What You Will Learn

This course covers advanced and computational mathematics in a structured way. You will explore a variety of core topics over 12 weeks.

• Mathematical Thinking and Problem Solving: You will learn logical reasoning, identify mathematical patterns, develop number sense, and apply strategies for solving complex problems. Activities include puzzle solving and mathematical games.
• Algebra: The course delves into polynomials, factorization, functions, graphs, sequences, and series. You will practice applications of algebra through graph visualization using computational tools.
• Geometry: You will study coordinate geometry, transformations, and geometric reasoning. Introduction to mathematical modeling will be included, with dynamic geometry software demonstrations.
• Trigonometry: You will explore trigonometric identities and graphs, and learn about real-world applications. There will be a focus on techniques for solving trigonometric problems.
• Calculus: The essentials of calculus will be covered, including limits, continuity, and derivatives. You will learn about applications of differentiation and optimization concepts, practicing visual understanding of derivatives.
• Integral Calculus: You will work with definite and indefinite integrals, learning how to find areas under curves and their applications in science and engineering.
• Linear Algebra: The course includes matrices, determinants, and systems of equations, with a focus on applications in technology and artificial intelligence. You will perform matrix computations using software tools.
• Probability and Statistics: You will learn key probability concepts, data analysis, and statistical reasoning, focusing on decision-making under uncertainty.
• Numerical and Computational Mathematics: This section covers numerical methods, error analysis, and approximation techniques. You will engage in hands-on computational exercises.
• Competitive Examination Preparation: You will practice quantitative aptitude, speed mathematics, and logical reasoning to prepare for competitive exams.
• Emerging Areas in Mathematics: You will explore topics like fractals, chaos, cryptography, and the role of mathematics in artificial intelligence.
• Research and Innovation: The final week covers how mathematics drives innovation, research opportunities, and career pathways, culminating in a capstone project analyzing a real-world mathematical problem.

This course develops from basic concepts to advanced applications, providing a comprehensive understanding of advanced mathematics.