What is mathematics?
Daniel J Velleman:
Ø High school mathematics is concerned mostly with solving equation and computing answers to numerical question.
Ø College mathematics deals with a wider variety of question, involving not only numbers, but also sets, functions, and other mathematical objects.
What ties them together is the use of deductive reasoning to find the answer to question?
Daniel J Velleman
When you solve an equation for x you are using the information given by the equation to deduce what the value of x must be.
Similarly, when matematicians solve other kinds of mathematical problem, they always justify their conclusions with deductive reasoning.
Deductive reasoning in mathematics is usulally presented of a proof.
What the objective of the mathematicians?
The objective of mathematicians is to discover and to communicate certain truths. Mathematics is the language of mathematicians, and a proof is a method of communicating a mathematical truths to another person who also “speaks” the language.
The objective of mathematicians is to teach you to develop and to communicate your own proofs of known mathematical truths.
The objective of mathematician is to discover to and to communicate previously unknown mathematical truths
Example:
n
|
Is prime?
|
2n - 1
|
Is prime?
|
2
|
Yes
|
3
|
Yes
|
3
|
Yes
|
7
|
Yes
|
4
|
No (4 = 2x2)
|
15
|
No (15 = 5 .3)
|
5
|
Yes
|
31
|
Yes
|
6
|
No (6 = 2x3)
|
63
|
No (63 = 9.7)
|
7
|
Yes
|
127
|
Yes
|
8
|
No ( 8 = 4x2)
|
255
|
No (255 = 17.15)
|
9
|
No (9 = 3x3 )
|
511
|
No (511 = 73.7)
|
10
|
No (10 = 5.2)
|
1023
|
No (1023 = 31x33)
|
Sumber : PPT
Materi Pembelajaran Membaca dan Membuktikan dalam Matematika STKIP Garut
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