Agenda, Semester Week 5

Agenda, Semester Week 5#

Polynomials and Induction#

This week will finalise our study of polynomials. The division algorithm for polynomials will be treated for determination of the multiplicity of a root of a polynomial.

Another topic that will be covered this week is induction, a method of proof that relies on recursive definitions. At its core, induction is a compact technique used to verify that proposed expressions indeed are valid.

Key Terms#

Long Day will cover:

  • The division algorithm for polynomials.

  • Factorised form of a polynomial.

  • The fundamental theorem of algebra.

  • Multiplicity of roots.

Short Day will cover:

  • Induction and the induction principle.

  • Base case and induction step.

  • Induction hypothesis.

Preparation and Syllabus#

Syllabus this week is the rest of Chapters 3 and 5.

  • For Long Day, read Sections 5.5 and 5.6.

  • For Short Day, read Sections 3.3 through 3.5.

Exercises#

Exercises for Long Day.

Exercises for Short Day.

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