This blog post has nothing to do with mathematics but just wanted to vent out my emotions.
I know that my opinions regarding the education system don’t matter since there always have been smarter people (i.e. people scoring more than me) around me in my home, school and college (and according to this system, only the opinions of top scorers matter). But, since WordPress allows me to express my opinions, here are the few comics which are in sync with my opinions:
© Bill Watterson
couldn’t find the creator of this comic
© Awantha Artigala
© Bill Watterson
I don’t think there is any solution to this problem since there are so many human beings on earth (i.e large variety of minds…).
Earlier I told about new mediums now available to enjoy maths. You can find a list of YouTube channels, to begin with here. And a list of dedicated math podcasts here.
In this post, I want to point out some episodes from the podcast “In Our Time” which discuss mathematics:
Apart from them, another podcast worth listening to is “The Wizard of Mathematics, Srinivasa Ramanujan” by Prof. Srinivas Kotyada on FM Gold:
If you are an average maths undergraduate student (like me), you might have ended up in a situation of choosing between “just completing the degree by somehow passing the courses without caring about the grades” and “repeating a course/taking fewer courses so as to pass all courses with nice grades only”. Following is a nice discussion from Reddit:
I found two documents that I was very proud of as a child. Both were the result of trying to understand the kind of things Ramanujan did in free time, a result of the little AMTI books I read as a child. I will share the second document in this post and the other one was in the previous post.
Following document was created in MS Word on my old Windows XP desktop. The calculations were done using some Microsoft advanced calculator:
I was not happy with the result though since the pattern didn’t continue which was supposed to continue according to Ramanujan.
I found two documents that I was very proud of as a child. Both were the result of trying to understand the kind of things Ramanujan did in free time, a result of the little AMTI books I read as a child. I will share one document in this post and another one in the next since both are not related to each other in substance.
Following is a calculation table generated using some spreadsheet software:
As you can see, it was motivated by the famous Taxicab number story.
If you are an average student (like me…) and are part of an insane curriculum (like having 5 advanced math courses in one semester) you may fail in few of your courses at college, even after trying your best to pass them. In such situations you may be able to control your panic by reading this Reddit post:
I will suggest you to go through the comments of that post.
Following are the four examples of sequences (along with their properties) which can be helpful to gain a better understanding of theorems about sequences (real analysis):
- : unbounded, strictly increasing, diverging
- : bounded, strictly decreasing, converging
- : bounded, strictly increasing, converging
- : bounded, not converging (oscillating)
I was really amazed to found that is a strictly increasing sequence, and in general, the function defined for all positive real numbers is an increasing function bounded by 1:
The graph of x/(1+x) for x>0, plotted using SageMath 7.5.1
Also, just a passing remark, since for all , and as seen in prime number theorem we get an unbounded increasing function for
The plot of x/log(x) for x>2. The dashed line is y=x for the comparison of growth rate. Plotted using SageMath 7.5.1