This is the second part of a two-course introduction to mathematical explorations, that lays the foundation for all the mathematics courses that follow, and is also taught through Inquiry-Based Learning (IBL).

The course provides the student the required transition from an intuitive understanding of the infinite to its axiomatic treatment. The student gets to see the role of formalism in providing a safe scaffolding to avoid erroneous inferences. This course provides an introduction to logic and the need for formalisation in logic, as well as practice in reading and writing formal proofs. Ordered sets and sequences are used to provide a rich landscape as content for assertions where students see the need for proof, and try their hand at providing rigorous arguments. Sequences on discrete as well as continuous domains provide examples for such arguments, and set up a foundation for algebra and analysis.