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Differential Equations: choose your way through to a twenty-first-century semes- Techniques, Theory, and Applications ter-long ODE course. Barbara D. MacCluer, Paul S. Bourdon, Thomas L. Kriete Barrycades and Septoku: Papers in Honor of Martin Gardner Introductory differential equa- and Tom Rodgers tions is the undergraduate course Thane Plambeck, Tomas Rokicki, whose content has been most Editors disrupted by mathematical ad- The set {1, 2, 3, 4} has partial vances of the last fifty years. sums 1, 3, 6, and 10. Barry Cipra Computing has elevated the im- noticed that the rearrangement portance of numerics, dynamical

Miscellaneous Book Series, Volume 129 (MBK/129) Volume Miscellaneous Book Series, {2, 3, 4, 1} yields partial sums 2, systems has had a similar effect 5, 9, 10, while the rearrangement on qualitative techniques, and {4, 3, 1, 2} gives sums 4, 7, 8, applications have extended very far from the classical Spectrum Book Series, Volume 100 (SPEC/100) 100 Volume Spectrum Book Series, and 10. That is, every number examples in physics and mechanics to biology, chemistry, from 1 to 9 appears as a partial sum exactly once. Richard public health, social science, and more. It is still possible Guy visualized these arrangements as a stack of logs as to teach real analysis from the textbook I learned it from pictured and dubbed the resulting object a barrycade. Note in the 1980s. It would be absurd and irresponsible to do that the breaks occur at every possible position once and the analogous thing in an ODE course. Today’s typical syl- only once. labus is the result of patching recent developments onto a Several questions im- syllabus first developed early in the last century. mediately suggest them- The authors of this book asked themselves how one selves: For which n is a might rethink the ODE course from first principles in barrycade possible? For A simple example of a barrycade. light of these advances. Their answer is to weave together a feasible n, how many theory, technique, and modeling. Differential equations essentially different ways are there? What other log lengths are presented as a method of modeling the real world with permit construction of a barrycade? mathematics. They are our best bet for predicting the future. The Gathering 4 Gardner (G4G) is a meeting of Martin Theory makes it possible to build, validate, and analyze Gardner fans that takes place in the spring of even-num- those models. And “analyze” means create techniques—an- bered years in Atlanta. Tom Rodgers conceived of and was alytic, graphical, numerical—to interpret those predictions the driving force behind the Gatherings until his death in of the future. Every section of this text carefully braids all 2012. It is an eclectic mix of mathematicians, computer three strands of this approach into a coherent picture. scientists, artists, philosophers, magicians, and it exists, to This is a book with a large vision of both its subject and quote the website, to “stimulate curiosity and the playful the appropriate way to teach that subject to undergradu- exchange of ideas and critical thinking.” It teems with the ates. The book has been in development and testing at the spirit of Martin Gardner, Tom Rodgers, and problems and University of Virginia for approximately fifteen years. The puzzles like the one above. This volume is a collection of exposition is well polished and extremely readable. There papers first delivered at a Gathering in recent years. With the are over 1,300 tested exercises and an online collection COVID-induced postponement of G4G this year, curling up of extensive modeling explorations. There is more than with the contributions of Neil Sloane, George Hart, Tanya enough material to fill a year-long course, or to pick and Khovanova, Erik Demaine, or one of the other brilliant The AMS Bookshelf is prepared bimonthly by AMS Acquisitions Specialist expositors represented here may just be the next best thing. for MAA Press titles Stephen Kennedy. His email address is skennedy @amsbooks.org.

August 2020 Notices of the American Mathematical Society 1033