This is the first part of a two-course introduction to mathematical explorations that lays the foundation for all the mathematics courses that follow. These two courses are taught using Inquiry-Based Learning (IBL): there are no lectures, there is no ​“covering” material in a textbook; instead students work together solving problems from carefully structured worksheets, and discuss, discover and raise questions.

In school, students do not get an opportunity to ​‘do mathematics’. Further, there is a sharp discontinuity between school mathematics and university mathematics in content. Students learn about notions like isometries, rigid transformations, and linear transformations, through algebraic, geometric, and computational explorations.

This course attempts to fill this lacuna by both allowing students to experience the process of doing and creating mathematics. It is structured so that students explore new ideas and themes, make guesses, come up with new structures and terms, and then prove their results. The topics are chosen from concrete linear algebra, providing continuity between school mathematics and university mathematics, by providing an entry to abstract spaces after building a foundation on concrete structures. The course activities involve significant exercises in reading and writing mathematics in a graded fashion. Students learn about notions like bases, dimension, linear transformations and orthogonality, through algebraic, geometric, and computational explorations.