Analysis of the problem
Preparing the mathematical problem
The way you analyze a problem depends on the type of problem. If the problem comes from the real world, you first need to set up mathematical problem that represents it. The mathematical problem is called a mathematical model.
Even if the problem begins more mathematically, it may not be stated clearly enough to solve. So your first job is often to clarify the problem: make assumptions, eliminate ambiguities. Sometimes you don't notice lack of clarity in the problem until after you've tried to solve it.
Solving the problem
Once the mathematical problem is clear, you want to solve it. To explore and solve problem, you can draw on variety of problem solving strategies.
Writing up a solution
When you think you've solved the problem, carefully write up a solution. A solution is more than an answer; the solution includes a justification for the answer. To help you write up a solution clearly, you might pretend you're explaining the solution to someone in your position before you solved the problem. From the solution your reader should be able to tell:
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