Introductory Problem Courses in Analysis and Topology
E.E. Moise - Introductory Problem Courses in Analysis and Topology
Published: 1982-05-05 | ISBN: 0387907017, 3540907017 | PDF + DJVU | 94 pages | 2.55 MB
in each chapter of this book, the student finds definitions, and theorems which are guaranteed to be true. The student's Job is to prove the theorems. in the problems that follow, various propositions are stated as if they were true, but many of them turn out to be false. Here the student's Job is to find out the truth, whatever it may be, and establish it with a proof or a Any adequate explanation of the workings and the advantages of problem courses would form an essay much too long for a preface. tollowing are some observations. student who has creative capacities deserves an opportunity to discover, use, and develop them; and this opportunity should come soon. it should not be postponed until the time comes to write a dissertation. the first few weeks of a problem course, the teacher is likely to see striking evidence of the need for such a course. At the beginning, it rarely happens that a student can write grammatical sentences which say what he really means. At the end of a problem course, almost all students can do this.