Moving Things Around

“Here, a sequenced and carefully curated collection of problem sets - not a grab-bag problem bank - guides students toward the awareness of connections between group and number theory. I feel that to realize the full potential for students to experience discovering these connections requires committing to a semester-length course; fourteen problem sets at roughly one per week. This would be more directed groupwork than lecture presentations, although strategic selections among this material could make for enlightening diversions in a traditional, lecture-based course.” - Tom Schulte, MAA Reviews

“...[T]hese problems were carefully and coherently sequenced to unfold an interesting mathematical story complete with plot twists and turns, ultimately building to a satisfying resolution of real mathematical substance. In other words, this was not a problem bank to be viewed as a companion resource for a course. Rather, these problem sets entirely define a complete mathematical course. To do justice to these problems and to allow students to experience the joys of discovering the beautiful and often unexpected connections the problems are designed to reveal, one needs to take the plunge and commit to making them the basis of the course. To me, that meant eschewing lecture presentations in favor of letting the problems tell the story. That would constitute my best advice to instructors using the materials: Let the problems tell the story. Go along for the ride, enjoy it yourself, and fight the urge to drive.” - Thomas Dick, The College Mathematics Journal