Sergei Yakovenko's blog: on Math and Teaching

Saturday, September 6, 2014

Polynomials, matrices and differential equations

Filed under: lecture — Sergei Yakovenko @ 10:33
Tags: ,

The transcendental elementary functions \sin x,\cos x, \mathrm e^x,\ln x are traditionally introduced in the high school/(pre)calculus courses in the way that obscures their inter-relations and properties. The text below is an extended version of the one-hour lecture delivered on Ulpana de-Shalit for undergraduate students. It purports to introduce these functions as solutions to linear differential equations in the way similar to radicals being introduced as solutions to algebraic equations.

Polynomials, matrices and differential equations, 11 pages (pdf).

Wednesday, July 9, 2014

Numeric indicators and real achievements

Filed under: opinion — Sergei Yakovenko @ 4:08

It is sometimes argued that the level of scientific research can be measured by various kinds of numeric indicators (number of publications, citations, the total of research grants obtained, PhD theses written etc.).

If you sincerely believe in this nonsense, here is how it works in another area (hat tip Yu.Sh.).

According to FIFA, the yesterday’s semifinal game Brasil vs. Germany in the mirror of numbers looked as follows:

Indicator Brazil Germany
Total attempts 18 14
Deliveries in the penalty area 19 11
Ball possession 52% 48%
On-target attempts 13 12
Saves 7 5
Score 1 7

Perhaps some navel gazing is required, dear administrations?

Wednesday, February 19, 2014

Correction to the exam: Problem 3, parts (6), (7)

Filed under: Uncategorized — innaento @ 11:46

There has been two misprints in Problem 3, parts (6), (7).

In part (6), the expression should be


(notice the correction in red!)

Also, in the Hebrew version, the denominator in the hint in part (7) should be 2^{-n} and not 2^n.

The English version of the exam has been corrected (here:

The corrections to the Hebrew version appears in RED here: (this file contains only the relevant page!)



Thank you very much to Menuha for pointing this out.

Thursday, February 6, 2014

Change of the deadline

Dear all,

the deadline for submission for the take-home exam was changed following the requirement of the Feinberg School. Please note that the exam should be submitted by the last day of February, 2014.

Good luck to everybody,


Monday, February 3, 2014

Exam: due February 28, 2014

Filed under: Uncategorized — innaento @ 10:37

Here is the exam:


Hebrew translation (handwritten): Hebrew_ver (note that Problem 3 has a misprint! Correction here:

It is due on Tuesday, March 4th Friday, February 28, 2014, by 23:00 (1 month from now).
Please let us know as soon as possible if there are any comments or remarks about the exam.
- You do NOT have to solve everything to get a good grade. Try to solve as much as possible.
- Try to write your solutions carefully and formally. But if you can’t manage, then write an informal solution – you will still get credit for it!
Good luck!

Tuesday, January 28, 2014

Exponent function – additional material

Filed under: Uncategorized — innaento @ 3:50

The following problem gives you a step-by-step definition and properties of the exponent function:


You do NOT need to hand it in.

Homework 5, problem 3.2 remark

Filed under: Uncategorized — innaento @ 12:04

Why the definition of the limit of a function f: R –> R at a point a through sequences is the same as the definition of the limit of a function at a point through epsilon, delta: Analysis _HW5_remark

Monday, January 20, 2014

Homework 5 – late hand-in

Filed under: Uncategorized — innaento @ 5:42

You can hand in Homework Assignment 5 until 30.1 (Thursday), but it might take time for me to check it.

Those who will hand in the homework until 24.01 (Friday) will get in back within a week.

Monday, January 13, 2014

Homework assignment 5 correction

Filed under: Uncategorized — innaento @ 11:23

In the definition of “limit of function f at point a” (page 2, line 5), should be

|f(x) – c| .

(NOT f(c) as it was written).

Thursday, January 9, 2014

Homework assignment 5 (due 23/01/14)

Filed under: Uncategorized — innaento @ 4:57

Homework assignment 5 can be found here: HW5_analysis

It is due on 23/01 (two weeks from now).

Let me know if you have questions or comments.

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