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Mathematics has evolved to a discipline that is mainly characterized by its method of proof; its concern for a progressive broadening of its concepts; and by the search for mathematical entities and operations that represent aspects of reality. It is a subject that is pursued by many for its own sake, and regarded as part of the mainstream of human culture. Mathematics pervades modern society with an impact which, already immense, is rapidly growing.

The two principal divisions of mathematics are pure mathematics and applied mathematics.

The pure mathematician is interested in abstract mathematical structures and in mathematics as an intellectual enterprise. The primary concern may not be with its utilitarian aspects or with the current needs of science and technology, although many problems in pure mathematics have developed from the sciences.

Some of the fields in which pure mathematicians work are:

• algebra;
• analysis;
• geometry;
• topology;
• number theory;
• foundations.

The applied mathematician is more interested in how mathematics can be used to study some aspects of the world. Mathematicians are engaged in the creation, study, and application of advanced mathematical methods relevant to scientific problems. Statistical science and methodology today is concerned with phenomena in which there is a background of uncertainty arising from inherent variability and the investigator is obliged to arrive at decisions from limited data. A key tool in statistics is probability.

Applied mathematics, which once referred to the application of mathematics to such disciplines as mechanics and fluid dynamics, has currently assumed a much broader meaning and embraces such diverse fields as:

• communication theory;
• theory of optimization;
• theory of games;
• numerical analysis.

Mathematics offers many vocational possibilities. Such fields as teaching, computing, applied statistics, and actuarial science offer opportunities for B.Sc. graduates. Opportunities to do original research in pure and applied mathematics are available in universities and research institutions. Employment is to be found in financially or technologically oriented business firms. The Department of Mathematics and Statistics, through its various programs, attempts to provide courses to suit the diverse interests within mathematics and statistics.

The Honours program demands of students a talent for abstraction in addition to a high level of competence in the use of mathematical tools. This program is intended for students who plan to work in an area where mathematical innovations may be needed. It is almost essential for students contemplating a career in mathematical research.

The Major program involves the same subjects as the Honours program, but is less demanding in terms of abstraction. It is designed primarily for students who will need mathematical tools in their work but whose creative activity will involve applications of mathematics to other areas. Within the framework of the Mathematics Major, various combinations of courses are suggested to meet the needs of different students. These include course suggestions for secondary school teachers, careers in management, and for careers in industry, government, or actuarial sciences.

It is possible for Major students to include a number of Honours courses in their programs. This will be an advantage for those students who plan to use their mathematics in graduate studies.

Students interested in a Mathematics program linked to other disciplines are advised to consider the B.Sc. Liberal program with a core component in Mathematics or Statistics, or our Joint programs with Computer Science, Physiology, and Physics.

In planning their programs, students are advised to seriously consider developing some depth in another discipline—preferably one for which mathematics has some relevance and use. Mathematics has been closely linked to areas such as computer science, physics, and engineering, but has recently come to play an increasingly important role in fields such as biology, linguistics, management, and psychology. Students should consider completing the requirements for minor programs such as those available in Cognitive Science, Computer Science, and Statistics.

Students considering programs in Mathematics and Statistics should contact the Department to arrange for academic advising.

The student's attention is called to the fact that a B.Com. degree with a Major in Mathematics is available from the Desautels Faculty of Management. In addition, the Schulich School of Music offers the B.Mus. degree with Honours in Theory with Mathematics option.

Students who want to get practical experience in industry before graduation are encouraged to participate in one of the following internship programs:

• The Internship Year in Science (IYS) is an academic program offered for a duration of 8, 12, or 16 months. It is reflected on the transcript and included in the program name (Bachelor of Science – Internship program). Eligible students usually take this program between their U2 and U3 years.
• The Industrial Practicum (IP) has a duration of four months and is usually carried out starting in May. It will appear as a 0-credit, Pass/Fail course on your transcript.

For more information on these programs, consult Industrial Practicum (IP) and Internship Year in Science (IYS).