Pedagogical knowledge of Mathematics
24th - 26th March 2018
Kerala School of Mathematics





This workshop will aim to touch upon some of these topics

Foundation

    Vector Spaces, Subspaces, Basis, Linear transformation, Quotient Space, Rank-nullity theorem, Matrix representations, Inner product Spaces


Diagonalization

    Eigenvalues and Eigenvectors; Geometric and Algebraic multiplicities, characteristic equation, spectral theorem for a symmetric operator in a f.d. inner
    product space. Structure of a single linear transformation, Algebra of Projections, Equivalence of Matrices and Similarity of Matrices


Isomorphism Theorems

    Isomorphism theorems, Linear Functionals, Dual bases, Operator Adjoints, norm, orthogonal direct sums,The Riesz Representation Theorem


Algebraic Structures

    Groups, Subgroups, Ring, Ideals, Quotient Rings, Maximal Ideals, Quotient fields, PIDs, UIDs, Fields and Algebras


Module

    Modules, Submodules, Homomorphisms , Quotient Modules, The Cyclic Decomposition of a Primary Module












The student is best taught who is told the least

- Robert Lee Moore