Pure Mathematics · 2021

CSS 2021 Pure Mathematics Paper

5 questions from this paper.

  1. Q1
    State and prove Lagrange's Theorem for finite groups.
    Past paper Group Theory 20 marks
  2. Q2
    Find the inverse of a 3x3 matrix using the Adjoint method and verify that A*A^-1 = I.
    Past paper Linear Algebra 20 marks
  3. Q3
    Define a Vector Space. Show that the set of all polynomials of degree at most n forms a vector space over the field of real numbers.
    Past paper Vector Spaces 20 marks
  4. Q4
    State and prove the Cauchy-Riemann equations in polar coordinates.
    Past paper Complex Analysis 20 marks
  5. Q5
    Determine the radius of convergence of the power series sum((n!)^2 / (2n)!) * x^n.
    Past paper Calculus 20 marks

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