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Mathematics

Question Description

After reading the two articles, I'm actually surprised I didn't previously realize how important the writing portion of math is. I always thought that showing work was required, but I didn't know to what extent and how to actually prove things correctly. Before I would show work to explain to a teacher, as if they know what I am already talking about, but I am just clarifying my work. However, these articles introduced the fact that when I write proofs or show work, I should have the intention to be writing things out to someone who has no experience or understanding of a certain topic. The one example in Dr. Cheng's essay was x=y. During a math problem, I would usually think this was obvious and didn't find the need to prove this out. But in fact, x=y is a math proof that needs to be justified through its work. One question that came to me while reading this was, how do I know to what extent I need to be "writing" my math work? Something I recently started doing was writing out each step in a math problem, and taking a different colored pen to write the Theorems or explanations next to each step. I'm not sure if this is correct according to Dr. Cheng and Dr. Su's guidelines, however, I believe it helps peers who read my work to better understand the background of why I am doing certain things in each step. From both articles, I can't really say I disagree with anything because I haven't formally been doing these steps in any math form, however, I think these processes will take a lot of time to learn and master. I was not taught to write math in this way, so all the steps and etiquettes are new to me. I do agree that when proving theorems or problems, the beginning/middle/end way is a good way to look at things. The middle is exactly what we have to do to get from the start to the end, and although it's a lot of work, taking these steps will definitely help mathematicians better understand problems.

Reading material:

Read Dr. Francis Su's article on writing mathematics. (Links to an external site.)

(Links to an external site.)Read this essay by Dr. Cheng on how to write proofs

I have attached my post too, so you can know my views and don't contradict anything in reply


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A WELL WRITTEN SOLUTION 1 A well Written Solution Your name Institution Course Professor Date A WELL WRITTEN SOLUTION 2 I think Dr. Su’s guideline makes more sense to me. I, therefore, agree with him that developing a mathematical solution would be determined by a number of factors. Dr. Su mentioned a number of factors namely knowing your audience, setting an invitational tone, the use of complete sentences, use of words so that the equations may be in context, and use avoiding short forms when composing formal writing. One of the factors that I think would greatly influence the manner in which one would present mathematical writing is an audience. Not all of us has the capability of comprehending mathematical concepts. Even so, different people are in different professions, and so a particular way of expressing some mathematical concepts to them would fail to make sense. But even after identifying the audience to be addressed, Dr. Su goes ahead to show us how to present the solution in an elegant manner. A well-organized work should begin with what is important as a way of helping the audience to stay in focus. I will therefore apply Dr. Su’s mathematical guidelines to solve an integration as follows: Problem: Solve the integral of 132x2dx Solution The integral of 132x2dx can be written as ∫ 132π‘₯ 2 𝑑π‘₯ Now, solving ∫ 132π‘₯ 2 𝑑π‘₯ would be as follows: Move 132 outside the integral sign as follows: ∫ 132π‘₯ 2 𝑑π‘₯ = 132 ∫ π‘₯ 2 𝑑π‘₯ Let us now apply the power rule on x2: π‘₯3 132 ∫ π‘₯ 𝑑π‘₯ = 132 +𝐢 3 2 A WELL WRITTEN SOLUTION Implying: 132 ∫ π‘₯ 2 𝑑π‘₯ = 44 π‘₯ 3 + 𝐢 Note that a constant C is always introduced during integration, as shown above. 3 A WELL WRITTEN SOLUTION 4 Reference Su, F., 2015. Some Guidelines for Good Mathematical Writing. MAA FOCUS. ...
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