Learning Objectives By the end of this module, you will meet this learning objective: · Apply the operations of formal/mathematical logic Module Overview Welcome to the first module for discrete mathematics, which is one of the core components of mathematics. Modern computer science and information technology is built almost entirely on discrete math, which includes areas such as set theory, logic, relations, graph theory, and analysis of algorithms. Understanding the topics presented here is fundamental to understanding logic, sets, computability, and many more computer science topics. By studying discrete math, you learn how to think logically, rigorously, symbolically, and creatively. In this first module, we focus on logic, which has its own unique language and way of defining what is true and false. For careers in computer science, data science, machine learning, software engineering, and more, you need to be fluent in the language of logic. In this module, you learn how to think and write like a mathematician. You will learn about propositions, which are statements that can be labeled as either true or false. You will also learn different ways to form new propositions from old ones. Working with propositions, you will learn logical operations, notation, and how to create a simple truth table to show the truth value of a statement and its negation. By the end of the module, you should understand both mathematical conventions and the basics of mathematical reasoning. Some propositions require quantifiers, which are expressions or phrases that indicate the number of objects that a statement pertains to. Examples of quantifiers in English are all, some, many, few, most, and none. Predicate logic, which is an extension of propositional logic, adds the concept of predicates and quantifiers to the meaning of statements. Mathematical logic that studies sets, or collections of objects, is called set theory. The logical operations are translated into set operations, which are explored further in this module. Finally, at the end of this module, Cartesian products are presented. Module at a Glance
This is the recommended plan for completing the reading assignments and activities within the module. Additional information can be found in the module Resources section and on the module table of contents page. 1. Review the Module One resources. 2. Post your initial response for the discussion by 11:59 p.m. EST on Thursday. 3. Complete the participation activities in zyBooks. 4. Complete the challenge activities in zyBooks. 5. Complete the problem set and submit it in Brightspace. 6. Post peer responses to the discussions.