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Week 8: The Big (Scary) O: Part 1

Greetings my spooky readers! 

 I hope you all have had a wonderful Hallow's Eve munching on candies or partying it up and didn't have to think about all those assignments you haven't done yet! 

 So while you're still working on all those "leftover" candies that you bought so you could "give" them to the trick-o-treaters (but really we all know you saved the good ones for yourself) let's tackle a big topic: the BIG O. (cue spooky music here)

 Because I am a little short on time today, I would just like to introduce the concept of the big O. So, if we were to label, big O would be an asymptotic notation for a set of functions. It's kind of like giving the upper limit of a function. The notation O(f(x)) would be saying that the set of functions within O would never grow faster than f(x). This is helpful in computer programming for when we want to calculate the maximum number of steps that a function may take. In other words, big O tells us to overestimate the number of steps as much as possible. 

 Now if I were to tell you that there's this thing that gives us an upper bound, then you are most likely going to ask me, "is there also a lower bound or some sort of in between estimate?" And the answer to that is, of course! 

 Within the asymptotic notations, we have learned 3 in class: O (the upper bound),  Ω (the lower bound), and 𝝦 (the tight bound). If you have done a bit of rudimentary integration, you might be able to understand when I compare this concept to the right endpoint, left endpoint, and midpoint approximations of the integral.

 That's it for today folks! I hope you can understand my haphazard explanation of something that I am still trying to fully grasp, and thanks for reading, as always!

Lana :)
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