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Deductive Mathematics: An Introduction To Proof And Discovery For Mathematics Education, Andrew Wohlgemuth
Deductive Mathematics: An Introduction To Proof And Discovery For Mathematics Education, Andrew Wohlgemuth
Mathematics and Statistics Faculty Scholarship
Mathematics has two fundamental aspects: (1) discovery/logical deduction and (2) description/ computation. Discovery/deductive mathematics asks the questions:
1. What is true about this thing being studied?
2. How do we know it is true?
On the other hand, descriptive/computational mathematics asks questions of the type:
3. What is the particular number, function, and so on, that satisfies ... ?
4. How can we find the number, function, and so on?
In descriptive/computational mathematics, some pictorial, physical, or business situation is described mathematically, and then computational techniques are applied to the mathematical description, in order to find values of interest. The …