This book is intended for students who have definite plans to study management and economics as their fields in college and graduate school. Even though there are similar and competing books in this area, they sometimes turned out to be too burdensome and long for students who need mathematical languages necessary to understand materials in management and economics courses at junior or upper levels. We think this book includes essential and comprehensive mathematical tools beyond the precalculus level. We tried to present mathematical logic and proof as simple as possible for those who do not have strong backgrounds in mathematics, but do have creative minds. We also tried to supply realistic examples from management and economics for those who are preparing their future in those fields. We designed this book to be sufficient for one-semester long class.