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What textbooks would you recommend?

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- Thread starter PFuser1232
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For people who are starting college in the late 2010s or 2020s, this rigor may be unfamiliar or too hard. Textbooks that introduce those topics are not written in a rigorous fashion, so it may be impractical to find an introductory text that meets your standards.f

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What textbooks would you recommend?

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Spivak or Apostol calculus? Serge Lang basic mathematics for pre cal.

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Spivak or Apostol calculus? Serge Lang basic mathematics for pre cal.

Is Spivak Calculus better than Simmons/Stewart Calculus?

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Yes, still in high school. I finished most of my subjects early though, so I know some basic differentiation and integration.

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Both books compliment each other well. Avoid watching youtube videos as soon as you get. Getting stuck is the best process of the learning experience.

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Both books compliment each other well. Avoid watching youtube videos as soon as you get. Getting stuck is the best process of the learning experience.

What about Simmons calculus?

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Science Advisor

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except that this time I need a more rigorous treatment of those topics.

Having read some of your posts on the forum, I'd say you have an high standard of rigor - a very high standard relative to the general population taking introductory courses. Textbooks that introduce those topics are not written in a rigorous fashion, so it may be impractical to find an introductory text that meets your standards.

(In the decade after Sputnik threw a scare in the USA education system, there were efforts to produce textbooks that were in harmony with respectable mathematics - versus being in harmony with convenient ways to teach students to work typical problems. An example of such a text is the 3rd edition of Calculus With Analytic Geometry by Johnson and Kiokemeister. The 4th edition takes an even more sophisticated approach but also has a slew of misprints. The last time I looked at Calculus books was in the 1980's and they were much less rigorous than J&K 3rd edition.)

Doing mathematics in a rigorous fashion can be laborious and slow, but mentally satisfying. You have to decide how to compromise the goal of "covering the material" with working in a way you enjoy. To cover material, you have to endure the fact that some aspects will not be presented rigorously. For example, the organization of mathematics education places the rigrorous approach to the properties of the real numbers in a graduate or advanced undergraduate course. Those who get to that course have been required to work with the real numbers in math courses for many years before they arrive.

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