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3 Improved clarity.

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Once students have been exposed to linear algebra and vector calculus, build calculus on manifolds along using many examples; i.e. go from real $\mathbb{R}$-abstract multilinear till to the de Rham complex, illustrating in $\mathbb{R}^3$. All that easen differential geometry, differential topology riemannian Riemannian geometry, ect etc.

2 fix latex

once exposed to linear algebra and vector calculus, build calculus on manifolds along many examples i.e. go from real $mathbb{R}$-abstract \mathbb{R}$-abstract multilinear till the de Rham complex illustrating in$mathbb{R}^3$. \mathbb{R}^3$. All that easen differential geometry, differential topology riemannian geometry, ect

once exposed to linear algebra and vector calculus, build calculus on manifolds along many examples i.e. go from real $mathbb{R}$-abstract multilinear till the de Rham complex illustrating in $mathbb{R}^3$. All that easen differential geometry, differential topology riemannian geometry, ect