**Academic Year/course: 2017/18**

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**30208 - Discrete mathematics**

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Syllabus Information
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__Syllabus Information__

**Academic Year:**

**Subject:**

**Faculty / School:**

326 - Escuela Universitaria Politécnica de Teruel

**Degree:**

443 - Bachelor's Degree in Informatics Engineering

**ECTS:**

**Year:**

**Semester:**

**Subject Type:**

**Module:**

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**5.1. Methodological overview**

#### The learning process designed for this course is based on the following items:

- An active engagement of the student during the lectures.
- An effective scheduling on the part of the student, studying the subject on a regular basis and trying to solve the proposed problems.
- Previous preparation on the student's part of the material to be covered during the computer lab sessions.

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**5.2. Learning tasks**

#### The program offered to the student to help them obtain the expected learning outcomes comprises the following activities...

- Lectures.
- Computer lab sessions.
- Tutorials.

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**5.3. Syllabus**

**1. Logic**

Connectives, truth tables, logical equivalence, tautologies, valid and invalid arguments, introduction to predicate logic.

**2. Number theory**

Principle of induction, Euclidean division, Euclidean algorithm, Bézout's identity, fundamental theorem of arithmetic, congruences, Chinese remainder theorem, modular binary exponentiation, Fermat's little theorem, Euler's theorem, RSA.

**3. Combinatorics**

Permutations, combinations, rule of sum, rule of product, binomial coefficients, pigeonhole principle, inclusion-exclusion principle, recurrence relations.

**4. Graph theory**

Basic concepts, Eulerian graphs, Hamiltonian graphs, matrix representations of graphs, isomorphisms of graphs, trees, Kruskal's algorithm, Prim's algorithm, Dijkstra's algorithm.

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**5.4. Course planning and calendar**

### Planning

The amount of time required to obtain the expected learning outcomes is estimated at 150 hours, distributed as follows:

- 45 hours of lectures (3 hours per week)
- 12 hours of computer lab sessions (6 sessions of 2 hours each)
- 90 hours of independent learning
- 3 hours of final written exam

### Scheduling

The schedule of the face-to-face classroom sessions is set by the institution, and can be found in its webpage. Dates for the assessment tests will be announced well in advance.