Math calculus:
Essential knowledge: real numbers, complex numbers, polynomials, functions, methods for finding roots of functions, inverse functions, limits, derivatives, continuity, integrals, definite integrals, Taylor polynomials, extremes of functions (minimum, maximum)
Recommended knowledge: multivariable calculus - vector functions, partial derivatives, differential equations, integrals, multiple (double, tripple) integrals
Calculus 1 | Professor Leonard - YouTube, Calculus 2 | Professor Leonard - YouTube, Calculus 3 | Professor Leonard - YouTube
Multivariable Calculus | Professor Leonard - YouTube
or
Calculus I (Differential Calculus) - YouTube, Calculus II (Integral Calculus) - YouTube, Calculus III (Multivariable Calculus) - YouTube
or
Calculus 1 | Khan Academy, Calculus 2 | Khan Academy, Multivariable Calculus | Khan Academy
Linear algebra:
Essential knowledge: points, vectors, vector spaces, matrices, determinants, linear transformations, linear maps, linear combinations, linear dependences and independences, matrix transformations (scalar product, multiplication, inverse, transpose), eigenvalues and eigenvectors, dot product, cross product, angle of two vectors, length of vectors, orthogonal vectors, linear systems, solving linear systems
Recommended knowledge: none
Linear Algebra: Geometry and Algebra of Vectors - YouTube
or
Linear Algebra | Khan Academy
or
Introduction to Linear Algebra, Sixth Edition (2023)
Geometry:
Essential knowledge: cartesian coordinates, spherical coordinates, 2D & 3D Euclidean space, points, lines (linear equation, parametric equations), lines intersection, distance of the point from the line, planes (linear equation, parametric equations), planes intersection, line intersection with plane, distance of the point from the plane, parametric functions
Recommended knowledge: normals and tangents to curves and surfaces, curvature, spline curves, spline surfaces, Bézier splines
Geometry | Math Fortress - YouTube
and
Mathematics of animation curves | Khan Academy
Probability and statistics:
Essential knowledge: elementary probability
Recommended knowledge: random variable, probability, distribution function, cumulative distribution function, expected value, variance
Statistics and Probability | Khan Academy
Workbooks for all subjects:
- Online Helping Engineers Learn Mathematics (HELM) – https://bathmash.github.io/HELM/
- HELM PDF chapters – https://www.lboro.ac.uk/departments/mlsc/student-resources/helm-workbooks/
Recommended topics in mathematics, according to the chapters in the HELM workbooks:
03.4 Solving Simultaneous Linear Equations
03.5 Solving Inequalities
06.1 The Exponential Function
06.3 Logarithms
06.4 The Logarithmic Function
07.1 Introduction to Matrices
07.2 Matrix Multiplication
07.3 Determinants
07.4 The Inverse of a Matrix
08.1 Solution by Cramer’s Rule
08.2 Solution by Inverse Matrix Method
08.3 Solution by Gauss Elimination
09.1 Basic Concepts of Vectors
09.2 Cartesian Components of Vectors
09.3 The Scalar Product
09.4 The Vector Product
11.1 Introducing Differentiation
11.2 Using a Table of Derivatives
11.3 Higher Derivatives
11.4 Differentiating Products and Quotients
11.5 The Chain Rule
12.1 Tangents and Normals
12.2 Maxima and Minima
13.1 Basic Concepts of Integration
13.2 Definite Integrals
13.4 Integration by Parts
13.5 Integration by Substitution and Using Partial Fractions
22.1 Basic concepts of Eigenvalues and Eigenvectors
35.1 Sets
35.2 Elementary Probability
The entrance test will cover the above topics.