Probability and Statistics

Introduction to Probability50Conditional Probability and Independence9Discrete Probability Distributions52Continuous Probability Distributions51Descriptive Statistics53Inferential Statistics50Regression and Correlation34Non-Parametric Tests31

Research Methods in Mathematics

Types of Research Designs51Sampling Methods59Data Collection Methods50Ethical Considerations54Descriptive Statistics50Inferential Statistics53Data Visualization50Software for Data Analysis56Writing Research Reports53Presenting Research Findings50Disseminating Research52

Calculus and Analysis

Definition of a Limit56Properties of Limits51Continuity32Definition of a Derivative57Applications of Derivatives55Definition of an Integral52Applications of Integrals10

Mathematical Modelling

Gradient and Intercept41Equation of a Line10Parallel and Perpendicular Lines53Parabolas51Quadratic Equations51Applications of Quadratic Functions23Trigonometric Ratios23Trigonometric Identities57Applications of Trigonometry25Laws of Exponents32Logarithms20Exponential and Logarithmic Functions31Limits and Continuity21Differentiation44Applications of Differentiation18

Algebraic Structures

Definition of a group51Properties of groups59Examples of groups42Definition of a ring59Properties of rings48Examples of rings56Definition of a field34Properties of fields51Examples of fields52

Optimization and Control Theory

Basic Concepts of Optimization53Introduction to Control Theory51Linear Programming59Integer Linear Programming43Unconstrained Nonlinear Optimization57Constrained Nonlinear Optimization50Time-Domain Analysis57Frequency-Domain Analysis56Classical Control Design53Modern Control Design58

Number Theory and Cryptography

Prime Numbers56Integer Factorization53Modular Arithmetic43Number Theory in Cryptography50Symmetric Encryption57Asymmetric Encryption56Hash Functions56Digital Signatures54

Numerical Analysis

Introduction to Numerical Integration55Newton-Cotes Formulas36Gaussian Quadrature46Introduction to Numerical Differentiation57Finite Difference Methods56Numerical Differentiation Using Interpolation47Introduction to Numerical Solution of ODEs53Single-Step Methods56Multi-Step Methods43Introduction to Numerical Solution of PDEs59Finite Difference Methods for Elliptic PDEs42Finite Difference Methods for Parabolic PDEs52Finite Difference Methods for Hyperbolic PDEs41

Geometry and Topology

Lines and Angles54Triangles46Quadrilaterals52Circles44Transformations42Vectors53Coordinate Geometry35Trigonometry55

Partial Differential Equations

Introduction to First-Order PDEs39Method of Characteristics57Applications of First-Order PDEs46Classification of Second-Order PDEs53Separation of Variables55Fourier Series and PDEs51Finite Difference Methods54Finite Element Methods30Applications of Numerical Methods52