mathematics, posts by tag: math - LiveJournal

 Hello. I am a math teacher and writer. I just joined this community . I like math, history and art. I've been writing a lot  about a book series called “CAIUS ZIP – The Time Traveller”
The main idea behind the “CAIUS ZIP – The Time Traveller” series is to show the history made by great men and how mathematics and other subjects were important in their decisions. Caius Zip is a young man that participates in these discoveries and in the great battles. In each adventure, he acquires maturity and learns that to get out of trouble he must use his most important ability that he unknowingly uses very well: the power of deduction.
 Mathematics is always present in the solution of enigmas, tactics and decision making in epic battles and during the investigation of a mystery. 

I d like to invite you to read some page:

CAIUS ZIP, The Time Traveller,  IN:  

NAPOLEON BONAPARTE IN RUSSIA

How some mathematical calculations can be crucial

for taking strategic decisions in this battle of empires

http://www.caiuszip.com/napoen.htm
  .

All convergent series representations have a closed form.
All real numbers have a series representation.

this means that any and every mathematical constant has numerous series representations. and every series rep. even though it is not known... does have a closed form, as hideous as it may be. example:
I bet it's some polynomial involving powers of Pi and.. stuff.
i can neither prove nor disprove it, i wouldn't even know where to begin. but a hunch tells me it's probably true. Any ideas? discuss. or is this just another blind alley?

I was just wondering if anyone had participated in/heard of/has any connection to the Math in Moscow program for undergraduates. I've been accepted for the fall and will spend a semester in "Fairytale Moscow."

Any info on traveling to Russia or studying in a more mathematically rigorous country would be extremely helpful!

So getting ready for this semester, I read a little and found the definition of a metric space. Now it seems strange that this section was skipped over in my intro analysis course, as everything we talked about in Rⁿ is in fact just using a metric space. Then I got to thinking, well... I don't actually think I've used anything except metric spaces, ever. I know in non euclidean geometry where you can work with objects on spheres, things will get wonky and you won't have a metric space, but what is this called? Also, what else is there, if anything?

So, I've been sitting in on some science classes at the school where I teach math. I was never that good at the concept of 'significant figures' in science-- or, at least, it failed to make sense to me except as a list of rules. Now, as an adult I'm still trying to piece all of this together. I hope this won't seem to dense to all of you. (And I hope there are some good math/science people here who can help me out!)

Let's say I have two instruments that will give me measurements. One is more accurate and gives me three significant figures the other gives me only one.

INSTRUMENT A: 2.71

INSTRUMENT B: 0.0003

So now I'd like to add these numbers following the rules for significant figures. I add them in the normal manner then round to one significant figure because instrument B has only one significant figure of accuracy. then round to two decimal places because it's the lowest number of decimal places.

2.71 + 0.0003 = 2.7103 --rounds to--> 3
2.71 + 0.0003 = 2.7103 --rounds to--> 2.71?

So that is my answer.

Now a reading of 2.71 on A and 0.0003 on B means that

2.705 < A < 2.715
0.00025 < B < 0.00035 (right?)

Where A and B are the "unknown true value" of the thing being measured. Now I could also add these inequalities, right?

2.70525 < A+B < 2.71535

Isn't that interval a better answer? Why bother with the rounding? Why don't they do it this way instead of rounding? Rounding bothers me.

--------
And for multiplication:
Significant Figure Method: multiply them in the normal manner then round to one significant figure because instrument B has only one significant figure of accuracy.

2.71 * 0.0003 = 0.000813 --rounds to--> 8 * 10^-4

Using intervals:

2.705 < A < 2.715
0.00025 < B < 0.00035

possible bounds:
2.705 * 0.00025 = 0.00067625
2.715 * 0.00025 = 0.00067875
2.705 * 0.00035 = 0.00094675
2.715 * 0.00035 = 0.00095025

0.00067625 < AB < 0.00095025

I am looking for native English speakers to help me improve the translation of a course in undergraduate mathematics. The course consists of two parts: Algebra and Geometry, each part has 12 sections. The translation of first 5 sections of Algebra and first 4 sections of Geometry are availble from

http://www.loria.fr/~sustreto/list…

If you want to help, please, do not hesitate to contact me. You can contribute by putting your suggestions on the wiki

http://wiki.loria.fr/wiki/Math_cou…

This is purely non-comercial work, I am doing it for fun, beacause I think that this course is worth being translated into English. The translation is under Creative Commons Attribution-NonCommercial-ShareAlike license.

You know you're going it alone when someone asks you how you're doing, and you reply,
"Oh, I'm okay. I think I can get this bijective map from the additive reals to the positive multiplicative reals -- Oh. Never mind. Yeah, I'm okay."