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390 Quick Answers 3 March

Exam topics? Remember the exam is sooner than you think (3 classes from now). Friday will be the last day for material on the exam. Someone asked - yes, you may use examples that I don鈥檛 discuss in class. 1600 is a decent cutoff for the exam.

Also of course remember your annotated bibliography is due by classtime on Friday. It must be in .pdf to get formatting correct. Oh, and _one_ paragraph to wrap together. One per source to wrap together makes no sense. Those who will present at GREAT Day need a title and abstract for Monday. A catchy but on-topic title is appropriate. The abstract should be a description of what you鈥檙e going to talk about, it should not be everything that you鈥檙e going to say about it. It should make sense to other math. majors.

Again we will have some delay. I will finish some 6.1 material on Friday, but will do all of 6.2 then also. 6.2 is a bit light. I鈥檓 pushing quartics and complex to Friday. Again, be careful on timing between 6.1 and 6.2.

I have a question 鈥� when I put individual comments to you in your my-learning submission - do you see them?

Lecture Reactions

Again, just because you use combinatorics in probability, does not mean it _is_ probability or statistics. Arithmetic is not calculus, but it is used in calculus. We have discussed no probability nor statistics 鈥� although Cardano was a first for probability, and we will discuss him today.

ben Gerson was not the first to use induction, al Karaji did about 200 years before. It is reasonable to believe the two were independent, and neither caught on very much at the time, I think. Why did I focus on ben Gerson and not al Karaji? I don't have a good answer - but we were rather busy during Islamic work, and less so in chapter 5.

I think Oresme's work with ratios is a step toward working more with fractions than ratios, which is more what you are familiar with. We have seen in our original source work that before this it was more discussed in terms of ratios.

Graphing as we saw in Oresme is new and a _big deal_. Notice we have graphs long before coordinates. That will be another big deal. Graphs are plotting points at heights perpendicular to a base.

One theme of last class was the question of how influential a mathematician is. Clearly since we don't use his notation, Chuquet wasn't very influential. To be clear, I don't know of any others referring to his work or style. He didn't have the audience. There are many other similar stories. We see them from time to time. It is very fair to say that Chuquet was comfortable with the rule for multiplying two powers of the same base. Chuquet used a dot with an exponent where you would write an x.

We still have no equations, and basically none of our notation. Lots of words. You'll see a little today of original pre-translated sources. They will start to look more familiar in the next couple classes. Watch carefully. The writing we see is matched in their work. They are not secretly using mathematical notation. Keep this in mind in our work today and next time especially.

Why do we skip 140 years? I think it's fair to say that Europe is still waking up.

Reading Reactions

Quarantine means forty and references the biblical 40 days, but the first use for disease was for 30 days. That is the best of my understanding of a somewhat complicated situation.

Jeff is probably overreacting to mathematics going from _all_ of the liberal arts. In particular, it sounds as if he is a showing a little personal grudge there. There's no real downgrade in Renaissance times, if anything, it is rising again, as we see.

How do languages get to be "the language of science"? Good question to which I don't have a good answer 鈥� it has generally gone from Greek, to Arabic, to Latin, to French, to English, as far as I know.

del Ferro was the first to solve cubics algebraically. He taught Fiore. Tartaglia (Niccolo Fontana) devised it independently. Cardano probably stole from Tartaglia, then found del Ferro鈥檚 notes and claimed that he knew from them. That鈥檚 the short version. Jeff tells the longer version better. Yes, it鈥檚 all true. The mathematics we will discuss is mostly del Ferro鈥檚 method. We'll see some narrative from this tale. I think it's fair to say this is the first big priority dispute. Oh, and I said we would notice when people start to want credit. We're there. Finally, if your livelihood relies on you solving problems in competitions, you want to not tell others how you do it.

"Cosa" is the Italian word for "thing", which was used as the variable.