Learning Resources
Outcomes
In this lesson you will learn
- The difference between deductive and inductive reasoning
- how to develop and analyze mathematical arguments and proofs
- prove, using the principle of mathematical induction
By the end of this section students will be able to:
- develop and evaluate mathematical arguments and proofs
- represent a series in expanded form and using sigma notation
- prove, using the principal of mathematical induction
Introduction
In developing your mathematical background, you should have explored, practiced and mastered various problem-solving strategies. In this section a new strategy, useful for many kinds of problems, is introduced.
This section, as the name suggests, explores the concept of proof by mathematical induction. Basically, you will learn about deductive and inductive proofs and use the principal of mathematical induction to prove statements involving natural numbers. The statements to be proven will vary in nature and involve algebraic, geometric and trigonometric properties.
This section of study should take approximately 4 hours to complete.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- how to represent a series in expanded form and using sigma notation
- how to sum geometric series
- how to sum arithmetic series
- algebraic fluency
- the set of Natural numbers
- exponent laws
- how to translate a verbal description of a statement into a mathematical one