Functions of One Real Variable for Competitive Mathematics Exams

Succeeding in competitive mathematics examinations requires a rock-solid grasp of real analysis and calculus. This text-based course breaks down the core theories of single-variable functions into clear, digestible explanations, helping you build the analytical skills needed to solve challenging exam problems. You will transition from understanding abstract definitions to confidently proving and applying key mathematical theorems. What you'll learn: Understand foundational concepts of real numbers, bounds, and sequence convergence; Analyze limits, continuity, and uniform continuity of single-variable functions; Apply differentiability theorems, including Mean Value Theorems and Taylor's formula; Evaluate Riemann integrability and calculate indefinite and definite integrals; Practice solving exam-style problems using rigorous logical reasoning. This course begins with essential definitions and foundational set theory before guiding you through limits, continuity, differentiation, and integration. It is designed for students and math enthusiasts preparing for competitive exams, requiring only a basic high school algebra background. Begin your journey toward mathematical mastery today.