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Discrete Mathematics
- Centre
- Faculty of Science and Technology
- Degree
- Bachelor's Degree In Mathematics
- Academic course
- 2024/25
- Academic year
- 2
- No. of credits
- 6
- Languages
- Spanish
- Basque
- English
TeachingToggle Navigation
Study type | Hours of face-to-face teaching | Hours of non classroom-based work by the student |
---|---|---|
Lecture-based | 36 | 54 |
Seminar | 6 | 9 |
Applied classroom-based groups | 18 | 27 |
Teaching guideToggle Navigation
AimsToggle Navigation
COMPETENCES
M06CM01 - To be familiarized with the main types of mathematical proof and with the techniques of solving problems (observation-conjecture-proof).
M06CM06 - To know how to solve combinatorial problems using basic techniques, generating functions and recurrence relations.
M06CM07 - To be familiarized with combinatorial identities and the main families of numbers with combinatorial meaning.
M06CM08 - To know the concepts, techniques and basic results of the graph theory and to be familiarized with some of its multiple applications.
LEARNING RESULTS
To know how to solve combinatorial problems with a certain degree of complexity.
To be familiarized with families of numbers that are present in many areas of Mathematics.
To use skillfully combinatorial expressions and identities, inequalities, recurrence relations and generating functions.
To be familiarized with graphs, their main properties, and some of their multiple applications.
TemaryToggle Navigation
1. BASIC COMBINATORICS: Basic resources in the combinatorial reasoning. The principle of inclusion and exclusion. The pigeonhole principle.
2. COMBINATORIAL IDENTITIES: Binomial and multinomial coefficients. Binomial and multinomial formulae. Related identities.
3. GENERATING FUNCTIONS AND RECURRENCE RELATIONS: Generating function of a sequence of numbers. Applications to combinatorial problems. Recurrence relations and combinatorial problems. Recurrence relations and generating functions. Obtaining the general term.
4. MAIN FAMILIES OF NUMBERS: Numbers of Fibonacci. Numbers of Catalan. Numbers of Bell. Numbers of Stirling. Partitions of natural numbers.
5. GRAPHS: Basic concepts. Paths. Trees. Planar graphs. Coloring.
MethodologyToggle Navigation
In the M classes the theoretical contents will be developed.
In the S classes the students will work and present problems ans tasks.
In the GA classes exercises will be solved.
Assessment systemsToggle Navigation
GUIDELINES
Final exam (70%), partial test (15%), and preparing and presenting tasks (15%).
The minimum grade required to pass is 5 points (over 10) provided that at least 4 points (over 10) are gotten in the final exam (compulsory).
WITHDRAWAL OF CONTINUOUS ASSESSMENT SYSTEM
The student must give written notice of widthdrawal of countinuous assessment system in a period of 9 weeks since the begining of the course. In this case, the final grade will be the grade of the exam (100%) and at least 5 points (over 10) are required to pass.
DECLINING TO SIT
A student who does not take the final exam will obtain <
Compulsory materialsToggle Navigation
The recommended materials will be available at the virtual platform.
BibliographyToggle Navigation
Basic bibliography
D.I.A. COHEN, Basic Techniques of Combinatorial Theory, Wiley, New York,1978.
J.M. HARRIS, J.L. HIRST, M.J. MOSSINGHOFF, Combinatorics and Graph Theory, Springer, New York, 2008.
N. HARTSFIELD, G. RINGEL, Pearls in Graph Theory, Dover, New York, 1994.
R.L. GRAHAM, D.E. KNUTH, O. PATASHNIK, Concrete Mathematics, Addison-Wesley, Reading, Mass., 1994.
In-depth bibliography
V.K. BALAKRISHNAN, Combinatorics, Schaum’s Outline Series, McGraw-Hill, 1995.
R.C. BOSE, B. MANVEL. Introduction to Combinatorial Theory, Wiley, New York, 1984.
F. GARCIA MERAYO, Matemática Discreta, Paraninfo, Madrid, 2001.
J. HEBER NIETO SAID, Teoría Combinatoria.La Universidad del Zulia, 1996. http://www.jhnieto.org/tc.pdf
D.A. MARCUS, Combinatorics: A Problem Oriented Approach, The Mathematical Association of America, 1998.
R. J. TRUDEAU, Introduction to Graph Theory, Dover Pulications, Inc, Nueva York, 1993.
N. Ya. VILENKIN, Combinatorics, Academic Press, New York, 1971.
H.S. WILF, Generatingfuntionology, Academic Press, Boston, 1990. http://www.math.upenn.edu/~wilf/gfology2.pdf
Journals
The Electronic Journal of Combinatorics http://www.combinatorics.org/
The Fibonaccy Quarterly http://www.fq.math.ca/
GroupsToggle Navigation
16 Teórico (Spanish - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
---|---|---|---|---|---|
1-1 | 17:00-18:00 | ||||
1-5 | 16:00-17:00 | ||||
1-12 | 15:00-16:00 | ||||
1-15 | 14:00-15:00 | ||||
8-10 | 16:00-17:00 | ||||
13-13 | 16:00-17:00 |
16 Seminar-1 (Spanish - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
---|---|---|---|---|---|
6-7 | 16:00-17:00 | ||||
9-11 | 16:00-17:00 | ||||
12-14 | 16:00-17:00 |
16 Applied classroom-based groups-1 (Spanish - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
---|---|---|---|---|---|
2-15 | 17:00-18:00 | ||||
13-15 | 15:00-16:00 | ||||
15-15 | 16:00-17:00 |
46 Teórico (Basque - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
---|---|---|---|---|---|
1-1 | 17:00-18:00 | ||||
1-5 | 15:00-16:00 | ||||
1-14 | 16:00-17:00 | ||||
1-15 | 14:00-15:00 | ||||
10-10 | 15:00-16:00 |
46 Seminar-1 (Basque - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
---|---|---|---|---|---|
6-12 | 15:00-16:00 | ||||
7-7 | 15:00-16:00 | ||||
11-11 | 15:00-16:00 | ||||
14-14 | 15:00-16:00 |
46 Seminar-2 (Basque - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
---|---|---|---|---|---|
6-12 | 14:00-15:00 | ||||
7-7 | 14:00-15:00 | ||||
11-11 | 14:00-15:00 | ||||
14-14 | 14:00-15:00 |
46 Applied classroom-based groups-1 (Basque - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
---|---|---|---|---|---|
2-15 | 17:00-18:00 | ||||
8-8 | 15:00-16:00 | ||||
13-13 | 15:00-16:00 | ||||
15-15 | 15:00-16:00 | 16:00-17:00 |
66 Teórico (English - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
---|---|---|---|---|---|
1-1 | 17:00-18:00 | ||||
1-5 | 15:00-16:00 | ||||
1-14 | 16:00-17:00 | ||||
1-15 | 14:00-15:00 | ||||
10-10 | 15:00-16:00 |
66 Seminar-1 (English - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
---|---|---|---|---|---|
6-12 | 15:00-16:00 | ||||
7-11 | 15:00-16:00 | ||||
14-14 | 15:00-16:00 |
66 Applied classroom-based groups-1 (English - Tarde)Show/hide subpages
Weeks | Monday | Tuesday | Wednesday | Thursday | Friday |
---|---|---|---|---|---|
2-15 | 17:00-18:00 | ||||
8-13 | 15:00-16:00 | ||||
15-15 | 15:00-16:00 | 16:00-17:00 |