Math Book Gets Real With Complex

The [Math Sorcerer] loves books. His latest acquisition is the famous Real and Complex Analysis, which is a very stout math book.  How stout? Well, there are several chapters on holomorphic functions, including how to do a Fourier transform on such a function. There’s also an appendix about Hausdorff’s maximality theorem. What are those? Beats us; read the book. You can also watch the short video review of the text below.

The author asserts right up front that the exponential function is “undoubtedly the most important function in mathematics.” Undoubtedly. [The Math Sorcerer’s] videos remind us of browsing a bookstore or a library. You don’t get a book summary as much as a preview of what’s in it, so you can decide if you want to read it.

We have to admit that his book list isn’t light reading. The second video below covers Elementary Quantum Mechanics. Calling a quantum mechanics textbook elementary is an excellent oxymoron right up there with “random order” or “seriously funny.”

Suppose your calculus and differential equations aren’t up to snuff. In that case, the channel does offer videos, often featuring books, ranging from “Math for Super Beginners” and “Learn Calculus Fast,” which might be the first step in a long path to where you can enjoy either of the two books he mentions.

We like things that make learning math faster and easier. However, maybe you can go too fast.

22 thoughts on “Math Book Gets Real With Complex

    1. I think they’re using “elementary” to mean something different than its usual meaning, lol! Mathematicians are fond of that. Take the word “normal”, for example.

  1. Loved baby and papa Rudin text books for UW-Madison classes. He was still teaching at Madison in the 80s when I was taking classes but I never had him as a prof. Math 521/Elementary Analysis was the only class I took three times before grasping the concepts. I still consider those books and classes as central to my education.

  2. Wearing my eye patch, I was reading “Graphs in VLSI” last night. Does anyone here make use of Graph Theory in their work/hobby?

    I realise this is tangential (sorry) to the OP, but it’s still mathsy.

  3. Elementary is better understood in the sense of “Elements,” which is contrasted with “introductory.” The word in this sense different from “for dummies.”

    A good teacher knows that there are no dumb questions, but a great teacher knows that there are levels of maturity, and brevity is the heart of wit, but the humiliation of the student, who hears the professor say, “It’s obvious,” at the conclusion of a proof.

    Thus the great teacher fosters the budding intellect, and lavished love and patience upon the student, though he hails from a modest upbringing, or she lives in public housing projects.

    I know this from experience. I purchased the analysis book at a library book store, recently.

  4. “…Suppose your calculus and differential equations aren’t up to snuff…”

    In that case, it is suggested that you obtain a copy of that world-renowned book, Calculus Made Easy, by Sylvanus P. Thompson. It is such a superb, user-friendly introduction, and the gateway to the mastering of advanced calculus, that it has sold well over a million copies (as of 1998) since being first published in 1910 has never been out of print; and makes the understanding–and mastery–of calculus so easy that the book has never been adopted (and in some cases, stridently rejected) by the mathematics faculty of most all major colleges and universities!

    And one more thing–
    Calculus Made Easy is such a superb book that it was completely revised and updated by none other than Martin Gardner**, and published in 1998.
    The easiest, most enjoyable way, absolutely least painful way (there really never was any pain, as made imminently clear by this book ) to master the calculus–

    Calculus Made Easy
    Sylvanus P. Thompson and Martin Gardner
    St. Martin’s Press
    ISBN 0-312-18548-0

    **“For more than half a century, Martin Gardner has been the single brightest beacon defending rationality and good science…He is also one of the most brilliant men and gracious writers I have ever known.”–Stephen Jay Gould (from the dust-jacket)

    1. People don’t flunk calc because it’s hard.
      They flunk because they aren’t ready.

      Point them to a similar book for algebra and trig.
      If that stumps them, point them to a similar book that teaches adding fractions.

      Alternatively, just go traditional and let them get an A in ‘calc for business majors’. Downside: They’ll go through life thinking they ‘get calc’. Dunning-Kruger never sleeps, so inevitable.

      1. I have a book, “Table of Integrals, Series, and Products”, of which over 1,000 pages are solutions of integrals. I don’t for an instant believe that calculus is not hard. There are a lot of principles to learn, and many are difficult to apply. Some involve having to guess the form of the answer before the details can be worked out.

    2. My father, not a math person, had that book from his highschool days, and he gave it to me when I started calculus (in the old Ontario grade 13 days.) It teaches you the tools of calculus in a clear way, with only the most heuristic proofs. It meant that I could concentrate on the more detailed proofs of the highschool course–notvtoo mention the full rigour of the university course.

  5. I’m not a native speaker, so I’m not completely sure how to read the tone of ““undoubtedly the most important function in mathematics.” Undoubtedly.” Is that condescending?

    However, hackers here love the Fourier transformation. Without that function, there wouldn’t be Fourier analysis. (By the way, that’s chapter 9 in that book).

  6. “Is that condescending?”

    No, but it is more an expression of the author’s–Rudin–personal opinion than it is of actual fact. Any statement as to which is “…the most important function in mathematics…” will be a statement with no universal acceptance among mathematicians…or others, for that matter (some claim that the linear function is the most important).
    A statement such as that can only be ‘personal opinion’, and would immediately call into question the remainder of the book’s contents.

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