Description of Program [25 pages] PDF format
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Mathematical Modelling and Industrial Mathematics Resources |
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Industrial mathematics is a process that begins with a problem from industry. A mathematical model of the problem is then formulated. By `mathematical model' we mean a collection of mathematical equations and mathematical structures the equations refer to which capture the abstract attributes of the problem. Once a mathematically consistent model is produced, its accuracy is judged by comparing its behaviour to known realizations of the real system the problem addresses. Next, an algorithm for obtaining a solution is proposed. The algorithm is a series of mathematically deduced steps beginning with an initial situation and leading to a final outcome of the model. The algorithm is typically implemented on a computer. Solutions from this algorithm are compared with observations or experiments and the mathematical model is then re-evaluated based on these comparisons. In addition to offering a solution to the problem, a satisfactory working mathematical model can be used to make predictions and to investigate underlying assumptions and structures inherent in the problem - a procedure which may be impossible or very difficult to do any other way. The industrial mathematician is involved in all aspects of modelling, analysis, and computation - which brings him or her into collaboration with managers, computer scientists, engineers, etc - but the industrial mathematician is mainly concerned with bringing the abstract power of mathematical analysis to bear upon the problem, a task for which he or she is uniquely qualified.
Modern manufacturing and service industries have changed drastically in modern times due to the explosion in information management and technology. Fast and inexpensive computing, word processing and communications have necessitated sophisticated methods to meet new demands. Mathematical sciences are the enabling factor in realizing and implementing these methods. In recent years the mathematical community has responded to this growing need for mathematically trained personnel in industry. Organizations such as the Fields Institute, The Mathematics of Information Technology and Complex Systems (MITACS), and the Pacific Institute for the Mathematical Sciences (PIMS) in Canada, and the Society for Industrial and Applied Mathematics (SIAM) and The Institute for Mathematics and its Applications in the United States have been promoting the interaction of mathematics with industry and continue to develop ways to meet industry's demand for mathematically trained scientists.
The proposed program will develop and maintain strong links with industry. This will ensure that students are receiving the most relevant, state-of-the-art knowledge in applied mathematics. Faculty will work together with people from industry to present current problems to the students. Students will gain exposure to 'real-life' mathematics and experience with potential employers. Industry will benefit by having highly trained individuals (students and faculty) analyze their problems.
It has been emphasized in reports written by the mathematics community on mathematics in industry that teamwork, communication skills, and breadth of knowledge are qualities that industry looks for in individuals and are, to a large extent, qualities that are absent from a traditional mathematics program. The proposed program differs significantly from traditional mathematics programs because of its emphasis on communication/teamwork skills, breadth of applied knowledge, exposure to real-world problems, and modelling exercises which will form the backbone of the student's studies throughout his or her undergraduate carreer.
Industry typically hires a mathematical scientist to work with engineers, business people, and managers in an interdisciplinary team. Managers feel that a mathematical scientist is smart, open-minded and one who can quickly learn the particular aspects of the job. The following qualifications are fundamental for a job in industry: breadth in the mathematical sciences and technology, ability to abstract essential mathematical/analytical characteristics from a situation and formulate them in a fashion meaningful for the context, computational skills (including numerical methods and data analysis), flexible problem-solving skills, communication skills (especially the ability to formulate goals and express results in ways that managers and colleagues can understand), the ability to work with other scientists, engineers, managers and business people, and a willingness to follow through to ascertain what real impact the modelling/analysis has in the enterprise.
The proposed program is dedicated to ensuring that graduates acquire the above qualifications. To this end the initial years of the program will be devoted to learning basic mathematical, technological (computer science) and analytical skills that are needed to address current problems in industry. Courses will include both theoretical and computational mathematics. In the latter years of study students will be able to take courses from other departments (such as engineering, computer science and business). The final years of the program will emphasize the development of problem-solving skills and teamwork. Students in their final year will work on projects based on problems from industry and will be required to write reports and present their solutions to an audience.
For more information about this program, please contact Randall Pyke, email: rpyke@ryerson.ca.