توابع محدب: توابع محدب

We believe that mathematics is best learned by examining in depth the major ideas in as familiar a setting as possible, and then seeing how they can be generalized. Chapter I takes up the very concrete and historic case of convex functions defined on an interval of the real line. This material appears as a logical extension of what the student has learned in his calculus course, has immediate applications, motivates most of the generalizations to come later, raises most of the important questions that will be studied in the rest of the book. The topic of convex sets is an excellent introduction to the fascination of advanced mathematics. This text brings together all the basic ideas on convex functions, includes a list of problems with varied difficulty levels, and can serve as a reference for other interested parties. A knowledge of undergraduate level linear algebra, advanced calculus, and introductory measure theory are advised as prerequisites