Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious ... Read More
Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious ... Read More
Description
Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student. Written by a noted mathematician and historian of mathematics, this volume presents the fundamental conceptions of the theory of curves and surfaces and applies them to a number of examples. Dr. Struik has enhanced the treatment with copious historical, biographical, and bibliographical references that place the theory in context and encourage the student to consult original sources and discover additional important ideas there. For this second edition, Professor Struik made some corrections and added an appendix with a sketch of the application of Cartan's method of Pfaffians to curve and surface theory. The result was to further increase the merit of this stimulating, thought-provoking text — ideal for classroom use, but also perfectly suited for self-study. In this attractive, inexpensive paperback edition, it belongs in the library of any mathematician or student of mathematics interested in differential geometry.
Reprint of the Addison-Wesley Publishing Co., Reading, Massachusetts, 1961 edition.
Details
Price: $15.95
Pages: 256
Publisher: Dover Publications
Imprint: Dover Publications
Series: Dover Books on Mathematics
Publication Date: 1st April 1988
Trim Size: 5.5 x 8.5 in
ISBN: 9780486656090
Format: Paperback
BISACs: MATHEMATICS / Geometry / Differential
Author Bio
Dirk J. Struik: A Birthday Celebration Dirk. J. Struik was born in Rotterdam in 1894 and spent most of his teaching career at MIT; he retired in 1960. His Lectures on Classical Differential Geometry, reprinted by Dover in 1988, is still a highly regarded classic, as is his Concise History of Mathematics, one of the first Dover original books in mathematics and first published by Dover in 1948, which reached its current fourth revised edition in 1987.
Professor Struik died on October 21, 2000, twenty-one days after his 106th birthday. Professor. Thomas F. Banchoff of Brown University, longtime friend and colleague of Dr. Struik and an advisor to Dover for the past 30 years, here tells the story of his friend's memorable 100th birthday celebration:
"Dirk Struik was 97 at the time I asked him what he planned to do on his hundredth birthday. He said that his family always had a party, but I then thought of a bright idea, a public celebration lecture where he would sit in the front row and hear people from his past say laudatory things about his contributions. I blurted out, 'What about a lecture on your hundredth birthday?' Without hesitation, he agreed, and that was the start of a grand event.
"Well over two hundred fifty people attended his lecture, about a third who knew him from his mathematical writings, another third acquainted with his work in history and politics, and, according to one wag, the rest wanting to see a hundred-year-old man stand up for an hour. Joan Richards gave a sterling introduction covering the many aspects of his long career. The talk itself was full of personal reflections about the characteristics of these almost legendary figures in modern mathematics and the audience was most appreciative.
"Dirk Struik went on giving lectures, in the United States and in the Netherlands for the next four years. He was a good friend to many people in his long life, and his books on so many subjects will continue to provide inspiration and encouragement to generations of students and teachers." — Tom Banchoff
Table of Contents
PREFACE BIBLIOGRAPHY CHAPTER 1. CURVES 1-1 Analytic representation 1-2 "Arc length, tangent " 1-3 Osculating plane 1-4 Curvature 1-5 Torsion 1-6 Formulas of Frenet 1-7 Contact 1-8 Natural equations 1-9 Helices 1-10 General solution of the natural equations 1-11 Evolutes and involutes 1-12 Imaginary curves 1-13 Ovals 1-14 Monge CHAPTER 2. ELEMENTARY THEORY OF SURFACES 2-1 Analytical representation 2-2 First fundamental form 2-3 "Normal, tangent plane" 2-4 Developable surfaces 2-5 Second fundamental form 2-6 Euler's theorem 2-7 Dupin's indicatrix 2-8 Some surfaces 2-9 A geometrical interpretation of asymptotic and curvature lines 2-10 Conjugate directions 2-11 Triply orthogonal systems of surfaces CHAPTER 3. THE FUNDAMENTAL EQUATIONS 3-1 Gauss 3-2 The equations of Gauss-Weingarten 3-3 The theorem of Gauss and the equations of Codazzi 3-4 Curvilinear coordinates in space 3-5 Some applications of the Gauss and the Codazzi equations 3-6 The fundamental theorem of surface theory CHAPTER 4. GEOMETRY ON A SURFACE. 4-1 Geodesic (tangential) curvature 4-2 Geodesics 4-3 Geodesic coordinates 4-4 Geodesics as extremals of a variational problem 4-5 Surfaces of constant curvature 4-6 Rotation surfaces of constant curvature 4-7 Non-Euclidean geometry 4-8 The Gauss-Bonnet theorem CHAPTER 5. SOME SPECIAL SUBJECTS 5-1 Envelopes 5-2 Conformal mapping 5-3 Isometric and geodesic mapping 5-4 Minimal surfaces 5-5 Ruled surfaces 5-6 lmaginaries in surface theory SOME PROBLEMS AND PROPOSITIONS APPENDIX: The method of Pfaffians in the theory of curves and surfaces ANSWERS TO PROBLEMS INDEX
Elementary, yet authoritative and scholarly, this book offers an excellent brief introduction to the classical theory of differential geometry. It is aimed at advanced undergraduate and graduate students who will find it not only highly readable but replete with illustrations carefully selected to help stimulate the student's visual understanding of geometry. The text features an abundance of problems, most of which are simple enough for class use, and often convey an interesting geometrical fact. A selection of more difficult problems has been included to challenge the ambitious student. Written by a noted mathematician and historian of mathematics, this volume presents the fundamental conceptions of the theory of curves and surfaces and applies them to a number of examples. Dr. Struik has enhanced the treatment with copious historical, biographical, and bibliographical references that place the theory in context and encourage the student to consult original sources and discover additional important ideas there. For this second edition, Professor Struik made some corrections and added an appendix with a sketch of the application of Cartan's method of Pfaffians to curve and surface theory. The result was to further increase the merit of this stimulating, thought-provoking text — ideal for classroom use, but also perfectly suited for self-study. In this attractive, inexpensive paperback edition, it belongs in the library of any mathematician or student of mathematics interested in differential geometry.
Reprint of the Addison-Wesley Publishing Co., Reading, Massachusetts, 1961 edition.
Price: $15.95
Pages: 256
Publisher: Dover Publications
Imprint: Dover Publications
Series: Dover Books on Mathematics
Publication Date: 1st April 1988
Trim Size: 5.5 x 8.5 in
ISBN: 9780486656090
Format: Paperback
BISACs: MATHEMATICS / Geometry / Differential
Dirk J. Struik: A Birthday Celebration Dirk. J. Struik was born in Rotterdam in 1894 and spent most of his teaching career at MIT; he retired in 1960. His Lectures on Classical Differential Geometry, reprinted by Dover in 1988, is still a highly regarded classic, as is his Concise History of Mathematics, one of the first Dover original books in mathematics and first published by Dover in 1948, which reached its current fourth revised edition in 1987.
Professor Struik died on October 21, 2000, twenty-one days after his 106th birthday. Professor. Thomas F. Banchoff of Brown University, longtime friend and colleague of Dr. Struik and an advisor to Dover for the past 30 years, here tells the story of his friend's memorable 100th birthday celebration:
"Dirk Struik was 97 at the time I asked him what he planned to do on his hundredth birthday. He said that his family always had a party, but I then thought of a bright idea, a public celebration lecture where he would sit in the front row and hear people from his past say laudatory things about his contributions. I blurted out, 'What about a lecture on your hundredth birthday?' Without hesitation, he agreed, and that was the start of a grand event.
"Well over two hundred fifty people attended his lecture, about a third who knew him from his mathematical writings, another third acquainted with his work in history and politics, and, according to one wag, the rest wanting to see a hundred-year-old man stand up for an hour. Joan Richards gave a sterling introduction covering the many aspects of his long career. The talk itself was full of personal reflections about the characteristics of these almost legendary figures in modern mathematics and the audience was most appreciative.
"Dirk Struik went on giving lectures, in the United States and in the Netherlands for the next four years. He was a good friend to many people in his long life, and his books on so many subjects will continue to provide inspiration and encouragement to generations of students and teachers." — Tom Banchoff
PREFACE BIBLIOGRAPHY CHAPTER 1. CURVES 1-1 Analytic representation 1-2 "Arc length, tangent " 1-3 Osculating plane 1-4 Curvature 1-5 Torsion 1-6 Formulas of Frenet 1-7 Contact 1-8 Natural equations 1-9 Helices 1-10 General solution of the natural equations 1-11 Evolutes and involutes 1-12 Imaginary curves 1-13 Ovals 1-14 Monge CHAPTER 2. ELEMENTARY THEORY OF SURFACES 2-1 Analytical representation 2-2 First fundamental form 2-3 "Normal, tangent plane" 2-4 Developable surfaces 2-5 Second fundamental form 2-6 Euler's theorem 2-7 Dupin's indicatrix 2-8 Some surfaces 2-9 A geometrical interpretation of asymptotic and curvature lines 2-10 Conjugate directions 2-11 Triply orthogonal systems of surfaces CHAPTER 3. THE FUNDAMENTAL EQUATIONS 3-1 Gauss 3-2 The equations of Gauss-Weingarten 3-3 The theorem of Gauss and the equations of Codazzi 3-4 Curvilinear coordinates in space 3-5 Some applications of the Gauss and the Codazzi equations 3-6 The fundamental theorem of surface theory CHAPTER 4. GEOMETRY ON A SURFACE. 4-1 Geodesic (tangential) curvature 4-2 Geodesics 4-3 Geodesic coordinates 4-4 Geodesics as extremals of a variational problem 4-5 Surfaces of constant curvature 4-6 Rotation surfaces of constant curvature 4-7 Non-Euclidean geometry 4-8 The Gauss-Bonnet theorem CHAPTER 5. SOME SPECIAL SUBJECTS 5-1 Envelopes 5-2 Conformal mapping 5-3 Isometric and geodesic mapping 5-4 Minimal surfaces 5-5 Ruled surfaces 5-6 lmaginaries in surface theory SOME PROBLEMS AND PROPOSITIONS APPENDIX: The method of Pfaffians in the theory of curves and surfaces ANSWERS TO PROBLEMS INDEX
