Practice Proof Of Bijection (1.7) - Overview 41 - Discrete Mathematics

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6 sample questions

Question 1.
What is the order of a finite field?
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Think about how we describe the size of a mathematical structure.
Question 2.
What does the characteristic of a finite field represent?
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Consider how many times you can add one before returning to zero.
3Question 3.
What is the characteristic of a finite field?
- A prime number
- A composite number
- A non-integer
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Recall the definition of field characteristics.
4Question 4.
True or False: The elements of a minimal spanning set are always unique.
- True
- False
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Think about redundancy in spans.
Question 5.
Construct a finite field of order 49 and explain the choice of irreducible polynomial.
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Consider how the degree of the irreducible polynomial corresponds to the structure of the finite field.
Question 6.
If given a finite field of order 9, demonstrate how to show that it is constructed using an irreducible polynomial.
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What properties must the polynomial possess to be irreducible in this context?

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