Krantz est surtout connu comme auteur de très nombreux livres qui comprennent, en plus de manuels, des guides de développements de carrières pour les mathématiciens débutants et des recueils d'anecdotes sur les mathématiciens. En 1992, il a reçu le prix Chauvenet[3],[4] et en 1994 le prix Beckenbach [5],[6] de la Mathematical Association of America (MAA). De 2010 à 2012, il a été rédacteur en chef des Notices of the American Mathematical Society[7]. Il est le fondateur et rédacteur en chef du Journal of Geometric Analysis.
Série "Textbooks in Mathematics" CRC Press (sélection)
Differential equations. A modern approach with wavelets, CRC Press, (ISBN978-0-367-44409-9)
Complex variables. A physical approach with applications, CRC Press, , 2eéd. (ISBN978-0-367-22267-3)
Elementary introduction to the Lebesgue integral, CRC Press, (ISBN978-1-138-48276-0)
The Elements of Advanced Mathematics, CRC Press, , 4eéd. (1reéd. 1995) (ISBN978-1-138-50631-2)
Essentials of Topology with applications, CRC Press,
Partial Differential equations and complex analysis, CRC Press,
Manuels
Function theory of several complex variables, American Mathematical Society, , 2eéd. (1reéd. 1992) (ISBN0821827243)
Geometric analysis and function spaces, American Mathematical Society,
Complex analysis: the geometric viewpoint, Mathematical Association of America, , 2eéd. (1reéd. 1990) (ISBN0883850354)
A Panorama of Harmonic Analysis, Mathematical Association of America,
avec Harold R. Parks, A primer of real analytic functions, Birkhäuser, , 2eéd. (ISBN0817642641)
avec Harold R. Parks, Geometry of domains in space, Birkhäuser,
avec Harold R. Parks, Geometric Integration Theory, Springer,
avec Harold R. Parks, The implicit function theorem, Birkhäuser,
Cornerstones of Geometric Function Theory – Explorations in complex analysis, Birkhäuser,
avec Lina Lee, Explorations in harmonic analysis – with applications to complex function theory and the Heisenberg group, Birkhäuser,
avec Robert E. Greene, Function theory of one complex variable, Wiley,
Real Analysis and Foundations, Chapman and Hall, , 2eéd.
Elements of topology - theory and practice, Taylor and Francis,
"demystified"
Calculus demystified, McGraw Hill,
Differential Equations demystified, McGraw Hill,
Discrete Mathematics demystified, McGraw Hill,
"Handbooks"
A Handbook of real variables, with applications to differential equations and Fourier analysis, Birkhäuser,
A Handbook of complex variables, Birkhäuser,
Handbook of logic and proof techniques for computer science, Birkhäuser,
"A guide to"
A guide to topology, Mathematical Association of America,
A guide to real variables, Mathematical Association of America,
A guide to complex variables, Mathematical Association of America,
Guides pour mathématiciens
A mathematician's survival guide: graduate school and early career development, American Mathematical Society, (ISBN082183455X)
Survival of a Mathematician - from Tenure to Emeritus, American Mathematical Society,
How to teach mathematics, American Mathematical Society, (ISBN0821813986)
An episodic history of mathematics: mathematical culture through problem solving, Mathematical Association of America, (ISBN0883857669)
Techniques of Problem solving, American Mathematical Society,
Mathematical Publishing - a guidebook, American Mathematical Society,
TeX
Handbook of Typography for the mathematical Scientist, CRC Press,
avec Stanley Sawyer, A Tex Primer for Scientists, CRC Press,
Divers
Mathematical Apocrypha, Mathematical Association of America,
Mathematical Apocrypha Redux, Mathematical Association of America,
The proof is in the pudding: the changing nature of mathematical proof, Springer, (ISBN978-0-387-48744-1)