Fundamental mathematics
    On creative mathematical problems at school
    Linear cyclic systems
    Using knowledge of planimetry for solving some systems of algebraic equations
    Solving algebraic equations rationally
    Solving problems using substitutions
    Application of the derivative for proving identities, inequalities and solving equations
    Function limits

Algebra
    Matrices and systems
    Elementary row operations
    Row echelon rows
    System of linear equations
    Gauss method for Systems of linear equations
    Gauss and Jordan elimination methods
    Dijkstra algorithm for finding the shortest paths in a graph
    Matrices, Determinants, Systems of Linear Equations

Calculus
    What is a sequence?
    Bounded Sequences
    Increasing and Decreasing Sequences
    Converging and Diverging Sequences
    Some Basic Properties of Sequences
    Calculating the Limit of a Sequence
    What is a Series
    Understanding Sigma Notation
    The Sn Notation
    Converging and Diverging Series
    Application of Series - Estimating the square root of a number
    Functions of a real Variable
    Limits and Continuity
    Properties of Continuous Functions, Asymptotes of Graphs, Derivatives
    Rules of Differentiation, Derivatives of Elementary Functions, Differential
    L'Hospital's Rule, Monotonicity, Local Extrema
    Global Extrema, Convexity and Concavity, Investigation of the Behaviour of a Function
    Indefinite Integrals, Integration by Parts, The Substitution Method
    Integration of Some Rational, Irrational and Trigonometric Functions

Difference and differential equations
    Difference equations - basic definitions and properties
    Differential Equations of the 1st order
    Linear Second Order Homogeneous Differential Equations with Constant Coefficients
    Linear Second Order Non-homogeneous Differential Equations with Constant Coefficients

Geometry
    Cartesian coordinates
    Polar coordinates
    Cylindrical coordinates
    Spherical coordinates
    Homogeneous coordinates
    Geometric transformations
    Euclidean transformations in the plane
    Euclidean transformations in the space
    Composite Euclidean transformations in the space
    Affine transformations
    Axial affinity
    Projective transformations
    Central collineation
    Matrices of transformations
    Creative space
    Monge method
    Orthogonal axonometry
    Matrices of projection methods
    Superposition of geometric figures
    Metric problems in projection methods
    Views of planar figures in projection methods
    Curves in the extended Euclidean space
    Curves in plane
    Curves in space
    Approximation and interpolation curves
    Surfaces in the extended Euclidean space
    Translation surfaces - theory
    Homothetical surfaces - theory
    Prismatic and pyramidal surfaces - views
    Cylindrical and conical surfaces - views
    Intersection points of lines and surfaces - views
    Developable surfaces - theory
    Surfaces of revolution - theory
    Special types of surfaces of revolution - theory
    Quadratic surfaces of revolution - theory
    Helical surfaces - theory
    Envelope surfaces - theory
    Intersections of surfaces - theory
    Intersections of elementary surfaces - views
    Notes on Geometry of Elementary Solid Cells
    In-homogeneous Bezier Solid Cells
    One-Parametric Deformations of Solids
    Free-Form Deformations of Solid Cells

Multivariable calculus
    Limit and Continuity
    Vector algebra
    Functions of Two and More Variables, Domains of Definition, Graphs, Limits
    Continuity, Partial Derivatives of Functions of Two Variables, Total Dierentials, Tangent Planes
    Local, Constrained and Global Extrema for Functions of Two Variables
    Double Integrals, Basic Properties, Fubini´s Theorems
    Double Integrals in Polar Coordinates
    Triple Integrals, Basic Properties, Fubini´s Theorems
    Triple Integrals in Cylindrical and Spherical Coordinates

Numerical analysis
    Basic notions: numerical methods, modeling, types of errors, correctness, stability
    Introduction to numerical solving of algebraic equations
    Function approximation (by Lagrange's interpolation polynomial)
    Least square method
    Spline interpolation
    Solving systems of linear equations - exact methods. Gauss's method (Gauss's elimination)
    Gauss-Jordan method
    Calculating determinants
    Matrix inversion
    Preparation of system of linear algebraic equations with positive defined matrix in order to apply the iterative approximation method
    Bisection method for solving equations with a single unknown
    Power method for solving the partial eigenvalue problem
    Jacobi's method (method of rotation)
    Numerical differentiation
    Numerical integration (Newton-Cotes quadrature formulas)
    Example of coefficient instability of the Gauss elimination method for solving linear system of algebraic equations
    Gauss-Zeidel method
    Method of simple iteration for solving systems of linear algebraic equations (Jacobi method)
    Double sweep method for tri-diagonal system of linear equations (Thompson's method)
    Method of consecutive iterations for solving nonlinear algebraic equations
    Introduction to the numerical integration
    Euler method for numerical solving of ordinary differential equations and systems
    Modified Euler method
    Euler-Cauchy method
    Euler's Method for ordinary differential equations using Mathematica
    Modified Euler's method for ordinary difference
    Euler's-Cauchy Method using Mathematica
    Euler's Method for systems of ordinary differential equations using Mathematica
    Mesh method for solving boundary value problem of the mixed type using Mathematica
    Two-order Runge-Kutta Method using Mathematica
    Two-order Runge-Kutta Method for systems of ordinary differential equations using Mathematica
    Fourth-order Runge-Kutta Method using Mathematica
    Fourth-order Runge-Kutta Method using Mathematica
    Optimising the Parameters of Polarised Electromagnetic Construction Using Mathematica
    Examples on Variational Methods for Solving Boundary Problems for Ordinary Differential Equations (ODE) of the Second Order (Galerkin and Ritz methods)
    Some more about the systems of linear equations
    The square root method
    Solving systems of linear equations - approximate methods
    Introduction to finite difference method for solving partial differential equations
    Finite difference method for solving PDE of parabolic type
    Examples for finite difference method for solving PDE of parabolic type

Optimisation
    Basic concepts in mathematical optimization
    Elements of dynamical optimization - basic notions
    Graphs, definitions, representations
    Network planning (problem of finding the shortest and longest path in a network)
    One-dimensional resource distribution problem. Bellman's functional equations
    Bellman's optimality principle
    Bellman-Ford algorithm
    Dijkstra algorithm for finding the shortest paths in a graph

Probability and statistics
    Rlo

History of mathematics
    How the Greeks might have discovered and approximate irrational numbers
    Development of the School of Mathematics in Cluj-Kolozsvár-Klausenburg (1872-1919)