A Calculus III lecture at ETH by Eugene Trubowitz

A calculus 3 lecture at ETHZ

Scanned lecture notes taken by Oliver Knill of a lecture given by Eugene Trubowitz

These notes of a calculus III lecture given by Eugene Trubowitz in the third semester at ETHZ (this is in the second year of the undergraduate studies) covered the topic of the Riemann Zeta function. As with the other course for the first two years, the course was mandatory which means for example that it was impossible to take an alterative or similar course instead. Also, as with most courses, there was no book, we had to digest the lectures or die

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. I found it actually quite effective to learn things from good lectures without being distracted with reading too much from different sources. It kept me focussed.

The lecture starts with a discussion of entire functions, mentions the formula of Euler (now often called "the golden key"), proves the functional equation for the Riemann Zeta function and ends with the Rieman hypothesis. At that time, I color-coded my handwritten lecture notes as follows: blue: questions, red: definitions, yellow: results, orange: important formulas.

While in the US, its difficult to get into a good university, it is quite hard also to be forced out from a US university. While at ETH, everybody with a highschool diploma (which about 15 percent of the Swiss population got then) can enroll, the exams would decide whether a student belongs there. Failing either at the first year or second year examination twice would mean to be "out". During the time of my studies, I estimate 20 percent of the initial math and physics class finished with a degree. While many things have changed since I was there, the basic things are still the same. I guess that the drop ratio could increase more, as highschool diploma become more common. Note that many nonhighschool diploma in Switzerland are equivalent to highschools in the US and part of highschool would overlap with the first part of college in the US.