BOOLEAN ALGEBRA

These boolean algebra resources were developed by Richard Singer while teaching at Webster University. They have been used with undergraduate mathematics and computer science majors. They have also been used in a master of arts program for secondary and middle school mathematics teachers, and some of these teachers have used portions of these materials for enrichment study with their own students. Titles and descriptions of these units are given below. Clicking on the title will allow it to be downloaded as a Microsoft word file.

Discussion about any of these resouces would be highly appreciated.

Basic Boolean Concepts: The main text introduces the concept of a boolean lattice, and related concepts of boolean equations. This material is prerequisite for all the other units. The appendix discusses atoms and boolean inequalities. These ideas are only used in a few places in later units.

Solving Attribute Puzzles: This unit is purely recreational, using boolean algebra to solve more challenging attribute puzzles.

Various Logic Puzzles: This unit is purely recreational, using boolean algebra to solve a variety of logic puzzles.

Representing BIT Functions: This unit, and the next two for which it is prerequisite, are oriented towards technological applications involving digital control systems. It uses the concept of boolean atoms to show how any BIT function can be represented as a atomic lattice polynomial. It also shows how to find reduced representations.

Digital Control Devices: This unit illustrates the use of bit functions in the construction of digital devices, with emphasis on circuits for computers.

Solving BIT Equations: This unit uses boolean polynomial representations to solve bit equations, with applications to feedback circuits.

Boolean Lattice Theorems: This unit organizes boolean lattices laws as an axiomatic system. It also relates boolean concepts to the broader concepts of contemporary algebra. This unit is primarily theoretical, but it is a prerequisite for the unit below which it involves both a recreational and a technological application of boolean concepts.

Boolean Group Applications: This unit has two independent parts, sketching the application of boolean groups to error correcting codes and playing Nim.