Arbias Hashani

When I ask anyone who is not a mathematician (and even some who are) what a “number” is, they never define what a “number” is, but say something along the lines of “well a thing you add to get another thing, like 2+2=4”. But here we had defined “+”, which I do not know of, have not defined and do not have much care for; I asked a different question. We see numbers as “left and right” on some big “interval”, this is also wrong. We will see this by the end of the first lecture.

The motivation behind this course is to build some proper rigour into understanding what, how and why analysis is/operates/works.

(When probability is taught wrong, it leads to bad knowledge of quantum physics, statistics(bizarrely), stochastic models, differential equations. Anything with randomness.)

When real analysis is taught wrong, it leads to bad knowledge of everything taught later on in maths: probability, calculus (vector calculus too), geometry, complex analysis, Fourier analysis, group theory, just a few to name, really cannot be taught without some specific and excellent knowledge of real analysis.

It makes sense (which through out this blog I will be saying… a lot) to begin with my notes for the course “An Introduction To Real Analysis”.

But… What if you have no mathematical knowledge? No worries. The prerequisites are nothing. Especially not calculus (integration or differentiation). But you should have some mathematical ability, what do we assume? That you know that a “real number” is. That is all. You do not even need to know what addition or multiplication are. To be honest; I hope you do not.

If you do have some mathematical knowledge, the notes will not be so interesting but the excercises should keep (some are very difficult, some very easy) you awake. And if you have a lot of mathematical knowledge, you may wish to simply download these notes for your own need; to teach others as a lecturer, as a prerequisite to your course, or just to have some real analysis notes, which is always handy.