Is This Calculus Book Too Advanced for Beginners?

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Discussion Overview

The discussion revolves around the appropriateness of a calculus book for beginners, specifically focusing on the content of the first chapter, which includes foundational mathematical concepts. Participants explore whether this content is relevant to calculus and if it is suitable for someone without prior knowledge of these topics.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants question the relevance of foundational topics like rational and irrational numbers to calculus.
  • Others suggest that the chapter serves as a review to prepare readers for calculus concepts.
  • One participant notes that the book may be more aligned with "analysis" rather than a traditional calculus textbook, indicating a theoretical approach to calculus.
  • There is a suggestion that pure mathematics books may be too advanced for beginners, as they often assume prior knowledge of various mathematical fields.
  • Several participants mention popular calculus textbooks and their structure, emphasizing that typical calculus books focus on limits, derivatives, and integrals.
  • One participant highlights the necessity of understanding earlier mathematical subjects to effectively solve calculus problems, particularly in integration.
  • Another participant contrasts two approaches to learning calculus: starting with calculus concepts or first mastering the properties of real numbers.
  • A participant seeks clarification on whether their book is considered one of the harder or easier texts for beginners.

Areas of Agreement / Disagreement

Participants express differing views on the suitability of the book for beginners, with some arguing it is too advanced while others believe it provides necessary foundational knowledge. No consensus is reached regarding the book's appropriateness for novice learners.

Contextual Notes

Participants note that the book's content may be more aligned with real analysis than typical calculus, which could affect its accessibility for beginners. There is also mention of varying definitions of "analysis" in different educational contexts.

Who May Find This Useful

This discussion may be useful for students considering different calculus textbooks, educators evaluating curriculum materials, and individuals interested in the foundational concepts necessary for understanding calculus.

Miike012
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The contents of the first chapter is...
Rational numbers
Irrational numbers
Real Numbers
Relations of Magnitude between real numbers
Algebraical operations with real numbers
the number (2)^(1/2)
Quadratic surds
The Continuum
The continuous real variable
Points of condensation
Weicrsrass's theorem...

My Question Is... What does any of this have to do with calculus? And because I don't know about any of it... will I benefit from reading it?
 
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Miike012 said:
The contents of the first chapter is...
Rational numbers
Irrational numbers
Real Numbers
Relations of Magnitude between real numbers
Algebraical operations with real numbers
the number (2)^(1/2)
Quadratic surds
The Continuum
The continuous real variable
Points of condensation
Weicrsrass's theorem...

My Question Is... What does any of this have to do with calculus? And because I don't know about any of it... will I benefit from reading it?

To answer your first question, no. Calculus mostly deals with derivatives and integrals. This looks to be like some kind of review chapter to get you familiar with mathematical concepts before delving into calculus.

To answer your second question, if you're not sure about any of the stuff, like real numbers, Algebraical operations with real numbers, etc., I would definitely read this chapter. You'll get a decent foundation of those topics and better understand what's going on in the subsequent chapters.
 
I would say that what you have (Courant and Hilbert?) is not, strictly speaking, a calculus book but an "analysis" book. Analysis (though I believe that, in Europe, "analysis" is often used to mean what people in the United States just call "calculus") is, essentially, the theory behind Calculus.
 
The book that I downloaded is called a course in pure mathematics by g.h. hardy.
Have either of you heard of this book?
 
Pure math is the name for all of math except applications, so it would be logical for a book on pure math to contain just about anything. The problem with pure-math books is that they usually are intended for people who have been introduced to the basics of most fields of pure math, and would be way above the head of the average calc student. The topics listed sound more like real analysis than calculus. A calc book would be likely to go in order of: limits, derivatives, and integrals, sometimes with a chapter on the applications of derivatives in between derivatives and integrals.

EDIT: I've never heard of it. But it should be known that I'm not a very well read person.
 
TylerH said:
EDIT: I've never heard of it. But it should be known that I'm not a very well read person.

It's an excellent book written by a great mathematican, but it's not a beginner's textbook on calculus.

Sorry, but I know know what the best (and/or most popular) beginning calculus texts are these days. I can't even remember what books I learned it from, and that was so long ago they are probably out of print anyway!
 
Back when I was in college "Thomas's Calculus" was the standard- and its still in print, though completely revised by people other than Thomas!
 
I teach Calculus
What you will soon discover when learning Calculus is that solving problems will very often involve the Calculus for half or less of the solution. Knowing nearly all the subjects taught earlier is required to be able to set up or finish a problem. Algebraic manipulation, Complete the Square, Algebraic Long Division, Trig Identities, Exponentials, Factoring and more are all necessary to complete problem solutions. This is especially true when covering Integration.

Thomas, Smith & Minton, and Stewart are the three most popular texts but there are several others. Banner is used at Princeton.
 
calculus is a subject that studies properties of functions of real numbers. hence one can either start right in with the calculus ideas, but only a fuzzy grasp of the nature of real numbers, or one can first try to understand well the properties of real numbers that are needed in calculus. the second approach is only taken with the brightest and perhaps most patient students. your book is of the latter kind. if you prefer the opposite approach, try calculus made easy by sylvanus p. thompson.
 
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Mine is the latter kind? What does that mean? That it is the harder one that only the "brightest" kids can do?
 
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