Home Page for Math 56, Section 1, Spring 2008: History of Mathematics
Class Meetings: MWF 1:50-2:55, Bailey 201
(This page was last updated on 30 May 2008.)
Texts: Math through the Ages, Berlinghoff and
Gouvea; The History of Mathematics: A Reader.
Additional readings will be provided during the course.
| Instructor: |
Kim Plofker |
| Email: |
plofkerk@union.edu |
| Office: |
Bailey Hall 206A, phone 6674 |
| Office hours: |
Tu-Thur 10:00-11:00 AM, 3:30-4:30 PM; Wed 4:30-5:30 PM |
Course Description: Open to all students with a
mathematical background up to and including pre-calculus, "History of
Mathematics" traces the development of mathematical ideas and methods
in literate cultures from ancient Egypt and Mesopotamia, to
Hellenistic Greece and medieval China, India and the Islamic world, up through the
dawn of calculus at the start of the Scientific Revolution in
early modern Europe. We will examine the interlinked changes
and intercultural transmission of basic numeracy, arithmetic, geometry,
trigonometry, algebra, practical computation and approximation, and concepts of
the infinitely large and small.
The course will stress both the technical mastery of mathematical
concepts and methods, and the historically informed comprehension of
their role and development within the larger intellectual context.
Students are expected not just to study standard mathematical knowledge and its
chronological development, but also to examine the ways in which
they think about math, and how practical and philosophical issues change
the way mathematical ideas are perceived. The writing-intensive course
work is designed to focus on careful reasoning and articulation of the
results of these inquiries.
First handout and first week's assignments
Photocopy of clay tablets (accessible from Union
College internet domain)
Week 1:
- Written Assignment 0 (due at start of class Wednesday April
2): See back of the
first handout
- Readings for Friday April 4:
- Math through the Ages, pp. 5-14 ("Beginnings")
and pp. 65-70 ("Keeping Count")
- History of Math Reader, pp. 31-32 (BM 13901),
pp. 40-42 (Section 1.E4), and pp. 43-45 (Section 1.E6)
- Journal entry on first readings (due at start of class Friday April
4)
Week 2:
- Readings for Monday April 7:
- Math through the Ages, pp. 85-90 ("Broken Numbers")
- History of Math Reader, pp. 14-24 (Section 1.D,
Egyptian Mathematics)
- Readings for Wednesday April 9:
- Readings for Friday April 11:
- Math through the Ages, pp. 107-110 ("Measuring
the Circle") and pp. 139-144 ("A Cheerful Fact")
-
Assignment 1 due Friday April 11
Week 3:
- Readings for Monday April 14:
- Readings for Wednesday April 16:
- NO READINGS for Friday April 18
- Journal entries for Weeks 2 and 3 due Friday April 18
Week 4:
- Readings for Monday April 21:
- Math through the Ages, pp. 14-24 ("Greek
Mathematics")
- History of Math Reader, pp. 61-73 (sections
2.E1 and 2.E2)
- Readings for Wednesday April 23:
- Math through the Ages, pp. 155-160 ("On Beauty Bare")
- History of Math Reader, pp. 99-110 (sections
3.A-3.B3)
- Readings for Friday April 25:
Week 5:
-
Assignment 2 due Monday April 28
- Readings for Monday April 28:
Theme: Circles and lines in the universe: Greek cosmology, astronomy
and trigonometry
- Math through the Ages
- pp. 163-166 ("In Perfect
Shape: the Platonic Solids")
- pp. 185-190 ("Half is Better:
Sine and Cosine")
- History of Math Reader
- pp. 76-79 (Section 2.E5,
Plato's cosmology)
- pp. 148-150 (Section 4.A1, Measurement of a
Circle---Warning: tough math!)
- Readings for Wednesday April 30:
Theme: Cones and parabolas in Greek mathematics
- Math through the Ages, p. 169 (1 page!)
- History of Math Reader, pp. 153-154 (Section
4.A3,
Quadrature of the parabola)
- NO READINGS for Friday May 2
Week 6:
-
Take-home Midterm due Monday May 5
- NO READINGS for Monday May 5
- Readings for Wednesday May 7:
Theme: Post-Greek mathematics in India and the Islamic world
- Math through the Ages,
- pp. 24-32
- pp. 127-130 ("A Square and Things")
- History of Math Reader, pp. 228-231 (Section
6.B1)
- Readings for Friday May 9:
Theme: Post-Greek mathematics, continued
- Math through the Ages,
- pp. 32-34
- pp. 93-98 ("Something Less than Nothing?")
- Journal entries for Weeks 4, 5 and 6 due Friday May 9
Week 7:
- Readings for Monday May 12 (not required to write up in course
journal):
- Readings for Wednesday May 14:
Theme: Algebra emerges in early modern Europe
- Math through the Ages,
- pp. 35-37 (not a typo! ends in mid-section)
- pp. 113-118 ("The Cossic Art")
- History of Math Reader, pp. 276-282 (Section
9.A)
- Readings for Friday May 16:
Theme: The increasing formalization and power of algebra in the
Scientific Revolution
- Math through the Ages,
- pp. 37-42
- pp. 133-136 ("Solving Cubic Equations")
-
Assignment 3 due Friday May 16
Week 8:
- Readings for Monday May 19:
Theme: Combining algebra and geometry in early modern math
- Math through the Ages,
- pp. 72-76 ("Reading and Writing Arithmetic")
- pp. 169-174 ("Shapes by the Numbers")
- Excerpt,
Descartes' Geometry (only the part in English!)
- NO READINGS for Wednesday May 21
- Readings for Friday May 23:
Theme: Mathematics and nature in the Scientific Revolution
- Journal entries for Weeks 7 and 8 due Friday May 23
Week 9:
- Readings for Wednesday May 28 (extended from Monday May 26):
Theme: Emergence of calculus ideas
- Math through the Ages, pp. 42-47
- History of Math Reader, pp. 356-359 ("Fermat" and
Section 11.C1)
- Readings for Friday May 30:
Theme: Concepts of infinity in calculus
-
Assignment 4 due Friday May 30
Week 10:
- Readings for Monday June 2:
Theme: Mathematics of games and chances
- "Field trip": class on Wednesday June 4 meets in Schaffer Library's Special
Collections section
Meet on front steps of library at 1:50 Wednesday
- NO READINGS for Wednesday June 4
- Readings for Friday June 6:
Theme: The origin of computers
- Math through the Ages,
- pp. 223-228 ("Machines that Think?")
- pp. 231-234 ("The Arithmetic of Reasoning")