390 Quick Answers 22 January
Syllabus questions:
Hi, my name is Jeff.
We will learn math. history until about 1950.
The text will give you background, the historical connections and
context. I will fill in the mathematics because the text is
intended (as it says on the back) as a supplement. You are a
college mathematics student taking a history of mathematics course,
so I am trusting that you are interested to learn both history and
mathematics.
You have a wide range of freedom in your history topic. I will
be happy to talk to you about it when we meet. If you want to
know if we will discuss it in class, the index would be a good place
to start - and also a quick way to get an overview of the
course. Make sure that your topic is something that is not
discussed for more than a week in the associated math. class (and is
not discussed in depth in this class).
Excellent question - what should you take notes on? The most
important part is to keep the parts that you personally find
interesting or will find useful in your mathematical lives
(teaching, learning, or creating). For the course keeping a
timelines of dates, location, names, and mathematics created would
be great. Beyond that grouping items in themes would be
helpful.
Mostly the course format has remained unchanged while I've been at
Geneseo, with the addition of lecture reactions after
pandemic. I find them much more valuable than attendance at
lectures. I want to know what you think, not just that you
were there.
Please enjoy learning and don’t worry about grades. I am
certain that this class has the lowest responsible:presented
information ratio of any … maybe ever taught (ok, for any where you
are responsible for any of the information presented).
Please read more carefully, in all ways. Thoughtfully,
critically. Reread things that don't appear likely to be
true. Think about possible meanings other than the unlikely
ones.
Exams will be in-class submitted via mylearning. Please bring
computers on those days. You may _not_ access any materials
during the exams. In the weeks before the exams we will talk
about some likely topics. The first exam is 75 minutes
(classtime), the second is 150 minutes (finals time). You will
have a score of 100 for each exam. +1 on the midterm for
visiting just once in the first two weeks. The exams have many
many many topic questions, and you select very few of them.
One of the topics is always "make up your own topic". We will
discuss topics in class and online when we get close.
What is not good enough on reactions? Insufficiently
reflective, insufficient number, insufficient breadth (only
addressing the beginning of reading or lecture). A nice idea -
if you have a question about something that is easily looked up - do
so, report back to me in your reactions. If you must
miss a lecture, contact me before the lecture occurs, then also
discuss it with classmates. Together there are ways to still
complete your lecture reactions. 10 points for each set of
reactions, one for each of ten reactions on Thursdays and
Sundays. Please make sure your reactions are _reactions_
not summary. Questions, connections, thoughts, something that
_you_ contribute to each. Read each assignment
carefully: 5 reading reactions and 5 lecture reactions each
day. Please please look at the samples. Do a
good job. I will notice patterns and deduct if needed.
We need one more office hour.
We need a code word for the feedback form, which is to be used any
time for feedback, not for the end of the semester.
Let's talk about the midterm. The day after returning seems an
awful choice. I'm open to that or either the Friday before
(best for me, but a bit rushed as it would be 4 days after the
material on the exam) or the Friday after. I am not open to
any other dates.
You will _never_ be working problems in this course. You will
talk _about_ mathematics, but never _do_ mathematics. Because
we'll never be solving problems, there's nothing in the book to
worry about getting ahead on. You can read at any pace that
allows you to do reading reactions in a timely fashion. I know
in the past some would do the reading enough in advance that they
could complete reactions by 5:30p after class. You could write
all your reading reactions tomorrow for the entire course, and then
just wait to write lecture reactions as they happen. It's up
to you.
Honestly, office hours aren’t so crucial for us. They are a
place for any questions you have at all, but since we're not working
problems, they are not like math class office hours. Which is
why you only get to pick one (that, and you’re last first
meeting). Office hours will be in person in classrooms to
allow for distance. If this is uncomfortable, please tell
me.
How will I decide which reactions to comment on? More likely
on ones that are questions or information added. "I like this
… " probably not. Or correcting misconceptions. Simple
things you can look up are better looking up and reporting than
asking. It's better to say "I didn't know this word and I
looked it up and it means … " than "what does this word
mean?". Because our enrollment is atypically low, I will also
include some comments from past years that are not asked
about.
GREAT day presentation is for those wishing to satisfy the
department’s oral presentation requirement (satisfied by INTD 302
for secondary candidates). Everyone writes a research
paper. Some choose to present at GREAT day.
Why is learning history of mathematics valuable? To see the
big picture, to see how things connect, to remember that it is a
human endeavour and not just things that appear from some mystical
experience, or from some superhuman authority. Also to
remember that mathematics is influenced by culture. The
textbook will mostly tell you the stories, and I will mostly tell
you the mathematical details. We will both vary. You
will not be responsible for reproducing the mathematics. And
the details will be sketchy sometimes. It is a very important
opportunity to learn that those who say mathematics is only details
are wrong. We can learn the ideas without needing to process
all of the complexity.
We do not have a “unit” on women and non-western cultures.
They are incorporated throughout the course. It will take time
for women to be incorporated, but we’ll get there. This is
history, I cannot change it.
This course is an excellent capstone putting all your learning
together. It also an excellent introduction or a menu, showing
things that you can learn more about later. This applies both
to mathematics and history (humanities).
Your feedback is sent anonymously to me and only me. I am
likely to discuss it here if I get it.
Please tell me of any challenges in accessing the text.
For the reading schedule, a part of the book referenced means the
whole part. So, 1.2.2 for Monday is all of 1.2.2 and 1.3 for
Monday is all of 1.3, i.e. 1.3.1 is a part of 1.3 as is 1.3.3.
Naturally, if there is ever anything that I haven't answered to your
satisfaction during class, please come talk to me about it.
Sunday is the last day to write reactions for credit to the course
as a whole. Remember always at most one reaction from quick
answers.
First reading:
General warning: best very very cautious to avoid "this is
weird" because it's different. Look to find value, not to
dismiss. For now, remember that we're learning about
mathematics a very long time ago. Work to understand and
appreciate, not to judge.
We will look at many original sources and see the notation
used. It will be a long while before anything like our
notation is actually used for anything.
There’s no other known reason for 11, 13, 17, 19 being together and
of interest. Is it possible that there is another one?
Sure. This is history. We have this ambiguity
often. Especially with something so old. We have the
artifact - it doesn't come with a caption plate.
Tally marks in one way or another are as old as history.
Counting is in fact older than humanity. Nonhuman animals
compare sizes. Counting days is not sophisticated. "Hm,
this flooding seems to happen regularly, I wonder how long is
between ..." The earliest origin for "months" is lunations,
i.e. "moonths", which are about 30 days.
Raise your hand. Why groups of 5? Ok, you can put your
hand down now.
We will say something about Roman numerals in a few classes, but
suffice it to say that they are probably the least useful system
ever invented, and have never been used for mathematics, only for
labels.
Egyptians did not have formulas as we think of them, but expressed
their work as processes.
Egyptians did not invent emoticons. They are _like_
them.
Just like any textbook, Jeff is mostly not reporting _his_
conclusions, but consensus conclusions.
It seems natural to me that the larger number a symbol represents
the more complicated it would be, as it would be used more
rarely. Raise both hands. Why groups of 10? …
ok. Also please remember groups of powers of ten is not base
ten or place value.
"how are we to know what mathematics was used to build the
great pyramids?" Mostly - we don't.
Egypt - pyramids - parts of pyramids? It's not hard for me
to imagine why the frustum volume would be helpful.
Number of bricks to fill the base of a pyramid as a step in
construction.
Fractions are needed in regular daily life for all people (at least
all that count). Whenever you have a part of something
perceived as a whole, some piece of a larger collection.
Egyptians understood 2 divided by 13 (not the symbols, but the
idea). I think they would have viewed 2/13 as a question, not
an answer. The closest unit fraction to 2/5 is 1/3 and
from that 1/15 is missing. That is why they do that and not
1/5 + 1/5.
Here’s something about why 2/3: it’s the most common non-unit
fraction (obviously), it could be 1/2 + 1/6. Here’s something
parallel: when you type in Word and you type fractions like
1/4 it turns to a “nice” symbol, but doesn’t do the same with
12/13. So, some fractions we have nice symbols for and some
not.
The papyri are named after the person that the artifact was
discovered by or where it is now kept, not after the person who made
it. This is different from more modern works. Jeff says
that Ah-Mose likely copied from another source. Ownership and
credit for ideas is a rather Western concept, not something that we
will see in that way for a while.
We will talk about false position. It is _not_ guess and
check.