12.1.1-12.1.4
Section 12.1.1- 12.1.4 Blog Entry
Having read sections 12.1.1-12.1.4 in the text:
Difficult:
One thing that I was not sure about was why 0! is equal to 1. How can we prove that 0! = 1 or is this statement a set idea/value that if assumed allows the rest of the factorials to be calculated? Also, how are the binomial coefficients (n k) = (n n-k) [couldn't figure out how to use superscripts in this blog] as stated on page 789? From the way that the text refers to the identity, it seems as if the binomial coefficients (n k) = (n n-k) can be equal only when k=0, but I'm not sure when it would equal each other in different cases. On page 790, the text refers to applying the counting principles to expand the binomial theorem (x+y)^n but I wasn't quite sure (and couldn't quite remember) how to write the expanded form when given values of n and k. When looking at the solutions section of the example, I was a bit confused when the text stated "A term of the form x^k . y^(n-k) occurs (n k) times since there are (n k) ways of selecting the factor x k times from among the n facotrs (x + y)."
Reflective:
In all of my previous math classes, I never felt as if I was able to delve and completely understand the ideas behind probabilty and statistics. During Algebra 2 when I first encountered counting principles such as permutations and combinations, I think I was more set on using the equations rather than truly understanding the logic behind the topic which made it more difficult as we began to encounter more complicated/challenging cases and began combining counting principles as in section 12.1.4. I think the text's way of writing out the definition/equation for a permutation was a bit confusing for me to understand at first since I had always approached it a bit differently. I think the ellipses/repeating multiplication symbols within the equation P(n,k) = n(n-1)(n-2) ... (n-k+1) made me forget about having the same number of descending factors (k) as parentheses on the right side of the equation and led me to think that there were more factors in between (n-2) and (n-k+1) that had to be multiplied to calculate the permutation. Although the examples of counting principles have always been centered around marbles in a bag or a deck of cards, I think that encountering it in a life sciences model/scope would be very interesting and more related to the career fields that interest me. I see now that using these counting principles in certain situations could be a much more effective, specific, and logical way of going about solving a real-life problem.
Having read sections 12.1.1-12.1.4 in the text:
Difficult:
One thing that I was not sure about was why 0! is equal to 1. How can we prove that 0! = 1 or is this statement a set idea/value that if assumed allows the rest of the factorials to be calculated? Also, how are the binomial coefficients (n k) = (n n-k) [couldn't figure out how to use superscripts in this blog] as stated on page 789? From the way that the text refers to the identity, it seems as if the binomial coefficients (n k) = (n n-k) can be equal only when k=0, but I'm not sure when it would equal each other in different cases. On page 790, the text refers to applying the counting principles to expand the binomial theorem (x+y)^n but I wasn't quite sure (and couldn't quite remember) how to write the expanded form when given values of n and k. When looking at the solutions section of the example, I was a bit confused when the text stated "A term of the form x^k . y^(n-k) occurs (n k) times since there are (n k) ways of selecting the factor x k times from among the n facotrs (x + y)."
Reflective:
In all of my previous math classes, I never felt as if I was able to delve and completely understand the ideas behind probabilty and statistics. During Algebra 2 when I first encountered counting principles such as permutations and combinations, I think I was more set on using the equations rather than truly understanding the logic behind the topic which made it more difficult as we began to encounter more complicated/challenging cases and began combining counting principles as in section 12.1.4. I think the text's way of writing out the definition/equation for a permutation was a bit confusing for me to understand at first since I had always approached it a bit differently. I think the ellipses/repeating multiplication symbols within the equation P(n,k) = n(n-1)(n-2) ... (n-k+1) made me forget about having the same number of descending factors (k) as parentheses on the right side of the equation and led me to think that there were more factors in between (n-2) and (n-k+1) that had to be multiplied to calculate the permutation. Although the examples of counting principles have always been centered around marbles in a bag or a deck of cards, I think that encountering it in a life sciences model/scope would be very interesting and more related to the career fields that interest me. I see now that using these counting principles in certain situations could be a much more effective, specific, and logical way of going about solving a real-life problem.
posted by Jhan at
1:53 PM
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