on the birth of modern mathematics beginning in the Renaissance and continuing to the early 1900's.

Topical strands will be pursued in historical fashion and the mathematical developments are tied to

social and political contexts where appropriate. Evolving ideas about mathematics, proof, and the

major controversies among mathematicians, both personal and mathematical, are part of the cultural

history of mathematics. As a synthesis course, students will reason analytically about the material,

write short essays and a major term paper, and present a brief overview of their term paper orally.

Each student will be responsible for leading one part of class discussion as part of a group during the term.

Some student works, with names removed, will be copied and provided to the assessment office

for use after the course is completed.

GRADING:

which
includes short essays, two exams, the term project with oral
presentation, and a final exam.

Points used as the basis of the grade will be:

Points used as the basis of the grade will be:

Homework (200); Two
exams (200); Class Participation (50); Term Paper (150); Final (200).

**EXAM
DATES**

**POLICIES**: **The
GMU
Honor
code
is in effect at all times and students are expected to be****
fully aware of its
requirements. **
Group work may be part of the course and group members

will truthfully report on non-contributing members.

reason and requires prior notification except in extreme circumstances.

**
DON'T**** ARRANGE TO LEAVE BEFORE THE FINAL
AND EXPECT
TO TAKE IT EARLY.
GIFTS:
None will be given as
grades. If you need a particular grade, you are responsible
for
earning it. I will work with
you to achieve your goal.
**

**
****IMPORTANT
DATES:
** 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

For more information, see http://registrar.gmu.edu/calendars/spring-2015/

Exam 1 – Tentative – Thursday, Feb. 19

Exam
2
– Tentative – Thursday, March 26

Final
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 of Chapter 7) Contributions of China
- 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;
Logarithms
and Decimals.

- 2/10: (Chapter
14) Analytic Geometry; Descartes,
Fermat,
Pascal.

- 2/12: (Section 13.5, Chapter 15) Calculus before Newton and Leibniz
- 2/17: (Chapter 16) Newton and Leibniz
- 2/19:
Exam 1

- 2/24: (Chapter 16 continued) Newton and Leibniz continued.
- 2/26: (Chapter 17, section 1) Differential equations: Bernoullis, Euler.
- 3/3: (Section 17.2) Multivariable
calculus.

- 3/5: (Sections 17.2,
17.4): More multivariable.
Foundations issues, round 1.

- 3/10,12: SPRING BREAK
- 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. Vector calculus.
- 4/7: (Sections
24.1-24.3) Nineteenth Century Geometry,
part 1.

- 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.
- 4/16:
(supplement) Godel and Turing. Von Neumann and
computers.

- 4/21: Presentations in
class.

- 4/23: Presentations in class.
- 4/28: Presentations in
class.

- 4/30: Presentations in class if needed. Review.

GETTING HELP: You can get help from Professor Sachs during office hours.

The library staff is very helpful in finding resources for projects.

MODIFICATIONS TO 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.