We explore the possibility of a calculus only over the rational numbers. This leads us to the important role of the axiom of completeness in the important theorems from first semester calculus.
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Books I like:
Abstract Algebra:
Judson(online): http://abstract.ups.edu/
Judson(print): https://amzn.to/2Xg92wD
Dummit and Foote: https://amzn.to/2zYOrok
Gallian: https://amzn.to/2zg4YEo
Artin: https://amzn.to/2LQ8l7C
Differential Forms:
Bachman: https://amzn.to/2z9wljH
Number Theory:
Crisman(online): http://math.gordon.edu/ntic/
Strayer: https://amzn.to/3bXwLah
Andrews: https://amzn.to/2zWlOZ0
Analysis:
Abbot: https://amzn.to/3cwYtuF
How to think about Analysis: https://amzn.to/2AIhwVm
Calculus:
OpenStax(online): https://openstax.org/subjects/math
OpenStax Vol 1: https://amzn.to/2zlreN8
OpenStax Vol 2: https://amzn.to/2TtwoxH
OpenStax Vol 3: https://amzn.to/3bPJ3Bn