Mathematical Knowledge

Dear All,

Next week we will be starting to examine the famous discipline of Mathematics. What is mathematics? Why do we all have to study it? Why do some people love it and others hate it? What kind of knowledge does mathematics give us? What methods are used in mathematics to generate this knowledge? What do words such as axiom, theorem, conjecture and proof actually mean? Why does mathematics seem to be so useful in other subjects? Why does it appear to us that the entire universe obeys relatively simple laws that can be expressed mathematically? Big questions.

A couple of things you could do while waiting impatiently for these lessons to come around? OK, why not ask your mathematics teacher about the subject? Why did s/he decide to learn and teach this subject? What would s/he say is the best thing about doing mathematics? And so on...

Also, try answering the following questions yourself. On Tuesday, we will all meet in the Auditorium in order to discuss them and move on into more exciting territory...

1. Mathematics is a subject about
A. logical thinking
B. illogical thinking
C. things that exist in nature
D. things that do not really exist at all
E. things that are certain
F. things that are not certain

2. Problems in mathematics can best be solved by using:
A. clever tricks
B. experiment
C. computers
D. graphic calculators
E. trial and error
F. investigations
G. discussion
H. the answers in the back of the textbook

3. Mathematics is a subject that should be studied by:
I. people who are interested in it
J. engineers and other people who want to apply it
K. people who are challenged by it
L. people who want to become better thinkers
M. people who are intrigued by aesthetic qualities
N. people who want to become better artists
O. people who want to improve their overall academic performance
P. people who want to improve their college entrance exams
Q. all Diploma Programme candidates
R. people who are poor at it

4. Which of the following best describes mathematics?
A. a body of knowledge
B. a practical tool
C. a cornerstone of philosophy
D. the perfection of the logical method
E. the key to understanding nature
F. an intellectual game
G. an aesthetic experience

5. Which of the following quotations best captures the essence of mathematics?
A. A mathematician is a blind man in a dark room looking for a black cat which isn’t there. (Charles Darwin)
B. Pure math is a game. It’s fun to play it for its own sake. It’s more fun than applying it. Most of the math that I teach is never used by anyone. Ever. (Ted Williams, Prep School Mathematics Teacher)
C. If you ask your mother for one fried egg for breakfast and she gives you two fried eggs and you eat both of them who is better in arithmetic, you or your mother? (Carl Sandburg)
D. Mathematics is a game played according to certain simple rules with meaningless marks on paper. (David Hilbert)