Seminar

Code:

M4104

Acronym:

M4104

Level:

400

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2018/2019 - A

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Master in Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:M	3	Plano de Estudos do M:Matemática	1	-	3	21	81

Teaching language

Suitable for English-speaking students

Objectives

Foster students' autonomous work as well as critical thinking and familiarity with scientific research.

Learning outcomes and competences

Ability to synthesize and understand the main apects and propelling ideas behind the results instead of loosing time and effort in the detailed understanding of all the technical steps.

Ability to prepare the structure of a presentation and to be able to transmit the main ideas of a research work in mathematics.

Working method

Presencial

Program

Presentation, critical analysis and discussion of scientific works. The topics covered depend on the interests of the student and faculty researchers participating in the Seminar.

Mandatory literature

Casacuberta C; Mathematical research today and tomorrow. viewpoints of seven fiels medalists. ISBN: 3-540-56011-4

Comments from the literature

[8] J. G. Kingston and J. L. Synge. The sequence of pedal triangles. Amer. Math. Monthly, 95(7):609–620,
1988.
[9] M. R. Leadbetter. Extremes and local dependence in stationary sequences. Z. Wahrsch. Verw. Gebiete, 65(2):291–306, 1983.
[10] I. Mulvey. Recurrent Ideas in Number Theory: The Multiple Birkhoff Recurrence Theorem Used to Prove van der Waerden’s Theorem. Math. Mag., 70(5):358–361, 1997.
[11] W. Parry. On the β-expansions of real numbers. Acta Math. Acad. Sci. Hungar., 11:401–416, 1960.
[12] M. Ram Murty. Prime numbers and irreducible polynomials. Amer. Math. Monthly, 109(5):452–458,
2002.
[13] N. Samet and B. Tsaban. Superfilters, Ramsey theory, and van der Waerden’s theorem. Topology Appl., 156(16):2659–2669, 2009.
[14] P. Samuel. About Euclidean rings. J. Algebra, 19:282–301, 1971.
[15] J.-P. Serre. On a theorem of Jordan. Bull. Amer. Math. Soc. (N.S.), 40(4):429–440, 2003.
[16] S. K. Stein. Unions of arithmetic sequences. Math. Ann., 134:289–294, 1958.
[17] M. Yamagishi. Elliptic curves over finite fields and reversibility of additive cellular automata on square grids. Finite Fields Appl., 19:105–119, 2013.

Teaching methods and learning activities

Stimulus to the reading and search of alternative sources for the understanding of the contents. Presentation and discussion of the proposed subjects.

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Apresentação/discussão de um trabalho científico	90,00
Trabalho escrito	10,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Apresentação/discussão de um trabalho científico	2,00
Frequência das aulas	21,00
Trabalho de investigação	50,00
Trabalho escrito	8,00
Total:	81,00

Eligibility for exams

N/A

Calculation formula of final grade

The students will be evaluated for the written report and, most of all, for the corresponding oral presentation.