Rather than teach mathematics and the structure of proofs simultaneously, this book first introduces logic as the foundation of proofs and then demonstrates how logic applies to mathematical topics. This method ensures that readers gain a firm understanding of how logic interacts with mathematics and empowers them to solve more complex problems. The study of logic and applications is used throughout to prepare readers for further work in proof writing. Readers are first introduced to mathematical proof-writing, and then the book provides an overview of symbolic logic that includes two-column logic proofs. Readers are then transitioned to set theory and induction, and applications of number theory, relations, functions, groups, and topology are provided tofurther aid in comprehension. Topical coverage includes propositional logic, predicate logic, set theory, mathematical induction, number theory, relations, functions, group theory, and topology.
