Sunday, December 30, 2007

College Advising - Organic Chemistry Vs. Biochemistry

Which course is more difficult: organic chemistry or biochemistry?

Well it depends on how your mind processes information! Orgo is analytical; its all about finding patterns and some spatial recognition (looking at and manipulating molecules in 3-D), and predicting the most likely outcome. Orgo is almost like algebraic chemistry. In algebra there are negative numbers and positive numbers, and there are a few operations (adding, multiplying, etc) that u can do to these numbers. Once you know how multiplication works, you can multiply any two numbers. In orgo there are big molecules; a big molecule may have slightly negatively charged areas and slightly positively charged areas; these slightly charged areas are usually the places where the big molecule will react with other reagents. All you have to do is determine which parts or 'functional groups' (like hydroxyl groups) make that big molecule slightly negative or slightly positive. Orgo is also like a 3 month IQ test; maybe that's why many people say it’s so hard. But it doesn’t have to be so hard. Like multiplication, orgo never changes. The exam questions never change; if I take the same IQ test 5 or 6 times, eventually I could score high. All you have to do is breathe and realize that nearly 90% of orgo questions just ask you 'where is the positively charged area of the molecule? Here? Ok, now you know that opposite charges attract, so if my reagent is negatively charged, what’s going to happen? Oh, well duh, the two are going to react and yield this product'.

If orgo is all about breaking down things and analyzing each atom or molecule or functional group, then biochemistry is more about looking at the BIG picture to come up with generalizations. Yes, you do analyze molecules in biochemistry, but there isn’t as much emphasis on analysis. The emphasis is more practical. Histidine has slightly charged regions, and so histidine is slightly acidic because histidine's ring is able to donate its Hydrogen. So what? Well histidine is a good pH buffer because its pKa is close to physiological pH (7.4), and it’s no surprise that hemoglobin contains many histidine residues in order to (for example) buffer the pH of the blood. Biochemistry can be easy if you take each relevant biochemical fact and put them together to see the BIG picture. In other words, grow a biochemical rationality so you can say things like ‘oh, it makes sense that eukaryotes have compartmentalized organelles; this allows each cell to perform many different reactions (at different pHs and substrate concentrations) at the same time'.

So! In conclusion, neither course is necessarily harder than the other is. And that’s not really important. The important thing is that orgo is all about knowing a few general rules and taking molecules apart, while biochem is all about synthesizing information derived from orgo to come up with many general rules and being able to connect these general rules together. If u realize this and are able to differ your approaches when you take these courses, you’ll find both courses easier than what everyone makes them out to be. Don’t believe the hype; decide how to look at these courses yourself today and in 3 months you can decide how to celebrate your A’s!

Poetry - Avis Choreographs Docility

This is a poem I wrote for a friend about our views on education.

Avis Choreographs Docility

Chattering chicks waddle to their pens–
Tattered by their creased city
Telling them of careless cares,
Tattered by the other chicks with
Their innate sense to pilot at will,
Tattered by their feathered cages,
Tattered by their pupils who see
Covers of books but not their pages– 8

…Happy-go-lucky nonetheless
Chicken-scratch… essays at first chance
Hatch… rhythms called success
Wobble then waltz… a tottering dance…
Avis–part swan: cakewalk on a lake
Of cerulean echoes and crimson bark:
Poised as a palm, supple as a brook
Whose stream curves out a question-mark; 16

A lyrical query, she muses over
Every step of every beat:
An epistemic salsa of how
To spin ideas at the webs of their feet;
Part owl: adorned tassels keep
Philosophy drawn to her mind’s eye;
Before dusk, she hunts those that prey
On her flock: pedantries lurk nearby… 24

Uncultured cultural quacks; Oh no,
She dares not call a forest a tree,
Just to swoop unseen but blind
Down to the ground and pick up debris–
No! ...she relents only to her heart
To perceive those musical utensils–
The sound, the sound of education:
Errors, and scribbles, and weathered out pencils; 32

And verb, six, seven, eight
Viva, baile, cante, swoon!
‘I see Cygnus in the sky’,
Scribe the dapper, dapper hip-hop saloon;
Tethers now cut; and so ashes now fly
Their pulse as high as the moon–
Magenta spews from the freshest dragon’s mouth;
A c o n s t e l l a t i o n revives the gentle south. 40

Algebra - Numbers Divisible by 9 (Friendly Version)

How do you know when a number is divisible by 9? If the sum of its digits is divisible by 9, then the original number is divisible by 9! For example, 6525 is divisible by 9 because the sum of its digits (6 + 5 + 2 + 5 = 18) is divisible by 9 (18/9 = 2). But, how and why does this happen?9 times 1 is 9, and 9 is divisible by 9; 9 times 2 is 18, and 18 is divisible by 9; 9 times 3 is 27 and 27 is divisible by 9; so, in general, 9 times any number is divisible by 9. 9x is divisible by 9; 9y is divisible by 9. It doesn't matter; x can be a number or a long sum of numbers; just as long as you multiply by 9, you can always divide a 9 out. Let us remember 9x. We want to get a number in the form of 9x. Then we know it has to be divisible by 9.Take 6525 for example! Now ask yourself if the mathematical sentences are true or not.
Is sentence below true?
6525 = 6(1000) + 5(100) + 2(10) + 5(1)
Yes; look at the metric system: 6m + 5dm + 2cm + 5mm = 6525mm
Is sentence below true?
6525 = 6(999 + 1) + 5(99 + 1) + 2(9 + 1) + 5
Again, yes because 10 = 9 + 1; 100 = 99 + 1, and so on.

Is the sentence below true?
6525 = 6(999) + 5(99) + 2(9) + 6 + 5 + 2 + 5
Yes, because we are allowed to distribute numbers like this. For example, x(x + 2) = x^2 + 2x, or 25 = 5(5) = 5(2 + 3) = 5(2) + 5(3) = 10 + 15 = 25. Now notice that the numbers on the right are the sum of the number 6525, which is 6 + 5 + 2 + 5 = 18, and 18 is divisible by 9 because 9 times 2 =18, and again 9 times any number is divisible by 9.

Is this sentence below true?
6525 = 9(111)(6) + 9(11)(5) + 9(2) + 9(2)
Yes, because all we did was factor out a 9 from each term. The last term was the sum of the digits 6525.This sentence below is true because we can factor a 9 from each term, we couldnt have done this if the sum of the digits in 6525 was NOT divisible by 9, so we need the sum of the digits to equal a number that's divisible by 9 in order to factor it out at this step!
6525 = 9[6(111) + 5(11) + 2(1) + 2]

Now remember, we said 9 times ANY NUMBER is divisible by 9, well let's make that number [6(111) + 5(11) + 2(1) + 2], now we have shown not only how but why if the sum of digits are equal to a number divisible by 9, that number MUST be divisible by 9, and vis versa. Here are all the steps in order:
6525 = 6(1000) + 5(100) + 2(10) + 5(1)6525 = 6(999 + 1) + 5(99 + 1) + 2(9 + 1) + 5
6525 = 6(999) + 5(99) + 2(9) + 6 + 5 + 2 + 5
6525 = 9(111)(6) + 9(11)(5) + 9(2) + 9(2)
6525 = 9[6(111) + 5(11) + 2(1) + 2]
6525/9 = 6(111) + 5(11) + 2(1) + 2725 = 666 + 55 + 2 + 2 = 725

Grammar - The Grammar of 'Either'

What is the grammatical function of the word 'either'? If you are confused, you're not alone!
Let's look at 'either' when it is used as a pronoun: 'Marry either of the two women.' sounds grammatically correct and it is. 'Marry any of the three women.' not only sounds better than 'Marry either of the three women.' but is also the grammatically correct choice. Just as 'between' is used to talk of 2 and only 2 entities and 'among' for 3 or more entities, 'either' is used to talk of 2 and only 2 entities while 'any' for 3 or more entities. In other words, use 'either' when talking about two things and use 'any' when talking about more than two things.

Nothing seems straightforward in grammar though. During the Old English (6th cen to 10th cen) and early Middle English (10th cen to 13th cen) periods, 'either' was taken to mean 'each of two' or 'both'. It wasn't until the late Middle English period where 'either' took on the disjunctive sense of meaning 'one or the other (but not both)'. The disjunctive sense was also covered by the word 'outher'; but, 'outher' became obsolete around the 16th cen, and so 'either' once again denoted the two prior meanings. Over the next 5 centuries the two prevailing meanings competed with each other. Eventually, the disjunctive meaning became dominate in Modern English.

Nonetheless, the original meaning has left a remaining residue of confusion in current language speakers. The Oxford English Dictionary actually recommends that the original meaning "must often be avoided on account of [its] ambiguity".

However, using 'either' is preferred over 'any' for whence a sentence talking of 3 or more entities yields an ungrammatical sentence. Thus, the sentence, 'President Nixon was either a good president, a bad president, or the best president' is a grammatical exception and therefore correct since using 'any' in this situation would yield an ungrammatical sentence.

Abstract Algebra - Numbers Divisible by 9 (Technical Proof)

This is a technical proof of how if you sum the didgets of any number and that sum is divisble by 9, then the original number is divisible by 9.

Let ai denote a digit in mod 10 and let a1a2…an denote a positive integer with an n number of digits. Then, 9a1a2…an Î Z+ if and only if 9Si = 1, n ai Î Z+.

Proof. Factoring out a 10n from the nth digit gives

a1a2…an – 1an
= 10(n – 1)a1 + 10(n – 2)a2 + … + 10(n – (n – 1))an – 1 + 10(n – n)an
= 10(n – 1)a1 + 10(n – 2) + … + 10an – 1 + an

Since [(10n – 1) + 1] = 10n,

= [(10n – 1 – 1) + 1]a1 + [(10n – 2 – 1) + 1]a2 + … + [(10 – 1) + 1]an – 1 + an.

Distributing ai to each term gives

= (10n – 1 – 1)a1 + a1 + (10n – 1 – 1)a2 + a2 + … + (10 – 1)an – 1 + an – 1 + an

Because 9(10n – 1) "n Î Z+, 9 can be factored out from each (10n – 1) to leave (S i = 0, n 10i).

= 9a1(S i = 0, n – 1 10i) + 9a2(S i = 0, n – 2 10i) + … + 9an – 1 + a1 + a2 + … + an (5)

The number a1a2…an – 1an contains the sum Si = 1, n ai. Let 9Si = 1, n ai = R. Factoring out 9 from each term gives

a1a2…an – 1an = 9a1(S i = 0, n – 1 10i) + 9a2(S i = 0, n – 2 10i) + … + 9an – 1 + 9R
= 9[a1(S i = 0, n – 1 10i) + a2(S i = 0, n – 2 10i) + … + an – 1 + R]

Because a1a2…an – 1an can factor out 9, 9a1a2…an – 1an. This could not have occurred if R did not factor out nine as well. Further, if 9a1a2…an – 1an, then a1a2…an – 1an gives a 9R term by equation (6). 9R = Si = 1, n ai and 9Si = 1, n ai. QED