Foundational Number Systems for Competitive Mathematics

Number systems are the bedrock of competitive mathematics, yet understanding bases beyond decimal requires focused study. This course provides a clear, conceptual foundation in number bases (radices) and computational theory, enabling you to confidently approach complex number theory problems found in math Olympiads and entrance exams. What you'll learn: * Understand the concept of place value, digits, and radix notation in various positional number systems. * Master techniques for converting integers and fractions between any two bases, including non-standard systems. * Apply properties of base systems to efficiently solve divisibility, uniqueness, and counting problems. * Practice fundamental modular arithmetic operations, congruence relations, and their use in number theory. * Learn how different bases are used in computational contexts and their theoretical implications for algorithms. The course begins with core definitions and the structure of positional numeral systems. We then move into practical conversion methods and algebraic manipulation of numbers in arbitrary bases, followed by in-depth coverage of modular arithmetic and its application to base theory problems. This course is suitable for absolute beginners in competitive mathematics and high school students preparing for math contests. No prior specialized mathematical knowledge is required. Start building your foundation in advanced number theory today.