Reading Reactions:
1. It's impressive that architects figured out
that the damage taken by the castle would be lessened if the angles of the
walls were changed. I also thought it was cool that architecture was
evolving based on developments in weaponry. In addition, I thought William
Louis's solution for increasing the rate of fire for the musket was
brilliant, even though it's so simple.
2. When I came across the term "nautilus" in this section, I had no idea
what this was referring to and researched the word. I had seen these
animals before but I had never known the proper name for them, so it was
cool that this reading helped make that connection for me.
3. Suzuki says "the rigors of working in the early hours of a cold,
Scandinavian winter proved too much for Descarte", and I did not
understand if he meant that Descarte died because of the cold or if his
teaching abilities impaired he could not handle the weather.
4. Leibniz seemed like an interesting figure from the time period. I
thought it was neat that he found the pattern within the sum of the
reciprocals of the triangle numbers to find the answer. It was also
interesting to learn Leibniz used the modern *dx* notation in his paper.
5. The reading stated that it was "impossible to turn lead into gold using
the means available in the 17th century", but I was unaware that lead
could be turned into gold using present day methods.
Reflection 1: Page 243 discusses how Peter's
autocratic power led to many changes. Suzuki specifies the change that all
European nobility were to be clean-shaven and that Peter literally walked
the streets with scissors to trim and shave those who disobeyed him. I
think it is funny to read facts in history like this. How can someone have
to power to say and do that?! It blows my mind.
Reflection 2: I feel overwhelmed as I am reading through this section.
Suzuki is jumping from person to person and discovery to discovery so
quickly. I have heard of many of these mathematicians (especially
Bernoulli and Cramer) so I would like to read more in depth about each of
them, but Suzuki is rushing through the mathematicians. I know there is a
lot of math history for Suzuki to cover, but what and who are the most
important to focus on?
Reflection 3: Wow, there are a lot of Bernoulli's!!! So, L'Hopital is
actually Guillaume Francois Antoine? Why is he called the Marquis de L'
Hopital? Another strange question that just came to mind is why are
mathematicians usually known by their last names? I have heard of a lot of
the mathematicians throughout this book, but I can only recall the last
names. My guess is that most discoveries, formulas, theorems, and rules
founded by mathematicians actually reference mathematicians last
names. Also, remembering one name is much easier than two!
Reflection 4: As I said in reflection two: along with the difficulty to
follow all of the people, is the difficulty for me to follow all of the
discoveries. I don't understand where the discoveries of these
mathematicians are coming from. I think this goes back to the fact that
Suzuki is trying to cover so much history in such a small amount of time,
but could we go over how Cramer came up with Cramer's Rule and how
Benoulli (all of the Bernoulli's) came up with his contributions to
probability and calculus? Could we also go over the theory of recurrent
sequences that Suzuki discusses on page 245-246 just to obtain a stronger
understanding?
Reflection 5: Some things I found interesting in today's reading was the
fact that the curve invented by Grandi and written about by Agnesi was
called the witch of Agnesi due to a mispronunciation/misread. Another
thing that caught my eye while reading was when Suzuki stated that
Lagrange turned down Fredrick's offer down in respect to another
mathematician, Euler (on page 249). Facts like this make me like certain
mathematicians even more! The last comment I would like to make is
regarding page 250 when Euler makes a comment about the existence of God.
This was entertaining to read.
1) I found it really interesting to read about
the beginning of restaurants. I would have thought that restaurants
came about much earlier than the late 1700's. It was interesting to
read that the proliferation of restaurants is sometimes attributed to the
flight of the nobles who left their chefs and cooks with no support, so
they turned to restaurants looking for work.
2) How many times have people decided to change the calendar up until this
point? The idea of a decimal calendar sounds terrible. Same thing
with decimal time. Was there a purpose to trying to make time use 10
as a base instead of 12?
3) Can you go over Gauss' work with the roots of x^n-1=0? This section was
long and complicated and I wasn't really understanding what was happening.
4) I thought it was cool how Gauss related number theory to
geometry. How exactly did he figure out that constructible polygons
correspond to the Fermat primes? This seems like a very weird connection
to make.
5) What is the principle of duality? Suzuki explained what it meant but
I'm still a little bit confused. Is this similar to the converse of
a statement or not at all?
Lecture Reactions (Both have only four; you are required to write five, at most one from the quick answers in the beginning)
The quick answers were relatively
straightforward. The explanation of the Poincare return map made a lot of
sense to me in terms of the orbit of the Earth. Having a realistic model
to imagine the moving points on helped, much more than the diagram even
did. I liked the article about the biopic on Rumanujan's work with Hardy.
Interesting about the critiques it received- not really any comment about
the mathematics- but should we really be surprised by that? I also liked
this article because I have emailed with Ken Ono before (applications to
Emory's math REU) so seeing his name was a fun little surprise. Your
explanation of the Hardy-Littlewood partnership helped explain the rules
even more clearly. While I don't think I was as opposed to the idea
of the partnership as some of my peers seemed to be, the rules as Suzuki
laid them out (which I would assume were in their original form) were more
confusing to me than their "translation."
The Fields Medalists for 2014 came from the US (Princeton and Stanford),
France, and England. I think this a very neat resource to have available
and I think it is fun to be able to look and see where some of the most
innovative mathematics is being done. Some of the names link to their home
websites from their universities, or their personal websites, but some
don't have any other information available. I wish that there was a short
list on the site or that each name linked to the type of problem they were
awarded the Fields Medal for or even for the field their work fell in. The
Clay Institute problems were organized more in this way and I liked
reading the description of each.
The many links on Hilbert problems were a little overwhelming, but also
incredibly interesting. That one person could come up with so many
different problems. I liked seeing the topics for all 23 (and reading
about the original 24th!), and being able to track so clearly which
problems have been solved and which haven't. I'm correct in thinking that
there are no prizes for solving the Hilbert problems, at least not more
than peer recognition and acclaim? So people are able to try to tackle
these questions as they see fit or are interested?
The image of the four-colored map was really interesting to see the
transformation. I thought it was a really effective visualization for the
reasoning behind the coloration. Of course, this theory can be applied to
many different graphs, so does the same type of "solution" picture apply
to those as well? Or does it depend on where you choose your "starting
point" and how many adjacent regions there are to that specific point?
There was a lot covered in the quick answers
today. Lots on history (which I enjoyed), a good amount on geography, and
plenty about the discovery of logarithms and use of negative and complex
solutions. I felt that the text for today was really rich mathematically
and didn't have a lot of historical context past that of the Tudor
dynasty, and this is reflected in the questions/comments of today's quick
answers. I am also expecting that this becomes more and more common as we
finish the book.
I liked being able to see examples of Recorde's actual text. It was
interesting to see the formatting they used at the time for including
examples along with text. I also really enjoyed the visuals of the maps of
the time. Being able to see the differences between the three options was
very interesting. The schematic map definitely helped me visualize how the
projections were done. The straight cylindrical map and the Mercator
projection both had distortions, especially around the edge of the
projections, but very different distortions in that. I appreciated your
comment that even now, maps have inaccuracies, especially towards the
poles, but that these errors do not pose too many problems because of the
lack of travel in these areas.
I enjoyed reading about Harriot because of all of the things he worked on.
The sonnet he wrote regarding the sign rule for multiplication was
relatively confusing. I think its interesting because this was a rule that
was relatively well known by this time. The examples they give in the text
were clear and concise and I liked that there were concluding sentences at
some points to explain notation in modern terms.
I liked that this section talked about Napier's logarithms because I had
read a lot about it in my research for my paper. I thought it was
interesting that you made the distinction in the quick answers that the
formal definition of exponential functions didn't appear until about 200
years after the idea of logarithms. It is my job to try to find as much
evidence against this statement as possible in the next week. I think his
tables are incredibly detailed, but I wish there was more explanation of
the methods he used to obtain those tables.