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In this article we introduce a new method of studying mathematics, CAM (Computer Assisted Mathematics) known as "Experimental Mathematics", by presenting an exemplary tonic on fractal. This method is essentially a child of our "Computer Age" and has been used effectively in the research of chaos, fractal and dynamical systems. Our scenario is the following. First of all, we draw a fractal figure on the display, making use of the super computer accompanied with the personal computer. On the basis of this figure we form a mathematical conjecture. To prove this we are confronted with the difficulty of long calculations and the complexity of formulas of the high degree rational functions. These tasks seem too hard and tedious to the human beings. So we entrust them to the computer and a useful software. (Hardwares are SX-1 E and PC 98, languages are FORTRAN and BASIC and software is REDUCE.) After these works completed, we resort to the mathematical logic. The mathematical induction finishes the proof of our conjecture. We emphasize here two points of view on the role of the computer. (1) Computer Graphics could be important sources of mathematical imaginations and thoughts. We should not treat CG so lightly as a hobby. (2) Computer assists mathematics in reducing complex formulas into simple forms as well as in doing difficult numerical calculations. Our conclusion is that CAM should be developed more intensively and systematically in the educations of mathematics in the university. The introduction of CAM will probably change the quality of the boresome traditional courses of linear algebra and differential and integral calculus and we hope it will give young students much more strong interest in the vivid mathematics and its applications.
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