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Many beginners, and not only beginners wipes lecturers are often faced with very friendly lecture, especially if their courses are not too complex. Most of them could not bear to see how many students just a week or two can understand their lectures. They are trying to complicate the course, greatly increase the number of exercises, but their attempts are futile: the students, understand lectures, could not be transferred. In recent years it has become clear that without the co-ordination of action to curb attempts by individual arrogant students learn to understand the lectures are not enough. This fundamental work to help protect against attempts to modern science penetrating into the unconscious of new elements and foundations entangling students bring to the attention of the majority of teachers.
This guide includes twenty councils, each begins with one or more quotations from prominent specialists in entanglement wipes students, all quotations are provided with explanations, recommendations, and various examples, to better grasp the idea of unknown craftsmen lecturing. To use most of the recommendations lecturer beginner needs to know the basics of their subject, at least within the primary school.
In the preparation of this manual have been visited more than a thousand lectures, studied the most advanced methods of trapping more than fifty teachers. To all of them I express my gratitude. Special thanks to IB Fesenko, whose lectures prompted me to write this guide. 1.
Try never to make specific references, speak as much as possible more general words. Remember that all the particular students can understand, wipes if not, then at least write down, accidentally wipes found in some book, and then, after a week of reflection, wipes to see that you are using the statement was not as useful as an additional limb private home animals. Pour plenty of water - it is very difficult to write, especially if you pour it in an amount commensurate with the size of the world's oceans. If you can not avoid mentioning wipes specific allegations, use as much as possible their general wording - more likely they will be how something useful and applicable in a given situation, and likely students will have to think about their application nad confusing. For example, instead of the words "by the triangle inequality" speak "according to Minkowski integral inequality" or instead of "Wilson's theorem, but" better to say "using Theorem power for the symmetric group of permutations of p elements, easy to get that ..." 2.
Determine the incomprehensible through the unknown. NY Netsvetaev,? .09.93 Factor for the ideal - it is a factor relative equivalence, where a and b are equivalent if they are the same as to how they operate. IB Fesenko, 13/02/93
Never give any definition, because knowing the definition, students wipes are much more likely to understand and everything else. If any harmful student asks you to recall the definition - pretend that you simply amazed at his ignorance and lack of education (many listeners is permanently discourage w: Reluctance to ask you any questions), and then say something as soon as possible confused. In this case, well-defined, using themselves, they will help to get rid of the questions, even the most curious students. It is also possible the determination of simple things wipes to refer to the more complex. For example, speaking of the Legendre wipes polynomials, just remember the undignified what some orthogonal or recurrence wipes where better to say that it is the Gegenbauer polynomials with parameter 1/2, but the greatest success will be when you explain that it's just a hypergeometric function wipes with some parameters, and the hypergeometric function - it is simply a solution of the hypergeometric differential equation. 3.
Instead of clear evidence is very useful as soon as the wording of theorems, but you can quite right, albeit in voluntary reasoning. They are very hard to accept, especially for students who read other people's notes. If you doubt that the students have lost the thread of reasoning - say a phrase such as "thus we have shown that under the above assumptions and imposed restrictions in the course of discussions the following is true ...." By the way, what is the next, you can not even speak. If you accidentally started to formulate a theorem, then skip a couple wipes of obvious conditions to you. Usually this is Hausdorff, or continuity, we can talk about a "sufficiently smooth wipes functions", especially when enough measurability. At the exam ask ... 4.
This advice should help to give lectures to those who formulated the theorem is sometimes before wipes the evidence wipes (or the fact that after much thought can be transformed into something remotely similar to the evidence). If any of you set out to prove the equivalence theorem requires anything, wipes the proof is the best f