Elementary set theory and solution sets of systems of linear equations. An introduction to proofs and the axiomatic methods through a study of the vector space axioms. Linear analytic geometry. Linear ...

Vector spaces, linear transformation, matrix representation, inner product spaces, isometries, least squares, generalised inverse, eigen theory, quadratic forms, norms, numerical methods. The fourth ...

Abstract Using the axiom of choice, we prove a generalized converse of the well-known fact that if X is a finite-dimensional vector space, then any linear functional on X is continuous with respect to ...

Properties of the real numbers, infimum and supremum of sets. Numerical sequences and series. Limits of functions, continuous functions, intermediate value theorem, uniform continuity. Differentiation ...