History of Mathematics Detailed Syllabus
(For a more general syllabus, see this.)
The chapters refer to our text, A History of Mathematics, an
Introduction A History of Mathematics, an Introduction
by Victor J. Katz, Addison-Wesley, third edition, 2009. Addison-Wesley.
Other material will be included as appropriate.
The material in the third edition is, for the most part, the same as the
material of the second edition, but it's been rearranged.
Last time I taught this course, I used
the second edition. Here's the Syllabus for the second edition.
- Chapter 1: Egypt and Mesopotamia
- Egypt: number system, multiplication and division, unit fractions,
the Egyptian 2/n table, linear equations and
the method of false position, geometry.
- Mesopotamia: sexagesimal (base 60) system and cuneiform notation,
arithemetic, Babylonian reciprocal table,
elementary geometry, the Pythagorean theorem,
Plimpton 322 tablet, square roots, quadratic equations,
tokens of preliterate Mesopotamia.
- Chapter 2: The beginnings of mathematics in Greece
- The earliest Greek mathematics: various Greek numerals, Thales, Pythagoras and
the Pythagoreans, difficult construction problems
- Plato and Aristotle: logic, magnitudes, Zeno's paradoxes
- Chapter 3: Euclid's Elements.
See
http://aleph0.clarku.edu/~djoyce/java/elements/elements.html with dragable figures,
and a
quick trip of the Elements
- Book I: Basic plane geometry through the Pythagorean theorem
- Book II: Geometric algebra and related constructions
- Book III: Intermediate plane geometry and the study of circles
- Book IV: Constructions of regular polygons
- Book V: The theory of ratio and proportions of magnitudes
- Book VI: Similar plane figures
- Books VII-IX: Number theory
- Book X: The theorey of irrational magnitudes
- Books XI-XIII: Solid geometry, the method of exhaustion, constructions of
regular polyhedra
- Chapter 4: Archimedes
- Chapter 5: Mathematical methods in Hellenistic times
- Chapter 6: The final chapters of Greek mathematics
- Diophantus and Greek algebra, Pappus and analysis
- Chapter 7: Ancient and medieval China
- Chapter 8: Ancient and medieval India
See also Outline of Mathematics in India
- The Hindu-Arabic place-value system and arithmetic
- Geometry
- Equations and indeterminate analysis
- Combinatorics, trigonometry
- Chapter 9: The mathematics of Islam
- Decimal arithmetic
- Algebra: quadratic equations, powers of the unknown, arithmetic triangle,
cubic equations
- Combinatorics
- Geometry: parallel postulate, trigonometry
- Chapter 10: Mathematics in medieval Europe
- Translations from Arabic into Latin in the 12th and 13th centuries
- Summary of early mathematics in western Europe
- Combinatorics
- The mathematics of kinematics: velocity, the Merton theorem,
Oresme's fundamental theorem of calculus
- Chapter 11: Mathematics around the world
- Mathematics at the turn of the fourteenth century
- Mathematics in America, Africa, and the Pacific
- Chapter 12: Algebra in the renaissance
- The Italian abacists, algebra in France, Germany, England , and Portugal
- The solution of the cubic equation
- Early development of symbolic algebra: Viéte and Stevin
- Chapter 13: Mathematical methods in the renaissance
- Perspective, geography and navigation, astronomy and trigonometry,
logarithms, kinematics
- Chapter 14: Geometry, algebra, and probability in the seventeenth century
- The theory of equations
- Analytic geometry: coordinates, equations of curves
- Eementary probability
- Number theory
- Projective geometry
- Chapter 12: The beginnings of calculus
- Tangents and extrema, areas and volumes, power series, rectification of
curves and the fundamental theorem of calculus
- Chapter 13: Newton and Leibniz
- Isaac Newton, Gottfried Leibniz, and the first calculus texts
Back to course page
This page is located on the web at
http://aleph0.clarku.edu/~djoyce/ma105/syll.html
David E. Joyce,
