Question: Can I use Geometry 2nd Edition by Harold Jacobs with the AskDrCallahan course?
Short Answer – No, not easily.
Longer Answer – Many have asked us if they could use the Second Edition of Geometry with our DVD set. The answer is no, at least not without a lot of grief to the teacher and student.
We initially were telling teachers and students they could use the 2nd edition. Several people told us they had been told the second edition was superior due to a better treatment of proofs. In support of those families, we attempted to develop the syllabus to develop a map between the two editions. We consulted with Harold Jacobs on the map. The resulting dialogue was interesting.
First, the two books cover basically the same material, but in different ways. But, the chapters and problem sets are different enough to cause a significant management issue for the teacher and student – even with a map.
Second, and more importantly, we came to believe that those who felt the 2nd edition was superior were wrong. This was further backed up by Jacobs when he wrote the following in an email back to us.
“There was more emphasis on two-column proofs in the second edition but, as is often the case with such proofs, the things to be proved were rarely surprising and almost always rather obvious. I endeavored in the third edition to build the exercises around more profound material and to give the student more freedom in developing proofs. For really challenging problems, this meant leading the student along in a Polya-like style. Forced into two-column format, some of the proofs in this edition would run 15-20 steps, much longer than the typical 4- or 5-step proofs in the earlier edition. In his foreword on page xii of the book, Andrew Gleason of Harvard University wrote that “This book restores the idea of proof to its rightful place in geometry. Whoever studies this text will know what a proof is, what has been proved, and what has not.” He, together with Dr. Peter Renz, who wrote the supplemental notes in the Teacher’s Guide, looked carefully at the content and structure of all of the exercises and gave his full approval. I feel very honored that he would take so much of his time to do this. Gleason, by the way, is a former president of the American Mathematical Society and one of our country’s most prestigious mathematicians. I hope this helps clarify what has changed between the second and third editions as well as why.”
We hope this clears up any misunderstanding. With the two books sitting side by side, we would clearly choose the 3rd edition for our children.