https://sandromagri.info/en/math123/notes/index.htmlOn the Teaching of Mathematics: Arnold Concise History of Mathematics - D.J.Struik Mathematics and its history - Stillwell Mathematics Form and Function - Mac Lane Pi Greek Elements of Mathematics - StillwellHugoensandro@freenetst.it (Sandro Magrì)sandro@freenetst.it (Sandro Magrì)2020- All rights reserved.Sat, 15 Mar 2025 11:43:44 +0100https://sandromagri.info/en/math123/notes/insegnamento_matematica/index.htmlTue, 11 Mar 2025 22:30:23 +0100sandro@freenetst.it (Sandro Magrì)https://sandromagri.info/en/math123/notes/insegnamento_matematica/index.htmlON THE TEACHING OF MATHEMATICS Vladimir Igorevič Arnol’d uspekhi Matematicheskikh Nauk (1998) English translation Viktor Goryunov,Russian Mathematical Surveys, vol.53, no.1, 1998, pp.229-234 transl.it. Sandro Graffi in CRITICAL POINTS NO. 3 (MAY 2000) Local copy PDF Mathematics is a part of physics.Physics is an experimental science, part of the natural sciences. Mathematics is that part of physics where experiences cost little.https://sandromagri.info/en/math123/notes/post100/index.htmlSat, 15 Mar 2025 11:43:44 +0100sandro@freenetst.it (Sandro Magrì)https://sandromagri.info/en/math123/notes/post100/index.html1st ed. 1948, 4th revised and updated 1987, 6th reprint New York 2020 “Mathematicians grow very old; it is a healthy profession. The reason you live long is that you have pleasant thoughts. Math and physics are very pleasant things to do.” [“Mathematicians age a lot; it’s a very healthy profession. The reason you live long is that you have pleasant thoughts. Mathematics and physics are very pleasant things to do.”] Dirk Jan Struik (1894-2000)https://sandromagri.info/en/math123/notes/post190/index.htmlFri, 14 Mar 2025 23:12:42 +0100sandro@freenetst.it (Sandro Magrì)https://sandromagri.info/en/math123/notes/post190/index.htmlJOHN STILLWELL - MATHEMATICS AND ITS HISTORY - 3rd ed. 2010 Of the prolific Australian mathematician I have already reviewed two volumes: “Elements of Mathematics: From Euclid to Gödel,” 2016 “From Pythagoras to Turing. elements of philosophy in mathematics,” 2018 both review concepts in mathematics that one already encounters in high school, with a different point of view, and the second, in Italian, focuses on the most important ideas for the history of philosophy. This is a much more ponderous and comprehensive volume of more than 650 pages, with a concise and unified exposition of mathematics, including early undergraduate mathematics, organized according to the historical development of the subject. The edition to consult is the fully revised third edition of 2010, avoid the earlier ones and the “concise” edition of 2020.https://sandromagri.info/en/math123/notes/post170/index.htmlFri, 14 Mar 2025 23:12:35 +0100sandro@freenetst.it (Sandro Magrì)https://sandromagri.info/en/math123/notes/post170/index.htmlSaunders Mac Lane - MATHEMATICS FORM AND FUNCTION 1st ed. 1986, reprinted 2012 " Incredibly beautiful. … If you know the maths read it for the simple joy and new perspective. If you don’t know the maths read it to get a sense of what beautiful things exist and what’s out there to learn." [Incredibly beautiful. … If you know math read it for pure pleasure and new perspectives. If you don’t know math read it to get an idea of how many beautiful things exist out there to learn.] (Anomymous Online Reviewer)https://sandromagri.info/en/math123/notes/post110/index.htmlFri, 14 Mar 2025 23:04:27 +0100sandro@freenetst.it (Sandro Magrì)https://sandromagri.info/en/math123/notes/post110/index.htmlTells Eugene Wigner (Nobel 1965) at the beginning of “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” “There is a story about two friends, who were classmates in classical high school, talking about their work. One of them became a statistician and was working on population trends. He shows a copy of his study to his former classmate. The essay begins, as usual, with the Gaussian distribution, and the statistician explains to his former classmate the meaning of the symbols for the current population, for the average population, and so on. His classmate was a little incredulous and was not sure if the statistician was making fun of him. “How do you know that?” she asks him. “And what is this symbol here?” “Oh,” said the statistician, “this is pi.” “What is it?” “The ratio of the circumference of the circle to its diameter.” “Well, now you are pushing your teasing too far,” said the classmate, “surely the population has nothing to do with the circumference of the circle. "https://sandromagri.info/en/math123/notes/post060/index.htmlFri, 14 Mar 2025 22:43:52 +0100sandro@freenetst.it (Sandro Magrì)https://sandromagri.info/en/math123/notes/post060/index.htmlJohn Stillwell - “Elements of Mathematics: From Euclid to Godel,” Princeton University Press, 1st ed., 2016 John Stillwell - “From Pythagoras to Turing. elements of philosophy in mathematics,” ETS Pisa, 2018 One thing that is very frustrating for students, both in high school and college, is the fact that they never take a course in mathematics. That is, they take programs in geometry, elementary algebra, trigonometry, analysis but they never see to a course that reveals the substantial unity of mathematics as a creation of thought, the many connections between the different branches seemingly far apart, the relationships with other sciences, the applications, the historical and social context. in this respect, Prof. John Stillwell’s books are very useful reading for everyone, and especially for high school and early college students. “Elements of Mathematics,” deals mainly with branches of mathematics already seen in high school, explained in a completely different way, with a new point of view. Each topic is covered clearly, concisely, and succinctly with basic principles, examples, problems, applications and connections to other areas of mathematics, historical notes, and philosophical implications. another volume by the same author, “Mathematics and its History,” which is slightly more advanced, more comprehensive and ponderous (about 660 pages versus 400 in this one), provides an overview of the mathematics one encounters in college; we will discuss this in detail in another post.