Friday, June 15, 2012

Proofs


Introduction to Proofs

Proofs are the heart of mathematics. Mathematics is a prerequisite for science… and understanding science is necessary for life.
If you are a math major, then you must come to terms with proofs--you must be able to read, understand and write them. What is the secret? What magic do you need to know?
There is no secret, no mystery, no magic. All that is needed is some common sense and a basic understanding of a few trusted and easy to understand techniques.

The Structure of a Proof

The basic structure of a proof is easy: it is just a series of statements, each one being either
  • An assumption or
  • A conclusion, clearly following from an assumption or previously proved result.
 Directly and inevitably to the desired conclusion- without any distractions about irrelevant details. Each step should be clear or at least clearly justified. A good proof is easy to follow. And that is all.
Biological effects of S-2-Amino-3-(3-phenylacetylimidazol-4-yl) propanoic acid:
HEP G2 cell viability test -

DMEM
0
1
5
10
25
50
[mM]








0.215
1.311
1.275
1.16
0.864
0.247
0.187
#1
0.21
1.333
1.403
1.049
0.874
0.251
0.185
#2
0.221
1.274
1.386
1.126
0.842
0.271
0.185
#3

1.264
1.332
1.042
0.797
0.253
0.189
#4








0.2153
1.2955
1.349
1.09425
0.84425
0.2555
0.1865
average
0.005508
0.032151
0.057879
0.058048
0.034219
0.01063
0.001915
Std.Dev










Additional detail:  each well contains 200ul. HEP G2 is the ATCC 'gold standard' for a hepatocellular carcinoma (liver cancer) cell line. Concentrations are expressed in millimolars [0mM], [1mM], [5mM], [10mM], [25mM], [50mM].  Column labelled 'DMEM' is only growth media - with no cells. The test wells all have 2,500cells per well. Microtitre plate was incubated for 3 days at 37*Celsius. Color developed with MTS (a tetrazolium salt)-commonly used for cell viability determinations. The plate was read on a microtitre plate reader at a wavelength of 492nm. Resulting absorbances indicate complete (100%) inhibition of HEP G2 at a concentration of [25mM]  (S)-2-Amino-3-(3-phenylacetylimadazol-4-yl)propanoic acid.

Rapid inhibition of difficult to treat cancer cell lines.
Independently confirmed, reproducible, effective and undisputed...
 

 quod erat demonstrandum

And that is all.