Recommend a Rigorous Calculus Book

[Sorgen]

I have an undergraduate degree in Mathematics from a Big 10 university. Right now I am looking for a Calculus text that would aid me in approaching philosophy and literature text.

Mostly what I'm looking for is a combination of Rigor (strictness in definitions and such) and problems that force you to examine them thoroughly from every angle.

Thanks!

 

[verty]

I don't understand this, do you mean something like a Bourbaki treatment of calculus? Perhaps "Folland - Real Analysis" or perhaps you want this stuff:

Differential Forms & Connections - Darling

 

[crownedbishop]

I have an undergraduate degree in Mathematics from a Big 10 university. Right now I am looking for a Calculus text that would aid me in approaching philosophy and literature text.

Mostly what I'm looking for is a combination of Rigor (strictness in definitions and such) and problems that force you to examine them thoroughly from every angle.

Thanks!

Calculus and rigor do not belong together. Baby Rudin should suffice for all your calculus needs. It has problems that require a deal of ingenuity that even Rudin admits in the preface. I think that qualifies for your examining thoroughly from every angle. I will tell you this, if you understand everything from baby Rudin, and do all the exercises you will probably not need a calculus text. I do not think there is anything of merit in a calculus book that is not in baby rudin. In my opinion, Rudin is the perfect literature, but perhaps not the easiest learning tool. If you want an actual real analysis text though, baby rudin is too easy and won't give you what you want. This text is a classic in the mathematical literature, and will make you appreciate conciseness. I personally prefer it over verty's suggestion of Bourbaki. I'm not sure what Bourbaki text you are recommending, since Bourbaki failed to even reach it's goal of proving Stoke's Theorem. I think the suggestion of Real Analysis by Folland is too abstracted away from calculus to be suggested. This all depends on what you want the text for. Do you want an actual real analysis book? Or do you want a book that holds your hand? Any calculus text is just a dumbed down version of parts of analysis. So, I would not recommend any calculus text if you actually want rigor. Here's what we need to know: what is your mathematical background? I know you said you have a mathematical degree in math, so you must have learned some analysis (I assume). Have you had any courses in real analysis? Have you learned measure theory? etc...

 

[verty]

What does "calculus approaching a philosophy and literature text" mean exactly? I hoped it meant "laying out the facts in a very coherent and justified way". But it is very confusing.

 

[rezeew]

I understand the importance of rigor in approaching any subject, including philosophy and literature. With that in mind, I would highly recommend "Calculus: Early Transcendentals" by James Stewart. This textbook is widely used in universities and is known for its rigorous approach to calculus. It covers all the fundamental concepts of calculus, including limits, derivatives, and integrals, in a clear and precise manner.

Additionally, the book includes numerous challenging problems that require a thorough understanding of the material and encourage critical thinking and analysis. This will be beneficial in your approach to philosophy and literature texts, as it will train you to examine them from different perspectives and think critically about the ideas presented.

Furthermore, the book also includes real-world applications of calculus, which can help bridge the gap between mathematics and other fields of study. This will be particularly useful in your pursuit of philosophy and literature, as it will demonstrate the practical relevance of calculus in these areas.

Overall, "Calculus: Early Transcendentals" by James Stewart is a highly recommended textbook for its rigor and thorough approach to calculus. I believe it will be a valuable resource in your pursuit of integrating mathematics into your study of philosophy and literature. Good luck!