This exploration of a selection of fundamental topics and general
purpose tools provides a roadmap to undergraduate students who
yearn for a deeper dive into many of the concepts and ideas they
have been encountering in their classes whether their motivation is
pure curiosity or preparation for graduate studies. The topics
intersect a wide range of areas encompassing both pure and applied
mathematics. The emphasis and style of the book are motivated by
the goal of developing self-reliance and independent mathematical
thought. Mathematics requires both intuition and common sense as
well as rigorous, formal argumentation. This book attempts to
showcase both, simultaneously encouraging readers to develop their
own insights and understanding and the adoption of proof writing
skills. The most satisfying proofs/arguments are fully rigorous and
completely intuitive at the same time.
General
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