This series begins with a file containing Professor Barbeau’s curriculum vitae. It is followed by a single file on courses he taught at the University of Western Ontario (1964-1966). The remaining files document his activities in the Department of Mathematics at
the University of Toronto. There are a few general files, followed by a report of the Committee on the Structure of the Governance of the Department (1973), and files on selected staff, the Fields Institute and the Fields Medal. This section concludes with two
boxes of index cards listing students registered in the Mathematics and Physics program between 1903 and 1966, along with cards on interested Commerce and Finance students, physics students, and students who received the Samuel Beatty Fund Scholarship
between 1953 and 1959. One use made of these cards was to compile statistics on the number of students registered in the Mathematics and Physics (M&P) program.
The main part of the series contains material relating to courses Professor Barbeau taught at the University of Toronto, beginning in 1969. It ends with files on a number of publications and organizations at the University of Toronto. For most courses of the courses in this series, Professor Barbeau inserted a memo providing the background and context of each. The material for each course ranges from memoranda, notes and reports, reading lists, and supplementary notes to problem sets, analysis, tests and examinations. Included is the occasional term paper. Until the 1980s, Professor Barbeau developed detailed mimeographed material for his courses; he then switched to typewriters and eventually to computers. Some files, such as those for courses 129, 133Y, and 1030F, contain manuals, drafts of papers, and supplementary notes. Course 439 has drafts of chapters for a work by Barbeau on ‘functional analysis,’ the topic of his doctoral thesis.
Professor Barbeau taught both at the undergraduate and graduate level at the University of Toronto, and also did a lot of outreach work with high school students and working professionals. His taught his first course at the University of Toronto in 1960-1961,
while taking his Master’s degree: calculus to pre-medical students. Later he taught the history of mathematical analysis, a course on chaos and dynamical systems, and a research course of Pell’s equation (the last not represented in this series). He also
developed a general course in mathematics for students in other disciplines, particularly engineering students (see, for example, MEC 362F and MAT 2432/335) and a course in mathematics for intending elementary students. At the graduate level, besides courses in functional analysis and Fourier series, he helped develop a course on problem solving for a Master of Science in Teaching program.
Professor Barbeau’s interest in introducing high school students to mathematics is well documented in this series. Beginning in 1970 and for a quarter century thereafter, he ran a number of courses for high school students. The first, in the summer of 1970 and 1971, was the John Honour Special Seminar in mathematics, while the longest running program, from 1985-1995, was a correspondence course in polynomials, initially for high school students in Metropolitan Toronto. It was soon extended across Canada. In the 1980s he also ran a quantum mechanics seminar (1986), a recreational mathematics and combinatorics course (1987-1988), and he also encouraged high school students to compete in the American High School Mathematics Examination competition.
Another area of outreach was working professionals who needed to upgrade their knowledge. There are two examples in this series, a mathematics seminar for secondary school teachers (1964, 1965) and”Operation alert for engineers”. Each fall between 1972 and 1975, the Faculty of Applied Science and Engineering offered an engineering update program in seven three-hour sessions, initially for about 40 working engineers from General Electric and later engineers from General Motors in Oshawa.
Professor Barbeau taught one of the sessions in each semester, on linear algebra and linear analysis.
This series ends with files on a number of publications and organizations at the University of Toronto. “Mathematical Mayhem” was a mathematical journal for gifted high school students and undergraduate students created by students at the University of
Toronto. In 1979, Professor Barbeau conceived of the idea of an essay contest in mathematics open to high school students, named in honour of Samuel Beatty, former Dean of Arts and head of the Department of Mathematics, which ran until 1982. The
quality of the submissions was sufficiently high that the trustees of the Samuel Beatty Fund published two volumes of the best essays.