دانلود کتاب مفاهیم ریاضی مدرن برای مهندسان، بخش اول: از حساب دیفرانسیل و انتگرال بی‌نهایت کوچک تا نظریه اندازه

Spring, 2023 – somewhere around Zermatt in Switzerland Two alpinists are traveling down from the Dufourspitze, the highest peak of Monte Rosa. Laurent is enjoying his first year of retirement by spending as much time as possible in the high mountains. For his entire active life, this passion remained sidelined by mathematics, his other passion. Especially since his wife passed shortly after their wedding, and they had no children, he has given himself no chance at a family life. Due to his grief, he has allowed his two passions to consume him, and, as he has lived in Paris for a long time, math has taken precedence over his more distant passion. They feel exhilarated at having climbed one of the highest summits of the Alps. Approaching the alpine hut, having left the dangers of the glacier behind, Pierre feels confident enough to open up to his old mathematician friend. These last few weeks, Pierre has been very preoccupied. His last son, Bernard, was hired a month ago as an engineer. Pierre is afraid that his son is not up to the task. When surrounded by the dangers of the high mountains, his worries had vanished. But, as he approaches solid ground, his son’s professional situation is creeping up again, disturbing his euphoria. Laurent and Pierre met long before they started mountaineering together. One coming from Annecy, the other from Grenoble – two big cities in the French Alps – they became very close friends during math´ematiques sup´erieures et sp´eciales at a highly prestigious French institution in Paris. Laurent entered the ´Ecole normale sup´erieure de la rue d’Ulm, initiating his brilliant career as a mathematician. Pierre entered the ´Ecole polytechnique and has grown increasingly distant from math as he progressed rapidly in the industry. Even though their career choices could have separated them, they have remained close thanks to a continuing dedication to mountaineering – through shared weekends or longer periods – for over 40 years. Walking downward from Monte Rosa, Pierre tells Laurent that his son has put himself at risk professionally: — Bernard has been asked to study via numerical simulations the feasibility of building a pharmaceutical plant, taking into account current environmental contingencies. I am afraid he lied about his skills to get hired. — You know, Pierre, I have been giving lectures to 25-year-old students for a long time. They brag that they find it hard to focus for more than seven minutes… I am not at all surprised. — If you allow me, it is not only about young people. I stopped watching television because of stupid things that people wrongly infer from math and science. Remember what this “Prof.” Harry Bannan said about the inflection point of the exponential function (sic) during the pandemic… Thinking about his dear friend’s rather harsh answer, Pierre reflects on his personal responsibility for his son’s education and situation. Bernard was born when Pierre was 40, from his second wife. Bernard has qualities, real ones, but he has always been spoiled and doesn’t realize that the more effort it takes to get things, the more valuable they are. Surely, he could have made something better of himself than entering into an engineering program whose selection is based on a math quiz. Based on his own education and his experience in the industry, Pierre knows that mastering applied math is essential to solving Bernard’s problem. He honestly thinks Bernard’s curriculum is not serious enough to tackle it. Perhaps Laurent might be able to help him? He ventures… — I’m not sure I’m the right person, you know. I am not particularly fond of this generation, says Laurent. As I have not had children, I do not really understand them. They speak too fast, too loud, they always zap from one thing to another, and they get bored so easily… It is so far from the life I chose for myself, where I can focus for days, weeks, or months even on a single math problem. And I am old and tired. — You’ve known Bernard forever; you know he isn’t a bad guy. True enough, he cannot focus for long. But he has the spirit of youth, and he wants to accomplish things. He wants to succeed in life. I honestly think you could help him acquire the necessary fundamentals. You would do me an immense favor by trying, at least. One week later – Caf´e Le Rostand in the Quartier Latin in Paris Bernard is sitting inside a caf´e. He is early for his 3:00 pm appointment. His father has told him that he absolutely had to be on time for his meeting with this exacting old man. Laurent had agreed to meet his old friend’s son (for a discussion) to assess his ability to be of help to him. Laurent would then decide whether he was ready to work to help Bernard with his pharmaceutical plant problem. Bernard had just completed his curriculum at CeePlus, an engineering school that was sadly not among the best, said his polytechnicien father. To the latter’s surprise, Bernard had managed to get a job at SofterWorld Consulting, one of the most demanding international companies. Together with all the other students of his school, he thought that math was merely a selection tool and was absolutely useless in real life. What a (capital) mistake! He was just starting to realize… Upon seeing Bernard, Laurent wants to understand precisely the situation in which Bernard finds himself. Bernard tells him that he had glorified himself throughout the interviews as being a French engineer, whose curriculum is more theoretical than the vast majority of curricula. In particular, he had to explain that French-trained engineers mastered math better than their counterparts from other countries. The department in which he has been posted is headed by Ann Winglett, a brilliant individual who obtained her PhD in applied math at MIT, following an MSc in pure mathematics at Orsay in France. She intends to use Bernard’s trial period to check whether his true skills match what he has told her. In particular, she wants to confront him with the engineers of the company who were not trained in France.