## PG as evolution of Perl for mathematicians in WeBWorK

2 years, 11 months ago
Disclaimer: The provided information can be useful to teachers, authors of courses. The majority of information is loose translation from English-speaking Wiki WeBWorK.

For a start: What is WeBWorK?

WeBWorK is the free system written on Perl for providing individual homeworks through a network. The system allows teachers to create courses from a set of homeworks which can be solved by students afterwards.

The student can will get access to homework from any computer. The system assumes input of formulas in any identical kind that removes excess cares from the student. Thanks to the fact that information on a correctness of a solution arrives immediately the student has an opportunity to solve a task.

The teacher is also not limited in the place of access. For drawing up a course both new tasks, and thousands of already ready tasks of several universities can be used. For suppression of writing off an opportunity to set specific features of a task for each student is provided. All information on students, courses and statistics of a solution of tasks is available to the teacher that allows to evaluate better progress of students as the general, and individual.

## 10 largest mathematical achievements of the last years

2 years, 11 months ago

Aperiodic mosaic of Sokolara-Taylor

Recently I work on the book "Mathematics of 1001", I do additions for the following edition which will be published abroad. Therefore I monitor the mathematical achievements which happened approximately since 2009. And I decided to provide you ten the most important events on this subject since then, as subjective increase in importance.

10. Sinjiti Motidzuki declared the proof to them abc-hypotheses. The event got to the end of the list as still its proof is not supported by a big circle of mathematicians. Otherwise it would win first place. For now, to disappointment of interested parties, it is in a limb.

9. Ternary problem of Goldbach. "Since 7, any odd number is the sum of three simple". Since 1937 this statement is right for enough large odd numbers, but in 2013 the Peruvian mathematician Harald Gelfgott verified this statement on the computer for numbers up to 1030. Irrespective of it it was made also by David Plath.

## Algorithms: theory and practice. Methods

3 years ago

In November we start online course "Algorithms: theory and practice. Methods" from Computer Science of the center. Course free, everyone is invited. It will be aware basic algorithmic methods are in detail sorted: greedy algorithms, method "separate and dominate", dynamic programming. For all algorithms the correctness and estimates for operating time will be mathematically strictly proved. We have tried to state material so that also algorithms, and how it would be possible to guess to their main ideas were clear. In addition to theoretical bases, subtleties of implementation of algorithms in programming languages C ++ will be told, to Java and Python. In particular, it will be told what the general practicians of writing of code allowing to minimize probability of error how to write and test code where it is worth using standard methods are but not to invent wheel.

We have carefully picked up tasks for material fixing. The majority of algorithms which you learn, you will need to program. It is the best way to be convinced that you have understood all parts. Solving such problems, you get valuable experience of writing and debugging of effective and reliable programs. Tasks on programming will help you to feel difference between bad (slow) and good (fast) algorithm. You are also waited by tests (where it is necessary to select the correct answers from offered) and theoretical tasks (in them it is necessary to prove the mathematical statement). At last, it is aware to eat also problems of the increased complexity — less standard tasks which are not obligatory for passing of course. Those who is already familiar with basic algorithms will be able to derive pleasure from solution of these tasks also.

## Non-overlapping sets and mysterious function of Akkerman

3 years ago
It will be a question of simple data structure — system of non-overlapping sets. In brief: non-overlapping sets are given (for example, graph connectivity components) and on two elements x and y it is possible: 1) to learn, whether are x and y in one set; 2) to integrate the sets containing x and y. The structure is very simple in implementation and was described many times in different places (for example, there is good article on Habré and still here and there). But it is one of those surprising algorithms, to write which it is possible, and here to understand why it works effectively absolutely hardly. I will try to state rather simple proof of exact assessment for the operating time of this data structure which is thought up by Zeydel and Sharir in 2005 (it differs from that horror which many could see in other places). Of course, the structure too will be described, and we will in passing understand and here inverse function of Akkerman about which many know only that it oooochen slowly grows.

## Oscilloscope on WebGL

3 years ago

In electronic music there is interesting direction — music for oscilloscopes which draws interesting pictures if to connect output of the audiocard to oscilloscope in the XY mode.
For example, Youscope, Oscillofun and Khrậng.

All beautiful videos generated by such music are created by means of record of work of the real oscilloscope on video camera. When I have looked for emulators of oscilloscopes in network, I did not manage to find such which draw soft lines as in the real oscilloscope.

It has moved me on sozdatsy the emulator of oscilloscope on WebGL: woscope.

In this post I will tell about that how exactly there is drawing of lines of oscilloscope in woscope.

## Ant optimization and network algorithms

3 years ago
As you could notice, we have calm here. But our creative search does not stop, and the first October publication will be devoted to ACO (Ant Colony Optimization)

Paying tribute to the author, we will not publish the last part of article containing example on JavaScript here, and we will suggest you to test it on the original site. Under cat you will find transfer of the theoretical part which is well telling about subtleties of ant optimization in different scenarios.

## Phase portraits "on fingers" or that can be learned about solutions of diffur, without solving it

3 years ago
Very often in a number of sciences the situation when the model of the considered process is reduced to differential equation meets. And, in the majority of real problems it is quite difficult to solve this equation, or it is absolutely impossible. And here the immemorial question at the top of the voice sounds: how to be?

3 years ago
On September 28 viktorpanasiuk has published task which solution is urged to lower costs of production of nebezizvestny confectionery, having made its goods more competitive in the market and more available to the buyer.

It was necessary to find as much as possible tolerance of mass of candy by its production that net the box consisting of 12 their pieces was not gone beyond by 310±7 grams in 90% of cases. To consider the distribution law normal.

The answer has been received that if root mean square deviation of mass of candy by production does not exceed =1,2248, this value is not limited on top.

Under cat you improvement of the received result on the module of some as it seems to me — reasonable expects, assumptions. Further it is stated insufficiently strictly, but nevertheless demands knowledge of the mathematical analysis and probability theory in volume of technical college.

3 years ago

## Task from area of financial calculations

3 years ago
In finance there are tasks of assessment of investment projects in which there is a number of indicators on which values the general assessment is given. These are such indicators as project payback period, the provided income, the net provided income etc. As a rule, for definition of each of indicators there are formulas in which, simply, it is necessary to substitute basic data, to calculate and receive result. But there is one of indicators which simple substitution of data in formula is not solved. This indicator is called "internal standard of profitability". Now there is big set of the different software for financiers which allows to conduct all calculations automatically, without reflecting how everything occurs inside.