3.4.5 Multinomial Theorem: Video

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MIT 6.042J Mathematics for Computer Science, Spring 2015
Instructor: Albert R. Meyer

License: Creative Commons BY-NC-SA

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I recently just programed a polynomial builder that takes in an array of terms and the degree at which it should be raised to and it foils it. I will be making a video on it soon. Keep in mind I am only a senior so if you see mistakes or improvements please let me know :)

emenikeanigbogu

Thanks a lot!! So interesting to know that computer science uses this theorem which I am just learning from an applied math course.

daniello

Nice video! One thing I want to add about the relation between bookkeeper's rule and operation of taking power: when a power is to be taken, given the power being an integer, then that can also be written as a multiplication of the term that is being taken power time itself for n-1 times given the power is n. Then for every iteration of that multiplication operation, since multiplication is a binary operation, you are required to choose 2 operands that which is the same for this case, and then from those operands which can be expressed as sum of i and j terms (each amount of terms for 2 of the operands), one has to choose 1 of i terms and 1 of j terms from the operands and after doing this action for every iteration (n-1 times) we get the result that is one term of the multinomial. Now, it is apparent that for the power of n, in the total n numbers must be multiplied after doing iteration that is multiplying 1 of i terms and 1 of j terms in every iteration. In the end, you basically choose from numbers in your base of power and order the appearance of when they are multiplied and you get the number of times a term is achieved from the expression

rusty

THANK YOU SIR A LOT!! WE JUST USED A SIMPLE PROBLEM OF COUNTING HOW MANY PERMUTATIONS OF A GIVEN WORD AND WE REACHED THE LEVEL OF MULTINOMIALS.AWESOME😊😀

shaikabutalhah