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Mathematical Methods in the Sciences
| Code: | M3012 | Acronym: | M3012 | Level: | 300 |
| Keywords | |
|---|---|
| Classification | Keyword |
| OFICIAL | Mathematics |
Instance: 2016/2017 - 1S 
| Active? | Yes |
| Web Page: | https://moodle.up.pt/mod/forum/view.php?id=114857 |
| Responsible unit: | Department of Mathematics |
| Course/CS Responsible: | Bachelor in Mathematics |
Cycles of Study/Courses
| Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
|---|---|---|---|---|---|---|---|
| L:B | 0 | Official Study Plan | 3 | - | 6 | 56 | 162 |
| L:M | 37 | Official Study Plan | 2 | - | 6 | 56 | 162 |
| 3 | |||||||
| L:Q | 1 | study plan from 2016/17 | 3 | - | 6 | 56 | 162 |
Fields changed: Calculation formula of final grade, Programa, Bibliografia Complementar, Bibliografia Obrigatória, Componentes de Avaliação e Ocupação
Teaching language
PortugueseObjectives
To learn Mathematics through some of its applications. To explore the use of Mathematics to solve problems within several scientific domains.
Learning outcomes and competences
The syllabus is the result of a judicious choice of examples of application of Mathematics to several sciences which build a substantial complement to the training of matematicians and science promoters. The list of topics includes elementary material and also results from recent research in Mathematics.
Working method
PresencialPre-requirements (prior knowledge) and co-requirements (common knowledge)
The fundamental contents of the two fisrt years of a degree in Mathematics (Linear Algebra, Algebra, Analysis, Differential Equations, Geometry, Probability).
Program
Triangulation. [Measurements in Astronomy.]
Estereometry. [An example given by Kepler.]
Spherical geometry. [Geodesy and map construction.]
Properties of the circle. [Contant curvature; arc theorem; wheels of constant width.]
Fórmula de Euler. [Symmetry in Chemistry; fullerens.]
Dynamical systems. [Mathematics and magic: dynamics of a card game.]
Iteration of matrices. [Genetics and linear algebra.]
Game theory. [Banach-Mazur, Euclides and Conway games: winning strategies. How to prove that R is not countable.]
Newton's method. [Successive approximations: intermediate value theorem; Heron's method. Chaos and fractals.]
Qualitative analysis of differential equations. [A Portuguese example of Volterra's model for prey-predator systems. Models in Biology and Environmental Studies.]
Approximate solutions of differential equations. [Nuclear deposits at the seabed. Models in Physics.]
Power series. [How to evaluate the depth of a well.]
Mass center. [The search for the geometrical and demographical center of Portugal. Mathematics in sport: jumps and football.]
Jordan curve theorem. [Construction of a pacemaker.]
Markov chains. [How a search engine like Google works.]
Mathematics of choice. [Redundancy in lottery games. Strategies in Economy.]
Lagrange multipliers. [Markowitz model for the selection of the optimal portfolio.]
What is math for? [Discussion concerning the talk http://on.ted.com/c0rby of the Spanish mathematician Eduardo Saenz.]
Estereometry. [An example given by Kepler.]
Spherical geometry. [Geodesy and map construction.]
Properties of the circle. [Contant curvature; arc theorem; wheels of constant width.]
Fórmula de Euler. [Symmetry in Chemistry; fullerens.]
Dynamical systems. [Mathematics and magic: dynamics of a card game.]
Iteration of matrices. [Genetics and linear algebra.]
Game theory. [Banach-Mazur, Euclides and Conway games: winning strategies. How to prove that R is not countable.]
Newton's method. [Successive approximations: intermediate value theorem; Heron's method. Chaos and fractals.]
Qualitative analysis of differential equations. [A Portuguese example of Volterra's model for prey-predator systems. Models in Biology and Environmental Studies.]
Approximate solutions of differential equations. [Nuclear deposits at the seabed. Models in Physics.]
Power series. [How to evaluate the depth of a well.]
Mass center. [The search for the geometrical and demographical center of Portugal. Mathematics in sport: jumps and football.]
Jordan curve theorem. [Construction of a pacemaker.]
Markov chains. [How a search engine like Google works.]
Mathematics of choice. [Redundancy in lottery games. Strategies in Economy.]
Lagrange multipliers. [Markowitz model for the selection of the optimal portfolio.]
What is math for? [Discussion concerning the talk http://on.ted.com/c0rby of the Spanish mathematician Eduardo Saenz.]
Mandatory literature
Abbott Edwin A.; Flatland o pais plano. ISBN: 972-662-303-0Anton Howard; Elementary linear algebra. ISBN: 0-471-66959-8
Braun M.; Differential equations and their applications. ISBN: 0387901140
Gardner Martin; The night is large. ISBN: 0-14-026372-1
Jennings George A.; Modern geometry with applications. ISBN: 0-387-94222-X
Hirsch Morris W.; Differential equations, dynamical systems, and linear algebra. ISBN: 0-12-349550
Kline Morris; Mathematics and the physical world. ISBN: 0-486-24104-1
Moise Edwin E.; Elementary geometry from an advanced standpoint
Niven Ivan; Mathematics of choice
Petit Jean-Pierre; Le geometricon
Stewart Ian; Les fractals. ISBN: 2-7011-0446-7
Polya G.; Mathematics and plausible reasoning. ISBN: 0-691-02509-6 (Vol. I)
Pólya George; Mathematical methods in science. ISBN: 0-88385-600-X
Rademacher Hans; The enjoyment of mathematics. ISBN: 0-691-02351-4
Rademacher H.; Higher mathematics from an elementary point of view. ISBN: 3-7643-3064-3
Wilson Alistair Macintosh; The infinite in the finite. ISBN: 0-19-853950-9
Complementary Bibliography
Elon Lages Lima; O teorema de Euler sobre poliedros, Matemática Universitária, Nº2, 57-74, 1985Curl, Smalley; Fullerenes, Scientific American (October), 1991
Rodrigues; Bolas, urnas e as lotarias de números, Matemática Universitária (Dezembro), 1982
José Filipe Queiró; Determinação do centro geográfico de Portugal, UP, 2010
Associação Atractor (publicado na Gazeta de Matemática); Controle biológico de pragas
Associação Atractor (publicado na Gazeta de Matematica); Rumos magnéticos, atracções polares
Associação Atractor (publicado na Gazeta de Matemática); A matematica do futebol
Associação Atractor (publicado na Gazeta de Matemática); À volta da roda
Maria Carvalho; Chaotic Newton sequences, Mathematical Intelligencer, Vol.24, pp.31-35, 2002
Maria Carvalho, Sílvia Cavadas (publicado no Boletim da SPM); Jogando no limite, 2014
Maria Carvalho, João Miguel Santos (publicado no Boletim da SPM); Dinâmica de um truque de cartas, 2014
Hull John; Introduction to futures and options markets. ISBN: 0-13-183252-2
Teaching methods and learning activities
The syllabus is presented in the lectures, where examples of problems from several sciences solved by mathematical results are extensively discussed, giving emphasis to objects, powerful mathematical methods and their applications. Reading suggestions, additional bibliography and other resources are available for students at the unit’s web page or the FCUP library. Students are encouraged to read mathematical works of unexcelled quality whose content connects Mathematics and other sciences, to work in advance on the proposed problems and to participate in their discussion, helping further to improve their knowledge and mastering of the powerful mathematical methods.
keywords
Physical sciences > Computer sciencePhysical sciences > Astronomy
Physical sciences > Chemistry
Health sciences > Medical sciences
Physical sciences > Mathematics
Physical sciences > Physics
Natural sciences > Biological sciences
Natural sciences > Environmental science
Social sciences > Geography
Evaluation Type
Distributed evaluation with final examAssessment Components
| designation | Weight (%) |
|---|---|
| Exame | 100,00 |
| Total: | 100,00 |
Eligibility for exams
Absences will not be registered.Calculation formula of final grade
According to the regulations of UP/FCUP and upon the students' agreement, the evaluation will consist of a written exam.
Classification improvement
Students may improve theirs grades on a second written exam.
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Page created on: 2024-10-06 at 17:26:45 | Acceptable Use Policy | Data Protection Policy | Complaint Portal
Page created on: 2024-10-06 at 17:26:45 | Acceptable Use Policy | Data Protection Policy | Complaint Portal