MTH 101: Elementary Mathematics I - Algebra and Trigonometry

This course establishes the foundational language of mathematics. It covers the core principles of set theory and applies them directly to the structure of the real number system. Mastery of this material is non-negotiable for further study in any quantitative field. The principles of set theory are the structural basis for formal logic, database theory, and computer programming. Understanding number systems as structured sets is the prerequisite for all higher mathematics, including algebra and calculus. This course provides the essential logical framework for these disciplines. By the end of this course, you will be able to use formal notation to define sets and their relationships, perform standard set operations such as union and intersection, use Venn diagrams to analyse set identities, and classify numbers within the real number system. This course is designed for first-year university students of mathematics, computer science, and engineering. It is also required foundational material for any professional in data analysis, software development, or other technical fields requiring rigorous logical thought.

This course provides a complete treatise of mathematical progressions. It formally defines sequences and series, with a specific focus on Arithmetic Progressions (APs) and Geometric Progressions (GPs). This material is the foundation for analysing patterns of growth, decay, and summation. These principles are foundational to finance, computer science, and physics. The course provides the tools to calculate compound interest, analyse algorithm complexity, and model physical phenomena. Mastery is required for calculus and financial mathematics. By the end of this course, you will be able to differentiate between sequences and series, apply all standard formulas for the nth term and sum of Arithmetic and Geometric Progressions, calculate the sum to infinity for a convergent GP, and solve problems involving arithmetic and geometric means. This course is designed for first-year university students in mathematics, economics, finance, and engineering. It is a mandatory prerequisite for the study of calculus and provides an essential foundation for financial modelling and algorithm analysis.

Quadratic equations are the bedrock of advanced algebra and the starting point for mastering non-linear mathematical models. This course provides a rigorous analysis of these equations, covering standard forms, solving methods like factorisation and completing the square, and the critical use of the discriminant to determine root nature. You will study turning points for optimisation, solve complex quadratic inequalities, and master the relationship between roots and coefficients to build equations from scratch. Mastering these models is essential for careers in engineering, physics, and finance where trajectories and profit levels must be calculated precisely. You will use these principles to describe projectile motion, design parabolic structures, and identify boundary limits in economic models. This is the mathematics of optimisation, providing the necessary tools to find the highest or lowest possible values in any system governed by second-degree polynomials. By the end of this course, you will solve any quadratic equation using multiple methods; use the discriminant to identify real, identical, or imaginary roots; and determine the location and value of turning points. You will master solving quadratic inequalities; identifying valid ranges for rational expressions; and using symmetric identities to evaluate root properties without solving the original equation. These skills form the essential foundation for calculus and mechanics. This course is built for first-year university students in mathematics, physics, engineering, and economics who need a solid algebraic foundation. It also serves secondary school leavers preparing for advanced entrance exams or technical professionals looking to refresh their analytical skills. Even those in data science or basic programming will benefit from the logical structuring and problem-solving techniques required to handle non-linear variables.

This course covers two critical topics in discrete mathematics: the principle of mathematical induction as a formal proof technique, and the binomial theorem for expanding powers of binomials. The course structure directly links the proof method to one of its most important applications in algebra. These topics are the foundation of algorithm verification, probability theory, and statistics. Mathematical induction is a core technique for proving algorithm correctness and establishing formulas for series. The binomial theorem is a powerful tool used directly in statistics for the binomial distribution and in financial mathematics. By the end of this course, you will be able to apply the principle of mathematical induction to prove mathematical statements, solve complex counting problems using permutations and combinations, and use the binomial theorem to expand any binomial expression for a positive integer exponent. This course is for first-year university students and is a fundamental prerequisite for computer science, statistics, and probability theory. It provides essential skills for competitive mathematics and advanced algebraic studies.

This course provides a complete introduction to the complex number system, from the definition of the imaginary unit to the Argand diagram and polar form. It then covers De Moivre???s theorem and its application to finding the nth roots of unity. This material extends algebra into two dimensions and provides essential tools for advanced mathematics. Complex numbers are an essential tool in engineering and the physical sciences. They are used extensively in electrical engineering to analyse AC circuits, in signal processing for Fourier transforms, in quantum mechanics to describe wave functions, and in fluid dynamics. This course provides the practical foundation for these applications. By the end of this course, you will be able to perform all arithmetic operations on complex numbers, represent them on an Argand diagram, convert between Cartesian and polar forms, apply De Moivre???s theorem to find powers of complex numbers, and calculate the nth roots of unity. This course is designed for first-year university students of mathematics, physics, and engineering. It is a critical prerequisite for the study of electrical circuits, signal processing, quantum mechanics, and any field that uses wave analysis or advanced vector mathematics.

This course provides a complete guide to trigonometry, from the principles of circular measure to functions of any angle. It covers the unit circle definitions and culminates in a full treatment of the addition and factor formulae. This is the mathematical language of cycles, waves, and angles. A command of trigonometry is essential for any field that models periodic or geometric systems. It is used extensively in physics to analyse waves and oscillations, in engineering for structural analysis and signal processing, and in computer graphics for rotations and 3D modelling. By the end of this course, you will be able to convert between degrees and radians, define the six trigonometric functions for any angle using the unit circle, and apply the addition and factor formulae to manipulate and simplify trigonometric expressions and solve equations. This course is a mandatory prerequisite for any student of mathematics, physics, or engineering. It provides the necessary foundation for the study of calculus, complex numbers, and vector analysis.