The discussion centers around the necessity of completing practice problems in Spivak's calculus book for effective self-learning. Participants explore the balance between problem-solving and understanding theoretical concepts, particularly in the context of proof-writing skills.
Participants do not reach a consensus on the necessity of completing all practice problems, and there are differing views on the importance of proof-writing skills in understanding calculus.
Some participants highlight their challenges with proof-writing and the need for additional resources, indicating that there may be gaps in foundational knowledge that affect their ability to engage with the problems effectively.
This book helps the student complete the transition from purely manipulative to rigorous mathematics. The clear exposition covers many topics that are assumed by later courses but are often not covered with any depth or organization:
For students who need a review of basic mathematical concepts before beginning "epsilon-delta"-style proofs, the text begins with material on set theory (sets, quantifiers, relations and mappings, countable sets), the real numbers (axioms, natural numbers, induction, consequences of the completeness axiom), and Euclidean and vector spaces; this material is condensed from the author's Basic Concepts of Mathematics, the complete version of which can be used as supplementary background material for the present text.
From - http://www.trillia.com/zakon-analysisI.html