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.
