MAT 300-02, History of Mathematics
Spring 2008, TR 6:15-7:30
 

In this course we study the history of mathematics from ancient to modern times.  The evolution of mathematical concepts and ideas is an important theme of the course. Some classical problems are worked using the methods of the day. However, technical details comprise only a part of the picture.  For that reason, we consider the cultural, philosophical, and technological frameworks within which these ideas evolved.  Further, we look at the individuals involved and their impact.  Finally, to the extent possible, we trace the paths by which our knowledge of those times has come.

 
Announcements:

Syllabus

Homework Assignments (includes reading assignments)

E-mail Assignments

E-Mail Assignment 1:

The answers to the following questions should be emailed to me by 4:00 pm on Tuesday, February 5  .In addition to the text, you may need to look at the handout containing the contents of the Rhind Papyrus and the Moscow Papyrus.

1.      In addition to two versions of Egyptian, hieroglyphic and demotic, what was the third language on the Rosetta Stone?
 

2.      The Rhind and Moscow papyri have problems involving the pesu of two "foods" made from grain. Name one of  those two "foods".   Note that both can be made from grain, but I do not want grain or the name of a specific type of grain as an answer.
 

3.      To what does the Egyptian term "seked" refer?

 

E-Mail Assignment 2:

The answer to the following question should be emailed to me by 4:00 pm on Thursday, February 7.

In Problem 10 on the Moscow Papyrus, the scribe gives a procedure for finding the surface area of what object? Give both the general geometric name and the name of the "physical" object referred to in the problem.  Note that the physical object woulr refer to something known to any Egyptian.
 

E-mail Assignment 3:

The answers to the following questions should be emailed to me by 4:00 p.m. on Tuesday, February 12. You will need to do the assigned reading in the text.

1. What numbers are characterized by the author of our text as regular sexagesimal numbers?

2. What do the initials BM and YBC, respectively, mean when referring to the classification of a Babylonian tablet?

3. According to the author of our text, what component of a circle did the Babylonians generally consider the defining component of the circle, the radius, the diameter, the circumference, or the area?
 

Email Assignment 4

Answers to the following questions should be emailed to me by 6:00pm on Tuesday, February 19.  All of the answers can be found in Chapter 1 in the text.

1.  Plimpton 322 is a tablet in the Plimpton Collection at Columbia University.  In the text's discussion of Plimpton 322, which column in Table 1.1 does not actually appear on the tablet (actually, for which is there not an equivalent column on the tablet)?  Your answer can be given in terms of the headings of the columns in Table 1.1 on page 18.

 2.  Although there are some tablets with different equivalent values, in most old Babylonian tablets involving circles, what numerical value was used to represent  the ratio of the circumference to the diameter?  (This numerical value represents the general Babylonian equivalent to π.)

 3.  What is a gnomon, in the context in which it is used in Chapter 1 of the text?

Email Assignment 5

The answers to the following questions should be emailed to me by 5:00pm on Tuesday, March 4.   You will need to do the assigned reading in the text and the assigned readings from the MacTutor History of Mathematics website.

  1. Identify the modern country in which each of the following cities is located.  There is a map on the insider back cover of your text that will prove useful.  Also note that only one of the four cities would actually lie in modern Greece.
         Athens
         Crotona
         Miletus
         Syracuse
     

  2. Many textbooks on the history of mathematics credit Thales with five theorems of elementary geometry:  State one of these theorems.
     

  3. The Pythagoreans worked with various figurate numbers, including the square numbers and the triangle numbers.  What is an oblong number?
     

Email Assignment 6

The answers to the following questions should be emailed to me by 5:00pm on Tuesday, March 11.  You will need to do the assigned reading in the text and the assigned readings from the MacTutor History of Mathematics website.

  1. Carefully state the problem of squaring the circle.  Note that I am using the word problem here in its mathematical sense, not in the sense of difficulty.
     

  2. Carefully state the problem of doubling the cube.  Note that I am using the word problem here in its mathematical sense, not in the sense of difficulty.
     

  3. An alternate notation for ratio uses a colon, so a:b is the same as a/b, or the ratio of a to b.  The problem of finding the geometric mean of two quantities a and b, i.e. find c such that a:c=c:b, is sometimes called the problem of finding the mean proportional.  Given two quantities a and b, what do we call the problem of finding two numbers c and d such that a:c=c:d=d:b ?
     

Tests

Test 1 Review Sheet

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Last revised:  March 7,  2008