IT-Universitetet i København
 
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Kursusbeskrivelse
Kursusnavn (dansk):Grundlæggende strukturer for beregninger - Diskret Matematik 
Kursusnavn (engelsk):Foundations of Computing - Discrete Mathematics 
Semester:Forår 2011 
Udbydes under:cand.it., softwareudvikling og -teknologi (sdt) 
Omfang i ECTS:7,50 
Kursussprog:Engelsk 
Kursushjemmeside:https://learnit.itu.dk 
Min. antal deltagere:12 
Forventet antal deltagere:25 
Maks. antal deltagere:50 
Formelle forudsætninger:Basic ability to program in some imperative programming language (Java, Python, C/C++/C#, etc.), using conditions, loops, arrays, methods/procedures/functions, and simple recursion. This may be obtained by following Object Oriented Programming - Introduction, or Introductory Programming or similar courses.
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Information about the course of study
This course is mandatory for students who are enrolled on This course is mandatory for students who are enrolled on on the Master of Science in IT, study programme Software Development and Technology, Development Technology track. See a description of the track here: Kandidat Software Development Technology
 
Læringsmål:After the course the student should be able to:

* Recognize if a concept is described by a formal definition, and recognize if a simple formal proof is correct, including those that use recursion and induction

* Express simple concepts in the language of mathematics

* Bound the growth rate of functions using asympotic analysis

* Solve recurrence relations, including divide-and-conquer relations

* Enumerate combinatorial structures, assess probabilities of events,
and compute expectations of random variables

* Model phenomena using discrete structures such as relations, graphs, logic, or finite-state machines
 
Fagligt indhold:The course is a standard introduction to discrete mathematics, but with focus on applications in the information technologies. In particular, the course develops the necessary terminology and conceptual tools needed for later courses such as Advanced Models and Programs, Algorithm Design, Database Tuning, Mobile and Distributed Systems and Efficient AI Programming). This includes:

* the analysis of algorithms, including basic randomised algorithms,

* models of computation, such as logic and automata

* databases, such as relations and functions

* models of networks (technological as well as social), such as graphs

The course emphasises the applicability of these by describing their applications, including a research article. Applications are expected to vary, but can include Google's PageRank algorithm, natural language processing, Bayesian spam filters, models for social networks, or data mining.

Central terms and concepts: Logic, sets and sequences, functions, sums, induction and recursion, permutations and combinations, discrete probability, recurrence relations, relations, graphs, trees, boolean Algebra, finite state machines, grammars.  
Læringsaktiviteter:14 ugers undervisning bestående af forelæsninger og øvelser

Around 14 lectures with exercise classes. Twice a week for the first 5 weeks. A larger project corresponding to half the course. All material will be made available on the Web.
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See the schedule here:
link to the time table
The schedule will be available shortly before the beginning of the term.
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NB!! Course restriction I!!
Please note that there is a course restriction between this course and the SDT course Modelling and Design.
If you have already taken Modeling and Design you need to register for the course Foundations of Computing - Algorithms and Data Structures.  

Eksamensform og -beskrivelse:X. experimental examination form (7-scale; external exam), 7-trins-skala, Ekstern censur

 

Litteratur udover forskningsartikler:Kenneth Rosen, Discrete Mathematics and Its Applications, 6/e, McGraw Hill, ISBN: 007288008  
 
Afholdelse (tid og sted)
Kurset afholdes på følgende tid og sted:
UgedagTidspunktForelæsning/ØvelserStedLokale
Mandag 12.00-14.00 Forelæsning ITU 4A16
Mandag 14.00-16.00 Øvelser ITU 2A52, 4A58
Torsdag 10.00-12.00 Forelæsning ITU 2A12
Torsdag 12.00-14.00 Øvelser ITU 2A52, 2A54

Eksamen afholdes på følgende tid og sted:
EksamensdatoTidspunktEksamenstypeStedLokale
2011-06-06 09:00-11:30 (sammen med Algor. & DS. til 13:30) Skriftlig eksamen ITU 4A14 og 4A16
2011-08-23 Re-exam - Please contact the course manager Skriftlig eksamen ITU 2A18 - ORAL EXAM
2011-08-23 Preparation Room Skriftlig eksamen ITU 2A03