Muslim Mathematician
Abu Ja'far Muhammad ibn
Musa Al-Khwarizmi
Born: about 780 in possibly Baghdad (now in Iraq)
Died: about 850
This is taken from a stamp from the former USSR
Sunday, 20 July 2014
Tuesday, 11 February 2014
Rate (mathematics)
Rate (mathematics)
In mathematics, a rate is a ratio between two measurements with different units. If the unit or quantity in respect of which something is changing is not specified, usually the rate is per unit time. However, a rate of change can be specified per unit time, or per unit of length or mass or another quantity.
A rate defined using two numbers of the same units (such as tax rates) or counts (such as literacy rate) will result in a dimensionless quantity, which can be expressed as a percentage (for example, the global literacy rate in 1998 was 80%) or fraction or as a multiple.
Sunday, 9 February 2014
Minimum Point of a Quadratic Graph
Minimum Point of a Quadratic Graph
Differentiating the function and setting its derivative to 0 is the fastest way however if you do not know calculus then an alternate method is to complete the square.
But for any quadratic in the form ax^2 + bx +c, where a, b and c are constants: the lowest point is when
x = -b/2a.
Monday, 9 December 2013
The Rule of Four
The Rule of Four
Mathematics should be expressed in the following four ways:
1. Algebraically
2. Numerically
3. Graphically
4. Verbally
In order to understand mathematics holistically, it is important that students connect each concept with the rule of four.
Click Here
Click Here
The beauty of this way of understanding mathematics is that it is so versatile; students can work with information presented in any one way and manipulate that information to find or interpret the information in other ways.
All students can learn
Three goals for the students:
1. Work accurately with basic operations:
2. Be able to apply basic operations to more complex problems.
3. Incorporate technology with the goal of higher level mathematics.
First and foremost my job is to ready my students for the next level of mathematics. Often, the level of mathematics dictates teaching methods.
When working with college-prep 9th graders in algebra, I focus heavily on a deep understanding of basic operations. The focus is essentially rote learning initially, and then we move to more involved problems. I teach and re-teach the basic skills that students will need to be successful when they reach algebra 2 and tackle the complexity therein.
When working with students in pre-calculus or calculus, I teach basic ideas fairly quickly and then move to complex applications of knowledge with the use of technology. I expose my students to the most rigorous IB or AP problems I can find or produce and sometimes much of class is spent discussing ideas rather than crunching numbers.
When working with college-prep 9th graders in algebra, I focus heavily on a deep understanding of basic operations. The focus is essentially rote learning initially, and then we move to more involved problems. I teach and re-teach the basic skills that students will need to be successful when they reach algebra 2 and tackle the complexity therein.
When working with students in pre-calculus or calculus, I teach basic ideas fairly quickly and then move to complex applications of knowledge with the use of technology. I expose my students to the most rigorous IB or AP problems I can find or produce and sometimes much of class is spent discussing ideas rather than crunching numbers.
"In order to understand Math, you must do Math."
Having too much
fun with the graphing calculator!
"Understanding of math is more than
following examples. It is the conceptual 'why' and 'how' and being
able to apply that."
"The
Rule of Three: Every topic should be presented geometrically, numerically and
algebraically."
Tuesday, 22 October 2013
Tuesday, 20 August 2013
Quotes on Mathematics
Quotes on Mathematics
As G H Hardy had aptly put it: “a mathematician, like a poet or a painter is a maker of patterns and that if his patterns are more permanent than theirs, it is because they are made with ideas.”
True beauty is a matter of maths
MATHEMATICS – The music of reason
As G H Hardy had aptly put it: “a mathematician, like a poet or a painter is a maker of patterns and that if his patterns are more permanent than theirs, it is because they are made with ideas.”
Friday, 28 June 2013
Expectation and Fair price
Expectation and Fair price
A person spins the pointer and is awarded the amount indicated by the pointer.
It costs $8 to play the game. Determine:
· The expectation of a person who plays the game.
· The fair price to play the game.
My work:
E=P(wins)(amount won)+P(loss)(amount lost)
E=1/3(-6)+2/3(-8)
E=1/3*-6/1 + 2/3*-8/1
E=-2/1+-16/3
E=-6/3+-16/3
E=-22/3=7.333
E=$7.33
Fair price=expectation + cost of play
Fair price= 7.33 +8.00
Fair price= $15.33
This just doesn't seem right to me, can someone tell me where I went wrong?
It costs $8 to play the game. Determine:
· The expectation of a person who plays the game.
· The fair price to play the game.
My work:
E=P(wins)(amount won)+P(loss)(amount lost)
E=1/3(-6)+2/3(-8)
E=1/3*-6/1 + 2/3*-8/1
E=-2/1+-16/3
E=-6/3+-16/3
E=-22/3=7.333
E=$7.33
Fair price=expectation + cost of play
Fair price= 7.33 +8.00
Fair price= $15.33
This just doesn't seem right to me, can someone tell me where I went wrong?
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