SYLLABUS, SPRING 2015
COURSE OVERVIEW: This course is a first course in
history of mathematics. We will focus
birth of modern
mathematics beginning in the Renaissance and continuing to the early
strands will be pursued
in historical fashion and the mathematical developments are tied to
and political contexts
where appropriate. Evolving ideas about mathematics, proof,
mathematicians, both personal and mathematical, are part of the cultural
of mathematics. As
a synthesis course,
will reason analytically about the
short essays and a major
term paper, and present a brief overview of their term paper orally.
student will be responsible
for leading one part of class discussion as part of a group during the
Some student works, with names
removed, will be copied and provided to the assessment office
for use after the course is
History of Mathematics: An Introduction
(Third Edition) by Katz
MEETING: Tuesday and
Thursday 1:30pm-2:45pm, Enterprise Hall, room 173
OFFICE HOURS: 201D
I, T, R 3:00-4:15pm or by
will be fair and impartial. It is based on a mixture of
includes short essays, two exams, the term project with oral
presentation, and a final exam.
the basis of the grade will be:
Homework (200); Two
exams (200); Class Participation (50); Term Paper (150); Final (200).
is in effect at all times and students are expected to be
fully aware of its
Group work may be part of the course and group members
will truthfully report on
members. Absence from exams must be for
reason and requires prior
notification except in extreme circumstances.
DON'T ARRANGE TO LEAVE BEFORE THE FINAL
TO TAKE IT EARLY.
None will be given as
grades. If you need a particular grade, you are responsible
earning it. I will work with
you to achieve your goal.
Last day to drop with no tuition
liability: Jan. 27
Last day to add classes: Jan. 27
Last day to drop with no academic liability: Feb. 20
Spring break: March 9- 15
Selective Withdrawal: Feb. 23 - Mar. 27
Exam 1 – Tentative – Thursday, Feb. 19
– Tentative – Thursday, March 26
Exam – Tuesday, May 12 1:30pm-4:15pm
We will cover selected
sections of most of
chapters 12 through 25 in the text. Schedule is tentative!
- 1/20: (Overview of
Chapters 1-6) Introduction. Overview of
early math including Greeks.
- 1/22: (Chapters 3, 4, 6)
Euclid's Elements. Archimedes. Late Greeks.
- 1/27: (Overview
Chapter 7) Contributions
- 1/29: (Chapter 8, Chapter 9) Contribution of India; Islamic; Cubics
- 2/3: (Chapter 9 cont., Chapter 12) Islamic math -- continued; Italian abacists.
- 2/5: (Chapter 12,
Section 13.4) Algebraic notation;
- 2/10: (Chapter
14) Analytic Geometry; Descartes,
- 2/12: (Section 13.5, Chapter
15) Calculus before Newton and Leibniz
- 2/17: (Chapter
16) Newton and Leibniz
- 2/24: (Chapter 16 continued) Newton and Leibniz continued.
- 2/26: (Chapter 17,
section 1) Differential equations: Bernoullis,
- 3/3: (Section 17.2) Multivariable
- 3/5: (Sections 17.2,
17.4): More multivariable.
Foundations issues, round 1.
- 3/10,12: SPRING
- 3/17: (Sections
19.1-19.3, 20.3-20.4): Algebra, Number
Theory, Geometry, Topology a la Euler
- 3/19: (Sections
21.1-21.3): Nineteenth Century Algebra and Number
Theory, part 1
- 3/24: (Sections
21.4-21.5): Nineteenth Century Algebra and Number
Theory, part 2
- 3/26: Exam 2
- 3/31: (Sections 22.1-22.3): Nineteenth Century Analysis, part 1. Foundations again.
- 4/2: (Sections 22.4):
Nineteenth Century Analysis, part 2.
- 4/7: (Sections
24.1-24.3) Nineteenth Century Geometry,
- 4/9: (Sections
24.5-24.6) Grassmann and Hilbert.
- 4/14: (Sections
25.1-25.2) Axiomatics, Set Theory, and
Topology circa 1900-1930.
(supplement) Godel and Turing. Von Neumann and
- 4/21: Presentations in
- 4/23: Presentations in
- 4/28: Presentations in
- 4/30: Presentations in
class if needed. Review.
GETTING HELP: You can get help from Professor
The library staff is very helpful in finding resources for projects.
SYLLABUS: I expect to survey the class early on
and based on your
backgrounds and interests, we may alter the topics significantly.
In that case I will redo this
document. I fully expect there to be minor changes.
The early part is much too fast. I truly
welcome your input on topics -- this is a great opportunity to explore things you wish to learn.