By the way, I totally used Japanese for my calculus assignment. Who would have known that indefinite integration could be used to determine how many kanji a student would learn over a given period of time, based on a statistically derived average learning curve? I am constantly amazed by how often I see calculus applied in the real world. Well, as real world as my made up learning curve equation was, but

*calculus can still be related to learning Japanese.*

So, here is the assignment (I used an image for the part that had equations since Blackboard's equation editor doesn't translate well to plain text):

Well, I'm cheesy and I cannot think of a great application that doesn't deal with the standard acceleration/velocity/displacement model, so I am going to explore how integration affects the rate at which a student of the Japanese language (or anything else for that matter) absorbs knowledge to a useful degree. This is also because I am about to go on leave to study in Japan for a month and I have been fervently studying in preparation, so it is pretty much all that I can think of right now.

Since 漢字 (Kanji, or those evil little squiggly Chinese characters) recognition provides a good model for proficiency as students of Japanese tend to learn more kanji as they become more proficient, I will use that aspect of the language.

Let us call LR the Rate at which a student learns kanji, K the number of kanji learned, and t is time.

The rate of being able to learn and recognize new kanji goes down as you learn more kanji, so we will say the average student learns new kanji at the rate of (t/500)^{0.5}over a certain period of time. If a certain student has learned 300 kanji over 500 days, write an equation relating the kanji the student learns to time.

At the rate this student is learning, he will have mastered all 1,945 joyo kanji (Japan's official list of common use kanji taught in schools) in about 1,639 days, or just under 4 and a half years. Quite the studious fellow, although all of the above numbers are completely made up and your mileage may vary. Of course, I have been studying for around 500 days and I know about 300-400 kanji, so maybe one day I will follow this curve. Of course, this can be applied to any subject: you can determine the learning curve based on statistical data to determine about how much information a student should learn over a specified period of time.

数学はおもしろいですね。 (Math is quite interesting, isn't it?)

じゃ、また来週ね。(See you next week!)

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