GREAT day is TOMORROW - please join us.  Our sessions will *all* be in Newton 201 (not as previously printed) 9:55 (note start-time change due to cancelation)-10:40a, 11:05a-12:05p, and 2:55-3:55p (and there's more mathematics elsewhere and more in 201 4:20-5:30p).  It is an entirely special day - and as you see I will be hosting a session during normal office hours.  

For those of you waiting, I am thinking about getting the 10% off papers back on Wednesday once GREAT day is over, and the 20% off papers back on the next  Monday.  We will see as it unfolds.  

I've said many times before - going back to the 17th century and before, it was probably reasonable to note what topics people seemed to be working on.  Beyond then, pretty much everything is being studied, and it's a matter of what Suzuki chooses as a focus.  On the other hand, if you examine a particular region at a particular time, it is reasonable to say they had a particular focus.  The U.S. is a good example of such a particular region.  

§10.1.4-

Suzuki does *not* say "Hamilton made the first major American contribution to mathematics" - he says he *inspired* it.  

I don't know how Dodgson attempted to find three right triangles with the same area.  He might've scanned a list of pythagorean triples and hunted for ways to find equal areas.  It seemed he was merely seeking examples.  As the footnote indicated, in fact, there are infinitely many triples of rational right triangles with equal areas.  

Nabla doesn't have any meaning connection to the harp, but the symbol didn't have a name before it was given the name nabla for this reason by Tait and his assistant.  This remains the name of the symbol.  The symbol is used to indicate gradient - studied in calc 3.  Among other things, it indicates the direction of maximum increase for a single-variable function of multi-variables.  (e.g. f(x, y)).  

I think unless otherwise noted "Peirce" refers to Benjamin Peirce.  I think Charles Peirce contributed to logic, among other things.  I haven't research Charles for this.  

Peirce was analysing Howland's handwriting.  In doing so he used data of other signatures to determine that there was 1/5 chance of downstroke matching.    Suzuki says that Peirce's arguments are "mathematically dubious".  Similar, but more careful, handwriting analysis is definitely still done.  Peirce's 3-year college math. program requires less than most of you completed in HS.  It was for all college students, so surely not intended to limit in any way.  (Our required curriculum for majors is mostly set by external demands - what graduate schools expect, what teachers need to know.  The electives are more about what what we want to teach.  Both change slowly from time to time.)

My guess is that Peirce wanted to study quaternions first, so they would seem natural to him, but regretted learning them after other arithmetic when he wasn't as young (age = 34).  I would say this is not directly related to the topic that most innovative mathematics is done at a young age.  The reason for this expectation i that innovation requires a fresh perspective, something people established tend not to have.  In spite of some societal impressions, within it is definitely viewed that mathematics is a young person's game.  We will read about the Fields medal in mathematics in chapter 11 - it is not awarded to anyone over 40 (with Andrew Wiles as the one exception).  

We will talk about idempotent and nilpotent today - it seems possible but not likely that you will see them (and even less likely that they will be emphasised) in a 330 class.  

It sounds as if Bowditch's criticism of Harvard's math. faculty was likely justified.  

Tait and Maxwell were USian.  It does seem reasonable to contact Europeans for questions.  

Sometimes silly wrong things can make you more famous than valuable contributions.  This was Newcomb's case - being made famous by saying that there wouldn't be airplanes.  

Definitely there was graduate education in Europe long before the US; same with PhDs.  

I'm guessing parents and students reacted negatively to math. requirements because it meant more work for them - I don't think they thought about what was good for them.  Seems typical.  

(x, y, z) is a right-handed system which obeys the right-hand rule for cross products.  (y, x, z) does not.  This is a matter of orientation.  (Suzuki is not trying to explain this, but is giving some historical context to the discussion.)  Hops are plants which are used in making beer (among other things).  They happen to grow in a distinctive fashion.

"I looked at Wikipedia to investigate Suzuki?s claim that Lewis Carroll's pseudonym was actually Latinized because at first glance Lewis Carroll didn't seem to resemble anything associated with Latin, but it turns out that *Lewis* was the anglicised form of *Ludovicus*, which was the Latin for *Lutwidge*, and *Carroll* an Irish surname similar to the Latin name *Carolus*, from which the name *Charles* comes."  Be careful about dismissing _Alice_ as a "children's story".  

Albert was the prince consort - he was married to the queen, but wasn't king.  

Last time:  quaternions are Hamilton's 4d "hypercomplex" numbers denoted by a + bi + cj + dk.   For these quaternions, there is no "the" square root of (-1) - it has three different square roots.  These numbers are more complicated than the complexes in this way.  By choosing to extend complex numbers beyond 2-dimensions, and requiring some properties, Hamilton discovered others.   Hamilton didn't think they were useful - merely very interesting and pleasingly coherent.  

A while ago:  Jacobi, I think it was, was responsible for the unification and formalisation of determinant.  The determinant is most certainly not an arbitrary quantity.  It has many geometric meanings - the simplest of which is the n-volume of the parallelipiped spanned by n-vectors.

See the beginning of 9.4 for the Prussian education model.