The course

Faculty of Mathematics and Statistics at the UPC
Centre for Mathematical Research UAB
University of Barcelona
Institute for Catalan Studies

From 11 January to 21 November

The Mathematics course from the Crazy about Science programme of the Catalunya La Pedrera Foundation is a course developed jointly by the Federation of Entities for the Teaching of Mathematics in Catalonia (FEEMCAT) and theCatalan Mathematical Society (SCM), aimed at 1st year A-Level students in the science and / or technology modality with a special interest in and talent for mathematics. The basic purpose of this course is to foster the scientific vocation of these young people and especially their enthusiasm for maths. The course has the support and collaboration of the Faculty of Mathematics and Computers of the UB, the Department of Mathematics of the UAB, the Faculty of Mathematics and Statistics of the UPC, the Pompeu Fabra University and the Centre for Mathematical Research (CRM).

 

The course will be held on 22 Saturdays from 11 January 2020 to 21 November 2020 at the facilities of the different Catalan universities where degree courses related to mathematics are taught. This situation allows students to discover, in situ and in a personalised way, the centres that offer studies directly related to the subject.

Each session consists of two parts. A first session is dedicated to the presentation of the subject (approx. 1h) and the other is held in a workshop format, which also includes a 30-minute break. Students are the protagonists of this second part because, individually or collaboratively, they think, reason, create, construct and apply mathematics with the support of the teachers.

Registration for the Crazy about Maths course will be open from 16 September to 24 October 2019 and among all those enrolled 25 students will be selected from 1st year of A-Levels to participate in this edition of the course within the 8th edition of the Crazy about Science programme that will take place in 2020.

Specific objectives

Students who have the opportunity to participate in the course:

  • Will interpret the presence of mathematics in current science and technology, as well as in close situations in everyday life.
  • They will practice the intellectual challenge of abstract and creative mathematical thinking, which fascinates the young and old, and which they may have already discovered in other driven programmes and competitions (Let's do maths, Stalmat, Kangaroo, Sprint problems, Marathon problems, More maths, Anemx + maths...).
  • They will have a clearer vision for deciding if they want to pursue a career in mathematics, but it will also help them follow pursuits in the sciences, engineering, economics, or others in which maths plays a significant role.

Academic studies

  • To foster among young people the scientific vocations linked to the world of maths, helping to guide their academic and professional future.
  • There is the opportunity for A-Level Research Work to be supervised by a reference research centre (Argó Programme at the UAB; Research work at the Faculty of Mathematics and Computers at the UB, Research work at the Faculty of Mathematics) and Statistics of the UPC).

Research

  • Bringing students closer to maths research and seeing what their fields of action are.
  • Discover the operation of the research centres linked to Maths.

Sessions

Opening session. Antoni Gaudi: Crazy about Geometry

Day: 11 January 2020

Opening hours: 10 am to 2 pm

Location: Faculty of Mathematics and Statistics of the UPC

Language: Catalan

Session given by: Claudi Alsina Català (Department of Architectural Structures, ETSAB, UPC)

The great architect Antoni Gaudí (1852-1926) was crazy about geometry: his creativity was based in many cases on his constant research into flat and spatial geometric shapes, geometric transformations and structural principles. In order to "understand Gaudí", one must know how to see the geometric secrets that support his spectacular projects. In this talk we will pay a detailed visit to these geometric secrets of Gaudí.

Session 2. Statistics: Beyond averages and percentages

Day: 25 January 2020

Opening hours: 10 am to 2 pm

Location: Faculty of Mathematics and Statistics of the UPC

Language: Catalan

Session given by: Pere Grima Cintas (Department of Statistics and Operations Research, UPC)

In this session we will talk about statistics, what it is and what it is for. We will see that many of the questions we ask ourselves in order to gain knowledge can only be answered by collecting and analysing data and that is why statistics are used. We will also discuss the possibilities of knowing the characteristics of a population by looking at only one sample and applying it to the estimation of the number of fish in a lake or the number of taxis in a city.


The second part will be in a computer classroom and we will use a spreadsheet to simulate the results of statistical studies. We will also discuss some issues with calculating probabilities.

Session 3. Maximums with minimal utensils

Day: 1 February 2020

Opening hours: 10 am to 2 pm

Location: Faculty of Mathematics and Statistics of the UPC

Language: Catalan

Session given by: Mireia López Beltran

Based on our own knowledge of the 4th year GCSE curriculum on the concepts of relative function and end, we solve the seemingly simple problem: "From a given segment AC find a point E between A and C, so that AExEC is maximum." This problem was posed by Fermat around the 1630s and will help us to work on maximums and minimums before systematising the solution of optimisation problems using differential calculus. The geometric and algebraic view of the proposed situation is strengthened and the use of ICT tools (GeoGebra and EXCEL) give a complete overview of the problems raised. There is good historical context and reflection that will help to consolidate the optimisation problems that are worked on in the 1st and 2nd years of GCSE.

Session 6. Decimal and positional necessarily?

Day: 29 February 2020

Opening hours: 10 am to 2 pm

Location: Faculty of Mathematics of the Univ. of Barcelona.

Language: Catalan

Session given by: Alberto Herrero Izquierdo (INS Lluís Domènech i Montaner, Canet de Mar)

Our numbering system is decimal and positional. But is there any reason for this to happen? Could it not be otherwise? Other cultures have opted for different numbering systems. Even today, dozens of scientific societies still propose a change based on 12. In this session we will take a closer look at numbering systems.
 

Session 1. Dynamics of presentation and activity in three acts

Day: 18 January 2020

Opening hours: 10 am to 2 pm

Location: Faculty of Mathematics and Statistics of the UPC

Session given by: Sergi del Moral Carmona (Institut-Escola Les Vinyes)

Language: Catalan

Have you ever been excited about seeing a movie? Do you think it is possible to get emotional solving maths problems? Do you think it is possible to get your pulse going as we answer questions with the help of mathematical tools and ideas? In this workshop we will do some special activities, ask you questions, conjecture, estimate results, discuss based on your own ideas and look for answers together.

Sessió 6 - La rebel·lió de Vincenzo Galilei. Quan la música formava part de la matemàtica

Dia: Dissabte 5 de març

Horari: 10h a 14h

Lloc: Facultat de Matemàtiques i Estadística de la UPC

Idioma: Català

Sessió a càrrec de: Santi Vilches i Maite Gorriz (INS Vilamajor, Sant Pere de Vilamajor. Inspecció a Catalunya Central)

La música ha estat un tret identitari ancestral de l'ésser humà que s'ha anat desenvolupant al llarg de totes les civilitzacions. La creació, l’evolució i l’afinació dels diferents instruments musicals s'ha convertit en una necessitat humana que ha generat un problema matemàtic obert. Els pitagòrics ja van intentar resoldre aquest problema proposant una solució que va ser qüestionada per Vincenzo Galilei. En aquesta sessió tornarem a qüestionar els cànons establerts i us encoratjarem a que feu la vostra pròpia proposta. Per fer-la no cal saber música sols cal tenir una mica d’imaginació i gaudir de la matemàtica i de la música. Durant la sessió podrem escoltar les vostres propostes matemàtiques. Que s'aixequi el teló!

Session 8. Looking for geometric properties with Geogebra

Day: 14 March 2020

Opening hours: 10 am to 2 pm

Location: Faculty of Mathematics and Statistics of the UPC

Language: Catalan

Session given by: Carlos Giménez Esteban (Sant Gabriel College, Viladecans)

The free GeoGebra programme is a very powerful tool for working on different parts of mathematics. Its dynamism makes it a very useful resource for conjecture and property tests, as well as for solving problems of all kinds.

In this workshop we will focus on the construction of dynamic geometric figures that allow us to conjecture and verify properties of a geometric nature. To begin with, we will do an introduction to the programme. This way, those who do not know, will also be able to reach the proposed buildings.

Session 11. History of Mathematics

Day: 18 March 2020

Opening hours: 10 am to 2 pm

Location: Faculty of Mathematics of the Univ. of Barcelona.

Language: Catalan

Session given by: Carles Dorce Polo (Department of Probability, Logic and Statistics, UB - INS Barres i Ones, Badalona)

The equations that we solve today without too much difficulty in secondary school were not the result of a person's inspiration one day, but rather they are the result of centuries of contributions that have set the course for what we are doing today. Starting with ancient Egypt, we will begin to solve 1st degree equations, and with the help of geometry we will solve second degree equation as thought out by the 8th-9th Century Arabs using cards, a ruler, scissors and glue, and 3rd degree equations following the ideas of talented 16th-century Italian teachers. In the eighth century, Baghdad became the world cultural centre, and from among the large number of scientists and philosophers who arrived there, the name Muhammad b stands out. Mûsâ al-Khwârizmî, not only introduced Indian numerals to the Arab world, but also wrote an algebra book that would continue to be used. The next logical step was to solve third-degree equations, but the only Arab attempts did not bring any numerical solutions and, during the Middle Ages, only Fibonacci, an Italian, was able to solve one.

This situation could not go on and so during the Renaissance, Bologna, Milan and Venice were the scene of one of the most interesting mathematical disputes in history. How did they come up with a universal formula to solve one of the hottest problems of the time? Throughout this process, we will be accompanied by the lives and anecdotes of some characters who shed light on this mathematical symphony.
 

Session 12. How and why you can travel in space

Day: 25 April 2020

Opening hours: 10 am to 2 pm

Location: Faculty of Mathematics of the Univ. of Barcelona.

Language: Catalan

Session given by: Arturo Vieiro Yanes (Department of Applied Mathematics and Analysis, UB)

Celestial mechanics tries to describe the movements of celestial bodies (planets, asteroids, natural or artificial satellites, etc.) under the action of mutual gravitational forces. Beyond their mathematical formalism, nowadays the basic ideas of celestial mechanics are applied to the description of the chemical reactions and the movement of atomic particles, in climatology models, and, of course, astrodynamics, which enables space travel. We will introduce the basics that describe the motion of planets and explain their consequences on planetary motion. In the workshop we will work on some elementary concepts related to the design of trajectories in space missions. With the help of computer software we will visualise the orbits of the 2-body problem and as an application we will discuss some aspects of the Cassini-Huygens mission, whose main purpose is to gather information about Saturn, its rings and moons.
 

Session 13. Biostatistics: Statistics applied to the Health Sciences

Day: 9 March 2020

Opening hours: 10 am to 2 pm

Location: Faculty of Mathematics of the Univ. of Barcelona.

Language: Catalan

Session given by: Miquel López Forner (INS Gabriel Ferrater, Reus)

The development and application level that Biostatistics has experienced in recent years has been spectacular. This progress is closely linked to the development, on the one hand, of computing and, on the other, a change of attitude on the part of all professionals in the area of Health Sciences. It has evolved into a scientific society where research has become an essential part of daily tasks. The interest in discovering new procedures through the accumulated experience has been decisive in the need for all healthcare professionals to be immersed in the training and learning of basic research methodology techniques and in data analysis.

In this session we will discuss what statistical tools a healthcare professional uses in his or her area of work. The contents of the session, divided into three blocks, can be summarised into:

Basic concepts of descriptive statistics, in their function of summarising, presenting and communicating the results of any study, as well as the techniques of extrapolating the conclusions of a population, based on what has been verified in a representative sample of this.

Basic notions of aspects such as probability, random variable... then focusing on diagnostic tests (application of the Bayes theorem), sensitivity and specificity and, finally, talking about the predictive value of a test.

Concept of statistical inference where forecasts of the population under study will be made.

Sessió 11 -

Dia: Dissabte 30 d'abril

Horari: 10h a 14h

Lloc: Facultat de Matemàtiques i Estadística de la UPC

Idioma: Català

Sessió a càrrec de: Albert Granados

Session 10. Taster of Industrial Mathematics at the CRM

Day: 28 March 2020

Opening hours: 10 am to 2 pm

Location: Auditorium of the Centre for Mathematical Research (CRM), UAB Campus. Event's Hall.

Language: English

Session given by: Tim Myers (Centre for Mathematical Research, UAB)

We will answer questions such as: What can cause a football team to win, how to stop ice from forming on the surface of an aircraft, or something as important as how we can conserve Rhinos? These are all questions that a mathematician can find a solution to. Mathematics can help engineering and other disciplines solve industrial needs. We have become accustomed to seeing mathematics in the language of other sciences, but mathematics as a discipline is also important when applied. In this talk we will try to see cases where having a mathematician working on a problem can make a difference.

Session 19. Mathematics helps Logistics at AMAZON
Session 9. Geometric fractals. Dimension and applications

Day: 21 March 2020

Opening hours: 10 am to 2 pm

Location: Rovira i Virgili University

Language: Catalan

Session given by: Antonio Garijo Real

Despite the fact that objects with complex geometry are part of nature and that scientists have been interested in understanding them since ancient times, fractals have gained a presence as a subject of mathematical study in recent decades, and especially since of the revolution of computers that have made it possible to visualise them more precisely.

In this workshop, we propose an approach to so-called (or, if you wish, perfect) geometric fractals, such as the Cantor set, the Sierpinski triangle, or the Koch curve. We will see how they are recursively constructed and understand their geometric complexity.
 

Session 14. Drawing pins, bubbles, chickpeas, papers, threads, coins ... maths that can be touched

Day: 16 May 2020

Opening hours: 10 am to 2 pm

Location: Faculty of Mathematics of the Univ. of Barcelona.

Language: Catalan

Session given by: Anton Aubanell Pou (Secondary Education and Applied Mathematics and Analysis Department, UB (retired), MMACA), Sergi Múria Maldonado (Secondary Education and Applied Mathematics and Analysis Department, UB), Jordi Font González and Francesc Massich.

This session will invite you to take a look at various mathematical experiences that come from manipulating materials: we will use strings to measure distances on maps, construct the Fermat point of a triangle with a ruler and a compass, and also make bubbles with soap (... will it be the same?), using drawing pins, we will try to make reasonings within amazing geometry where "circles" may not be round, we will discover conics by folding paper, we will try to figure out a random secret by throwing coins and even ourselves will become materials for doing maths.
 

Session 15. The forms that surround us
Session 16. Starry polyhedra and tessellations in space
Session 7. Generation of curves. Polyhedron workshop

Day: 7 March 2020

Opening hours: 10 am to 2 pm

Location: Faculty of Mathematics and Statistics of the UPC.

Language: Catalan

Session given by: Josep Rey Nadal, Manel Udina Abelló and Enric Brasó (Secondary Education - retired people and MMACA)

The session will contain a presentation of the Museum of Mathematics of Catalonia (MMACA). On the one hand, we will look at how some curves such as epicycloids, hypocycloids and others are physically generated and study some relevant aspects. We will see applications in features of planetary motion. GeoGebra will also be used to make generalisations. In the second part of the session we will build a sculpture with 72 pencils. It is about the creation of GW Hart consists of 4 interlaced hexagonal prisms that determine their intersection with a rhombic dodecahedron.

Session 17. The conical sections: from Apollonius to projective geometry
Session 18. The Congruent Number Problem (CNP)
Session 20. Ruled curves and surfaces: straight or curved?
Session 21. Closing conference. Magic and maths. Delivery of diplomas
Calendari 2022
Calendari 2022
Dissabte 22 de gener
Facultat de Matemàtiques i Estadística de la UPC
Antoni Gaudí: Boig per la Geometria
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 29 de gener
Facultat de Matemàtiques i Estadística de la UPC
Estadística: Més enllà de les mitjanes i els percentatges
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 5 de febrer
Facultat de Matemàtiques i Estadística de la UPC
Màxims amb estris mínims
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 12 de febrer
Sessió online
Decimal i posicional necessàriament?
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 19 de febrer
Facultat de Matemàtiques i Estadística de la UPC
Totes les superfícies del món
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 5 de març
Facultat de Matemàtiques i Estadística de la UPC
La rebel·lió de Vincenzo Galilei. Quan la música formava part de la matemàtica
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 12 de març
Facultat de Matemàtiques i Estadística de la UPC
A la recerca de propietats geomètriques amb Geogebra
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 19 de març
Universitat de Barcelona
Història de les Matemàtiques
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 26 de març
Universitat de Barcelona
Com i per què es pot viatjar a l'espai
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 2 d'abril
Universitat de Barcelona
Bioestadística: Estadística aplicada a les ciències de la Salut
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 30 d'abril
Facultat de Matemàtiques i Estadística de la UPC
Per definir
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 7 de maig
Auditori del Centre de Recerca Matemàtica (CRM), Campus de la UAB. Sala d'actes
Matemáticas que fluyen
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 14 de maig
UPF
Mathematics helps Logistic
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 21 de maig
Universitat de Barcelona
Fractals geomètrics. Dimensió i aplicacions
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 28 de maig
Universitat de Barcelona
Xinxetes, bombolles, cigrons, papers, fils, monedes...matemàtiques que es toquen
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 17 de setembre
Departament de Matemàtiques de la UAB
Les formes que ens envolten
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 1 d'octubre
Departament de Matemàtiques de la UAB
Políedres estrellats i tesselacions a l’espai
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 8 d'octubre
MMACA - Museu de Matemàtiques de Catalunya
Generació de corbes. Taller de poliedres
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 15 d'octubre
Departament de Matemàtiques de la UAB
Les seccions còniques: d’Apol·loni a la geometria projectiva
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 22 d'octubre
Departament de Matemàtiques de la UAB
El Problema del Nombre Congruent (CNP)
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 5 de novembre
Departament de Matemàtiques de la UAB
Corbes i superfícies reglades: rectes o corbes?
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 12 de novembre
Institut d'Estudis Catalans. Sala Prat de la Riba (Carrer del Carme, 47; 08001 Barcelona)
Conferència de cloenda. Màgia i matemàtiques. Lliurament de diplomes
Sessió teòrico-pràctica. De 10h a 14h
Calendari 2021
Calendari 2021
Dissabte 16 de gener
Sessió online
Antoni Gaudí: Boig per la Geometria
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 30 de gener
Sessió online
Estadística: Més enllà de les mitjanes i els percentatges
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 6 de febrer
Sessió online
Màxims amb estris mínims
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 20 de febrer
Sessió online
Totes les superfícies del món
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 27 de febrer
Sessió online
Decimal i posicional necessàriament?
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 6 de març
Sessió online
La rebel·lió de Vincenzo Galilei. Quan la música formava part de la matemàtica
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 20 de març
Sessió online
A la recerca de propietats geomètriques amb el GeoGebra
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 24 d'abril
Sessió online
Història de les matemàtiques
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 8 de maig
Sessió online
Com i perquè es pot viatjar a l'espai
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 15 de maig
Sessió online
Bioestadística: Estadística aplicada a les ciències de la Salut
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 22 de maig
Universitat de Barcelona
Xinxetes, bombolles, cigrons, papers, fils, monedes... matemàtiques que es toquen
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 18 de setembre
Departament de Matemàtiques de la UAB
Fractals geomètrics, dimensió i aplicacions
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 25 de setembre
Departament de Matemàtiques de la UAB
Les formes que ens envolten
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 2 d'octubre
Departament de Matemàtiques de la UAB
Poliedres estrellats i tesselacions a l'espai
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 9 d'octubre
MMACA
Generació de corbes, Taller de poliedres
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 16 d'octubre
Departament de Matemàtiques de la UAB
Les seccions còniques: d'Apol·loni a la geometria projectiva
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 23 d'octubre
Departament de Matemàtiques de la UAB
El problema del nombre congruent
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 30 d'octubre
Auditori del Centre de Recerca Matemàtica (CRM), Campus de la UAB. Sala d'actes
Matemáticas que fluyen
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 6 de novembre
UPF
Mathematics helps Logistic at AMAZON
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 13 de novembre
Departament de Matemàtiques de la UAB
Corbes i superfícies reglades: rectes o corbes?
Sessió teòrico-pràctica. De 10h a 14h
Dissabte 20 de novembre
Institut d’Estudis Catalans, c/Carme 47, Barcelona
Conferència de cloenda. Màgia i matemàtiques. Lliurament de diplomes
Acte de cloenda. De 10h a 14h