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I am a math major currently in my sophomore year. I have a sound base in one variable calculus and basic linear algebra. I am currently doing a course in multivariable calculus. I have completed reading Calculus by Apostol Vol 1 and 2 and reached nearly half-way through Baby Rudin.

I am currently thinking about reading Advanced Calculus by Loomis and Sternberg mainly because of its vast table of contents and applications in Classical Mechanics (I am a physics minor too). After going through the first few chapters lightly, I am certain that it would take a whole semester to complete this book.

My question is: Is it worth spending the whole semester (5 months) in this book?

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    $\begingroup$ You read math books at the speed of light. $\endgroup$
    – Git Gud
    Mar 4, 2014 at 17:15
  • $\begingroup$ @GitGud You think its not possible to finish in 5 months? $\endgroup$
    – Mathgrad
    Mar 4, 2014 at 17:21
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    $\begingroup$ I don't know the book. I just think that if you went through Apostol I, II and half of Baby Rudin in less than two years then you're very fast. $\endgroup$
    – Git Gud
    Mar 4, 2014 at 17:23
  • $\begingroup$ @GitGud Actually those were prescribed text books for the first 3 sem courses. $\endgroup$
    – Mathgrad
    Mar 4, 2014 at 17:35
  • $\begingroup$ You should get a copy of Arnold's text Mathematical Methods of Classical Mechanics. $\endgroup$
    – James S. Cook
    Mar 7, 2014 at 14:37

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It depends on what draws you to the text, and what prompts you to post this question:

  • Is it a matter of (mostly) enjoyment (that the prospect of digging into Loomis and Sternberg is enticing to you, so the question is more along the lines, "is it so fun/challenging that it would be a shame to miss out by not tackling it?"),
  • ...Or a question of necessity (e.g., Is studying Loomis and Sternberg in my best interest, mathematically?),
  • or both?

It seems to me that, having tackled Apostol I, II, and given that you're currently making your way through Rudin,, you will do just fine, mathematically, if you do not read it, or if you read it "recreationally." Having said that, if having perused its table of contents, you find it immensely appealing, so much so that you're willing to spend "down time" on the text, just for the sheer fun and challenge of it, then go for it!

To sum up: I do not think that Loomis and Sternberg is a prerequisite that any serious student of math ought to study. But it is certainly a fine text to work through if you you find doing so to be enjoyable, enriching, and/or helpful as a supplement to your current studies.

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  • $\begingroup$ It's a very challenging text, and especially appealing to very serious students, so if you like a challenge, go for it...it will certainly benefit you in terms of enjoyment and mastery! $\endgroup$
    – amWhy
    Mar 4, 2014 at 17:41

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