Problem sheet

Summation and Product Notation

summation · sigma-notation · product-notation

Exponentials and Logarithms

exponential · logarithm · log-likelihood

The Sigmoid Function

sigmoid · logistic-function · logit

Dot Product

vectors · dot-product · linear-algebra

Vector Norm and Unit Vector

vectors · norms · normalisation

Matrix Multiplication

matrices · matrix-multiplication · shapes

Binomial Coefficient

combinatorics · counting · integers

Solve a 2x2 System (Cramer's Rule)

linear-systems · determinant · cramers-rule

Inverse of a 2x2 Matrix

matrix-inverse · determinant · identity

Numerical Derivative (Central Difference)

calculus · derivatives · finite-differences

Derivative Rules and the Chain Rule

derivatives · chain-rule · product-rule

Trapezoidal Integration

calculus · integration · numerical-methods

Gradient Descent in 1D

optimisation · gradient-descent · learning-rate

Numerical Gradient of f(x1..xn)

multivariable-calculus · gradient · partial-derivatives

Taylor Series for exp(x)

series · approximation · taylor

Dominant Eigenvalue by Power Iteration

eigenvalues · linear-algebra · iterative-methods

Gradient-Descent Visualiser

Project idea · optimisation · visualisation · calculus