This book includes problems and projects (either in whole or in part) that my students worked on in my regular math classes, in my advanced math elective, or outside of school with my mentoring. The problems and projects include some that can be found in literature, some that I made up myself, and some (no doubt) that are both because what I made-up may have been made-up previously. I decided to compile some of the topics that my best students worked on and publish them for the benefit of other teachers, who could share them with their gifted students. Some of the problems and projects are presented with complete solutions, with every step detailed. Some are missing a number of the intermediary steps, which need to be filled in, and some are problems and projects that are only proposed without any solution offered. All the problems and applications are designed to challenge the best students and their teachers. The math disciplines range through geometry, algebra, trigonometry and calculus while the applications include physics, origami, investments and financial strategies, human modeling, etc.