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Section Daily Prep 10
Today we will discuss polynomials over finite fields and some of their properties and algorithms.
Subsection Learning Objectives
Subsubsection Basic Learning Objectives
Objectives
Before our class meeting, you should use the resources below to be able to learn the following. You should be reasonably fluent with these; we’ll answer some questions on them in class but not reteach them in detail.
State the definition and give examples of: polynomial ring over a field, coefficient, degree, monic polynomial, quotient, remainder.
Compute addition, subtraction, and multiplication of polynomials over a field.
Subsubsection Advanced Learning Objectives
Objectives
During our class meeting, we will work on learning the following. Fluency with these is not expected or required before class.
Apply the Division Algorithm to compute quotients and remainders for polynomials over a field.
State the definition and give examples of: irreducible polynomial, reducible polynomial.
Test low-degree polynomials over
\(\F_p\) for irreducibility.
State the Unique Factorization Theorem for polynomials over a field.
Subsection Resources for Learning
Use these resources to prepare for class and answer the questions below.
Guruswami, Rudra, & Sudan, Section 5.1, Appendices D.3, D.7, pp. 93-95, 524-526, 536-537
Roth, Section 3.2, pp. 51-56
No reference video for today, sorry. Today’s intro ideas really do work just the same over finite fields as the real numbers so your intuition will be good.
Subsection Important Terms
