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#iteachmath

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"An Invitation to Real Analysis" should be out in October. I hope the book helps students around the globe learn real analysis for many years into the future. In any event, getting to tell this story of numbers, sets, functions, sequences and limits, and function spaces is something I got to do in my time here on earth.

If you are teaching introductory real analysis in Winter/Spring 2026 or beyond, I am deeply grateful for your consideration. The book was written for courses covering material from basics of sets and proofs at one endpoint to metric spaces and selected applications in function spaces at the other. There are over 600 exercises at all levels of challenge. Selected hints, answers, and solutions are in the back, and a complete solution manual will be available for instructors.

Throughout, I've striven for readability, simplicity, networks of conceptual connections, and consistency of notation and terminology. Consistency was not as straightforward a goal as I first expected.

There are a few noteworthy choices--such as using descriptive terms in favor of eponyms, and counting starting from 0--that I believe are features even if at first they seem not to be. Other pedagogical choices include using adversarial games systematically to convey analytic definitions, acknowledging the "foreign language" aspects of analysis, and putting material in strict logical order to the extent possible so readers can easily tell at any stage what concepts and results are available for use.

I'll post further details, including the publisher's web page for the book, once I'm formally notified.

If you're in Austin for the WeTeachCS conference, don't miss our talks!
June 9, 9:45am Data Science: How to Thoughtfully Integrate Science, Math and Computer Science
June 9, 12:45pm Teaching CS and Math Concepts through Creative Calculations of Pi
June 10, 1:30pm Impacting student attitudes about CS through coding integration into science
#CS4Yall #CS4All #iteachmath

Mathematics Teaching 296 now available online atm.org.uk/Mathematics-Teachin

Design and cover photographs by me

Four free articles for non-members:

Everyone can think mathematically by Tom Francome
Tom Francome explores ways of developing the mathematical thinking of all students, including low attainers.
atm.org.uk/write/MediaUploads/

Book review Learning with AI by Ian Benson
Ian Benson reviews 'Learning with AI' by Joan Monahan Watson published by Johns Hopkins University Press (296 pages, $24.95)
atm.org.uk/write/MediaUploads/

Book review Breaking images by Pete Wright
Pete Wright reviews ‘Breaking images: Iconoclastic analyses of mathematics and its education’, edited by Brian Greer, David Kollosche, and Ole Skovsmose.
atm.org.uk/write/MediaUploads/

Ole Skovsmose—the man who put the critique in critical mathematics education by Peter Gates
Peter Gates has collated this obituary for Ole Skovmose.
atm.org.uk/write/MediaUploads/