Real Analysis (University)
Upon completion, students will be able to construct formal epsilon-delta proofs, evaluate the convergence of functions and series, and apply the structural prop
Real Analysis (University). This course is designed for advanced undergraduate mathematics students seeking a rigorous, proof-based foundation in the analytic properties of the real line and metric spaces. Upon completion, students will be able to construct formal epsilon-delta proofs, evaluate the convergence of functions and series, and apply the structural properties of metric spaces to solve complex analytic problems. This course is independent preparation and is not affiliated with or endorsed by the independent university-level study (not affiliated with any university); check the official site for current test formats and dates. Every lesson includes tutor notes, a practical lab, worked exercises and a 12-question quiz you must pass at 80%, followed by a pooled final exam and free and paid practice tests.
Curriculum
One complete track with its own final exam and certificate.
10 modules mapped to the official examination areas, from foundations to final mocks.
Course Foundation and Logical Prerequisites. Practice activity: Construct formal proofs for the Archimedean Property and the Density of Rationals in R..
- 1.1 Introduction to Real Analysis and Axiomatic Systems Lab90 min
- 1.2 Set Theory: Relations, Functions, and Cardinality Lab90 min
- 1.3 Methods of Proof: Induction, Contradiction, and Contraposition Lab90 min
- 1.4 The Ordered Field Axioms and the Real Number Line Lab90 min
- 1.5 The Completeness Axiom and the Least Upper Bound Property Lab90 min