Straight Lines and Curves by Vasiliyev
N. B. Vasilyev was the chief architect of Mathematical Olympiads in Soviet Union. This gem from erstwhile Soviet Union’s publication, explores loci of points in plane and space. The entire discussion is aided by geometric intuition. The authors occasionally use algebraic tools to augment the ideas. The holistic nature of the discussion is truly breathtaking.
This book is suitable for any middle school student passionate about mathematics. However mathematics enthusiasts of any age will be charmed by the scope and novelty of the topics.
Pre Calculus by Tarasov
This treatise from Tarasov, yet another Soviet mathematician, is truly a masterpiece. The entire book runs in conversation format (between teacher and student). Tarasov employs dialectical methods to elaborate intricate concepts of limit and continuity. This text is useful for forming a very strong conceptual foundation about the infinitesimals. Though even a junior school student may read it without much difficulty, college level students may also benefit from the clarity and elegance of Tarasov’s discussions.
Intuitive Topology by Prasolov
V.V. Prasolov’s work can at once be regarded revolutionary. This short text provides a highly visual introduction to the world of topology. The reader is at once introduced to the rich theory of knots, links, vector fields without much ado about point set topology. This allows for a constructive approach to this intricate subject. The text is suitable for school students, though college students may also benefit from it.