4.9 KiB
| title | TARGET DECK | FILE TAGS | tags | ||
|---|---|---|---|---|---|
| Polynomials | Obsidian::STEM | algebra::polynomial |
|
Overview
Given nonnegative integer d, a polynomial in n of degree d is a function p(n) of the form $p(n) = \sum_{i=0}^d a_i n^i$
The coefficients of p(n) are a_0, a_1, \ldots, a_d. Furthermore, a_d \neq 0.
%%ANKI
Basic
Using sigma notation, a polynomial p(n) in n of degree d is a function of what form?
Back: p(n) = \sum_{k=0}^d a_kn^k where a_d \neq 0.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Basic What four algebraic operations are permitted in a polynomial? Back: Addition, subtraction, multiplication, and exponentiation. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
END%%
%%ANKI
Basic
What is d in "a polynomial in n of degree d"?
Back: d is a nonnegative integer.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI
Basic
What is n in "a polynomial in n of degree d"?
Back: The polynomial's indeterminate.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Basic Which coefficient is special in a polynomial and why? Back: That attached to the monomial with highest degree because it cannot be zero. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Basic What are the coefficients of a polynomial? Back: The constants of the monomials found in the polynomial. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Basic What name is given to a degree-0 polynomial? Back: A constant. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Basic What name is given to a degree-1 polynomial? Back: A monomial. Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
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%%ANKI Basic What name is given to a degree-2 polynomial? Back: A binomial. Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
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%%ANKI Basic What is a binomial? Back: A polynomial containing two terms. Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
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%%ANKI Basic What is polynomial fitting? Back: The solving of a linear system to find the coefficients of a polynomial. Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
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%%ANKI Basic Polynomial fitting is a strategy for discovering what part of a polynomial? Back: The coefficients. Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
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%%ANKI Basic What is the degree of a polynomial? Back: The highest degree of the monomials with non-zero coefficients. Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
END%%
%%ANKI
Basic
How many data points are required to fit a polynomial?
Back: k + 1 where k is the degree of the polynomial.
Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
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Bibliography
- Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
- Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).