390 Quick Answers 24 January

Syllabus questions:

Hi, my name is Jeff.

Office hours were not included; they are here now, but I need your confirmation of them.   They are more central for my other classes, but I would always _love_ to discuss our topics in more detail.  Alas, that doesn't seem to happen very often.  Credited initial visits can be after class today or Monday (when I have office hours).  There will be many more visit chances next week between classes. 

Why MF, why 3:30?  Yes, our midterm exam is really on π day, and I'm sure that will a popular topic for it. 

We will learn math. history until about 1950.  This is because there is more mathematics after 1950 than before, and it takes too long to explain. 

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.  

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).  

The analysis of historical sources will be done during class-time.  It may show up in your research project (it would be great if it did!). 

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.  The final will have a section for questions after 1600, and a section for questions across all time. 

Reactions are like participation only better - I get to hear from everyone, and no one is uncomfortable speaking in class.  On of my favourite parts of this is hearing from students who would otherwise be quiet.  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.  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.   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?". 

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.  I believe in formative feedback in all parts of life.  It is much more valuable than summative feedback, and this is an example of that. 

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. 


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.

"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.   


Raise your hand.  Why groups of 5?  Ok, you can put your hand down now. 

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.  The calendar is one of the most basic, fundamental uses of mathematics.  We will discuss it occasionally. 

The Egyptians are also responsible for dividing our day into two 12-hour segments, which varied in length by the seasons.  10 of daylight, one of dawn, one of dusk, and 12 of night to balance the 12. 

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.  It is very reasonable to infer that the additive parts of the Roman system are influenced by the Egyptian system. 

For Egyptians, fractions were a question, not an answer.  7/12 is a division problem, like 7÷12, which has an answer 1/2 + 1/12.  It is a more basic presentation.  We will say more.  Here's something about having different symbols for fractions – when you type fractions, some are made into nice symbols like 1/4 and some stay like 123/324.  That difference is similar to the Egyptian difference.

Egyptians did not have formulas as we think of them, but expressed their work as processes. 

Just like any textbook, Jeff is mostly not reporting _his_ conclusions, but consensus conclusions.