Teaching Einstein s general relativity at introductory level
poses problems because students cannot begin to appreciate the
basics of the theory unless they learn a sufficient amount of
Riemannian geometry. Most elementary books take the easy course of
telling the students a few working rules stripping the mathematical
details to a minimum while the advanced books take the mathematical
background for granted. Students eager to study Einstein s theory
at a deeper level are forced to learn the mathematical background
on their own and they feel lost because pure mathematical texts on
geometry are too abstract and formal.
The present book solves this pedagogical problem in a unique way
by dividing the book into three parts. Essential concepts of
Riemannian geometry are introduced in Part I (four chapters)
through Gauss work on curvature of surfaces using only ordinary
calculus. A first acquaintance with Einstein s theory can then be
made. Only after this first brush with both physics and mathematics
of relativity, a proper, detailed mathematical background is
developed in the next six chapters in Part II. The third part then
recaptures all the basic concepts of general relativity and leaves
the student with a sound preparation for learning advanced
topics.
My aim has been that after learning from this book a student
should not feel discouraged when she opens advanced texts on
general relativity for further reading."
General
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