Sergei Yakovenko's blog: on Math and Teaching

Monday, January 29, 2018

Exam

Filed under: lecture,Rothschild course "Analysis for high school teachers" — Sergei Yakovenko @ 5:05
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Exam

The exam is posted online on Jan 30, 2017, and must be submitted on March 16, 2018 (the first day of the new semester).

Its goals are, besides testing your newly acquired skills in the Analysis, to teach you a few extra things and check your ability for logical reasoning, not your proficiency in performing long computations.
If you find yourself mired in heavy computations, double check whether you understand the formulation of the problem correctly. Remember, small details sometimes matter!

Please provide argumentation, better in the form of logical formulas, not forgetting explicit or implicit quantifiers. They really may change the meaning of what you write!

Problems are subdivided into items. The order of these items is by far non-random, you have to solve them from the first through the last, (solution of one item may be a building block for the next one). A complete solution of a problem is a proof of some important theorem in Analysis, so you will be discovering these results on your own. The Remarks will help you to place the freshly proved theorem on the general picture.

To get the maximal grade 100, it is not necessary to solve all problems. Problems are of varying length, variable complexity, various level of abstraction. No apriori points are assigned for solution of each problem, no summation at the end. You can get extra points for short and elegant argument or have some points removed for writing an obviously stupid things (honest errors will simply bring you zero points). You have all the time, try to solve as many problems as you can, we will appreciate and assess the results as objectively and honestly as possible.

You are assumed to work individually, which is, of course, impossible to verify, but please in any case avoid submitting isomorphic solutions: this is a bad taste for take-home exams.

You are absolutely free to write in English (easier for me) or Hebrew, submit handwritten pages or compuscripts, in a hard copy or by email (even scans will work). I we will encounter difficulties reading your submission, we’ll let you know.

If you believe you found an error or crucial omission in the formulation of a problem, please write me. If this will be indeed the case (errare humanum est), the problem will be either edited (in case of minor omissions) or cancelled (on my account). In case of any doubt don’t hesitate to leave your questions as talkbacks to this post, so that other people will be able to follow. Asking questions is never penalized!

Good luck to everybody!

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Lectures 11-13 (Jan 16, 23, 30)

Filed under: lecture,Rothschild course "Analysis for high school teachers" — Sergei Yakovenko @ 4:53

Infinite series

These three lectures were devoted to the general theory of numeric series and the issues of their convergence. Then we switched to studying power series (both formal and convergent). Finally, we used the convergent power series to move into the complex domain and discover fascinating phenomena there.

There two separate sets of lecture notes, on infinite series and operations on them and on functions of complex variable.

Lecture 10 (Jan 9, 2018)

Integration and antiderivation

Again, no new notes were prepared this time.

Lectures 8-9 (Dec. 26, Jan. 2)

Linear algebra and differentiable maps

The revised notes on the linear algebra are available here.

No new notes concerning differentiability are added this year. The only thing you need to understand about it is the idea that linear (affine!) approximations, if available, carry an important bit of information about maps that admit such approximations. Use the notes from the past years.

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