Brilliant Tutorials in Mathematics and Computer Programming

The name is the attractor. I certainly want to be brilliant, if only in my own estimation though not the world’s. About 272 days ago, we both signed up and paid $161.88 each. She is still mad at me because she paid for something that does not work. I pointed out that they say that they are hiring and proofreading high school math is exactly her kind of job. So, that ball is in her court. I still work the problems, even when the problems have problems. 

I usually work at night and sometimes I have to skip one (even two) sessions, but I earn battery charges that carry me over. 

So far, I have completed series in elementary algebra, geometry, and calculus in addition to Probability & Chance, Functions, and Vectors, and large sections of logic, data analysis, and some others. A few, I began and chose not to pursue. The lessons on Digital Circuits and Circuits are waiting for me to make time to haul out the breadboarding kits. (I want to see their answers.) 

The reviews are nice exercises at bedtime. I do most of the work in my head. Some got complicated and required pen and paper and some of those are long tutorials, which, if I quit, I lose my place and have to start over. (About the third pass, I have memorized the first several answers.) It’s bedtime reading. I do enjoy the learning.

Find sin(a+b). 

I worked this through over three nights and was able to conceptually integrate the lesson and the proof of the formula. 

The Pythagorean Theorem has over 300 published proofs (one of the them by Pres. James Garfield). The proof in Euclid’s Elements is one of the most complex and demanding and least intuitively obvious presentations of this well known truth. So, too, with this demonstration of the measure of the sines of two adjacent angles. Nonetheless, after several repetitions, I found it elegant.

But not everything works that well. I ran into bugs in their tutorials for polar coordinates and for modulo arithmetic. As I told Laurel when she discovered other errors, all that is required is to document everything with screenshots, write out a descriptive narrative to show your work, and send it to them. 

51 mod 3 = 0 and also 51 mod 17 = 0.
And 51 mod 2 = 1.
But not here.

The Polar Coordinates maths are inverted.

The iPhone can be a barrier. I stopped working in Python, computer science, and AI because it is easier on the keyboard and I seldom sit here before going to sleep. So, I do what I can in bed and let the rest slide until I can have some daytime hours free for fun and games. I did finish the packet on Algorithmic Thinking. 

For another overview, see Wikipedia here https://en.wikipedia.org/wiki/Brilliant_(website)

More pros and cons on Quora here https://www.quora.com/What-is-your-review-of-Brilliant-org

PREVIOUSLY ON NECESSARY FACTS

Elisha S. Loomis and the Pythagorean Proposition 

How the Martians Discovered Algebra 

The Man Who Loved Only Numbers 

G. H. Hardy’s ‘Apology’ 

Birth of a Theorem by Cédric Villani 

A Simple Truth 

Grigory Perelman’s Perfect Rigor by by Masha Gessen 

ChatGPT and the Historical Forms of Academic Dishonesty

 In one criminology class, our professor said that 80% of people are honest 80% of the time; about 20% of the goods on the market have no clear title. 

Back in 1968, at my small liberal arts college, at the end of the school year, several of my classmates found themselves faced with a final paper in world history that some of them could not complete. At least one of them had done (most of) the work. He gave his pals his paper to copy, which they did, apparently verbatim in small or large passages. However, our school had an Honor Code, a Pledge, which was to be written in full at the top of each examination or paper. (Usually, for quizzes and such, we just wrote "Pledged" at the top.) Also, as it happened, the center of the conspiracy copied a section directly from the assigned textbook without attribution. The textbook was a reference for our benefit. We never read from it in class; we had no assignments from it. So, at least one of my classmates may have assumed that the professor would not recognize the passage or passages. In any case, it did not occur to them that their nearly identical papers would betray them. Of course, they should have been expelled and of course they were not. The story is not unusual in any way.

We have one day a month assigned away from the workplace and on that day, we receive a task from a manager. They call this "Mental Spa Day." My work away from work included completing an introductory class about ChatGPT and then having ChatGPT write a story. "Use a favorite character from two of your favorite tv shows/movie/book – so, you have two characters; Have them meet while on vacation in ____________(location of your choosing);  Have them describe the location surrounding them;  Have them go on two adventures." This is the result.

My instructions to ChatGPT: Write a story in which the character of Temperance Brennan from the televisions series "Bones" meets the character of Sherlock Holmes as played by Benedict Cumberbatch in the television series "Sherlock." They are separately on vacation in Austin, Texas. They meet on a tour of the Lady Bird Johnson Wild Flower Center. While admiring the plants and other wildlife, they see a foot under a bush and discover a body. Call this "Intro One."

Title: Botanical Bones: An Unexpected Encounter

Intro One: Lady Bird Johnson Wildflower Center

In the heart of Austin, Texas, the Lady Bird Johnson Wildflower Center sprawled with vibrant colors and the fragrant scents of nature. Temperance Brennan, a forensic anthropologist known for her meticulous attention to detail, found herself on vacation in the Lone Star State, seeking solace amidst the blooming wildflowers.

Meanwhile, Sherlock Holmes, the enigmatic detective with a penchant for deduction, had chosen Austin as his destination for a much-needed break from the hustle and bustle of London.

Their paths converged unexpectedly on a guided tour of the Wildflower Center, where they found themselves admiring the indigenous flora and fauna.

[Edit in: 7 June 2024. I rarely edit entry to this blog after a work has been posted. I sometimes fix typographical errors such as "its" for "it's" though most errors survive because that is the record. In this case, I removed the story so that I can edit it and post it on 8 June as "Fan Fic by ChatGPT: Part 3."] 

The work needs editing. Among the weaknesses was the use of the same key word in a sentence: "...they forged a bond forged in the crucible of investigation..." However, it is a good beginning for someone who does not want to create and needs to fill a requirement. I have several books of newly published science fiction like this purchased last summer on a whim. I got through half of one and cannot read the others. I did read two novels by Marion Zimmer Bradley and four short stories by H. G. Wells. To produce literature at that level would require training ChatGPT, which is the intent of its creators: you recursively teach the program to develop what you want. At that level, you might as well do all the work yourself, or, at least you will have the learning experience of teaching the subject. 

In 2008, I had a class in symbolic logic. Our first exercises were to program a logic engine to produce certain truths. After a few weeks, we were on our own: the homework was to solve this or show that or demonstrate some other. Well, I had the logic program to do that. I just entered the Boolean expressions and turned the handle. That worked fine until the problems got harder. I had to do a lot of paper-and-pencil to know what to give the machine. Eventually, although there was one that took me five hours, it was easier just to do the work myself. 

I recently read some discussions on Reddit among professors who were worried (or not) about how to test their students in the era of interactive AI. Here at the University of Texas Austin, they have large lecture classes assigned to teaching assistants: your "professor" is some kid two years older than you. At Eastern Michigan University, we did not have TAs. If your name was in the book, then you were the person in front of the class. Granted, you might not know every freshman in an auditorium of 200, but you should know every senior in your seminar.  

Addendum: April 28. 11:23 AM. For the more recent topic here on the slide rule, I was going to add a comment about calculators. Then, I realized that my phone will do that, of course. I seldom use an actual calculator any more. But how about math class? If you have a phone, you do not need to do any calculations. You enter “Bill can mow the lawn …” in your search engine and you get lots of answers. 

PREVIOUSLY ON NECESSARY FACTS

Goofing to a Meltdown? 

Engines of Creation 

Lost in Translation 

Invisible Cheating and Visible Rights