There are no official requirements for this course but basic knowledge of technical drawing and descriptive geometry is recommended. The objective of the Graphic Expression subject is to prepare students so they can compose and interpret the necessary graphic documents to carry out their professional activity. For this purpose, the intention is to give you the knowledge about the systems and techniques of representation most appropriate to each case. Special attention will be given to the application of computer-assisted representation techniques, with a parallel development of spatial interpretation capabilities. Initiation to work in Autocad 2D.
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View four larger pictures. Pedro was his parents' only son. The first workshops of the company were in the Barceloneta district of Barcelona and it was in the primary school in that district that Pedro began his education. Robert Puig loved music and languages and had a huge influence on his son Pedro. At the primary school in Barceloneta, Pedro was taught by Josep Gra and he proved himself an outstanding pupil, excelling in writing and arithmetic.
At the age of eight, Pedro's father sent him to the Franklin Institute in Lyon in France where he spent fifteen months. As well as improving his French, he also learnt German during this time in Lyon. He completed his studies at the Institute in , winning the top prize. Later in Puig Adam entered the School of Industrial Engineers in Barcelona and as well as studying engineering at this school, he also studied mathematics in the School of Exact Sciences which was in the same building. After taking two engineering courses he gave up his studies in this area to concentrate on mathematics.
The professor who had the greatest influence on Puig Adam at this stage was Antonio Torroja Miret - , Professor of Descriptive Geometry and Geometry of Position at the University of Barcelona, who taught him projective geometry. Torroja Miret was the first teacher to introduce Puig Adam to rigorous mathematics, teaching him to both think rigorously and to write rigorous mathematics.
At this time classes were small and often Puig Adam would be the only student in Torroja Miret's classroom. Torroja Miret related an interesting episode many years later.
This happened in Puig Adam's first year at university see for example [ 3 ] :- Puig Adam was an outstanding student so imagine my surprise when, in April, I received the visit of his father, who saw that his son was studying with the ardour with which he always did, but was nervous, worried and expressing fear at every step. He wished, as a good father, to know my judgment, so that he could advise his son, if necessary, not to take the examination and to study the subject again in the following year.
That brilliant student I do not need to tell you what my answer was. What I want to add, in honour of his father, is that the son did not know about that episode or my encouraging reply until many years later. After graduating from the University of Barcelona, Puig Adam went to the Central University of Madrid to complete his doctoral studies. Puig Adam was always grateful to these teachers. Miguel Vegas, whose teachings and affection were invaluable to me. His wise observations led to the correction of many of its defects.
I do not know how to express my gratitude for his spontaneous and for me such a precious collaboration. In the thesis he states that the topic studied was During the following three years a number of famous mathematicians visited Madrid and gave lectures which Puig Adam attended.
Puig Adam took on a number of different teaching positions over the following years. Also from but continuing until , he taught mathematical analysis and infinitesimal calculus at the Catholic Institute of Arts and Industries in Madrid.
From to he taught at the Higher Technical School of Computing. They had been friends since meeting in Barcelona and so their wedding took place in Barcelona but they settled down to live in Madrid. Both were enthusiastic musicians and they both played the piano. However, he had only reached Lyon when he fell ill and was advised to rest for three or four months. He returned to Madrid and eventually decided not to take up the scholarship.
In he was appointed as professor of mathematics at the Institut de Sant Isidre in Madrid. We see from these titles that he was concentrating more on teaching mathematics.
He began working with Julio Rey Pastor on writing books for secondary school mathematics teachers. Not on a single day you must begin the Geometry lesson without having these, your good companions, next to you, nor finish studying it without leaving your table completely full of trimmings of paper and paper with figures I: Plane geometry. II: Geometry of space However, Puig Adam had many interests other than mathematics and teaching:- He cultivated a fine sense of humour, he enjoyed reciting and writing verses, playing hands of cards, performing, harmonizing and composing musical pieces, drawing portraits with charcoal and painting pictures.
A whole host of hobbies that combined with his teaching, research, literary creation, exquisite cultivation of friendships in conversations and visits or in maintaining an abundant correspondence.
The situation became unbearable when Franco' troops launched a major offensive against Madrid in October , so at that time he left Madrid and moved to Barcelona. There he taught from to at the Institut-Escola de la Generalitat de Catalunya and also as a professor at the Escola Central d'Enginyers Industrials de Barcelona. Although Puig Adam was back home in Barcelona and at first in a better position regarding the Civil War, nevertheless the situation grew worse as Franco' army, with air support from Germany and Italy, forced the Republicans back.
Many of the teachers at the Institutes where Puig Adam worked were either killed or fighting with the army. The health of Josep Estalella, the director of the Institut-Escola de la Generalitat de Catalunya, worsened and he died on 20 April Puig Adam took over the directorship of the Institut-Escola.
When Barcelona fell to Franco's Nationalists in January one might have imagined that Puig Adam would have been dismissed but in fact he was able to continue in all his teaching positions in Barcelona. He became a full professor at the School for Industrial Engineers in Although Puig Adam taught in an exemplary manner at the San Isidro Institute in the s, nevertheless the experience was not made easy by having classes of more than students.
There was also a lack of resources and the rigid regulations together with the need to prepare students for the various examinations and state tests meant that he was somewhat restricted in presenting mathematics in the way he thought best. There was a national decline in standards during these years which caused him great sadness but he tried to compensate by presenting his ideas in various international publications and delivered some wonderful conference lectures. His work did not receive the recognition it deserved during his lifetime, neither by the Administration nor, with some exceptions, by Spanish mathematics teachers.
However, today his contributions are very highly respected and a glance at the references below will show how much he has been appreciated in more recent times since only two references are dated while the remaining 25 are dated or later.
Let us end by giving Puig Adam's advice to mathematics teachers: Do not adopt rigid didactics, but adapt in each case to the student, constantly observing. Do not forget the concrete origin of mathematics or the historical processes of its evolution.
Present mathematics as a unit in relation to natural and social life. Carefully graduate the way towards abstraction. Teach guiding the student's activity towards creating and discovering. Stimulate this activity by arousing direct and functional interest towards the goal of knowledge.
Promote self-correction as much as possible. Obtain some mastery in the solutions before they become automatic. Ensure that the student's writing is a faithful translation of his or her thinking. Help all students to succeed in avoiding becoming demoralised. Other Mathematicians born in Spain.
References show. F B Pedraza et. Puig Adam 56 , 41 - Additional Resources show.
Pedro Puig Adam
View four larger pictures. Pedro was his parents' only son. The first workshops of the company were in the Barceloneta district of Barcelona and it was in the primary school in that district that Pedro began his education. Robert Puig loved music and languages and had a huge influence on his son Pedro. At the primary school in Barceloneta, Pedro was taught by Josep Gra and he proved himself an outstanding pupil, excelling in writing and arithmetic. At the age of eight, Pedro's father sent him to the Franklin Institute in Lyon in France where he spent fifteen months. As well as improving his French, he also learnt German during this time in Lyon.
Puig Adam Geometría Métrica - Tomo I.pdf
The need to provide a neural network for pattern recognition with invariance to a new transformation, projectivity, is considered. This invariance is justified when working with object images that can appear rotated in relation to an axis contained in its own plane. An invariable relation to the transformation is found, the double ratio of four points, and incorporated to the network as a restriction to the weights. A projectivity invariant pattern classifier has been simulated. Besides, some considerations about high order neural networks are expounded. Unable to display preview.