Mathematics Refresher


This course reviews the mathematical foundations necessary to absorb the body of knowledge of the ARPM Certificate
Downloadable materials
Univariate calculus
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Derivative and chain rule (instantaneous forward rate)
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Taylor polynomial (Taylor approximations)
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Fundamental theorem of calculus (transformation of a random variable)
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Integration by parts formula (the P&L of trading strategy)
Multivariate calculus
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Partial derivative, directional derivative, and gradient (Greeks; derivatives)
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Iterated integral (marginalization; e.g. uniform bivariate)
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Chain rule for multivariate function (Euler decomposition)
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Convexity and Hessian matrix (convexity analysis)
Downloadable materials
Calculus
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Change of variables and Jacobian (pdf of an invertible function; pdf of a copula)
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Relative extremum (mode)
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Unconstrained optimization problem (mode)
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Second derivative test (mean-variance trade-off)
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Constrained optimization problem (linear programming; convex programming)
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The method of Lagrange multiplier (views processing)
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Functional (e.g. mean; variance; median; mode)
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Euler-Lagrange equation (P&L optimization: Almgren-Chriss model)
Downloadable materials
Linear algebra
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Row operations and rank of a matrix
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Matrix manipulations (matrix algebra; matrix calculus)
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Linear independence, spanning, and basis (market completeness)
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Inverse of a matrix (pseudo-inverse)
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Trace and determinant of a square matrix (properties of trace; )
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Diagonalization of symmetric matrices (spectral theorem example)
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The Gram-Schmidt procedure (Gram-Schmidt)
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