Mathematics

4:00 AM

byeTed

$\forall x\in R\,\exists y\in R\,(x=y+y\vee x=y+y+1)$ is easily seen to be equivalent to $R/2R\cong\Bbb Z/2\Bbb Z\vee R/2R\cong\Bbb Z/\Bbb Z$. Now I wonder about $\forall x \exists y\exists z(x=y+y \vee(x=y+y+z\wedge\neg\exists w(z=w+w)))$.

cyberskull

@KevinDriscoll have you decided to move your question to M.O. yet?

Kevin Driscoll

@cyberskull A good question. I really should

cyberskull

go for it

cyberskull

5:21 AM

\o/ . /o\ . /o/ . /o\ . Y.M.C.A.

Jack M

5:51 AM

hey

cyberskull

hi

Jack M

6:36 AM

is it acceptable to post a question in here if after several days, it's only had a dozen views?

Tobias Kildetoft

@JackM the receptions tends to vary. But not much is going on here anyway right now, so you won't be interrupting anything

Jack M

@Tobias I might drop by when there's some more people in fact

although it's on field/galois theory if anyone is interested in that area?

or I might just wait for the bounty

Tobias Kildetoft

@JackM depends on the level. If too high, I would not be able to help

Jack M

2

Q: Proof of necessary condition for constructibility of a number

I'm reading a proof of the necessary condition for a real number to be constructible, and it seems to leave out a few details that I can't really fill in. This is what I understand so far. We have to prove that: If the point $(p, q)$ is constructible with straightedge and compass starting fr...

DragonLord

6:51 AM

I'm hoping to get the HP Prime soon

www8.hp.com/us/en/products/calculators/…

Does anyone have experience with this calculator? (I'm taking a linear algebra course this semester and will take prob&stats next (and final) semester.)

amazon.com/dp/B00CMWCT26

Jack M

@DragonLord why not just use a laptop?

DragonLord

Full-scale computing devices (PCs, tablets, smartphones) are not allowed during tests, but handheld calculators are. The touchscreen makes exploring math concepts much easier.

You can use the familiar panning and pinch-to-zoom gestures on graphs.

Jack M

oh, for tests

Tobias Kildetoft

they allow calculators that do algebraic manipulations but not computers?

DragonLord

I'm in college. The professor allows us to use any kind of handheld calculator, but expects us to show our work. I use my calculator during lectures to better understand concepts (though I often have my Nexus 7 out to read Wikipedia articles on Gaussian elimination et al. during class).

cyberskull

7:13 AM

@robjohn have you ever noticed how large the amazon.com link^^ is compared to all the rest?

DragonLord

1

Q: Amazon logo shown for Amazon links in chat is pixelated

When I post a link to an Amazon product page in chat, the Amazon logo is very fuzzy: Can someone increase the resolution of the Amazon logo?

bug chat logo

@cyberskull ^

cyberskull

@DragonLord Are you saying that someone has already increase the resolution of the Amazon logo?

28 mins ago, by DragonLord

HP PRIME GRAPHING CALCULATOR

Hewlett-Packard Calculators

Prime Graphing Calculator Handheld calculating in a sleek slim brushed metal design that looks great and performs even better. Enjoy a feature-rich calculating experience with familiar HP keypad and a large 3.5-inch diagonal multi-touch display. Explore math concepts with Dynamic Geometry CAS Advanced Graphing and spreadsheet applications. Save time and keystrokes with RPN and programmable functions and see intermediate results while you work. Easily switch between symbolic graphical and numerical table views with dedicated buttons. Be productive longer with a lithium-ion rechargeable battery - when you need to charge up the convertible charger works with the USB connection on your PC or a standard AC wall plug.

Just look at the difference!

Mathematics

Mathematics is the abstract study of topics such as quantity (numbers), structure, space, There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measu...

Jack M

it looks like the amazon link grabs the full product description, regardless of how long it is

cyberskull

7:30 AM

yes, it does look that way

cyberskull

7:44 AM

Connect wirelessly to a PC

Wireless connectivity and the HP Calculator Connectivity Kit allow you to connect to your PC.

DragonLord

8:14 AM

@cyberskull: This functionality requires a separately-sold accessory. Otherwise, you can use a Micro USB cable (supplied) to connect the calculator to a PC.

Chris's sis

10:42 AM

Greetings

Danny Cheuk

11:08 AM

Hey

Shahab

11:34 AM

hey

Jack M

would anybody be able to explain something from field/galois theory to me?

Nick

11:58 AM

@JackM: Maybe MathDoctorBob? youtube.com/watch?v=LUSWqVfWrM8

@JackM: There's also wikipedia en.wikipedia.org/wiki/…

Jack M

@Nick it's a very specific question, but thanks anyway

I already have two textbooks and some class notes to work from :)

Nick

@JackM: don't worry someone will help you out in a sec (it won't be me. I can't comprehend much of it) You may need to wait but in the mean time, I hope you that you can try to crack open the nut on your own. It may seem hard at first.

but as a great mathematician (I forget who) once said:

A problem worthy of attack proves it's worth by fighting back.

Jack M

12:15 PM

@Nick seems it was piet hein, the guy who wrote all those little haiku thingies

Nick

@JackM: Or it could be Erdos. No one knows.

what'sup

hi guys

can you tell me the new big questions Because i wasn't here .

Jack M

"why" is still pretty popular

Tobias Kildetoft

12:31 PM

"why not" is gaining on it though

Jack M

I'm not sure how long you've been gone though

those are both pretty old

Nick

Almost as old as the Answer to life, the Universe and Everything.

robjohn

@DragonLord Heh... my gravatar seems to annoy MSO

Nick

12:47 PM

@robjohn: You can't really blame him. it's a good design but it doesn't really reflect who you are, does it?

robjohn

@Nick You don't see me as mean and square?

Nick

@robjohn: I see your gravatar to be mean and square. You seem more like a circle to me. ( Maybe you're hectogon, I really can't tell the difference) and as far as statistics is concerned, you're like a mean deviation about median.

Tobias Kildetoft

►

it doesn't have a hectogon unfortunately. It only gets to dodecagon

robjohn

@TobiasKildetoft Decimalists the world around will be disappointed.

Tobias Kildetoft

@robjohn while it might have gone to hexadecagon, going all the way to hectogon seems like overkill

Nick

12:58 PM

Yeah, going beyond dodecogon in 2D geometry is like studying the properties of elements beyond Ununonoctium in Chemistry. They all exist (sort of) but they're completely useless to learn about.

robjohn

@Nick icosahedrons are dual to dodecahedrons and they are cool.

Tobias Kildetoft

@robjohn but now we have gone up a dimension

robjohn

@TobiasKildetoft Dang, I hate it when that happens...

Nick

@robjohn: 2D, my friend, with the exception of our humble noble circle.

You know what, Tesseracts are the coolest.

On the same note, I was wrong about chem. Unseptbium is sexy.

robjohn

@Nick Never saw that centerfold.

Chris's sis

1:13 PM

Greetings noble minds!

@robjohn Have you seen the first member of my new limits class, that is $$ \lim_{n\to\infty} e^{(\displaystyle -n^{2012}+n^{2011}/2-n^{2010}/3+\cdots+n/2012)} (1+1/n)^{\large n^{2013}}$$ ?

Nick

@robjohn: You've never heard centerfold, either. youtube.com/watch?v=BqDjMZKf-wg

robjohn

@Nick er, yes I have.

@Chris'ssis haven't seen that yet.

Chris's sis

@robjohn It's called "super limits class". (I gave them a name)

Nick

@robjohn: Wow, you're that old, you fossil

John Wilson

2:47 PM

hello

Jack M

3:02 PM

hi

Chris's sis

@Nick @robjohn is one of the most brilliant persons I've ever met. Be sure his mind is far younger than many apparently young people. By the way, someone around 50 years old is pretty young.

Tessa Danger Bamkin

3:35 PM

hello

combinatorics help? math.stackexchange.com/questions/505981/… im completely stuck. until then im going to try and do some other questions.

Nick

@Chris'ssis: Aww, shucks, i didn't mean to offend him. 50 is the new 20. And yeah, he is super smart. But I still think he's more like a circle. (Why? cuz I like pi)
See. I'm never serious.

Chris's sis

@Nick ok ;)

Nick

Ooh, I have a weird clock over here.

What is 11 supposed to be?

Tessa Danger Bamkin

I feel so hopeless at maths. art is much easier.

PGFTricks

3:52 PM

@Nick (1011) in binary.

anon

4:05 PM

@PGFTricks out of curiosity how does the strange 06 represent the binary string 1011?

Jack M

also what is the $g$ in $\ceil{g}$

$\roof{g}$ ?

PGFTricks

@anon 0B might be a number in hex.

anon

is it normal for hex digits to be lowercase letters rather than uppercase?

seems like it's being roundabout for the sake of being roundabout then

that clock is rather silly

PGFTricks

@anon Both are used.

anon

I see

PGFTricks

4:08 PM

Without seeing the labels we already know the value.

cyberskull

true dat^

anon

what lame starring

Chris's sis

@Nick $11$ is related to the hexidecimal system, that is $0b$.

I need to rest half an hour ... (back later)

cyberskull

later

marcelolpjunior

Help

$$\int \frac{x^2\;\;dx}{(x^2+4)^{\frac{3}{2}}}$$

Daniel Rust

4:18 PM

►

PGFTricks

I really need your contributions as mathematicians in my question:

2

Q: Is learning mathematics good to build personal character?

In my experience, people who are well trained in mathematics will have strong toughness and confidence in solving their daily life activities or problems. Is learning mathematics good to build personal character?

personality

cyberskull

"it depends"

Shahab

@PGFTricks: Do you want personal opinions?

PGFTricks

@Shahab Yes. Any opinion is OK.

Shahab

I do not believe mathematics helps in any way which is exclusive to mathematics

discipline of mind, perseverance and logical thinking faculty are strengthened by doing mathematics but all these can also be obtained through other ways

PGFTricks

4:29 PM

The question may be read as "What are the advantages of having strong math skill in our daily life?" Because I want to persuade kids who don't want to learn math.

Shahab

I have posted a similar question on the math stackexchange site because I am also interested in knowing about this

Daniel Rust

@Shahab Just because maths isn't the only thing which teaches those qualities doesn't mean they don't contribute to answering @PGFTricks's question

Shahab

@DanielRust: Yes, of course. I never said mathematics doesn't contribute to character building.

cyberskull

@PGFTricks Trying to persuade kids who don't want to learn math is a different question.

anon

outside of personal finances (a major component of which is just self-discipline and responsibility not math IMO) and proving to institutions that you know and can handle stuff, school math isn't really necessary for people to know or use who do not do any technical work.

Shahab

4:33 PM

@DanielRust: If you carefully read what I said, I said that I do not believe that it helps in a way which is not possible to do otherwise

7

Q: Studies on lack of mathematical education

I am looking for studies which compare students who did not receive mathematical education beyond basic mthematics and those that learned maths upto introductory calculus, with the assumption that both groups recieved similar education in other subjects such as social sciences and natural science...

soft-question education

Sadly I haven't had any response to this question yet.

PGFTricks

@cyberskull No. It is relevant. The answers I got will support me to persuade the kids with good reasoning.

marcelolpjunior

@PedroTamaroff

Boa tarde, espanhol sí?

sonicboom

In ring theroy...what are the units of Z_7 .... i.e. the integers modulo 7

I think it is all the elements of Z_7 itself - {0, 1, 2, 3, 4, 5, 6}

?

Daniel Rust

7 is prime so everything except 0 is a unit

Shahab

@sonicboom: In any Z_n the units are the elements which are not zero divisors

cyberskull

4:37 PM

@PGFTricks That is more of an educational psychology question, no?

marcelolpjunior

@PedroTamaroff Pedro?

Daniel Rust

In general, in $\mathbb{Z}_n$, the set of units is the set $\{1\leq i\leq n-1\mid \gcd(i,n)=1\}$.

cyberskull

Hi @TedShifrin how are you?

sonicboom

Ty guys

Ted Shifrin

hi @cyber ... just stopping by for a second on lunch break ... you making trouble?

cyberskull

4:42 PM

@TedShifrin Who me? ;-)

};-)

PGFTricks

@cyberskull I posted a new question: parenting.stackexchange.com/questions/8988/… for you! :-)

cyberskull

@PGFTricks Thanks honey! :D

PGFTricks

@cyberskull :-)

Shahab

@PGFTricks: Have you heard Lockhart's Lament

sorry, have your read Lockharts lament

PGFTricks

@Shahab Not yet.

Shahab

4:54 PM

Maybe the best way to get kids interested in mathematics is to present maths in an appealing and beautiful way.

When they learn how fun it can be they will be drawn towards learning more...Lockhart's Lament is an essay on what is wrong with the way currently maths is taught to children and how it can be remedied.

Essentially, the point being the intrinsic beauty of the subject is ignored

in the current teaching methodology

worrydream.com/refs/Lockhart-MathematiciansLament.pdf

PGFTricks

@Shahab Thanks for the link.

I am teaching algebra but the kids don't like variables, they like numbers. :-)

Shahab

@PGFTricks: No problem

I was browsing today and saw a great game for solving linear equations in one variable

PGFTricks

@Shahab What is that?

Shahab

scratch.mit.edu/projects/2477436

Jack M

to get back to the "personal character" thing

Shahab

5:01 PM

maybe your students will enjoy it.

Jack M

that @PGFTricks was asking about

cyberskull

@Shahab thanks for sharing

Jack M

I find that most kids (probably most adults) have this perspective on the world where there's "normal people" (them) and then "geniuses", and that certain things (math, science, good art) are only accessible to these mysterious "geniuses", and they shouldn't even try

realizing that that's false was a direct consequence of my learning mathematics

and I think that that's an important lesson for everybody

but again, that's not exclusive to math

Shahab

@cyberskull: No problem...I got stuck on level 10 and didn't bother after that.

cyberskull

:D

Shahab

5:07 PM

:) it may be a resource for students learning linear equations

@JackM: yes, what you say is definitely not an exclusive realization of learning mathematics.

by learning mathematics (not of)

cyberskull

32 mins ago, by cyberskull

@PGFTricks That is more of an educational psychology question, no?

PGFTricks

@cyberskull Yes. It includes that aspect.

cyberskull

@PGFTricks It is a very important aspect of learning.

@PGFTricks Here

Pedro Tamaroff

5:28 PM

@marcelolpjunior Hey.

Chris's sis

@marcelolpjunior Wouldn't we like to consider $$\int \frac{x^2\;\;dx}{(x^2+4)^{\frac{3}{2}}}=\int \frac{x^2+4-4\;\;dx}{(x^2+4)^{\frac{3}{2}}}$$?

robjohn

@JackM I am assuming $g=9.80665\,\text{m}/\text{s}^2$, that is the acceleration of gravity at the Earth's surface.

PGFTricks

5:44 PM

@cyberskull Thanks.

cyberskull

np

Kevin Driscoll

@robjohn That's the most accurate quote of $g$ that I've ever seen

cyberskull

@KevinDriscoll not even Physicists quote it that accurately?

Kevin Driscoll

HA! $g$ rarely comes up in research-level problems because the only people who do gravity are working on General Relativity or String Theory, and so they go WAY beyond needing $g$

and so most often it's just an intro physics thing and they use $10$ or $9.8$ or $9.81$ if theyre fancy

@cyberskull

the universal gravitational constant, $G$, however I have seen quoted to many more decimal places

cyberskull

@KevinDriscoll just don't ask him to quote $\pi$ ;-D

Kevin Driscoll

5:53 PM

No thanks @cyberskull, don't wanna be reading it all day

cyberskull

Indeed.

robjohn

@KevinDriscoll That's the value I've seen since I was a wee child. It is just a couple of digits more than $32.16\,\text{ft}/\text{s}^2$

Kevin Driscoll

@robjohn Clearly society is declining, I've never seen something more precise than $32$

cyberskull

we were taught to remember the speed of light to nine digits

Kevin Driscoll

6:08 PM

@cyberskull I'm a theorist $c = \hbar = 1$.

cyberskull

Yes, for correctly chosen units.

:-)

robjohn

6:49 PM

@cyberskull $299792.458\,\text{km}/\text{s}$ exactly

They define the meter that way :-)

after defining the second by cesium-133

Kevin Driscoll

@robjohn Indeed

robjohn

@Chris'ssis You impugn my simplicity...

Chris's sis

@robjohn my former work colleagues used to call me "genius" and I was proud of it. There is no worry about it.

@robjohn you should be proud and that's all. :-)

robjohn

@Chris'ssis :-)

Chris's sis

@robjohn How does it seem to you that limit I showed you above as difficulty level?

robjohn

7:05 PM

@Chris'ssis I haven't had a chance to work on it. Let me work on it.

Chris's sis

@robjohn Oh, I see. OK.

robjohn

It's pretty straightforward:
$$
\begin{align}
&\lim_{n\to\infty} e^{(\displaystyle -n^{2012}+n^{2011}/2-n^{2010}/3+\cdots+n/2012)} (1+1/n)^{\large n^{2013}}\\
&=\lim_{n\to\infty}e^{-n^{2013}\log(1+1/n)+1/2013-1/(2014n)+\dots}e^{n^{2013}\log(1+1/n)}\\
&=e^{1/2013}
\end{align}
$$

Chris's sis

@robjohn I see.

robjohn

@Chris'ssis It's nice, but if someone is familiar with series, it might not be that challenging.

Chris's sis

@robjohn true

cyberskull

7:39 PM

@KevinDriscoll Once you have defined the meter using the speed of light, you don't need to use cesium-133 to define the second, right?

Kevin Driscoll

@cyberskull No you still do

because the meter is defined as the distance light travels in vacuum in a certain amount of time