Code: | M3011 | Acronym: | M3011 | Level: | 300 |
Keywords | |
---|---|
Classification | Keyword |
OFICIAL | Mathematics |
Active? | Yes |
Responsible unit: | Department of Mathematics |
Course/CS Responsible: | First Degree in Mathematics |
Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
---|---|---|---|---|---|---|---|
L:B | 0 | study plan from 2016/17 | 3 | - | 6 | 56 | 162 |
L:CC | 0 | Plano de estudos a partir de 2014 | 2 | - | 6 | 56 | 162 |
3 | |||||||
L:F | 0 | study plan from 2017/18 | 2 | - | 6 | 56 | 162 |
3 | |||||||
L:G | 0 | study plan from 2017/18 | 2 | - | 6 | 56 | 162 |
3 | |||||||
L:M | 37 | Plano estudos a partir do ano letivo 2016/17 | 2 | - | 6 | 56 | 162 |
3 | |||||||
L:Q | 1 | study plan from 2016/17 | 3 | - | 6 | 56 | 162 |
Teacher | Responsibility |
---|---|
Jorge Manuel Martins da Rocha | |
Pedro Ventura Alves da Silva |
Theoretical and practical : | 4,00 |
Type | Teacher | Classes | Hour |
---|---|---|---|
Theoretical and practical | Totals | 1 | 4,00 |
Pedro Ventura Alves da Silva | 2,00 | ||
Jorge Manuel Martins da Rocha | 2,00 |
With this course, it is intended that students will know and understand some of the main results of Discrete Mathematics that, for its present relevance within Mathematics, and by its special applicability, inside and outside Mathematics, should be of general knowledge for mathematicians. In this course the students should also develop their ability to solve combinatorial problems and the ability do solve problemas looking for the more suitable structure.
Upon completing this course, the student should know and be able to apply the concepts and results covered in the course. It is intended that this unit contribute to the furthering of skills in the field of discrete mathematics. In summary, it is intended that upon completion of this class the student can:
-Understand and apply fundamental combinatorial techniques as well as understand when these can or cannot be applied.
-Use appropriate techniques and problem solving skills on new problems.
-Recognize mathematical structures (e.g. algebraic ones) in combinatorial problems, can formulate them and solve them using the corresponding techniques.
-Be mathematically creative and inquisitive, being capable of formulating interesting new questions in combinatorics.
Module AUTOMATA:
WORDS AND LANGUAGES: words, free monoids, languages.
RATIONAL AND RECOGNIZABLE LANGUAGES: rational expressions, finite automata, alternative versions, transition monoid, recognizability by a finite monoid.
CLOSURE OPERATORS: closure properties of recognizable languages, Kleene's Theorem.
DECIDIBILITY: minimal automaton of a rational language, syntactic monoid, decidable properties, pumping lemma.
Sharkovsky's Theorem
Dynamics of the shift mapping
Dynamics of the quadratic family
Sperner's Lemma and Brower's Fixed Point Thorem
Expositional classes with discussion of examples and resolution of exercises.
designation | Weight (%) |
---|---|
Teste | 100,00 |
Total: | 100,00 |
designation | Time (hours) |
---|---|
Estudo autónomo | 106,00 |
Frequência das aulas | 52,00 |
Total: | 158,00 |
Evaluation in the first season is performed through two mandatory tests, T1 and T2, one for each module, each one worth 10 points with a duration of 2 hours. The first test is done during the semester and the second during the first season of exams.
The final mark will be the sum of the marks obtained in each test. Approval requires a sum not inferior to 9,5 points. Those obtaining a grade higher than 18 in the exam or in the full collection of tests must do an extra short written exam to confirm their mark.
The second season exam consists of two independent tests, one for each module, each one worth 10 points with a duration of 2 hours. In any situation (seeking approval or improving their grade), in the second season the student may choose to do both parts or just one of them, R1 and R2, R1 or R2. They must transmit that intention to the professors before doing the exam. The final grade, CF, is the sum of the maximum grades obtained in each part of the evaluation: CF=max{T1, R1}+max{T2,R2}. Approval requires a sum not inferior to 9,5 points. Those obtaining a grade higher than 18 in the exam or in the full collection of tests must do an extra short written exam to confirm their mark.
All other evaluation situations unforeseen in the previous points, in particular improving grades from previous seasons and substitution exams previewed in the regulations, will be performed through a unique exam, not exceeding 3 hours of duration, which may be preceded by a simple oral exam to verify if the student is minimally prepared to realize the exam.