This textbook covers topics of undergraduate mathematics in abstract algebra, geometry, topology and analysis with the purpose of connecting the underpinning key ideas. Part 2 discusses the number systems of common practice, while the backgrounds needed to solve equations and inequalities are developed in Part 3.

This textbook covers topics of undergraduate mathematics in abstract algebra, geometry, topology and analysis with the purpose of connecting the underpinning key ideas. It guides STEM students towards developing knowledge and skills to enrich their scientific education. In doing so it avoids the common mechanical approach to problem-solving based on the repetitive application of dry formulas. The presentation preserves the mathematical rigour throughout and still stays accessible to undergraduates. The didactical focus is threaded through the assortment of subjects and reflects in the...