Hi everyone! This is Jordan and as you may or may not know I'll be dropping the occasional question here for you guys to think about and answer.
For the first week I have two small requests. I'm not 100% sure how much you have done or talked about in the class just yet, but answer this as you feel is appropriate.
*NOTE: PROMPT ONE IS REQUIRED FOR WEEK ONE.
Prompt 1.)
In your own words, explain what you think Number Theory is. That is, what kind of topics does it deal with, what kind of applications does it have, etc. Please note that I am not expecting you to do research on this, I just want to know what you guys think or expect. A short answer will certainly suffice.
*NOTE: PROMPT TWO IS NOT DUE UNTIL WEEK TWO.
Feel free to look it over and even do it early if you wish, but it will NOT be due until the second week!
Prompt 2.)
So this prompt is a bit more of the flavor you can expect from these blog posts. My question will come in parts:
Part a.) What is the sum of the first n integers for n=1, 2, 3, 4, 5, 6, 7, 8, 9, and 10?
*Note, that is to say, for n=6 you will simply calculate 1+2+3+4+5+6
Part b.) Is there a pattern as n gets larger? What do you intuitively think the pattern might be? If you don't see one immediately, try a few larger values of n (around 15 to 25.)
Part c.) Do you think it's possible to write a formula for the sum of the first n integers for any n (for instance, if I want to know the sum of the first 1,000,000 natural numbers, but don't want to write all of them out, is there a shorter formula that I can simply plug n=1,000,000 into?) If so, what do you think it might be (or if you're not sure, why do you think there is one?) and if not, why don't you think so?
Part d.) If you think there is a formula, can you justify (or prove) that it is correct? If you don't think there is one, can you prove that there isn't? (It's okay if you can't do this part, but just elaborate a bit.)
That's all for this week, I don't expect large elaborate solutions to these, and yes, if you look the question up you can probably find the answers, but that's not the point. These are meant to make you think and not necessarily about whether you're right or not. Just put down what you think is the case and why and you'll be fine. I don't expect long answers by any means, but I DO expect more than "no its not" or "i think its 12 but dont no y."
If you guys have any questions about anything (related to this assignment or not) let me know at jmartin5@tulane.edu
Ciao.
So, i'm going to do this as a comment, like i thought we were supposed to..
ReplyDeleteIn my own words i believe number theory is exactly how it sounds. The theory of how numbers work together and how you can add or subtract or multiply or divide to make them form a sequence or series.
Also, i think number theory is very helpful to people in trying to find common factors, lcd's, gcf's, and so on. This can also be very helpful to everyday basic math.
Lastly, i'd like to say although i didn't think so, i'm actually enjoying this class and appreciating that its giving me the ability to do mental math a lot quicker!