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How can mathematical modelling be integrated with complex network of biological system in comprehensive education? There are mutual agreements between academia from various fields that mathematical modelling is an important part of the curriculum. Immunology is a complex subject and for student to fully understand its complex interaction at molecular level requires computer supported models. This research tries to resolve the ever emerging problem of teaching immunology in higher education. The main objective is to develop multimedia educational software to enhance immunology teaching, with the use of a Computer Algebra System (CAS) that fully utilizes mathematical equation, modelling and simulation of complex network of gene regulation and metabolism. A survey was conducted among students in higher learning institutions, and the result clearly shows that the current teaching method is not feasible to the current learning style. To overcome this, new teaching techniques to support the required understanding need to be introduced. With the development of this educational package that uses new modelling and simulation techniques hopefully can aid in teaching some of immunology courses.

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This study uses the cylindrical algebraic decomposition algorithms implemented in Mathematica to produce procedures to analytically compute integrals over polynomially defined regions and their boundaried in two and three dimensions. Using these results, we can implement the divergence theorem in three dimensions or the Green's theorems in two dimensions. These theorems are of central importance in the applications of multidimensional integration. They also provide a strong correctness test for the implementation of our results in a computer algebra system. The resulting software can solve many of the two and some of the three dimensions lintegration problems in vector calculu stextbooks. The three dimensional results are being extended. The results in this paper are being included in an automated student assistant for vector calculus.

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