MATH 400 SYLLABUS, SPRING 2015 Professor Sachs

        COURSE OVERVIEW: This course is a first course in the history of mathematics. We will focus
        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.

TEXT: A History of Mathematics: An Introduction (Third Edition) by Katz (Addison-Wesley).

MEETING: Tuesday and Thursday 1:30pm-2:45pm, Enterprise Hall, room 173

OFFICE HOURS: 201D Science and Tech I, T, R 3:00-4:15pm or by appointment.

CONTACTS: email: rsachs@gmu.edu, phone: 993-1464

COURSE WEB PAGE: math.gmu.edu/~rsachs/math400

GRADING: Grading will be fair and impartial. It is based on a mixture of graded homework,

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:

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

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. Absence from exams must be for a valid
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 DATES

Exam 1 – Tentative – Thursday, Feb. 19

Exam 2 – Tentative – Thursday, March 26

Final Exam – Tuesday, May 12 1:30pm-4:15pm

MATERIAL COVERED AND TENTATIVE SCHEDULE

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.