1.Preface -- 2.Numbers and mathematical symbols: natural, rational, irrational and complex numbers/complex plane: formula reading, often used symbols in mathematical formulas -- 3.Equations: equalities and inequalities: expansions, series: fractional equations: equation solving techniques: various rules (such as Cramer's rule) to solve equations: introduction to basic functions (e.g. square, square root) -- 4.Trigonometry: trigonometric ratios, angles: trigonometric functions (sin, cos, tan) and their complex definitions: epicycles: Fourier series and transform -- 5.Vectors: geometric interpretation of vectors: vector addition/subtraction, scalar multiplication: projections: inner product (including related aspects such as correlation, independence and orthogonality) -- 6.Matrices: basic matrix manipulations e.g. multiplication and inversion with examples such as the Jacobian, affine transformation, and rotation: Principal Component analysis in matrix notation -- 7.Differentiation: limits and infinity: continuity of a function: the differential: basic differentiation rules: partial differential equations: introduction to dynamic systems -- 8.Integration: explanation in terms of antiderivatives and area under the curve: basic integration rules: convolution.