This Fall, I was encouraged to attend an undergraduate's class on Real Analysis. A subject of mathematical analysis. It is a basic or very fundamental to all mathematics' graduates in Concordia. It has been two weeks now and there's a lot that I've learn from the class.
During my undergraduate's I remembered that I took some mathematical subject being as my minor. Those days, I have Calculus, Algebra, Linear Algebra, Advanced Calculus, Vector Analysis, Mechanics and Complex Analysis. For all this types of subject I was learning on how to solve a problems given. To be specific, we were taught on solving problem technique per se.
In my Real Analysis class, we start with the study of the property of natural numbers (i.e. positive numbers, 1,2,3,..), next the rationals (i.e fractional number 1/2, 1/3, ...) and now we are learning to construct the real numbers from the rationals. How beautiful can it be rite?
We were using the fact that from the property of rationals the operation of addition and multiplication can also be done in the real number without assuming that that kind of operations are definitely works (in real life it is always true). But, how far that we know that it is always true? In this class, we were suppose to answer any such question with proves. Only then it is safe to say something implies to something. If no such proof, then it's just only and hypothesis. Nothing else. It's quite complicated and sometimes it can be a mental torcher, but it is worth it.
I think it is the best choice to sit in this class and learn 'new' things which for most people it is not really new.
p/s- Reals as we know as nombor nyata has long been used for counting.
During my undergraduate's I remembered that I took some mathematical subject being as my minor. Those days, I have Calculus, Algebra, Linear Algebra, Advanced Calculus, Vector Analysis, Mechanics and Complex Analysis. For all this types of subject I was learning on how to solve a problems given. To be specific, we were taught on solving problem technique per se.
In my Real Analysis class, we start with the study of the property of natural numbers (i.e. positive numbers, 1,2,3,..), next the rationals (i.e fractional number 1/2, 1/3, ...) and now we are learning to construct the real numbers from the rationals. How beautiful can it be rite?
We were using the fact that from the property of rationals the operation of addition and multiplication can also be done in the real number without assuming that that kind of operations are definitely works (in real life it is always true). But, how far that we know that it is always true? In this class, we were suppose to answer any such question with proves. Only then it is safe to say something implies to something. If no such proof, then it's just only and hypothesis. Nothing else. It's quite complicated and sometimes it can be a mental torcher, but it is worth it.
I think it is the best choice to sit in this class and learn 'new' things which for most people it is not really new.
p/s- Reals as we know as nombor nyata has long been used for counting.
