Logic, Computational & Advanced Mathematics
Build rigorous foundations of calculus through real numbers, limits, continuity, sequences, series, and proof-based reasoning.
Course structure
This course is published as a development map. Full lessons, practice, and assessments will be added after content review.
Complete these courses before beginning when they are available.
Learning outcomes
Module outline preview
Estimated times add up to the course’s planned learning time. Every module is in development.
Revisit formal proof and examine order and completeness properties of real numbers.
Use neighborhoods, bounds, open or closed sets, and distance-based reasoning.
Prove and apply convergence, boundedness, and subsequence concepts.
Use foundational theorems to establish existence and convergence results.
Formalize limits of functions with precise definitions and proof methods.
Analyze continuity through sequences, compositions, and intermediate-value reasoning.
Distinguish pointwise and uniform behavior on important sets.
Study rigorous consequences of differentiability and mean-value reasoning.
Define and analyze integrability using partitions and bounds.
Analyze convergence and the conditions needed for interchange-style reasoning.
Select applicable results and verify each hypothesis in proof problems.
Construct and revise cumulative proofs using core course definitions.
Course status
This course is not yet open for enrollment and does not include lessons, practice, assessments, or formal credit. You can review the outline while it is developed.
Recommended learning paths
These paths show a recommended order. Branches identify connected study that can follow once prerequisites are complete.
Learning path
Use proof-based reasoning to enter discrete, analytical, and abstract mathematical study.
End capabilityUse proof-based reasoning to enter discrete, analytical, and abstract mathematical study.