What You'll Learn
Order Axioms & Fields
Understand the properties of ordered fields, Archimedean properties, and identify why certain sets (like the set of rational numbers) are not complete ordered fields.
Neighborhoods & Limit Points
Grasp the formal definitions of neighborhoods and limit points, learning how to rapidly identify limit points for complex sequences and sets.
Open & Closed Sets
Analyze the topology of the real line to determine if sets are open, closed, both, or neither, using arbitrary unions and finite intersections.
Sequence Convergence
Master the concepts of monotonic and bounded sequences, distinguishing between limit points and actual limits of sequences.
Advanced Limit Theorems
Apply Cauchy’s limit theorems and the Sandwich theorem to quickly evaluate complex sequence limits.
Series Convergence Tests
Bypass tedious calculations using the Root test, Condensation test, and Comparison test to determine series convergence.
Alternating Series & Uniform Convergence
Evaluate alternating series using Leibnitz’s test and determine uniform convergence for sequences and series of functions utilizing the M-test.
Meet Your Instructor
Mr Narayan
15+ Years teaching Mathematics