Session 9: Algebra as Structure

In Session 8, we concluded our study of functions by looking at cyclic and inverse functions. You learned that cyclic functions have repeating outputs and that in an inverse proportion, the outputs get smaller as the inputs get larger, and vice versa. Finally, you found that many different kinds of functions can be drawn through the same two points.

Throughout the past several sessions, we've seen that functions are relationships between inputs and outputs. We have explored properties of different kinds of functions, situations where they arise, and how they can be expressed in tables, equations, and graphs. This session explores algebra as structure by taking a closer look at the properties of functions. Note 1

Part A:
Comparing Operations

Part B:
Guess My Rule

Part C:
Algebraic Structures

Part D:
Working with Algebraic Structures

Part E:
Summing Up

Homework

The main goal for Session 9 is to find out what is meant by "algebraic structure," a relatively modern branch of mathematics. To that end, in this session you will:
•	Explore important concepts in the study of algebraic structure
•	Explore a new algebraic structure
•	Solve equations in the new structure


	Throughout the session you will be prompted to view short video segments. In addition to these excerpts, you may choose to watch the full-length video of this session.


	Previously Introduced:		New in This Session:
	algorithm set solution set modular arithmetic		algebraic structure binary operation commutativity associativity distributivity closure identity element inverse group field

Next > Part A: Comparing Operations

Session 9: Index | Notes | Solutions | Video