Code: | M3026 | Acronym: | M3026 |
Keywords | |
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Classification | Keyword |
OFICIAL | Mathematics |
Active? | Yes |
Responsible unit: | Department of Mathematics |
Course/CS Responsible: | Bachelor in Mathematics |
Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
---|---|---|---|---|---|---|---|
L:B | 0 | Official Study Plan | 3 | - | 6 | 48 | 162 |
L:CC | 0 | study plan from 2021/22 | 2 | - | 6 | 48 | 162 |
3 | |||||||
L:F | 0 | Official Study Plan | 3 | - | 6 | 48 | 162 |
L:G | 0 | study plan from 2017/18 | 2 | - | 6 | 48 | 162 |
3 | |||||||
L:M | 0 | Official Study Plan | 3 | - | 6 | 48 | 162 |
L:MA | 0 | Official Study Plan | 3 | - | 6 | 48 | 162 |
L:Q | 0 | study plan from 2016/17 | 3 | - | 6 | 48 | 162 |
Teacher | Responsibility |
---|---|
Pedro Ventura Alves da Silva |
Theoretical and practical : | 3,69 |
Type | Teacher | Classes | Hour |
---|---|---|---|
Theoretical and practical | Totals | 1 | 3,692 |
Pedro Ventura Alves da Silva | 3,692 |
To become acquainted with a variety of combinatorial concepts and techniques, with emphasis on graph theory and enumerative combinatorics.
BASIC NOTIONS OF GRAPH THEORY: isomorphism, walks, subgraphs, connec- tedness, eulerian circuits, bipartite graphs.
ENUMERATIVE COMBINATORICS: recurrence relations, generating functions, per- mutations, derangements, involutions, Catalan numbers, Bell numbers.
PRINCIPLE OF INCLUSION-EXCLUSION: the Principle and its applications, Stir- ling numbers of the first and second kind.
GRAPHS AND MATRICES: adjacency matrix, incidence matrix, minimum polyno- mial and spectrum of a graph, spectrum of a bipartite graph.
TREES: forests and trees, alternative characterizations, Cayley’s Theorem, spanning trees.
COLOURINGS: colouring of the vertices of a graph, chromatic polynomial and chro- matic number, critical graphs.
PLANAR GRAPHS: Euler’s Formula, criteria for planarity, characterizations involving minors, Five Colour Theorem.
MATCHINGS: Marriage Theorem, systems of representatives, doubly stochastic ma- trices, perfect matchings, Tutte’s Theorem.
HAMILTONIAN CYCLES: Ore’s Theorem, necessary conditions for the existence of a Hamiltonian cycle.
Exposition by the teacher, discussion of exercises. List of exercises and other course materials are available on the course page at Sigarra.
designation | Weight (%) |
---|---|
Teste | 100,00 |
Total: | 100,00 |
designation | Time (hours) |
---|---|
Estudo autónomo | 114,00 |
Frequência das aulas | 48,00 |
Total: | 162,00 |