Discrete Structures (Free Online Course)

Discrete Structures (Free Online Course) : This provides a clear, accessible introduction to discrete mathematics that combines theory with practicality. Discrete mathematics describes processes that consist of a sequence of individual steps, as compared to forms of mathematics that describe processes that change in a continuous manner. The major topics we cover in this course are single-membership sets, mathematical logic, induction, and proofs. We will also discuss counting theory, probability, recursion, graphs, trees, and finite-state machines.

Understanding the terms “single-membership” and “discrete” is important as you begin this course. “Single-Membership” refers to something that is grouped within only one set and systems that can be in only one state at a time, at the same hierarchical level. Similarly, “discrete” refers to that which is individually separate and distinct. Each element of anything can be in only one set or one state at a time. This is a result of Aristotelian philosophy, which holds that there are only two values of membership, 0 or 1. An answer is either no or yes, false or true, 0% membership or 100% membership, entirely in a set or state, or entirely not. There are no shades of gray. This is much different from Fuzzy Logic (due to Lofti Zadeh), where something can be a member of any set or in any state to some degree or another. Degrees of membership are measured in percentages, and those percentages add to 100%. But, even in Fuzzy Logic (multiple-membership, multiple-state, non-discrete logic), one ultimately comes to a crisp decision so whether some specific action is taken or not. For this course, it is enough to understand the difference between single-state and multi-state logic.