Differential geometry/topology

[ice109]

it sounds interesting, what should i know before i try to study it and what would be a good intro book to read?

note this isn't just a book request

 

[quasar987]

I say this,

The classic text is DoCarmo's 'Differential geometry of curves and surfaces'.

You should know real analysis of several variables but of one variable is very viable.

 

[piercas]

Differential geometry and topology are two branches of mathematics that study the properties of geometric objects, such as curves and surfaces, using the tools of calculus and algebra. They have applications in various fields, including physics, engineering, and computer graphics.

Before diving into the study of differential geometry and topology, it is important to have a solid foundation in calculus, linear algebra, and basic geometry. Familiarity with concepts such as derivatives, integrals, vectors, matrices, and coordinate systems is essential for understanding the more advanced topics in these fields.

A good introductory book to start with would be "Elementary Differential Geometry" by Barrett O'Neill. This book provides a clear and accessible introduction to the fundamental concepts of differential geometry, including curves, surfaces, and manifolds. It also covers basic topics in topology, such as continuity and connectedness.

Another great book to consider is "Topology from the Differentiable Viewpoint" by John Milnor. This book focuses on the interplay between topology and differential geometry, and provides a deeper understanding of the geometric structures underlying topological spaces.

Ultimately, the best way to approach studying differential geometry and topology is to have a strong mathematical foundation and to practice solving problems and working through examples. It may also be helpful to seek out a mentor or join a study group to discuss and clarify difficult concepts.