Transactions of the American Mathematical Society, Vol. 176 (Feb., 1973), pp. 305-318 (14 pages) The theory of monotone matrix functions has been developed by K. Loewner; he first gives some necessary ...

This paper presents a conceptual analysis for students' images of graphs and their extension to graphs of two-variable functions. We use the conceptual analysis, based on quantitative and ...

Functions of two variables can be visualized in many ways: heat maps in 2D, contour curves in 2D, wireframes in 3D, surfaces in 3D. We begin by defining a function of two variables, building an array ...

Group, Subgroup, cyclic group and their properties. Order of Elements of group Coset decomposition, Lagrange’s theorem. Normal subgroup, Quotient Group, Homomorphism, Isomorphism, Automorphism of ...