Assignment #3 Outline

Topic: History of Coding and Computer Algorithms

Format: Visual Road Map

Bibliography: 

Bureau, T. G. (2020, November 5). Ada Lovelace Day: Commemorating the world's first computer programmer. TechGig. https://content.techgig.com/ada-lovelace-day-commemorating-the-worlds-first-computer-programmer/articleshow/78642521.cms

Encyclopædia Britannica, inc. IBM develops FORTRAN. Encyclopædia Britannica. https://www.britannica.com/technology/computer/IBM-develops-FORTRAN

Encyclopædia Britannica, inc. LISP. Encyclopædia Britannica. https://www.britannica.com/technology/LISP-computer-language

Hayward, D. (2020, October 7). A Brief History of Coding - BDM Tech Guides. BDM Publications. https://bdmpublications.com/brief-history-coding/

The History of Visual Basic. http://www.johnsmiley.com/visualbasic/vbhistory.htm

History - Open Dylan. https://opendylan.org/history/index.html

How Alan Turing Cracked The Enigma Code. Imperial War Museums. https://www.iwm.org.uk/history/how-alan-turing-cracked-the-enigma-code

McCracken, H. (2014, April 29). Fifty Years of BASIC, the Language That Made Computers Personal. Time. https://time.com/69316/basic/

McFadden, C. (2020, September 5). The Origin of Algorithms We Use Every Single Day. Interesting Engineering. https://interestingengineering.com/origin-algorithms-use-every-day

Mkhitaryan, A. (2017, October 13). Why Is C# Among The Most Popular Programming Languages in The World? Medium. https://medium.com/sololearn/why-is-c-among-the-most-popular-programming-languages-in-the-world-ccf26824ffcb

Python History - javatpoint. www.javatpoint.com. https://www.javatpoint.com/python-history.

The rise of C++. Nokia Bell Labs. http://www.bell-labs.com/about/history/innovation-stories/rise-c-plus-plus/

Nasar, Audrey A. (2016) "The history of Algorithmic complexity," The Mathematics Enthusiast: Vol. 13: No. 3 , Article 4. https://scholarworks.umt.edu/tme/vol13/iss3/4

The Golden Age of Medieval Islam

 One thing that I found very interesting from this reading was the inception of the word "algorithm". I had never put much thought into where the word came from, so it was interesting to find out. Apparently al-Khwarizmi's book "The Book of Addition and Subtraction According to the Hindu Calculation" was so important that it was the first Arabic math book to be translated into Latin. Today the word "algorithm" is used to describe the act of calculating something, but it is derived from the Latin interpretation of al-Khwarizmi to "algorismi". 

It was also very interesting to learn about al-Khayyami's achievements with ratios. Specifically, I had no idea that his view of the ratio of the diagonal of a square to the side (sqrt 2) or the ratio of the circumference of a circle to its diameter (pi) eventually lead to the introduction of positive real numbers. This is an achievement that has surely stood the test of time because we are still using positive real numbers today. 

Finally, it would be impossible not to mention al-Kashi's correct calculation of 2pi to 16 decimal places. Calculating the perimeters of inscribed and circumscribed polygons in a given circle having 805,306,368 sides. He even went as far as to describe how close he wanted his approximation to be and was correct. The time and effort that he put into this calculation show the true dedication that he had to his craft. 

Trivium & Quadtrivium

"Numbers were identified with the various gods. He considered odd numbers to be male and the even ones to be female."

I found this to be very interesting and it made me wonder what the thought process was here. This is obviously me stereotyping, but generally, speaking girls are better behaved in grade school. Once both genders are grown up I think it evens out a bit but during school, it is almost always the boys that give teachers a hard time. This is why this analogy makes sense to me, with boys being slightly more "odd" and less put together and females being more "even" and polished. 

"To qualify for a degree, he was required to participate in public disputations, either defending a proposition or opposing one defended by another student"

There was a couple of things that I found interesting. Firstly the use of the word "he" because back then university was only provided to men and not women, that is certainly one aspect that the modern university has changed for the better. Secondly, I find it interesting that the university used to require students to argue their opinions. I feel that this is something lacking from the modern university, where at times it feels like students are just being graded on their ability to memorize facts and figures. 

"education as the sole occupation of the first thirty-five years of a man's life. He would have the first twenty years spent on gymnastics, music, and grammar, the next ten on arithmetic, geometry, astronomy, and harmony, and the next five on philosophy. "

This was an opinion of Plato's. The first thing that sticks out to me is the subjects that he chose, particularly gymnastics and music. It is clear that Plato believed that a man should focus the majority of his education on the arts, which I found interesting. Additionally, this is a very long time! I have been in school for sixteen years and that is already a long time. On paper, it would appear that Plato's theory would result in a well-educated, more successful society, but I am not sure that is the case. My opinion is that the economy would suffer because people aren't entering the workforce until a later age and because there is no diversity of knowledge. Yes, a university education is important, but we also need trades workers and I don't think philosophy and astronomy are very important for those roles. 

False Position

My word problem: Two of a number and its square root are equaled to 36.




2x + √x = 36

Try 4: 2(4) + √4 =

8 + 1 = 9

36/9 = 4, therefore multiple 4 by 4

2(16) + √16 =

32 + 4 = 36




It worked!

Was Pythagoras Chinese?

Does it make a difference to our students learning if we acknowledge (or don't acknowledge) that non-European sources of Mathematics? Why, or how?

I think that it is important to study the history of math in a fully holistic manner. It doesn't make any sense to me why someone would study Greek math history but not Chinese? Are their discoveries any less impressive or important? I would think not. The arguments behind teaching math history as part of the curriculum; understanding the trial-and-error aspect of math, understanding that math is always evolving, would surely also apply to Chinese math history. I guess it is true what they say, history is written by those that create it and in our western world we are more attuned to the western history of math, I think that should change though. 

What are your thoughts on the naming of the Pythagorean Theorem, and other named mathematical theorems and concepts (for example, Pascal's triangle)

The naming of proofs and math concepts is a complicated subject. On one hand, the Babylonians and Egyptians understood the relationship between sides of a triangle prior to Pythagoras, so why should he go down in history as the master of the triangle? Is it because his way of thinking was very western? Prior generations had possibly placed less importance on individual fame and recognition, placed less importance on a formal proof process and Pythagoras has reaped the rewards of such. On the other hand, where do you draw the line? If not the Pythagoras Triangle then what? The Egyptian triangle? But then the Babylonians would be up-in-arms. I think that there is no solution to this problem and if Pythagoras was the one that made the theory famous, I'm fine with that.       

Why Teach Math History?

Pre-reading ideas about whether, why, and how math history should or could be incorporated into math teaching. 

As one of the few non-education majors, I am not sure I can say how I would implement it into "my own" math teaching. I can, however, put myself into the shoes of a high school student and think about what I would want to learn about. That being said, I see math history playing a minimal role in high school math education. I think that the history of math can be helpful if it provides context to complicated techniques, showing how a certain type of math was discovered could create real-world applications for math in the minds of students. Other than that though, I think it would just confuse kids and overload them with information that they don't necessarily need. 

Things that made me "stop and wonder"

"History can be torturous and confusing, rather than enlightening", this is exactly what I was trying to say, this has been phrased a lot more eloquently than I could ever say it, but I 100% agree. "Lack of time", I also agree with this, highschool math already has a ton of concepts packed into it, I feel that adding the history of math would increase that "knowledge overload" that I discussed above. "The active predisposition towards mathematics", I agree that this point is interesting. Math should be seen as ever-evolving and should inspire students to question everything and maybe even discover new are better ways to approach math. A few hundred years ago math looked a lot different than it does now and in a few hundred years with will look different again.  

Conclusion

I think that some very valid points were made for both sides and I now definitely now see the benefits of teaching the history of math to students more than I did prior to reading this. However, my main doubts remain and I think some of them were even strengthened and confirmed by the article. 

Alice Major on Mayan and Other Numbers

Is this something that you might want to introduce to your secondary math students? Why or why not?

I likely would not teach this to secondary math students. My reasoning is, although this is interesting, I'm not sure it would help the students understand math better. In high school, when students are learning concepts like pre-calculus and calculus, math can be very hard to grasp. I wouldn't want to complicate things any further

If you would use these ideas in your math class, how might you do so?

I think that these concepts can be applied and useful to a different age group. For example, in primary school when students are first learning to use addition and subtraction I could see this playing a role. The concepts and personalities of the numbers would obviously be simplified from what the Mayans used, to apply to primary students. I think that a video, showing numbers as personalities and how they interact could be extremely fun and useful to these primary school students. For example, showing a pair of fives as young and energetic twins, then showing a ten as a more mature and larger version of those fives, showing that two of those fives equal to that ten. This is a very rough example, but hopefully, you get the point. 

Do numbers have particular personalities for you? Why, how, or why not? What about letters of the alphabet, days of the week, months of the year, etc?

I have never thought about it like this, but now that I am thinking about it, definitely. I saw a meme a while back that said "I can't explain why, but the number eight, the day Thursday, and the month October all are the same", and I couldn't agree more. I tried dissecting the reason for it and I think it's all about being an even number and being close to the end of their respective spectrums. Eight is an even number and is very close to ten, October is an even-numbered month (tenth) and is close to the end of the year. I know technically Thursday is the fifth day of the week, with Sunday being the first but I think most people think of Thursday as the fourth day of the week and Monday as the first, which would make it an even-numbered day and close to the end of the week. Additionally, I see five and ten as being preppy and perfect, likely because of being seen as "round numbers". I see numbers 2,4,6 and 8 as being related because they are even. Three and nine are seen as the "rebels" to me, somewhat related to six, but a little rough around the edges. Then that leaves one and seven, I see one as being the baby of the group (self-explanatory) and I see seven as being the hipster. I think this personality comes from people choosing a number between one and ten, somehow seven is always the most common choice. This is likely because it doesn't fit into any of the usual categories (even numbers, multiples of five, multiple of three, close to zero, or close to ten), it is just kind of its own thing and I respect seven for that. After reading this story, I will definitely look at numbers differently.