SM/0129 - ARITHMETIC AND LOGIC
Academic Year 2019/2020
Free text for the University
MARINA MUREDDU (Tit.)
- Teaching style
- Lingua Insegnamento
|[60/65] MATHEMATICS||[65/10 - Ord. 2012] Generale||6||48|
Arithmetic and Logic course aims to give the student a picture, as complete as possible, of the mathematical understandings starting from
the invention of the positional numbering (Panini, I century a.C), passing through Fibonacci (1170-1250), until the formalization of the mathematical logic started with Boole (1815-1846). At the end of the course, the attentive and participant students should find themselves with a greater knowledge of the historical and current issues and problematics. I believe this course provides students with important tools through dissemination. In addition, the course focuses III and IV points of the Dublin descriptors: autonomy of judgment and communication skills. At the same time, I believe that it is not entirely in my power to change the learning capacity of students who have already reached the second year of the master's degree. Indeed, their ability to store complicated notions without any critical sense might cause some of the students believe that they have already reached the maximum level of their learning. That is a problem because with that lack of self sense, interest and modesty my efforts become vain.
Mathematics is now so well formalized that there is no longer any need of full comprehension about the issues. Indeed, those who stop to understand philosophy
that is at the base of mathematical reasoning will be like students who are content to be able to answer the questions that will be asked to the examination whether they understand what they are doing. Those exam questions give the students the opportunity to respond according to a pre-established cliché. In addition to the formalization of mathematics, to be able to give the possibility for everyone to follow with the same methods of learning, we also try to formalize the teaching of any subject with a succession of precepts suitable for zero the differences in assessment. This is not an accurate assessment if you realize how much human beings (thankfully) are much more complex than the most sophisticated and futuristic computer.
Another formative objective of this course is to discuss the establish understanding that mathematical knowledge is neither a sequence of theorems and demonstrations nor, much less, the ability to solve complicated problems in art. What I hope to achieve is to provide the students with a realization that teaching has no shortcuts, highways and prescriptions. Each step is determined by their depth of knowledge of the subject and the students they encounter; and if they really want to teach even a little math, they must continually change their tactics
and study social and intellectual history to realize the difficulties of ordinary people (in all times and in all places). My goal is to erase the concept of "trivial" from the classrooms: the phrase "But it's trivial!"; A phrase that hides the lack of understanding. As Einstein says: "You do not really understand something until you are able to explain it to your grandmother "
Numbers:Talete, Pitagora, Zenone, Euclide, Archimede, Eratostene, Diofanto,Panini, Brahmagupta, Al-Kwarizmi, Abu Kamil, Fibonacci, Pacioli, Del Ferro, Tartaglia, Ferrari, Copernico, Cardano, Viète, Keplero, Galilei, Nepero, Briggs, Fermat, Cartesio, Pascal, Cavalieri, Wallis, Newton, Leibniz, XIX century in France.
Verification of learning
Written test for student 36/48, Otherwise oral test.
Doneddu, Aritmetica Generale.
Other books, in particular: "Ifrah, Storia universale dei numeri".