Talk:Summation Notation

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Contents

Response to checklist

Original response to checklist, in black, written by Kate 14:05, 14 July 2011 (UTC)

You'll find my comments in red AnnaP AnnaP 22:33, 14 July 2011 (UTC)

References and footnotes

  • Images are all cited.
The one issue with this is that, based on a conversation we had last night, I went back to the blog where I found the cupcake liner picture to figure out if he minded his images being used, and it looks like he does. But I'm planning on baking cupcakes with friends this weekend, so I figure I'll just take a picture then and replace the current one on Monday.
  • All mathematical content is from my general knowledge (with corrections by Prof. Maurer), and so no references are provided

Good writing

Quality of prose and page structuring

  • Subject headings and/or first sentences make the purpose of each section clear
  • Each section is relevant to the topic
  • Page builds up from a one-sentence definition to examples of more complicated sums

Integration of images and text

  • Math writing is used far more often than images, as the point of the page is to explain a notational convention and few images are relevant

Links to other pages

  • The HelperPage template links back to Matrix and Markus-Lyapunov fractals

Examples, Calculations, Applications, Proofs

  • Many numerical examples and calculations are included, effort has been made to integrate them well into the text

Mathematical Accuracy and precision of language

  • To the best of my knowledge, all statements are accurate and error-free
  • I discussed this page with Prof. Maurer, and the only major change since then is the addition of the cupcake example
  • Definitions have been provided in green bubbles for sequence (& series), and dummy variable (which also has a small hidden section elaborating)

  • When you say this: Indexing with two variables can also be written using only one sigma: \sum_{i,j=1}^n {a_{ij}} = \sum_{i=1}^n {\sum_{j=1}^n a_{ij}}, you are summing to n in both cases. Since that isn't what you're doing above, you should offer a bit more explanation of that.
Kate 13:54, 15 July 2011 (UTC): Fixed.
  • In your polynomials section, I'd take your example one step forward and say p_3 (x) = a_0 x^0 + a_1 x^1 + a_2 x^2 + a_3 x^3 =a_0 + a_1 x^1 + a_2 x^2 + a_3 x^3 .
Kate 13:54, 15 July 2011 (UTC): Fixed.


Layout

  • Text is in short paragraphs, but is not broken up by images, as there are very few images relevant to this topic.
  • Hide/Shows have been used to:
  • Hide more challenging mathematical content at the bottom
  • Hide an additional explanation that not all readers may need closer to the top
  • Hide the answers to example problems that the reader is asked to think about
  • Hide the example problems, in case the reader isn't interested in them
  • Page has been viewed in a variety of window sizes, nothing weird happened

  • Did you think about making all of the subsections under "more on summation notation" simply their own sections. In think that might look/flow better.
Kate 13:54, 15 July 2011 (UTC): I hadn't thought about it, but now that you've mentioned it, I changed it.
  • In the summation and distribution section, add a bit more space between the two equations, and maybe label one "multiplication" and the other "division"
Kate 13:54, 15 July 2011 (UTC): done.

Older comments

Diana 18:35, 6/17: A lot of students are really confused by i when they first see this notation. You address it briefly in the "indexing" section, but I think it's worth saying more about it. For the layman, especially someone who's never done programming or logic, the idea of using i as a placeholder is often foreign.

Kate 13:40, 20 June 2011 (UTC): Can you tell me more about how it's confusing? I guess I'm so used to it that I'm not really sure what parts need to be expanded on or how to expand them.
The problem that Diana is talking about is sort of a more sophisticated version of how some kids in their pre-algebra class really struggle that x can mean any number. Then, some kids will struggle that you can make any variable any number--if it's unknown, they think it must be "x"! It's a very, very common problem with understanding the abstraction. So, this issue with indices is a similar problem with really getting the abstraction.
So, that's my explanation of the problem... now in terms of a solution, it may be best to have an entire paragraph on "dummy variable" instead of just your mouse over. I'd also suggest pointing this out with a sum that goes to something smaller than 20, as you do in the later sections. If you want me to, I can spend some more time working on the wording AnnaP 7/5
Okay, so I think I understand the problem better now. I'll try and figure out what should go in a paragraph about dummy variables. Do you think cupcake liners could be a good analogy? Like, when you make cupcakes, you set out all the cupcake liners where you intend to make cupcakes, but you don't actually have any cupcakes until you fill them with batter. So the cupcake liners are like indices, because they help define the pattern, but you don't actually have anything until you "fill" them with actual numbers or expressions.
I'm also thinking that no matter how good an explanation I give, the best way to actually understand it is to do a lot of example sums, which isn't really feasible in a website.
Cupcake liners might work--I'd suggest putting in a picture just to make sure everyone knows what you're talking about. Also, I'd specific that putting down the liners doesn't mean that you have to put the exact same thing in each. In fact, all of your cupcakes will be at least a little bit different!
I added this example in - is the way I did it ok? I didn't want to put it in there the first time I mention "dummy variable", because that's in my table, and then I wasn't sure where to put it, so I made a combination balloon-link and put the paragraph in a hidden section before the example problems. (Kate 18:57, 11 July 2011 (UTC))
Chris 7/13/11 The cupcake idea is excellent is terms of place-holding but problematic in terms of the fact that a cook wants each cupcake to be similar. I brainstormed for a while to come up with a better idea but couldn't find one. I think the value of the analogy outweighs the problems. I like the way Kate integrated it into the page and included the cupcake liners image.

As a minor point, your section on the matrix is specifically about a square (n by n) matrix. I'd suggest making it an n by m matrix, just to make your example a bit more generic. AnnaP 7/5

Changed.

xd 20:36, 14 June 2011 (UTC) I think it has all the general information it has. It is not possible for this page to be comprehensive and listing all the sums in closed forms. Maybe it is useful to put on some common sums like  \sum_{i=1}^{n} i =\frac{(1+n)n}{2}

done!
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