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Tuesday, September 05, 2006

Teaching Mathematics

How can teachers make math enjoyable? Well, once a year i prepare the math trail for fourth year high school students when the topic involves angles of elevation and depression. Each group of students should solve three problems involving heights of the school building, of the flagpole in front of the building, and of the gymnasium.

Before the students set out on the trail, I ask them qestios as motivation: Who wants to become an engineer or an architect? A good engineer can determine the height and the cost of a building by inspection and measurements. How about determining the height of the flagpole without actually climbing to measure it?

The students are very excited and after the activity some of them go on to take up engineering courses in college.

Wednesday, August 02, 2006

David Hilbert


The Mathematical Problems of David Hilbert

About Hilbert's address and his 23 mathematical problems
Hilbert's address of 1900 to the International Congress of Mathematicians in Paris is perhaps the most influential speech ever given to mathematicians, given by a mathematician, or given about mathematics. In it, Hilbert outlined 23 major mathematical problems to be studied in the coming century. Some are broad, such as the axiomatization of physics (problem 6) and might never be considered completed. Others, such as problem 3, were much more specific and solved quickly. Some were resolved contrary to Hilbert's expectations, as the continuum hypothesis (problem 1).
Hilbert's address was more than a collection of problems. It outlined his philosophy of mathematics and proposed problems important to his philosophy.

Although almost a century old, Hilbert's address is still important and should be read (at least in part) by anyone interested in pursuing research in mathematics.

In 1974 a symposium was held at Northern Illinois University on the Mathematical developments arising from Hilbert problems. A major mathematician discussed progress on each problem and how work on the problem has influenced mathematics. Also, 23 new problems of importance were described. The two-volume proceedings of the symposium was edited by Felix Browder and published by the American mathematical Society in 1976. See also Irving Kaplansky's Hilbert's problems, University of Chicago, Chicago, 1977.

Friday, June 16, 2006

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Monday, June 12, 2006

Numbers in Egypt



Numbers

The ancient were possibly the first civilization to practice the scientific arts. Indeed, the word is derived from the word Alchemy which is the ancient name for Egypt.

Where the Egyptians really excelled was in medicine and applied mathematics. But although there is a large body of papyrus describing their achievements in medicine, there is no records of how they reached their mathematical conclusions. Of course they must have had an advanced understanding of the subject because their exploits in engineering, and administration would not have been possible without it.

The Egyptians had a using seven different symbols. 1 is shown by a single stroke. 10 is shown by a drawing of a hobble for cattle. 100 is represented by a coil of rope. 1,000 is a drawing of a lotus plant. 10,000 is represented by a finger. 100,000 by a tadpole or frog 1,000,000 is the figure of a god with arms raised above his head.

The conventions for reading and writing numbers is quite simple; the higher number is always written in front of the lower number and where there is more than one row of numbers the reader should start at the top.


Raymond eto yung typing tutorial

Sunday, June 11, 2006

More Tricks!

Here are some more mental Math for you to try ....

Quick Square - Did you know that there is a quick way of squaring a two digit number which ends in 5? Just multiply the first digit by that number +1 and stick a 25 after your product and there's your answer ...^^
Example:
Q. What is 35 squared?
A. 3x4=12
.....now stick on the 25
.....the answer is 1225

Times Eleven - The eleven times table has always been very easy to learn up to 9 x 11. Here's a way of multiplying large numbers by 11 too:
Example:
Q. What is 324 x 11 ?
A. Write down the first digit... 3
.......Add the first and second digits .. 3 + 2 = 5
.......Add the second and third digits .. 2 + 4 = 6
.......Write down the last digit ........ 4
The answer is 3564

Multiplying by Four - Doubling a number is quite easy. We learn doubles as some of our first number facts. So multiplying by four is easily achieved by doubling, then doubling again.
Example:
Q. What is 742 x 4?
A. 742 x 2 = 1484
.....1484 x 2 = 2968
The answer is 2968

Hope you learn something ^^

Saturday, June 10, 2006

Mental Math Tricks

Tricks! What's the difference between a strategy and a trick? A trick is associated with magic, something happening without an obvious explanation. Mental arithmetic tricks are just the same. When you first learn them you may not know why they work but they are very useful nevertheless. They are even more useful when you are able to explain why they work and understand their limitations.
Here are some mathematical tricks for you to try ...
Multiply Up to 20X20 In Your Head
With this trick, you will be able to multiply any two numbers from 11 to 19 in your head quickly, without the use of a calculator. I will assume that you know your multiplication table reasonably well up to 10x10.
Now try this:
· Take 15 x 13 for an example.
· Always place the larger number of the two on top in your mind.
· Then draw the shape of Africa mentally so it covers the 15 and the 3 from the 13 below. Those covered numbers are all you need.
· First add 15 + 3 = 18
· Add a zero behind it (multiply by 10) to get 180.
· Multiply the covered lower 3 x the single digit above it the "5" (3x5= 15)
· Add 180 + 15 = 195
That is It! Wasn't that easy? Practice it on paper first!
Here's another one:
Square 2 Digit Number: UP-DOWN Method
Square a 2 Digit Number, for this example 37

-Look for the nearest 10 boundary
-In this case up 3 from 37 to 40.
-Since you went UP 3 to 40 go DOWN 3 from 37 to 34.
-Now mentally multiply 34x40
-The way I do it is 34x10=340;
-Double it mentally to 680
-Double it again mentally to 1360
-This 1360 is the FIRST interim answer.
-37 is "3" away from the 10 boundary 40.
-Square this "3" distance from 10 boundary.
-3x3=9 which is the SECOND interim answer.
-Add the two interim answers to get the final answer.
-Answer: 1360 + 9 = 1369


Confused? Practice.... practice... ^^

Friday, June 09, 2006

Finger Math

- 9X Rule To multiply by 9
1. Spread your two hands out and place them on a desk or table in front of you.
2. To multiply by 3, fold down the 3rd finger from the left, if multiply by 4, it would be the 4th finger and so on.
3. The answer is 27 ... now read it from the two fingers on the left of the folded down finger and the 7 fingers on the right of it.

This works for anything up to 9x10!