum acceptable performance which fulfills the course goals of understanding and applying formal representations in discrete mathema¬tics and understanding and applying formal representations in pro¬blems within discrete mathematics. |
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| Teaching material : | W W Chen, “Discrete Mathematics” web version 2008 rutherglen.ics.mq.edu.au/wchen/ln.html and supplementary material handed out during the course. |
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| Responsible teacher : | John Aasted Sørensen
, jaas@dtu.dk |
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