Mathematics at University

High school mathematics classes are very different than those at university. Yes, mathematics classes at university are more difficult, but it is more than just that. When you learn mathematics at high school, all of the classes are about solving problems. The students are presented with the theory, the teacher demonstrates how to solve the problem using the theory and then the students try it for themselves.

What happens at university? Firstly, the classes are now lectures and so mathematics is now presented to the student rather than co-created with the student. Some problems are demonstrated, but often the lecture is mostly theory. The drawback is that the student must choose to put in the time in doing the problems outside of the class.

Some universities provide one hour of tutorial time per week or per two weeks. In these tutorials, often a postgraduate at the university will help the students in solving problems from a problem set. While this is welcomed, often the postgraduate is not as approachable as a high school teacher. The same can be said about the lecturer. Yes, you will find some lecturers who are only too happy to offer one-to-one time helping the students but this is not the norm. Most lecturers have their time taken up by research and they view classes as a secondary role of their job. This, of course, is not true for all third level institutes.

In addition to this, the mathematics courses themselves vary. For example, a student taking a course in statistics would be solving many more problems than a student taking pure algebra. Most questions in pure algebra are not “problem based” but rather “proof based”. That is, in statistical classes the student will need to solve a problem and in pure mathematical classes students would mostly be proving a result. The former is more reminiscent of high school mathematics classes.

My advice for students entering a mathematics course at a university would be to stay on top of the questions or problems the lecturer assigns. You will not have the same time in class you would have had at high school for solving problems. Mathematics is not a spectator sport; you must work at it. Mathematics is presented to students as something to “watch” but it is something to work at. And of course, if you find yourself having trouble in your course, then seek help straight away!


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What Are The Greatest Changes In Shopping In Your Lifetime

What are the greatest changes in shopping in your lifetime? So asked my 9 year old grandson.

As I thought of the question the local Green Grocer came to mind. Because that is what the greatest change in shopping in my lifetime is.

That was the first place to start with the question of what are the greatest changes in shopping in your lifetime.

Our local green grocer was the most important change in shopping in my lifetime. Beside him was our butcher, a hairdresser and a chemist.

Looking back, we were well catered for as we had quite a few in our suburb. And yes, the greatest changes in shopping in my lifetime were with the small family owned businesses.

Entertainment While Shopping Has Changed
Buying butter was an entertainment in itself.
My sister and I often had to go to a favourite family grocer close by. We were always polite as we asked for a pound or two of butter and other small items.

Out came a big block of wet butter wrapped in grease-proof paper. Brought from the back of the shop, placed on a huge counter top and included two grooved pates.

That was a big change in our shopping in my lifetime… you don’t come across butter bashing nowadays.

Our old friendly Mr. Mahon with the moustache, would cut a square of butter. Lift it to another piece of greaseproof paper with his pates. On it went to the weighing scales, a bit sliced off or added here and there.

Our old grocer would then bash it with gusto, turning it over and over. Upside down and sideways it went, so that it had grooves from the pates, splashes going everywhere, including our faces.

My sister and I thought this was great fun and it always cracked us up. We loved it, as we loved Mahon’s, on the corner, our very favourite grocery shop.

Grocery Shopping
Further afield, we often had to go to another of my mother’s favourite, not so local, green grocer’s. Mr. McKessie, ( spelt phonetically) would take our list, gather the groceries and put them all in a big cardboard box.

And because we were good customers he always delivered them to our house free of charge. But he wasn’t nearly as much fun as old Mr. Mahon. Even so, he was a nice man.

All Things Fresh
So there were very many common services such as home deliveries like:

• Farm eggs

• Fresh vegetables

• Cow’s milk

• Freshly baked bread

• Coal for our open fires

Delivery Services
A man used to come to our house a couple of times a week with farm fresh eggs.

Another used to come every day with fresh vegetables, although my father loved growing his own.

Our milk, topped with beautiful cream, was delivered to our doorstep every single morning.

Unbelievably, come think of it now, our bread came to us in a huge van driven by our “bread-man” named Jerry who became a family friend.

My parents always invited Jerry and his wife to their parties, and there were many during the summer months. Kids and adults all thoroughly enjoyed these times. Alcohol was never included, my parents were teetotallers. Lemonade was a treat, with home made sandwiches and cakes.

The coal-man was another who delivered bags of coal for our open fires. I can still see his sooty face under his tweed cap but I can’t remember his name. We knew them all by name but most of them escape me now.

Mr. Higgins, a service man from the Hoover Company always came to our house to replace our old vacuum cleaner with an updated model.

Our insurance company even sent a man to collect the weekly premium.

People then only paid for their shopping with cash. This in itself has been a huge change in shopping in my lifetime.

In some department stores there was a system whereby the money from the cash registers was transported in a small cylinder on a moving wire track to the central office.

Some Of The Bigger Changes
Some of the bigger changes in shopping were the opening of supermarkets.

• Supermarkets replaced many individual smaller grocery shops. Cash and bank cheques have given way to credit and key cards.

• Internet shopping… the latest trend, but in many minds, doing more harm, to book shops.

• Not many written shopping lists, because mobile phones have taken over.

On a more optimistic note, I hear that book shops are popular again after a decline.

Personal Service Has Most Definitely Changed
So, no one really has to leave home, to purchase almost anything, technology makes it so easy to do online.
And we have a much bigger range of products now, to choose from, and credit cards have given us the greatest ease of payment.

We have longer shopping hours, and weekend shopping. But we have lost the personal service that we oldies had taken for granted and also appreciated.

Because of their frenetic lifestyles, I have heard people say they find shopping very stressful, that is grocery shopping. I’m sure it is when you have to dash home and cook dinner after a days work. I often think there has to be a better, less stressful way.

My mother had the best of both worlds, in the services she had at her disposal. With a full time job looking after 9 people, 7 children plus her and my dad, she was very lucky. Lucky too that she did not have 2 jobs.

Board Examination Study Tips

It is that time of year when feverish preparations begin – the Examination Fever. Many young students are getting ready for the biggest test of their academic lives, one that will determine their choice of career and how their futures will shape up. The 10th standard examinations or Board Examinations follow many patterns according to the syllabi and the academic councils the schools are affiliated to. Getting high marks and percentages overall in all subjects is key to enhancing chances of a good education in a reputed institution; therefore students should take extra steps in equipping themselves well in the preparations for exam study.Students at this level have six to seven subjects with allocation of marks and grades combined for a subject grouping. Mathematics and Science take predominance over other subjects like Social Studies, English or Other Languages. This is because for most technical courses post school and getting admitted into college depend on excellent percentages in these two subjects. While subjects like English depend on the student’s excellent uptake of grammar and presentation of answers in a neat format with the relevant points concisely written, Mathematics and Science depend largely on accuracy in answers and results.Some examination tips for High School• By understanding the format of exams corresponding to the syllabus undertaken, a student can work out a study schedule depending on subjects that need more attention and time. Having a timetable based subject-wise and topic-wise will greatly benefit your study schedule; always remember to complete the schedule as per the timetable you have prepared• Referring to previous question paper samples and guides helps obtain an insight into the kind of questions that can be expected and prepare a mental plan on how to answer the questions• Resorting to malpractices or depending entirely on memorizing content can be disastrous. In case of exam panic or a wrong move, the mind goes into a freeze making thinking and recollection difficult. It is better to understand content, rephrase questions on how best to bring out the answers and keep doing the tasks over and over to perfect the method and analyze and correct mistakes, especially in problem solving• One of the best ways to retain content the student has read is to write down points or make brief notes that will help to remember key points to prepare the flow of content• When in doubt, seek help. Parents, teachers, friends, guides are always around to help clear doubts. Published guides help but where they fail is the kind of one on one interaction that you can have with peers and superiors• Learn to practice time management which is very essential in answering question papers. Practicing writing speeds can help improve answering skills when time is of utmost importanceBesides these academic tips, there are several other areas that the student has to keep in mind when preparing for Board exams.i. Choose a study area without distractions and ambient noises from traffic, TV screens, computers and other gadgets that can be a disturbance or intrusion. Conversations with friends can be restricted to times when you take a break from studyingii. Getting proper nutrition, exercise and sleep recharges the body and fills it with energy resources which are very essential. Skipping meals and sleeping less will tire the body and mind and leave you exhausted by the time examinations arriveiii. Avoid places and situations that can cause anger and negative emotions to surface. The unnecessary anxiety and worry will not help in any wayiv. Always take constant breaks from study to re-energize the mind and body. Cramming the brain with too much information or too many facts in a short span of time is not a good idea. Take time off to indulge in a favorite hobby like listening to music, painting or photography; going for a short walk and meeting friends for a cup of coffee is a good idea provided this does not cut into your daily study schedule and you are able to get back into study mode again
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