1 x PREFACE
We began the project with an extensive survey of opinions about the
teaching of mathematical proof writing, and we want to thank all who
shared their thoughts and experiences:William Berlinghoff, Southern John Lawlor, University of
Connecticut State University Vermont
Charles Biles, Humboldt State Douglas Nance, Central Michigan
University University
Richard Chandler, North Carolina Gregory B. Passty, Southwest
State University Texas State University
Orin Chein, Temple University
Bradd Clark, University of
Southwestern Louisiana
William Coppage, Wright State
University
Carl Cowen, Purdue University
Robert G. Dean, Stephen F.
Austin UniversityGail Ratliff, University of
Missouri, St. Louis
Robert B. Reisel, Loyola
University of Chicago
Donald F. Reynolds, Indiana
State University
David Sprows, Villanova
University
Thomas Den=, Ashland College Louis A. Talman, Metropolitan
State College
Michael Evans, North Carolina
State University Raymond D. Terry, California
Polytechnic State University
Daniel Farkas, Virginia
Polytechnic and State Richard Thompson, University of
university Arizona
Dorothy Goldberg, Kean College James Vance, Wright State
of New Jersey University
Joel Haack, Oklahoma State
UniversityRobert W. West, University of
California, Irvine
Kenneth E. Hummel, Trinity
University\, The suggestions of many reviewers had a strong influence on the devel-
opment of the manuscript. I would like to thank Professors William
Berlinghoff, Charles Biles, Orin Chein, Robert Dean, Michael Evans, Joel
Haack, John Lawlor, David Sprows, Richard Thompson, and James Vance,
for an extraordinarily conscientious job of reviewing, criticizing, enhancing,
and sometimes praising my work. In particular, Professors Biles, Evans,
and Vance provided material, including several fine exercises, that I incor-
porated into the text. I am grateful to Professor Berlinghoff and his stu-
dents at Southern Connecticut State University, who used a late version
of the manuscript in their course and made a number of helpful suggestions.