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- My question is about the history of education in Physics and Maths.

I will basically focus on 18th and 19th century, I got to know from the biographies of Max Planck and few other that there were no organized syllabus in Universities for studying. Students had to take classes that they could understand and it was less like a lecture and more like a private tutoring by some professor to a small number of students.

I got this

information from cesaruliana (a user from another forum). And as I'm reading Arnold Sommerfled's Lecture on Theoretical Physics (on the guidance of @vanhees71) I came across this

So, I have given two examples where it was assumed by the instructors that the students know higher mathematics. If we focus on first quote, we find that up to 1850s textbooks (textbook in the sense that we use it today, an organized sequence of chapter with explanations and exercises) were not in general public use, only

In my second example Sommerfeld is assuming his students to be familiar with vector calculus, although the year was around 1945 - 1951 (and his lectures were meant for undergraduate courses) but it was Germany not the U.K. where universities by this time had adopted an organized course. Was it like that instructors used to teach students all by themselves without means of any textbooks? Do we have any record of lectures where an instructor doing something like this?

Any help will be much appreciated.

I got this

It is noteworthy that in the 1850s the Stokes' Theorem appeared in the examination for the math Tripos at Cambridge, as a question to generalize Green's Theorem to 3 dimension, from what we surmise that it was not explicitly taught.

information from cesaruliana (a user from another forum). And as I'm reading Arnold Sommerfled's Lecture on Theoretical Physics (on the guidance of @vanhees71) I came across this

Throughout this volume we shall make continual use of vector analysis, that is, calculus applied to vector quantities. Thus, while familiarity with vector algebra and with basic concepts of vector analysis is assumed on the part of reader...

So, I have given two examples where it was assumed by the instructors that the students know higher mathematics. If we focus on first quote, we find that up to 1850s textbooks (textbook in the sense that we use it today, an organized sequence of chapter with explanations and exercises) were not in general public use, only

*original publications*were there (original works of Stokes, Cauchy, Green, Hamilton). My point is the textbooks that we use today contains the explanation of some topic with examples and real life situations but the*original papers*doesn't intend to teach anything, their only purpose is to establish a result indisputably. So, how those students lear higher mathematics (like Vector Calculus) without the availability of textbooks?In my second example Sommerfeld is assuming his students to be familiar with vector calculus, although the year was around 1945 - 1951 (and his lectures were meant for undergraduate courses) but it was Germany not the U.K. where universities by this time had adopted an organized course. Was it like that instructors used to teach students all by themselves without means of any textbooks? Do we have any record of lectures where an instructor doing something like this?

Any help will be much appreciated.

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