"Undergraduate Texts in Mathematics" is a series of textbooks aimed at third- and fourth-year undergraduate mathematics students in North American universities. These texts aim to provide students and teachers with new perspectives and novel approaches, with motivation that guides the reader to an appreciation of the interrelations among different aspects of the subject. The books include examples that illustrate key concepts and exercises that strengthen understanding. "Kristopher Tapp's Differential Geometry of Curves and Surfaces" is a textbook that introduces the differential geometry of curves and surfaces. It is written for students who have completed a minimal one-semester course in multivariable calculus, linear algebra, and real analysis. The book includes over 300 color illustrations, green-boxed definitions, and purple-boxed theorems to help visually organize the mathematical content. It covers topics such as curves, surfaces, curvature, geodesics, and the Gauss-Bonnet theorem. The book also includes applications to physics and engineering, such as the study of conformal and equiareal functions in cartography, and the use of Green's theorem in drafting tools. The book is written to serve a variety of readers, from those seeking an elementary text to those bound for graduate school in mathematics or physics. It includes clear and colorful explanations of essential concepts, culminating in the famous Gauss-Bonnet theorem. The book is designed to make abstract ideas more understandable and engaging, with applications, metaphors, and visualizations that motivate and clarify the rigorous mathematical content. The book is structured into six chapters, each covering a different topic in differential geometry. It includes an appendix on the topology of subsets of R^n, and a section on recommended excursions. The book is accompanied by image credits and an index. The book is written in a way that emphasizes geometric concepts, with local coordinate formulas placed near the end of each chapter. These formulas empower the reader to compute various curvature measurements in particular examples, but they do not define these measurements."Undergraduate Texts in Mathematics" is a series of textbooks aimed at third- and fourth-year undergraduate mathematics students in North American universities. These texts aim to provide students and teachers with new perspectives and novel approaches, with motivation that guides the reader to an appreciation of the interrelations among different aspects of the subject. The books include examples that illustrate key concepts and exercises that strengthen understanding. "Kristopher Tapp's Differential Geometry of Curves and Surfaces" is a textbook that introduces the differential geometry of curves and surfaces. It is written for students who have completed a minimal one-semester course in multivariable calculus, linear algebra, and real analysis. The book includes over 300 color illustrations, green-boxed definitions, and purple-boxed theorems to help visually organize the mathematical content. It covers topics such as curves, surfaces, curvature, geodesics, and the Gauss-Bonnet theorem. The book also includes applications to physics and engineering, such as the study of conformal and equiareal functions in cartography, and the use of Green's theorem in drafting tools. The book is written to serve a variety of readers, from those seeking an elementary text to those bound for graduate school in mathematics or physics. It includes clear and colorful explanations of essential concepts, culminating in the famous Gauss-Bonnet theorem. The book is designed to make abstract ideas more understandable and engaging, with applications, metaphors, and visualizations that motivate and clarify the rigorous mathematical content. The book is structured into six chapters, each covering a different topic in differential geometry. It includes an appendix on the topology of subsets of R^n, and a section on recommended excursions. The book is accompanied by image credits and an index. The book is written in a way that emphasizes geometric concepts, with local coordinate formulas placed near the end of each chapter. These formulas empower the reader to compute various curvature measurements in particular examples, but they do not define these measurements.