Maths 460: History of Mathematics
(3)
Syllabus
1.
Prerequisite: Maths 161 or
165.
2.
Course
Description: The
development of mathematics from prehistoric times to the seventeenth century.
Topics may include number concepts and numeration, algebra, geometry, trigonometry,
analytic geometry, and calculus.
3.
Course
Objectives: Students will become familiar with the significant
problems, concepts, treatises, and people from the history of mathematics, as
well as with certain historical and social factors which have influenced the
development of mathematics. Present day mathematical concepts will be revealed
to the student in historical context, showing the motivation for the original
work on these concepts. The student will develop a more sophisticated notion of
how the various branches of mathematics are dependent upon one another, while
seeing how mathematics as a discipline survives and flourishes. Further,
students will develop an awareness of the sources in the history of
mathematics.
4.
Course
Rationale: The
various branches of mathematics are often falsely described as static
and independent
of one another. One of the best ways to dispel these notions is to explore the
history of mathematics. Through history, one sees not only the marked
interdependence which exists among the branches of mathematics, but also the
dynamic nature of mathematics, even up to the present day. Further it is
important for prospective mathematics teachers to be aware of historical
content which may be used to illuminate mathematical concepts and motivate the
study of mathematics.
5.
Course
Content: The history of mathematics is
a broad subject. Material may be chosen from, but is not limited to, the
following list of topics.
i.
Prehistoric Mathematics.
ii.
Egyptian Mathematics: Introduction to Egyptian history. Number system; arithmetic
methods, including the use of unit fractions; method of false position;
quantity problems; plane and solid geometry; Pythagorean identity; Rhind and
Moscow papyri.
iii.
Mesopotamian Mathematics: Introduction to
mesopotamian history. Sexigesimal number system; arithmetic, including
extensive use of mathematical tables; motivation for algebra—area versus
perimter of a closed planar curve; algebra, including quadratic equations;
Pythagorean identity and Plimpton 322.
iv.
Greek Mathematics: Introduction to Greek history. Early proof
structures; logic and foundations; plane geometry; solid geometry;
constructibility; problems from classic documents (e.g., Euclid’s Elements).
Several important figures include Thales, Pythagorus, Hippias, Hippocrates,
Zeno, Plato, Aristotle, Eudoxus, Euclid, Ptolemy, Archimedes, Apollonius,
Diophantus, Nicomachus, and Pappus.
v.
Oriental and Indian Mathematics.
vi.
Arabic Mathematics:
Al-Khwarizmi and the appearance of algebra; solutions to quadratic equations;
solutions to cubic equations.
vii. Medieval Mathematics: Gerbert and the abacus; Boethius and the
school tradition; Jordanus; Fibonacci.
viii.
Renaissance Mathematics: Regiomontanus; the translation of Greek into Latin; Cardano,
Tartaglia, and the solution of the cubic equation; Bombelli and the birth of
complex numbers; Ferrari and the quartic equation; the Cossists.
ix. Mathematics of the 17-th century: Emergence of symbolic algebra; analytic
geometry; decimal system; logarithms; the binomial theorem and infinite series;
birth of calculus; celestial mechanics; the brachistochrone problem and the
catenary curve. Important figures include Stevin, Napier, Viete, Descartes,
Fermat, Pascal, Roberval, Barrow, Newton, Leibniz, and the Bernoullis.
6.
Course
Format: Lecture/discussion.
7.
Method
of Evaluating Student Performance: Typical components are homework assignments, projects, and
take-home exams (possibly involving group work), in-class exams, student presentations, oral exams, and term
papers. The evaluation and weight of these components are at the discretion of
the instructor. Students may be evaluated on their understanding of the content
material for the course, their ability to solve problems related to the course
material, and on their ability to communicate mathematically to others verbally
or in writing.
8.
Evaluation
of the Course: The
instruction of the course is evaluated by departmental student evaluations and
peer evaluation. The course is reviewed and revised periodically by the
Departmental Undergraduate Programs Committee.
J. Lorch, 1/15/02 (Adapted from C.V. Jones,
9/88)
V. Mascioni, 4/07/04