Math education from a female perspective

Why did I give up on math? Ask my mom
https://www.washingtonpost.com/posteverything/wp/2015/08/04/why-did-i-give-up-on-math-ask-my-mom/

But it’s unfair to pin all the blame on my mother. There were other factors, such as indifferent or incompetent teachers and my growing sense that girls who like math are suspect to boys — and at 12, what boys thought was suddenly very important.


Girls Get Higher Math Scores When Taught By Female Teachers
http://www.ischoolguide.com/articles/20763/20150804/higher-math-scores-female-teachers-researchers.htm

This new study also found that when female students switched from a male to a female teacher, their math test scores increased by 8.5 percent of the standard deviation than the boys.
Meer said he felt that the increased performance in mathematics is due to the girls feeling more comfortable when taught by a female instructor.

Judges wrangle over the definition of the number "one"

http://www.independent.co.uk/news/science/what-exactly-does-one-mean-court-of-appeal-passes-judgement-on-thorny-mathematical-issue-10350568.html

What is the meaning of one? It’s a question that has occupied the minds of the greatest thinkers such as Philo of Alexandria, who believed that the numeral one was God’s number and so the basis of all other numbers.

Two millennia later, in the august surroundings of the Royal Courts of Justice in London, three judges in the Court of Appeal last week also deliberated on the meaning of one. They came to the conclusion that one does not necessarily mean one at all – because it can actually include anything greater than or equal to a half and less than one-and-a-half.



When will I ever use this?

http://www.maa.org/sites/default/files/pdf/Mathhorizons/supplement/MH-CoreyWeb.pdf

The most asked question in math class is some variation of "When am I ever going to use this?”  In fact, I began typing this question into a search engine, and every one of the
10 popular completions for "when am I ever going to use . . .” dealt with school mathematics. Now, as a student, I know this question is a compelling one. Of course, some students ask it as a challenge to the teacher, using it to mean “Prove to me that I need this in my life.”  However, some students ask it sincerely, honestly wanting to know how it might be used in the future.

91% of health-related web searches go to third parties

http://www.scilogs.com/next_regeneration/the-invisible-web-undermines-health-information-privacy/




Don't follow the advice at the end.  Ghostery is now owned by an ad agency. 
http://lifehacker.com/ad-blocking-extension-ghostery-actually-sells-data-to-a-514417864
Use the Disconnect extension instead.
https://disconnect.me/

AdBlock slows down your browser and is not the best choice.
http://www.digitaltrends.com/computing/using-adblock-plus-with-firefox-may-slow-your-computer-to-a-crawl/
uBlock is a better alternative.
http://lifehacker.com/ublock-is-a-fast-and-lightweight-alternative-to-adblock-1625246461

But even these will not protect you.  
You need to manage cookies that sites use to track you. 
Get a browser extension like Better Privacy to delete supercookies.

Use search engines that don't track you, like DuckDuckGo, StartPage, or PrivateDuck.

Get a good VPN to mask your IP address, so that your IP address (web identiy) is masked to the websites you request.  You browse through a secure tunnel, and even your internet service provider can't track your surfing.

For more advanced users:
Get a browser add-on the prevents surreptitious tracking info going to Facebook (even when you not on Facebook).
http://webgraph.com/resources/facebookblocker/

Turn off geolocation on your browser.  It's supposed to improve your browser experience, but it can tell websites exactly where you are:
http://diveintohtml5.info/geolocation.html
http://techlogon.com/2013/04/23/how-to-disable-geolocation-in-ie-chrome-or-firefox/
Leaving this on defeats the security of a VPN.  They'll know where you're browsing from anyway. 

Use a browser add-on to block WebRTC.
http://thehackernews.com/2015/02/webrtc-leaks-vpn-ip-address.html
Leaving this on also defeats the security of a VPN.  Your true IP address can be directly accessed.

Warning: You may find that some videos and other media don't work on some websites.  Allowing yourself to be tracked is the price you pay to watch the video. Temporarily disable protection if you really have to see it.

This is why it's hard to teach (and learn) probability

https://www.quantamagazine.org/20150730-the-slippery-eel-of-probability/

There is a famous problem in probability known as Bertrand's paradox whose statement is simple: What is the probability that a random chord of a circle is larger than the side of the equilateral triangle inscribed in the circle? To do this you have to determine the density of such chords by “counting” how many are larger than the side of the triangle and dividing that by the total number of chords. The answer can be ¼, ⅓ or ½, depending on how the chords are counted. All of these answers are correct in different circumstances.

Japan's Atomic Bomb Projects

Projects plural!  I had no idea about these!  They got the U-238 from Germany via submarine and had figured out thermal diffusion of uranium hexaflouride by the time we dropped ours on them!



 
        

I believe it was Sin-Itiro Tomonaga who told Feynman "What took you so long?"  he was expecting the A-bomb to be dropped on Japan at least one year earlier.  Understood everything about it. Indeed, the people at Los Alamos were in fact just screwing around, trying to get things perfect, when 70% of perfect would have worked just fine.  Groves finally had a fit and told them to quit horsing around and get a bomb out to Tinian right away. We were losing 200 men a day at that stage of the war. 

Of course to be fair, the plutonium (Nagasaki) bomb was far more complicated, and instantly made the uranium (Hiroshima) bomb obsolete. Little Boy was so crude that we never even tested it.  We never built another one, although we had already cast the casings for it.

That the Japanese had exploded a uranium bomb left me absolutely gobsmacked.  We built an entire city just to filter UF-6.  Where would the Japanese get the uranium?  Central Africa (The Belgian Congo?)  Hardly. Colorado? *  Don't think so.  And how on earth could they separate the light isotope?  Well, Germany was the answer to #1, and they were using thermal diffusion for #2...no city necessary.  The U.S. Navy had a thermal program but it didn't go anywhere.  It was working, but we already had the Oak Ridge filters up and running, not to say Hanford, Washington for the Plutonium.  Interesting that the Iranians are investing in centrifuges, another method we did not use.

Everybody knows E = mc^2, but that has absolutely nothing to do with how atomic bombs work.  The first lecture everyone got when they arrived at Los Alamos was the fact that electrical potential, not relativity, is the driving concept.  Stop me if you've heard this.

Let's make a uranium nucleus.  Get a proton and hold it in one place.  Now take another proton at infinity, and bring it in to the first at a distance R.  The work you have just done is integral (infinity to R) of k qXq/x^2 dx.  Now take another proton and bring it into the first two.  The work is integral (infinity to R) of k qX2q/x^2 dx.  Then integral (infinity to R) k qX3q/x^2 dx, k being Coulomb's constant.  Keep adding until you bring the 91st proton in.  That is the work you have done in assembling a uranium 92 nucleus.

Now add the 55 integrals for barium 56 and the 37 integrals for strontium 38.  You will see that the uranium work FAR exceeds the work done in assembling the other two.  That's the secret of the atomic bomb.  (Lecture #1, The Los Alamos Primer, by Robert Serber.)

Keeping it really simple, let the first integral have a value of 1.  Then uranium is 1 + 2 + 3 +...+91  = 91X92/2 = 4186 units of work.

Barium clocks in at 1 + 2 + 3 + ... 55 = 55X56/2 = 1540 and strontium is 37X38/2 = 703.  So barium and strontium add up to 1540 + 703 = 2243.

So each reaction unleashes 4186 - 2243 = 1943 units of work (energy).   Of course, all three radii are slightly different, but this is only a first-order approximation after all.  Notice that nowhere does "relativity" explain any of this.

Poor Einstein.  He always protested that he had absolutely nothing to do with the atomic bomb, aside from signing the letter to Roosevelt.  Blame Charles-Augustin Coulomb instead.