by commutativity of multiplication, distributivity, the existence of a neutral element 0 for addition, and the commutativity of multiplication once again. Thus, we have that
x*0 + x*0 = x*0.
For clarity, define
A = x*0.
Then we have that
A + A = A
A + A + (-A) = A + (-A), by the existence of additive inverses.
A + (A + (-A)) = (A + (-A)), by associativity of addition
A + 0 = 0, by the definition of additive inverses
A = 0, by the definiton of the neutral element 0 of addition
Because the concentrated effort needed to "not do something" seems to increase the likeliness that you will do exactly that, especially under stress. For some reason, it seems that it is not the will or intent of the thinker that is important, but what the thinker is actually thinking that controls reflexive actions.
Well, yeah. I knew that from watching Homer's antics on the Simpsons. This doesn't dp anything to explain why if you incessantly think "Don't do x; don't do x" then you wind up doing x. But maybe I'm expecting too much from an article in the Sports section.
It also tends to work better than not telling anybody about it at all.
If you tell people that you are quitting something, there is a social pressure on you to follow through on your promise. Your friends and family might also be willing to help you achieve your goal, which can be encouraging and push you that much further.
Well worth it, if you ask me. Best of luck to the author.
Some schools are fighting back against this. For example, I know that the UCLA math department has a policy that professors are required to search for a replacement textbook once a textbook goes beyond the third edition, unless there is a significant addition of material (e.g. entirely new chapters needed as a result of recent developments). The idea being: "If the author hasn't got it by the third edition, they'll never get it."
I believe this eliminated the majority of calculus/linear algebra/diff-eq texts from introductory courses, so it has become easier to find used copies.
I'm glad I'm not the only person who has #3. For some reason, I seem to get miraculous insights into problems when I'm exercising, so I've taken to keeping a tiny pen and a couple index cards within reach at all times. While running, this has sometimes resulted in me crouching on the side of a street, scribbling madly while constantly looking for oncoming cars, but when I get back home and finally finish that tricky proof or implement that evasive idea into code, I find it is well worth the trouble.
I keep thinking I should get a voice recorder (my MP3 player can record, but starting up recording takes several seconds). But the sound of my own voice makes me uncomfortable, and I'm doubtful I would follow up.
I also get ideas e.g. when driving. A voice recorder could capture those.
Recently, I discovered while trouble-shooting something else that my old cell phone has a sort of half-*ssed recorder built in (requires extended button press; voice notes limited to 1 minute, despite having a 1 GB card in the thing). I imagine this feature is available on iPhone, Android, etc.?
While I am now an Apple fan, this reminds me of the ridiculous excuses Apple fanboys gave me when they compared their early-generation iPods to my MP3 player at the time (a Rio Karma).
"It doesn't support gapless playback because in modern times, you should focus songs not albums!"
"It only holds 10 gigs, because you should only listen to your best songs on the go!"
"You don't need a button for skipping tracks, because you should spend your time listening to music, not switching between songs!"
Does anybody here know somebody that has used this program to aid their learning of computer science concepts? It's certainly an admirable cause, but is this a better introduction to programming than something like Logo, which has been used to teach programming to kids for many years?
Alice is impressive, and you can see the obvious programming influence, but it seems like "Moviemaker with control flow and objects" more than anything else. What problem is it trying to solve?
For me, the hardest part of learning elementary computer science was not things like OOP or if-statements, it was data structures, algorithms, and the difficulty of keeping many different interactions in your headspace. It seems like in many CS programs, the data structures or algorithms class is the "weeder" that separates the CS majors from the wannabe CS majors. Personally, I believe the drop-off at this level is more important to address than how many students enroll in CS 101.
Step one is to "break the ice" and get them interested in computers.
Step two is to figure out if they're any good at that.
A good childhood should be spent breaking the ice on numerous possible interests and finding out what works with you and what doesn't. Everybody gets abundant opportunity today to figure out whether they like sports, of all kinds; we could do with more (good!) opportunities to figure out if you like programming, or many of the other interests and hobbies that few children ever get exposed to. Most won't be any good at programming. That's OK, because everybody should be trying lots of things, and you won't be terribly good at most of them. (Where "good" here includes some concept of enjoying it enough to want to do it on your own, along with raw talent.)
These are the times when I wish that this technology was open-source (correct me I'm wrong), so if it was lacking, it could be added. I would love to have some similar way of turning commutative diagram sketches into TeX-ready form. It would save me hours of times fiddling with the current LaTeX packages.
if you use pgf/tikz in latex, you can do commutative diagrams pretty easily in a matrix style environment where you then indicate how to draw arrows between various entries and such. It takes an hour or two of playing with to get a hang of the notation, but its pretty nice, despite its quirks
No way. There are tons of people in the sciences with very interesting lives, they just don't have people knocking down their door to write popular biographies like Feynman, Erdös, or Tesla.
I say that living mathematicians like John Nash Jr., Shing-tung Yau, and Alexander Grothendieck have much more interesting lives than the examples you mentioned.
Let x \in R. Then we have that
by commutativity of multiplication, distributivity, the existence of a neutral element 0 for addition, and the commutativity of multiplication once again. Thus, we have that For clarity, define Then we have that which gives us our desired result.