Is Principles of Mathematics a Good Book for Learning Calculus from Scratch?

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Discussion Overview

The discussion revolves around the suitability of various calculus books for beginners, particularly focusing on whether "Principles of Mathematics" by Allendoerfer is a good resource for learning calculus from scratch. Participants explore the prerequisites for understanding calculus and the theoretical foundations of differentiation and integration.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant seeks recommendations for a calculus book that starts from the very beginning and explains the theory behind differentiation and integration.
  • Another participant argues that no book exists that does not assume some prior knowledge, suggesting that different books have varying prerequisites.
  • A recommendation is made for "Practical Analysis in One Variable" by Estep, which is noted for covering basic arithmetic without assuming much prior knowledge.
  • "Basic Mathematics" by Lang is also recommended as a comprehensive resource for foundational knowledge needed before tackling calculus.
  • One participant asserts that "Principles of Mathematics" by Allendoerfer is indeed a suitable book, highlighting its coverage of fundamental topics leading up to calculus and its rigorous approach.
  • Another participant expresses enthusiasm for "Principles of Mathematics," indicating a desire to explore it further.

Areas of Agreement / Disagreement

Participants express differing views on the availability of a suitable calculus book for absolute beginners. While some recommend specific titles, others maintain that all books will require some prior knowledge, indicating a lack of consensus on the best starting point.

Contextual Notes

Participants mention varying levels of assumed knowledge in different books, but do not resolve the specific prerequisites for "Principles of Mathematics" or other suggested texts.

Darth Frodo
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Can anyone recommend a good calculus book that starts from the very beginning and also explains the theory behind differentiation and integration. If it were to go from HS to Freshman year that would be great!

Thanks!
 
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There is no such book, I fear. Every book will assume some knowledge, some books will require more knowledge than others.

A book I like is "Practical Analysis in One Variable" by Estep. It goes over integers and rational number arithmetic and stuff, so you could say that it doesn't assume very much.

In any case, let me also recommend you "Basic mathematics" by Lang. This book contains literally everything you need to know in order to start calculus.
 
Great! Thanks micromass! Yeah I already picked up Lang's book based on your numerous recommendations! I also wrote down that calculus book from reading your blogs, just wasn't sure if it was a good starting point.

Thanks again! Very helpful as always!
 
there is such a book!

Principles of Mathematics by Allendoerfer

This is the book that first got me into mathematics. It covers everything from functions, counting, induction, building up to calculus. And it is also a fairly rigorous book ( has delta-epsilons )
 
Last edited:
wisvuze said:
there is such a book!

Principles of Mathematics by Allendoefer

This is the book that first got me into mathematics. It covers everything from functions, counting, induction, building up to calculus. And it is also a fairly rigorous book ( has delta-epsilons )

Ooh, sounds like an exciting book. I need to check it out.
 

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