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| MATH0063-1 | Discrete mathematics I
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| Duration : | 25h Th, 15h Pr |
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| Lecturer : | Pierre Mathonet |
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Language(s) of instruction :
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| French language |
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Organisation and examination :
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| Teaching in the second semester |
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Course contents :
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| This course is an introduction to discrete mathematics.
Various topics of this field of mathematics could be introduced in a first-year lecture series.
I chose some of these topics because they are interesting on their own, but also because they will allow us to review and deepen some of the concepts introduced in algebra (matrix calculus, polynomials, finite rings, permutations...), geometry (vector and affine spaces, inner products...), analysis (differential equations), or statistics.
More precisely, we will deal with the following topics (among others).
We will study the theory of Boolean and pseudo-Boolean functions and see how they provide a natural framework for the theory of cooperative games, and if time permits, for the theory of coherent systems.
We will introduce some elements of cryptography (the theory of ciphers), starting from the most ancient and simple cryptosystems and finishing with the celebrated RSA system. Doing so, we will use elements of algebra and arithmetics introduced during the first semester.
Finally we will study the theory of recurrent sequences, that are similar to the linear differential equations with constant coefficients introduced in analysis. |
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Learning outcomes of the course :
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| At the end of this lecture series, the students should have basic knowledge of some areas of discrete mathematics. They should be able to use them to solve new problems. This should also reinforce concepts introduced and used in other lecture series in the first year of mathematics through applications or analogies. |
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Prerequisites and co-requisites/ Recommended optional programme components :
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| Some basics of mathematics (secondary school-college) are necessary.
Some parts of the lectures also rely on the other lecture series of the first year of the Bachelor of Mathematics. |
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Planned learning activities and teaching methods :
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| The theory is explained on the blackboard and/or using data projector. Students are encouraged
to ask questions and to participate. The practical sessions are mainly dedicated to solve exercises corresponding to the theory considered during the lecture sessions. Those sessions are also useful to obtain extra informations or enlightenments on the concepts presented during the lecture sessions.
I strongly suggest that the students form small groups to discuss the topics of discrete mathematics and exchange their knowledge. They should then make lists of particular points that they do not understand and ask for explanations, either from me or from Miss M. Ernst.
This can be done by making an appointment or at the end of the lectures or exercise sessions.
It should not be considered as normal not to understand particular points of the lectures, and is it most likely that I will not go through this point once again during the lectures if I am not asked to do so, but rather use it to explain another one. It is very unlikely that the situation will become better without an action taken by the student... |
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Mode of delivery (face-to-face ; distance-learning) :
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| The students are supposed to attend the lectures of theory and practice.
The schedule of the lectures and exercise sessions is established by the Department of Mathematics, and is available on its website
http://www.deptmath.ulg.ac.be/ |
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Recommended or required readings :
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| Some lecture notes were written during year 2011-2012 and will be available on my web page
http://www.geodiff.ulg.ac.be,
Moreover, a new version of these notes will be available at the beginning of the second semester on the same site.
A printed version will also available (at very low price). Please contact the Secretary of the Department of Mathematics (D. Bartholomeus, office 0/28, building B37).
Many textbooks on discrete mathematics are also available at the library of mathematics (building B52). |
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Assessment methods and criteria :
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| The final examination consists of two parts, a written one and an oral one.
The written part is devoted to the resolution of problems and exercises, concerning the topics developed during the lectures and exercise sessions.
The oral part is devoted to the theory developed during the lectures but also includes direct applications of it.
In order to avoid stress for the exam, a list a major questions that will be asked during the exam will be provided at the end of the lectures.
As usual in mathematics, it is expected that the students be able to state definitions and results and provide their proofs, except otherwise stated.
The final result is an arithmetic mean of the results obtained by the students for the two parts of the exam. |
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Work placement(s) :
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Organizational remarks :
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Contacts :
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| Feel free to contact me for any question, preferably by e-mail (P.Mathonet@ulg.ac.be) to make an appointment or for very short questions, or come to my office (Building B37, Grande Traverse 12 - Sart Tilman, office 0/27).
You can also try to call me on the phone 04/366 94 80.
For questions regarding lectures and exercises, feel also free to contact Miss M. Ernst (building B37, office 0/66). |
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| Items online : |
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| Useful material |
| As already mentioned, lectures notes and other useful material will be available soon on my web page. |
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