I am out of job again. Very funny how the unemployment net keeps getting me caught. Have lost my job teaching beautiful high school student Further Maths.
Wish I knew how to go back to teaching. Love teaching.
I wonder how many people are out there without a job.
Right now, thinking of doing commensalism with my parents. Wish they do not notice I won’t be contributing any money to the home, just making sure I wake up late, when they are out, watch the tv, if PHCN wants me to and do some home cleaning.
It feels so bad being out of a job. And for one I love really. Teaching Further Maths.
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A student cannot be greater than his master.
There is no count to the number of lessons we can learn from the simple formulas found in our maths.
I was sleeping yesterday when, after a religious service, the thought occurred to me: a student cannot be greater than his master. Right, yeah, I do believe that. But how is that translated in the maths? I wanted to know.
I was thinking about it when the thought of sets and subsets came to mind. I thought of all the maths problems I had solved and of my maths teachers , both those loved and hated; those feared and respected. I realized one truth then: The solution space of a student, any student, is a subset of his teacher’s.
The solution space of a student cannot be greater than his master’s. A student cannot do much maths, cannot solve more advanced maths than his teachers. One would never realize it unless you take the count yourself. I’d give a reward to anyone who can prove than he can solve more complex maths than his teacher? Excepting – exceptions are always the rule in life.
Excepting:
THE STUDENT HAS TO DO A CHANGE OF PARADIGMS. I recall this term from one of Steven Corby’s books. I think it was the “Seven habits of highly successful people?” Please forgive me if I am wrong.
So, how can we do a paradigm change in solution space and maths solutions.
1. By derivation. A derivation is like a creative activity. To be able to derive a solution space different from the teacher(s)’s, the student has to be a teacher himself. A derivation is like creating a complexity out of simple objects. But although this is a paradigm change, yet there must, I say, must still be taints of the inspiration and influences of his original teachers. So, there can be no total claim that the new teacher can have a solution space greater than his own teachers, just a more complex derived space.
2. Or By intersection. While still keeping the original solution space, by intersecting with another school of thought, a school of thought with a different paradigm, he can create a new solution space that is greater than his original teacher(s)’s.
But the two options above result in complexities and complexities result in more problems to solve. What if the teacher does not succeed? Then back to the original solution space of his teacher(s) is he/she going to be going to.
You see why I have to agree with that maxim: A student cannot be greater than his teachers?
I was sleeping yesterday when, after a religious service, the thought occurred to me: a student cannot be greater than his master. Right, yeah, I do believe that. But how is that translated in the maths? I wanted to know.
I was thinking about it when the thought of sets and subsets came to mind. I thought of all the maths problems I had solved and of my maths teachers , both those loved and hated; those feared and respected. I realized one truth then: The solution space of a student, any student, is a subset of his teacher’s.
The solution space of a student cannot be greater than his master’s. A student cannot do much maths, cannot solve more advanced maths than his teachers. One would never realize it unless you take the count yourself. I’d give a reward to anyone who can prove than he can solve more complex maths than his teacher? Excepting – exceptions are always the rule in life.
Excepting:
THE STUDENT HAS TO DO A CHANGE OF PARADIGMS. I recall this term from one of Steven Corby’s books. I think it was the “Seven habits of highly successful people?” Please forgive me if I am wrong.
So, how can we do a paradigm change in solution space and maths solutions.
1. By derivation. A derivation is like a creative activity. To be able to derive a solution space different from the teacher(s)’s, the student has to be a teacher himself. A derivation is like creating a complexity out of simple objects. But although this is a paradigm change, yet there must, I say, must still be taints of the inspiration and influences of his original teachers. So, there can be no total claim that the new teacher can have a solution space greater than his own teachers, just a more complex derived space.
2. Or By intersection. While still keeping the original solution space, by intersecting with another school of thought, a school of thought with a different paradigm, he can create a new solution space that is greater than his original teacher(s)’s.
But the two options above result in complexities and complexities result in more problems to solve. What if the teacher does not succeed? Then back to the original solution space of his teacher(s) is he/she going to be going to.
You see why I have to agree with that maxim: A student cannot be greater than his teachers?
What Pascal’s triangle taught me about life? Understand your habits
This here is Pascal’s famous triangle. By the way, Blaise Pascal was a French mathematician and philosopher.
Here’s how the triangle works? Each level is the power to which you want to raise a term to. Level one means raising some terms like (x + a) to power 0 which will always result in 1. Level 2 is (x + a)1 which will result in (x + a) as answer. Level 4 means (x + a)4 which results in the coefficients 1 4 6 4 1 and hence the answer x4 + 4x3a + 6x2a2 + 4xa3 + a4. This blog was not conceived to teach you Pascal’s triangle but the beauty of the triangle.
This is how it works? To get to a higher level, you need to have a knowledge of the pattern of coefficients of the level before it. This is how it helped me resolve some problems in life. To get to a higher state in life or before I start complexing my life, I need to understand the simplicities I was dealing with, otherwise, I would be lost in the maze of complexity which is our daily life. Generating a complexity from the preceding solutions involves mastering the solutions that you have been dealing with and the ability to understand the pattern for that solution whenever it arises again. I’m not talking about understanding what happened in the past in order to resolve the present. No. Pascal’s triangle is all about understanding the patterns of your past and present way of living before adding or removing one or more layers to it.
Imagine say five or three years ago. Those years ago, you must have been on a different status of life before now, maybe you progressed somewhat or it was the opposite. Did you understand the patterns in your life? Habit is something that everyone has. Did you understand what you did regularly and what made you succeed? Did you use those patterns to build upon the present or someone just gave you a lift? Understanding patterns and using them to get to where you want to can make a big difference between living a simple or complex life.
Without Pascal’s triangle, solving a problem like (x + a)6 would take me considerable time, even if I try to simplify things down to (x + a)2 three times and multiply the results. Understanding the pattern in Pascal’s triangle and building upon those patterns simplified the resolution. I found a “wow!” experience in the beauty behind the maths.
What are some scenarios that can make life complex?
1. You just got a raise in the office and your employer requires you work some extra hours? Take time to reflect on the habits or patterns in your life that made you succeed. Name that habit. Ask yourself questions just as: how would this new situation impact on my present habit of success? How would my life be if I worked the extra hours? The extra hours represent a layer of complexity to your present life. What do you need to give or take to make the extra hours conform to the present habits of success? You should never compromise on a formula for success, no matter what.
2. You discover that your source of income has been compromised. You might go financially bankrupt in the short term if things continue the way they are. What do you do? Do you allow the situation to overwhelm you and make you involve yourself in unbecoming business transactions? Donning the mantra of simplicity is what learning from Pascal’s triangle can do. Evaluate the solutions you have and the pattern of those solutions. Filter them into groups: sources that are still viable and those that will soon fall into the red. Work on the viable ones. How can you use the viable ones as a pattern to solve the problem of lost revenue? If the lost revenue cannot be recouped, then the pattern of viable sources should be what you must have in your hands before you allow the stress of the situation to overwhelm you. Evaluate your strength. In the words of Pascal’s triangle: staying at the pattern for success while scouting for solutions.
I hope you got the idea of the beauty behind Pascal’s triangle. I am presently using it to resolve some biting financial problems. You can also.
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
Here’s how the triangle works? Each level is the power to which you want to raise a term to. Level one means raising some terms like (x + a) to power 0 which will always result in 1. Level 2 is (x + a)1 which will result in (x + a) as answer. Level 4 means (x + a)4 which results in the coefficients 1 4 6 4 1 and hence the answer x4 + 4x3a + 6x2a2 + 4xa3 + a4. This blog was not conceived to teach you Pascal’s triangle but the beauty of the triangle.
This is how it works? To get to a higher level, you need to have a knowledge of the pattern of coefficients of the level before it. This is how it helped me resolve some problems in life. To get to a higher state in life or before I start complexing my life, I need to understand the simplicities I was dealing with, otherwise, I would be lost in the maze of complexity which is our daily life. Generating a complexity from the preceding solutions involves mastering the solutions that you have been dealing with and the ability to understand the pattern for that solution whenever it arises again. I’m not talking about understanding what happened in the past in order to resolve the present. No. Pascal’s triangle is all about understanding the patterns of your past and present way of living before adding or removing one or more layers to it.
Imagine say five or three years ago. Those years ago, you must have been on a different status of life before now, maybe you progressed somewhat or it was the opposite. Did you understand the patterns in your life? Habit is something that everyone has. Did you understand what you did regularly and what made you succeed? Did you use those patterns to build upon the present or someone just gave you a lift? Understanding patterns and using them to get to where you want to can make a big difference between living a simple or complex life.
Without Pascal’s triangle, solving a problem like (x + a)6 would take me considerable time, even if I try to simplify things down to (x + a)2 three times and multiply the results. Understanding the pattern in Pascal’s triangle and building upon those patterns simplified the resolution. I found a “wow!” experience in the beauty behind the maths.
What are some scenarios that can make life complex?
1. You just got a raise in the office and your employer requires you work some extra hours? Take time to reflect on the habits or patterns in your life that made you succeed. Name that habit. Ask yourself questions just as: how would this new situation impact on my present habit of success? How would my life be if I worked the extra hours? The extra hours represent a layer of complexity to your present life. What do you need to give or take to make the extra hours conform to the present habits of success? You should never compromise on a formula for success, no matter what.
2. You discover that your source of income has been compromised. You might go financially bankrupt in the short term if things continue the way they are. What do you do? Do you allow the situation to overwhelm you and make you involve yourself in unbecoming business transactions? Donning the mantra of simplicity is what learning from Pascal’s triangle can do. Evaluate the solutions you have and the pattern of those solutions. Filter them into groups: sources that are still viable and those that will soon fall into the red. Work on the viable ones. How can you use the viable ones as a pattern to solve the problem of lost revenue? If the lost revenue cannot be recouped, then the pattern of viable sources should be what you must have in your hands before you allow the stress of the situation to overwhelm you. Evaluate your strength. In the words of Pascal’s triangle: staying at the pattern for success while scouting for solutions.
I hope you got the idea of the beauty behind Pascal’s triangle. I am presently using it to resolve some biting financial problems. You can also.
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