A First Course in Differential Geometry by Lyndon Woodward and John Bolton, University of Durham | Books - Cambridge University Press

Take a closer look at this interesting introductory textbook originates from a popular course given to third year students at Durham University for over twenty years, first by the late L. M. Woodward and later by John Bolton (and others).

A First Course in Differential Geometry

Differential geometry is the study of curved spaces using the techniques of calculus. It is a mainstay of undergraduate mathematics education and a cornerstone of modern geometry. It is also the language used by Einstein to express general relativity, and so is an essential tool for astronomers and theoretical physicists...

It includes many exercises to test students' understanding of the material, and ends with a supplementary chapter on minimal surfaces that could be used as an extension towards advanced courses or as a source of student projects.

• Explains some of the main classical highlights of the geometry of surfaces (Theorema Egregium, geodesics, Gauss–Bonnet Theorem) using a minimal amount of theory, while presenting some advanced material suitable for self-study at the end
• Builds up geometric intuition by providing many examples to illustrate definitions and concepts, and drawing analogies with real-life experiences
• Includes many exercises at the end of each chapter. Students can challenge their understanding of the contents through problem solving, and brief solutions are given to about a third of the exercises

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Enjoy reading this mathematic book! 

Source: Cambridge University Press