ABSTRACT
Logic is the foundation for all of mathematics. The reason that mathematics is so portable, and that its ideas live forever, is that our methodology is so rigorous and based on solid rules of reasoning. This chapter begins with sentential logic and elementary connectives. This material is called the propositional calculus. A more advanced course in logic will explore other logical methods. The chapter discusses the concept of truth, and begins to describe what a mathematical proof is. An atomic statement is a sentence with a subject and a verb but no connectives. In everyday conversation, people sometimes argue about whether a statement is true or not. In mathematics there is nothing to argue about. In practice a sensible statement in mathematics is either true or false, and there is no room for opinion about this attribute. The formula seems to describe what is going on in nature is convenient, and is part of what makes mathematics useful.
