Here is the concluding part of the slides on Tensor Algebra
Next lecture: Tensor Calculus
Here is the concluding part of the slides on Tensor Algebra
Every member of this class (SSG 516) is entitled to a fully licenced copy of the Mathematica Software Version 10.4 once you are registered in the LG Laboratory. I will empower Mr Adeyeye and Mr Emmanuel Olowosulu to install and license all who show interest during the week. Find out from Emmanuel how much you need to pay to register at the LG Lab. We will be using the software for class work once we complete the work on Tensor Analysis. You will be better off if you can already work with the software before we get there. The ability to use this powerful software is a useful skill in its own right and can mean a lot for your future.
Here is a link to the recommended text
These are the problems to prepare for your test on Friday
The first set of slides are introduced here. Please go through them and be prepared to ask questions on Monday morning. I will be glad to have open questions we can discuss on this site.
Judging by the posture of the Labour Unions and discussions in the News Media, we are, once again in another iteration of the perennial palava on “Minimum Wage”. On the face of it, the issues of “Minimum Wage” or, if you like, “Living Wage”, easily draws adherents and crowd support. After all, have we not been hearing the million, billions or trillions in every currency imaginable losing their way into private accounts, tax havens or used to settle different kinds of political favours? Are we not daily treated to the iniquitous payments (it is injustice to call it wages or income) to Senators and House of Assembly members and Pension Managers and NERC Commissioners, etc.? Why must we suddenly say “there is no money when it comes time to “settle” the poor workers? Is it possible for a fair minded person to refuse to join the chorus for an increase in “Minimum Wage” especially when we consider the fact that the present value of seven thousand five hundred is far below the transport fair needed by most workers just to get to work? The arguments for minimum wage is compelling. Unfortunately, it is also wrong. In fact, it is my view, and I am not an economist, that incessant demand for “Minimum Wage” misses the larger issue of Income Inequity that creates and feeds the under development in our society.
It is amusing (or depressing depending on how you look at it) that different “armed” unions such as NMA, ASUU etc., demand higher wages from various governments by arguing on Internationalization. “A doctor or University Lecturer here has the same training as the one in Turkey” blah blah blah – so the argument go. One way or the other, most successful Unions are able to bluff their ways into forcing governments to pay them more allowances. Interestingly, some of these allowances may indeed include the computation into their wages, the salaries of a couple of servants they should be entitled to! We still talking about doctors, lecturers, parmacists and other professionals in government work or the public service. The matter takes a different turn if we bring our “onorebus” into the matter. This group of Nigerians already know that the monies they pay themselves amount to daylight robbery and they must forever keep it secret.
Based on a US Minimum Wage of 12 dollars an hour, the least paid full time worker in that country will earn at least 28,000 dollars if he works for 25 days in one month. President Obama makes 15 times that much. In most developed countries, it is hard to find individuals working for the same government making double digit the number of times another person is earning, no matter how skilled. I am NOT the highest paid person where I work, but I know for a fact that I get paid up to 50 times some unlucky fellows in the same or similar establishments. A person making twice my income is therefore getting three figure multiples of what some other people are getting in the same public service.
Before going further, let me be certain to define my terms. Of course, a football coach in a US university can negotiate to be paid a fraction of what monies he can make in the year. Such a person may, in fact earn more money than the President of the College. Furthermore, there is no statue binding private firms to peg what they can pay to board members and operatives on whose labour they build their prosperity. In such controlled environments, “Minimum Wage” makes a lot of sense.
Welcome to Nigeria! Here, you can have a person’s wage so calculated to include 3 stewards, 2 drivers, etc. If you increase minimum wage, this fat cat’s wages increase exponentially! Are labour leaders saying they are not aware of this? A system that allows a government worker to earn 50 times, one hundred times or more money than another from the common patrimony of us all is iniquitous. And we are not talking socialism here – just common sense! The absence of a limit on the maximum wage a person can earn from the public purse, compared to the least paid worker is gross injustice!
If it were just a matter of justice, then we can argue that people complaining should work their way to the top instead of merely grumbling about the success of others. However, the matter hurts our nation even more than that. It makes us unproductive.
Thirty five years ago, I had the opportunity in living in a Western country for a period of five years. I was surprised that the highest paid officer with a doctorate degree in my office earned about three times the least paid employee who had only a high school diploma. In that society, everybody tries to be part of the labour force one way or the other. With my Yoruba upbringing, was astonished by the fact that 18 year olds were expected to contribute to the funds used to maintain the home. In fact, ten year olds picked up empty bottles of soda and take them to the depot to collect small payments they use to start their personal account. My boss’ daughter worked as a waitress during school holidays and young people cleaned the streets, mowed lawns and did so many odd jobs such as painting, hedge trimming, carpentry etc. so to support themselves and not become too dependent on their families. It turns out that the average 25 year old from that society would not just leave school as a complete novice in everything but would have had substantial work experience and useful skills in addition to any post secondary education!
I think I have the answer to the question “Why don’t such things happen here”? Why do we continue to be dependent until we are into our forties? Why do able-body young adults simply loaf around and expect parents to supply all their needs? Why do we have cities and towns filled with garbage, unkempt fields and open sewers with able bodied people just tip-towing around, each expecting that someone, somewhere should do the needful? Why are we not having our houses, bridges and public facilities regularly painted and renewed? Why are the gutters always full of debris, and when they are removed, they become untreated, smelly refuse on the streets for weeks, months or years?
I think I have an answer. It is to be found in the fact that the wage iniquity we operate does not make contributing labour in these ventures sufficiently rewarding. In order to Illustrate consider two middle-class wage earners in Nigeria and England. Let us assume that the Nigerian earns 400,000 Naira a month while the counterpart in England earns 5000 UK Pounds after tax. If these people have three young adult children between the ages of 16 and 22. The Nigerian parent will necessarily be responsible for all the fees, the incidental expenses, clothing and feeding of the children. The UK parent here has more than two million Naira each month. Yet, he cannot afford to do for his children, what the Nigerian parent would feel obligated to do! To pay fees, housing and expenses for each child may require at least 1,000 pounds per month. The children in the UK will have no choice but to either get school loans or find paid employment. In the UK, the developed labour system allows a young adult to find unskilled labour jobs that will pay him 1000 pounds per month. In Nigeria, a similar job will pay him a maximum of 20,000 Naira! The parents will prefer that he loafs around and “read his books”. He will read those books while his counterparts elsewhere are learning life skills! The unskilled to semi skilled labourer will eventually learn to paint, to maintain lawns, to run a small supermarket alone; to serve foods and drinks in a hotel; to wash dishes using a heavy-duty dish washer and many other things that can even stimulate him to take one of these things as a lifetime calling in an entrepreneurial role! Our young adults here are “reading their books” because the parents are using yesterday’;s tools to solve today’s problems.
The same wage iniquity that we thought was helpful to us has come back to bite! It should stop. Labour leaders ought to stop fighting for minimum wage! Instead, they should insist that Governments in Nigeria must be limited by a maximum wage. Nobody in any government role ought to be able to earn more than 20 or 30 times. If we succeed in forcing a debate in this line, it will then become impossible for governments to secretly increase the salaries of some people while pretending that the Minimum Wage others are looking for is too much! If 10,000 Naira per month is too much for some people; then 300,000 per month is the maximum anybody else should earn. If some people are so great that they deserve to earn 1.5 million Naira per month, then by the principle of Maximum Wage, the least paid public servant should earn 50,000. Away with the anachronistic, colonial and slavish mindset that allows us to compute somebody’s wage while adding a number of other human beings that he is entitled, by government rules to be his servants!
Classes will continue after undergraduate exams next week.
These Questions and Answers follow the lectures on Tensor Calculus. Work through them for your next test: