MaThematics Essay Samples and Topic Ideas
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Mathematics Mathematical writing is often not immediately understood and takes time and though before comprehension. When reading the mathematical text, the most difficult part is the mathematical formula. This is represented in the form of signs and letter. The letters may be Roman or Arabic, but each has a specific meaning. At the same time, certain combinations represent different meanings as well. Getting to understand the logic behind the formula derivation, proper use and how certain calculations came to require concentration and deeper understanding of the text. It takes me more than three rounds of reading the text for me to intuit and understand it fully. However, I have to make close...
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mathematics as my program. Mathematics is what I like and have been enjoying the subject so much. Mathematics is useful in daily operations. Using mathematics, the economy of a country is determined and viable advice given to authorities based on the calculations. I feel motivated to provide solutions to such problems that need mathematical skills and knowledge. The University of Waterloo is known for providing the best mathematics program in Canada. I, therefore, chose The University of Waterloo because my wish is to get the quality education in mathematics. My educational goal is to get a better education. Once I have the excellent education, I will be able to assist people who need help. My...
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Mathematics Page 156 Question 4 b. n3+(n+1)3+(n+2)3Is divisible by 9 for all n≥1Proof The base case in this situation is n=0 which implies that n3+(n+1)3+(n+2)3=03+13+23=9 This is divisible by 9. Therefore, the basis holds true for n=0The inductive hypothesis becomes n=k≥0, k3+k+13+(k+2)3 is also divisible by 9 → k3+k+13+(k+2)3=9p…(i)By inductionn=k+1, equation (i) becomes (k+1)3+(k+2)2+(k+3)3=9p-k3+k+33…(ii) Simplifying (ii) we have =9p-k3+k+33=9p-k3+k3+9k2+9k+27=9p+9k2+k+3=9(p+k2+k+3)This implies that (k+1)3+(k+2)2+(k+3)3 is also divisible by 9 therefore, n3+(n+1)3+(n+2)3is divisible by 9 for all n≥1 d. 83 – 3n Is divisible by 5 for all n≥1Proof If n=1 then, 8n-3n= 81+31=5 this can...
Mathematics Week 3 Homework Page 79 Determine whether each of the following relations is a function with domain {1, 2, 3}. For any relation that is not a function, explain why it isn’t. f = {(1, 1), (2, 1), (3, 1), (4, 1), (3,3)} Solution: This is not a function there are two different pairs of the form (3,-) in f f = {(1, 2), (2, 3), (4, 2)} Solution: With the given domain, this is not a function since a pair of the form (3,-) does not exist. f = {(1, 1), (1,2), (1,3), (1,4)} Solution: This is not a function since more than one pair of the form (1,-) exists. e. f = {(1, 4), (2, 3), (3,2), (4,1)} Solution: This is function since the pairs of the (1,-) and (3,-) exists. Suppose A is the set of...
Mathematics Page 42 1. List the (distinct) elements in each of the following sets: {x Z | xy = 15 for y Z}Solution: C = { 1, 3, 5, 15, -1, -3, -5, -15} (both positive and negative of 15) e. {a N | a <-4 and a >a} Solution:It is impossible to list the elements since they are infinite in number. “N” refers to natural numbers and therefore "-4" is irrelevant. 2. List five elements in each of the following sets: d. {nN|n2 + n is a multiple of 3} Solution:The numbers are in the form n2+n=3p for some integer P hence: n={3,5,6,8,9} 9a. List all the subsets of the set {a, b, c, d} that contain Solution i.) four elements - {a,b,c,d}ii.) three elements - {a,b,c}, {a,b,d}, {a,c,d}, {b,c,d}iii.) two...
Problem 1 Question 1The determination of the median height can be arrived at by taking the functional value of f (48). The value x should be substituted for 48. This should look like follows: F(48)= 3.1√(48)+19 =3.1(6.928)+19 =21.47+19 =40.5 Question 2 The calculation obtained above indicates a median height of 40.5 inches. However, the actual height is said to be 40.2 inches. The meaning of this analysis is that the model has overestimated the height by the difference of 40.5-40.2 which is 0.3 inches. Question 3 It is appropriate to determine the height of the girl during birth, considered as month zero. Once this has been achieved, it is good to substitute 0 in place of x. The function looks like...