Undergraduate Real Analysis

I am teaching undergraduate real analysis for the first time in the fall. This means that I will need to choose a textbook soon: I am looking for advice in the comments. Here are the textbooks I am considering so far:

These texts seem to be at the correct level for my students—we have used Abbott and Ross here before. I think that Beardon is intriguing—he hammers on limits at the beginning of the text, and then shows that everything else (derivatives, integrals, etc.) is a mere consequence of the notion of a limit—but I cannot find any reviews online (save for one on Amazon).

Here are some textbooks that I am not considering:

  • Rudin—too advanced
  • Pugh—too advanced
  • Spivak—too calculus-y, not analysis-y enough

Convince me if I am wrong to disregard these (keeping in mind that Ross/Abbott is definitely the right level). In particular, I would really like to use the fabled Calculus by Spivak, but it seems more like advanced calculus than real analysis.

While I am at it: I am teaching complex analysis in the spring of next year. So far, I am considering Churchill. I would love ideas for this text, too.

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9 Responses to “Undergraduate Real Analysis”

  1. Adam Glesser Says:

    Thanks for pointing out the link to Trench’s book. Finding quality—yet free—material at that level is more difficult.

    My undergraduate experience in analysis was Strichartz’s The Way of Analysis (which I loved) and then Rudin (which I did not love, but have grown to appreciate). The only problem with Strichartz is that there seem to be many students who don’t appreciate the exposition, which is quite excellent, but long-winded at times. Personally, I love it and think it really leads the student into analysis at a great pace.

    • bretbenesh Says:

      Hi Adam,

      Other professors here are using Trench this semester, with good reviews so far.

      And I ordered a desk copy of Strichartz’s book—thanks for the tip!

  2. Jackie Says:

    I used Ross in a baby analysis/intro to proofs class as an undergrad. I recall thinking it was a good book, and I’m sure there was a lot of material in the book that we didn’t cover in that type of course.

    If you go with the free book, you could suggest one of the other books as a supplement and/or put a copy on hold in the library. Printing out 600 pages certainly isn’t free, though.

    For Complex, I used a Springer book by Bak and Newman the first time I took it. I certainly didn’t “get it” the first time, but I remember it being a good extra resource the second time around.

    • bretbenesh Says:

      Hi Jackie,

      Thanks for the help—one vote for Ross.

      The free book would cost $20-28, which would be about 60% of the cost of a book like Abbott or Ross. I used one in linear algebra last semester, and I was quite pleased with the savings ($28 vs. $150). However, I think that the book was a bad fit for the school, so I probably won’t be using it again. Our school is currently using the free analysis text, so I should have a fairly detailed report by the time I need to decide (the students I have spoken to like it so far).

      I haven’t heard of Bak and Newman. I will look into it—thanks!

  3. Derek Bruff Says:

    My copy of Rudin has a big crack in the spine. It received that crack when I kicked it across my apartment in frustration my first year of grad school.

    Good call on Rudin.

  4. bretbenesh Says:

    Hi Derek,

    Did kicking it make you feel better?

  5. Derek Bruff Says:

    Much. And the book’s presence on my bookshelf is a frequent reminder to me just how hard learning can be.

  6. bretbenesh Says:

    That alone makes it worth the money; your students should really appreciate that you learned out of Rudin.

  7. Abbott wins « Solvable by Radicals Says:

    […] that I am teaching real analysis next semester, and I asked for help in deciding which textbook to use. I started by considering texts by Abbott, Beardon, Ross, and […]

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