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Methods in problem solvingучебный курс
- Автор: Alexei Belov
- Год создания: 2011
- Курс на иностранном языке
- Описание: 1. The main objective is to make student to meet with non-standard problem - on any level. This happens in some percentage of cases and there is responsibility problem. It is very hard to demand to produce something non-standard. The only way as I see - to make term paper plus low credit for course. They can find the solution but at least they should write it in qualified way. That is all can be done for majority of students. 2. Another objective of the course - to see perspective students and show them joy of mathematics. 3. All BIU students, including talented ones know almost nothing on the problem solving methods (and, by the way, when we started with Lev IMC - almost all students from all universities, excluding some students from Tel-Aviv). Same stuff I did in China. For all students for all levels I have to teach following subjects (which are understandable even for kids): a) Invariants, mostly Parity (chessboard with + and -, signs in each row and column can be interchanged, when possible to get all +) many elementary stuff. 2-3 classes - level does not matter. b) Pigeonhole principle in elementary forms. 2 classes c) Invariants in geometry (is it possible cut the circle in some pieces and rearrange into square every cut is the straight line or circle - sum of convex arches - sum of concave), pigeon hole principle in geometry (there exist two opposite sea points on the earth). 1 class. d) Reduction and optimization process. (Each classmate participated in two trips, in each of them girls was >20%, prove that number of boys is less then 2/7 ) 2 classes. e) Seminvariants. (Each parliament member has \le 3 enemies. Prove that parliament can be divided in two parts such that in each part everybody has no more than 1 enemy. enemy relation is mutual. divide somehow and if somebody has 2 or more enemies in his part - he or she moves to another part, number of enemy relations in parts decrease (2 brakes, at most 1 new). 1 class f) Boundary principle. (On each cell of chessboard some number is written, each number in a cell is the mean of its neighbors. Prove that the numbers are equal. Consider maximal one) 1 class g) Extremal principle. equivalence two main definitions of convex figure. 1 class, joining semiinvariant with boundary principle. some specific subjects: (which can vary a little bit) h) Information theory. Guessing number via questions with answers ``yes'' or ``no''. why 1 ``trit''=\log_23 bits? 1 class f) Fast multiplication, RSA - promotion of subjects - advertise to deal cryptography and computer algebra. I strongly disagree with dividing course for advanced students and usual ones. My reasons are following: 1. In this situation weak students does not spoil situation and does not trouble good students. 2. From other hand, public discussion with good students is reasonable to see for other. If class made from bad students it does not work at all. We kill dialog. 3. The reason of class is also to catch perspective. Without public dialog it will be killed. What is reasonable to do: A. I think, I have to note active students and provide this information for other perspective scientific advertisement and sent them Olympiad invitations. B. Instead of having course of problem solving but for advanced and usual students, it is reasonable to have same course as it is in Fall semester, but in Spring semester somehow continuation - ``reading'' course for advanced students - they produce more complicated papers (solutions of some problems, may be not for publication in math journal, but sometimes good enough for popular journals publications such as solution of problem). In some journals I can guarantee publications. May be not for everyone but some. I am responsible for problem corner.
- Добавил в систему: Белов Алексей Яковлевич
Прикрепленные файлы
| № | Имя | Описание | Имя файла | Размер | Добавлен |
|---|---|---|---|---|---|
| 1. | Задание | zadanie2012.pdf | 74,3 КБ | 1 декабря 2016 [AlexeiBelov] | |
| 2. | Задание | problemsfall11.pdf | 56,4 КБ | 8 ноября 2016 [AlexeiBelov] | |
| 3. | 88300_grading_policy.pdf | 88300_grading_policy.pdf | 58,7 КБ | 8 ноября 2016 [AlexeiBelov] | |
| 4. | Задание | zadaniefall132.pdf | 71,5 КБ | 8 ноября 2016 [AlexeiBelov] | |
| 5. | preselection.pdf | preselection.pdf | 18,0 КБ | 8 ноября 2016 [AlexeiBelov] | |
| 6. | 88300_grading_policy_go6rqcq.pdf | 88300_grading_policy_go6rqcq.pdf | 14,8 КБ | 8 ноября 2016 [AlexeiBelov] | |
| 7. | Задание | fall14.pdf | 31,2 КБ | 8 ноября 2016 [AlexeiBelov] | |
| 8. | Задание | fall14adv.pdf | 25,9 КБ | 8 ноября 2016 [AlexeiBelov] |