Abstract:
1.Bicomplex Hamilton numbers and their applications: the Gibbs and Heaviside vector calculus. 2. Hypercomplex numbers of Grassmann and Clifford and their applications: geometric theories of matrix determinants and the inverse matrix; oblique-angled vector bases: vectors, polyvectors, and their co-vectors; tensor calculus, covariance and contravariance. 3. Algebraic theory of spatial rotations: groups and Lie algebras. 4. Spin matrices of Pauli and Dirac. Élie Cartan' theory of spinors. The geometric algebra of D. Hestenes. Symplectic geometry of phase space. 5. Quantum statistics of fermions: Grassmann variables, superanalysis by F. Berezin.
