the world of integrating by parts.

"If numbers aren't beautiful - I don't know what is" - Paul Erdos

So anyway, my first pattern my teacher wishes for me to notice, while exploring that sea of number lore in private, is how to do integrals of two functions. It's really the same pattern as the derivative of two things multiplied together, only now you're just doing the integral of the thing.

Really it's sorta intereting - I just need to plug away, another interesting thing is the relation between the sin and arc sin, which shows how the graph looks when you just replace the x and y's of each function.

Things

" What would really be a lesson that everybody should learn is that things come out of nothing - things evolve out of nothing. The tiniest seed in the right situation turns into the most beautiful forest, and then, the most promising seed in the wrong situation turns into nothing...
it gives people confidence.. that's how things work.. you can say.. 'Well, I know that things come from nothing very much and start from unpromising beginnings, and I'm an unpromising beginnigng - I could start something"

Mathematics is not so much ability as attitude

..the renee tape is one of his favaroites because of how beautifully it illustrates what he considers to be the secret to learning mathematics: Twenty-two minutes pass from the moment she says, "Ahhhh. That means something now." That's a long time. "If I put the average person in the same situation.. I'm guessing that after the first few attempts, they would have said, "I don't get it. I need you to explain it."..Schoenfield once asked a group of.. students how long they would work on a homework question before they concluded it wasn't theirs to solve.. the average was two minutes. But [she] persists. She experiments. She goes back over the same
issues time and again. She thinks out loud. She keeps going and going.
She won't give up.

"Oh! it's... " Her facelights up... Ohhh okay. Now I see.. That means
something"

He teaches a course.. I pick a problem that I don't know how to solve, 'he says' I tell my students, 'You're going to have a two-week take-home exam [or in my case.. 6 days to do a homework assignment]..' I know your habits. You're going to do nothing for the first week and start it next week, and I Want to warn you now: If you only spend one week on this, you're not going to solve it. If, on the other hand, you start working on it the minute you get the assignent,
[it might not work the first second.. but by week two [or in my case day 5] you'll have solved it.

Mathematics is not so much ability as attitude. Success is a function of persistence and doggedness and the willingness to work hard for twenty two minutes to make sense of something that most people would give up on after thirty seconds.

Profile of one before

Homeward serenely she walked with God's benediction upon her.
When she had passed, it seemed like the ceasing of exquisite music.

He grasped ideas about the laws of the heavens by simply doodling in sand - his own passionate excitement was so overwhelming the war amongst his brethren was something unnoticed.
This man, this 'God's mind's penetraitor',was confronted by one of his generations currents, a frail enemy soldier, and asked what was he doing - "Dear Sir, leave me be, for the completion of this chart, will show at once a diagram of a relation hidden for generations, and, if you agree, we shall be honored for eternity and remembered by far more a number than that of the current living. Hark, look at this, grasp your mind around the meaning of this idea - see this circle see this idea.. see how beautiful.." and at once he was stabbed.

Archimedes grasped the Mind of God - and in turn, was smote by an Earthly sword. The man Achilles brought empires to their knees, and crumbled the tainted dynasties of those long ago - still, the name Archimedes is remembered like his, showing the discoverer of ideas, as well as that conquerer of Nations, also wins immortality.

"He smote his breast and chided thus his heart - Endure my heart, for worse has thou endured."
- Virgil

Mathmatical ignorance diminishes, discriminates, and says No - Mathematic incite expands, unites, and says yes.

The Universe is number is a blog spot blog where my readers must know with their new knowledge, they shall - in future - reform the world! A site where, for only a few minutes in time - they may see that the Universe all around them is cloaked in number - where, after the trivialities of their day to day affairs & habits - visiting this blog allows an escape comparable to riding on the wings of Prometheus, allowing flights of imagination so orgasmic that these numeric states of affliction become like opium - a drug one can take at any time - where with my knowledge and posted quantity revelations - you may face the world with a type of mathematic drunkenness -where, you may see and finally feel true what William James has described before: Mathematical ignorance diminishes, discriminates, and says No - Mathematic passion expands, unites, and says yes.

' Our waking consciousness.. rational, as we call it, is but of one type, whilst all about it, parted from it by the filmiest of screens, there lie potential forms of consciousness entirely different. The consciousness produced from states of calculation and moments of incite - the sudden discovery of relations once hidden, are in a word, like breathing in the fumes left from creation, where we, with our meager human faculties, are now at once taping into the laws and nature of things - and by so doing our most mystical faculties are now being stimulated. The early child gets a taste of this at that first realization that every circle surrounding us, from the cradle to the grave, has a hidden relation - the diameter measured of the sun is 1/3.14th its circumference, and what holds true for that massive object in the sky is true from the 1/8th inch hole of the eye. Realizations like this are free and, simply for contemplating, admiring, and understanding nature's relations, she in turns stimulates human nature's pleasure centers - how wonderous!