The Official Course Description

Course Number: Math 103

Course Title: Quadrivium: Mathematics and Metaphysics in the Premodern World

Instructor: Daniel Newsome

Time: Tuesday/Thursday, 8:30-9:50

Room: Hegeman 102

Class size: 22


What does the Music of the Spheres sound like? What influence did astrology have on mathematics?  Why does Newton's rainbow (ROYGBIV) have 7 colors? Does mathematics exist if there is nobody to think about it? These questions are addressed by the quadrivium, a term coined by the 6th century philosopher Boethius for the mathematical program of the medieval university. The quadrivial disciplines make up 4 of the 7 Liberal Arts: arithmetic, music, geometry and astronomy.  Taken as a whole the quadrivium is the metaphysics of Pythagoras and Plato.  Number is the structure of the universe and One-ness is its source. This course will explore each of the quadrivial disciplines using primary sources in English translation and show how mathematics was seen as the structure of everything.  Primary authors will include Plato, Euclid, Ptolemy, Boethius, Martianus Capella, al Khwarizmi, Sacrobosco, Fibonacci, Oresme, Alberti, Cardano, and Kepler.  Other than a working knowledge of basic algebra, the class requires only a willingness to explore new ideas and construct convincing arguments.

Prerequisite: Passing score on Part I of the Mathematics Diagnostic. Class size: 22


Class by Class Operations


The general goal of this course is to introduce you to premodern mathematics.  If you were at the University of Padua in 1350, what would you have learned?  This is a mathematics course, but a lot of the mathematics will be somewhat unfamiliar.  Much of this premodern material was written in prose and not in the familiar algebraic language that many of you have come to know and love.  Numbers were a different animal, x-y graphs were basically unheard of, and the equal sign (if used at all) was Gemini or a Taurus on its side.  This was a period when astrology and astronomy were interchangeable, numbers had meaning, music had powers, and geometry remembered that it started with "geo." 

Because this course fulfills a mathematics requirement, there will be regular mathematical assignments.  These assignments will often anachronistically use modern notation.  If this course were a history course I might attempt to only use period notation, but I fear that such a restriction would slow us down too much.  Historically accurate notation varies from place to place, author to author, and year to year. Nevertheless, you will be reading a lot of primary documents (in translation) which will use historically accurate notation.  You will be reading it a lot, but not necessarily producing it yourself. 


Every week will have required readings.  These readings will be more lengthy than the typical math course, but probably less than your typical history course.  Every week you will also have some sort of mathematical homework.  Throughout the term you will also be required to write several short essays, as well as a variety of assignments in other media (drawing, design, music, etc.) 


Your grade will be determined as follows:

1/3: Attendance, Punctuality, Attention, Preparedness, and Participation

1/3: Homework – Completeness, Correctness, and Timeliness

1/3: Exams and Quizzes


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As I get older I am using technology less and less in the classroom.  For a class on premodern mathematics this makes a lot of sense.  I have found that my classes go better and are more engaging for everyone when I am not letting a PowerPoint slide show determine the flow.  Twenty years ago, when PowerPoint was a novelty, it may have held everyone's attention, like a TV at a diner, but the novelty is gone and now it is just a way to avoid thinking on your feet.  As a result of my increasingly Luddite tendencies, I do not want homework submitted electronically unless specifically requested.  I want paper.  I'll provide most mathematical homework assignments on paper in class.  You will do the homework on paper and turn it in on paper.  It is simply too much work grading electronic assignments and filing them away and sending them back and figuring out how to comment on them.  Some teachers are good at this. I'm not. 

This is the first time I have taught this course.  It's the learning curve, Beta-version.  I would very much appreciate your input on everything we do. Feel free to tell me what you are thinking.  If a reading or homework assignment is totally terrible, let me know.  If you really liked a particular assignment. Let me know.  If you want to dig into a particular topic that I'm not covering, let me know.  Maybe it can be mixed in or you can work on it independently.


About homework: To liberally paraphrase Benjamin Franklin, Homework, like fish, begins to smell after 3 days.  If you are late with a homework assignment, it very quickly begins to rot.  I don't want to read it if it is more than one class session late. If it is one class session late, it will be graded as if it were a rotten fish.  I probably won't even read it.  You might get some credit, but it stinks, I might just throw it out. 


There is an unfortunate law in the world of teaching:  Good students require little work on the teacher's part and lazy students require lots. This is exactly the opposite of what we want.  As teachers we want to spend more time with students who give a shit and less time with students who can't seem to get to class on time.  But this is never the reality.  This is what makes college professors bitter.  The lazy student always needs an extension, is late, is absent, is sleeping or is tired, is overworked, has too much homework from other classes, etc.  All of this crap inevitably entails requests for extensions, alternate test times, and innumerable emails going over things already covered in class.  This eats up a lot of time that I don't have.  Legitimate issues are legitimate issues, I'm totally fine with a legitimate issue, but some students redefine "legitimate" in order to rationalize their own laziness. If you can't wake up when your alarm clock goes off, you need to take a semester off and figure that one out.  A student who takes five classes in a semester had better be good at time management.  It's not my problem a student took too many classes.  I've got my own problems with my own time management. The point is, I have a very busy teaching schedule this term.  Don't infringe on my time because you are lazy or undisciplined.  I will not be all that sympathetic when I hear about a series of unfortunate events that always seem to crop up when assignments are due.  Legitimate reasons need to be legitimate.  If they are, I'm perfectly happy to accommodate.  If they are not, once again, you may want to take a semester off so that you can paint some houses or hang some sheet rock or dig some ditches.  Many people go to college AND work a job. 


Summary: Be a good student or drop the class.  I don't have time for slackers. 


That being said, if you are having any problems what-so-ever, come and talk to me.  Come to my office hours or email me to make an appointment. I'm not quite as mean as the above paragraph sounds like.


This course is graded and is not offered as pass/fail. 



ADA Statement

The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Amy Shein ( to determine if you may be eligible.  Definitely talk to me and let me know how I can be of assistance.


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