390 Quick Answers 1 March


Exam topics?  Remember the exam is sooner than you think (4 classes from now).  Monday will be the last day for material on the exam.  Someone asked - yes, you may use examples that I don’t discuss in class.  1600 is a decent cutoff for the exam. 

Also of course remember your annotated bibliography is due by classtime on Monday.  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’re going to talk about, it should not be everything that you’re 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 Monday, but will do all of 6.2 then also.  6.2 is a bit light.  I’m pushing quartics and complex to Friday.  Again, be careful on timing between 6.1 and 6.2. 

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


Lecture Reactions

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. 

Levi ben Gerson did some applied work (trigonometry), but clearly also did theoretical work (as he indicated).  The induction work was on the theoretical side.  ben Gerson definitely understood the point of induction - that by proving a base case and induction step he knew it was true for all values.  At least he created these ideas independently, if not being the first in history.  And the permutation/combination proofs at the end seem useful. 

Geometric series had been known long before, to the ancient Greeks. 

Oresme improved on Greek compounding of _ratios_.  Because they are ratios, not equivalences, this is not related to transitivity, but, as Oresme indicated, more related to multiplying 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. 

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

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. 

It's fun to me how much you enjoyed and were comfortable with Chuquet.  I'm glad that you see that this is progress.

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. 

Doctors relied on astrology thus were "mathematicians in the ancient sense", not what we call mathematicians. 

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 … 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’s notes and claimed that he knew from them.  That’s the short version.  Jeff tells the longer version better.  Yes, it’s all true.  The mathematics we will discuss is mostly del Ferro’s method.  We'll see some narrative from this tale.  I think it's fair to say this is the first big priority dispute. 

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

Remember  -- if you make your reputation by competing in contests, then you want to keep your methods secret so that you can solve problems that others cannot.