Tarski's Algorithm and Decidable Real Algebra

Understanding whether mathematical statements can be systematically proven or disproven is a cornerstone of modern logic and computer science. This course provides a clear, accessible guide to Tarski's quantifier elimination algorithm and the decidability of the first-order theory of real numbers. You will explore how geometric and algebraic assertions can be formalized and systematically decided without relying on heuristic proofs. By breaking down foundational logical concepts into clear explanations, this text-based guide bridges the gap between formal logic and automated theorem proving. What you'll learn: - Understand the fundamentals of first-order logic, signatures, and formulas over the real numbers - Master the principles of quantifier elimination and how it establishes decidability - Apply algebraic techniques to translate geometric problems into polynomial systems - Explore modern cylindrical algebraic decomposition and automated decision procedures - Analyze computational complexity and boundaries between decidable and undecidable theories The course begins with foundational terminology, real closed fields, and formal syntax before walking you through the mechanics of quantifier elimination algorithms and their applications to automated geometry theorem proving. This course is designed for curious beginners, mathematics students, and computer science enthusiasts with an interest in formal logic. No advanced background in model theory is required. Start reading today to discover how algebraic logic enables automated mathematical reasoning.