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The form of mathematics that does not work within the framework, definitions, rules, or rigor of formal mathematical models.

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The study of topics such as quantity, structure, space, and change.

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- Visual evidence (ex. Mandelbrot's computer generated graphics that were used to illustrate the Fatou-Julia theory)
- Coincidences (ex. 1986884 = 1 + 196883: 1986884)" Sheer coincidences in math are often not merely sheer; they’re often clues—evidence for something missing, yet to be discovered. " (http://www.math.harvard.edu/~mazur/papers/Math.presentation2.pdf)
- Numerical evidence comes in a variety of forms:
* proof by induction
*proof by construction
*proof by exhaustion
*proof by probability
*statistical proof

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Practitioners of mathematics are mathematicians:

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Practitioners of mathematics are mathematicians:

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mathematicians conduct research in order to develop and understand mathematical principles. They also analyze data and apply mathematical techniques to help solve real-world problems.

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Focus Question: What physical materials do we use to make knowledge?

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Focus Question: What physical materials do we use to make knowledge?

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Mathematics is the abstract science of number, quantity, and space. Mathematics can be studied it its own rights like with pure mathematics or as it is applied to other disciplines like physics and engineering like in applied mathematics. In mathematics, we use proofs and evidence in numbers to support the knowledge we are creating. In mathematics, a proof is a deductive argument for a mathematical statement. Proofs use logic but also include some about of language to admit its truth.

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Explain what the practitioners of your assigned Area of knowledge does with the facts they have obtained with the physical material utilized: 

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Explain what the practitioners of your assigned Area of knowledge does with the facts they have obtained with the physical material utilized: 

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Sometimes, the abbreviation "Q.E.D" indicated the end of a proof. This abbreviation is Latin for "that which was to be demonstrated." A more common alternative is to use a square of rectangle to state it during and oral presentation and show that the mathematical formulas and equations have come to a valid conclusion. When enough evidence has been gathered, the evidence is used to create mathematical theories. When mathematicians have created and proven mathematical theories, they share it with others who can verify their results.

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Provide 3 instances of physical material that your assigned AOK uses to produce evidence

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Provide 3 instances of physical material that your assigned AOK uses to produce evidence

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- Microscopes can be used to produce evidence in the field of pure mathematics
- Computers can display data and figures, which can be used as evidence for mathematical theories
- Math tutorials are a method of learning to help transfer knowledge of a particular math subject.
- Mathematical proofs is a type of argument that uses deductive reason perceive something as truth.