spekcular is correct. One could draw the following graph very roughly capturing how these concepts developed:
Grassman’s exterior algebra -> Differential forms
Cartan’s Exterior Derivatives -> Differential forms
Quaternions -> Clifford Algebra
exterior algebra -> Clifford Algebra -> geometric algebra
Differential forms are a particular kind of tensor and tensors can be defined in terms of multilinear maps. As spekcular says, the standard curriculum covers differential forms, tensors and vectors. This entails becoming familiar with multivectors, the wedge product and multilinear algebra, making geometric algebra a relatively small delta to pick up.
On the other hand, the standard course will also prepare you for mathematical topics like lie derivatives, differential geometry and de Rham cohomology.
Other than physics, the standard approach equips you with the mathematical machinery underlying many topics in machine learning and statistics like Hamiltonian monte carlo, automatic differentiation, information geometry and geometric deep learning.
The central advantage of geometric algebra over the standard approach isn't that it's better or more general, it's that pedagogical material for it is generally leagues and magnitudes better than those for the standard course.
Grassman’s exterior algebra -> Differential forms
Cartan’s Exterior Derivatives -> Differential forms
Quaternions -> Clifford Algebra
exterior algebra -> Clifford Algebra -> geometric algebra
Differential forms are a particular kind of tensor and tensors can be defined in terms of multilinear maps. As spekcular says, the standard curriculum covers differential forms, tensors and vectors. This entails becoming familiar with multivectors, the wedge product and multilinear algebra, making geometric algebra a relatively small delta to pick up.
On the other hand, the standard course will also prepare you for mathematical topics like lie derivatives, differential geometry and de Rham cohomology.
Other than physics, the standard approach equips you with the mathematical machinery underlying many topics in machine learning and statistics like Hamiltonian monte carlo, automatic differentiation, information geometry and geometric deep learning.
The central advantage of geometric algebra over the standard approach isn't that it's better or more general, it's that pedagogical material for it is generally leagues and magnitudes better than those for the standard course.