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New mathematics often comes about by probing what is already known. Mathematicians will change the parameters in a familiar calculation or explore the essential ingredients of a classic proof. Almost magically, new ideas emerge from this process. This book examines elementary functions, such as those encountered in calculus courses, from this point of view of experimental mathematics. The focus is on exploring the connections between these functions and topics in number theory and combinatorics. There is also an emphasis throughout the book on how current mathematical software can be used to...

A Guide to the Evaluation of Integrals

Special Integrals of Gradshetyn and Ryzhik: the Proofs provides self-contained proofs of a variety of entries in the frequently used table of integrals by I.S. Gradshteyn and I.M. Ryzhik. The book gives the most elementary arguments possible and uses Mathematica^(r) to verify the formulas. You will discover the beauty, patterns, and unexpected connections behind the formulas.

Volume II collects 14 papers from Revista Scientia covering elliptic integrals, the Riemann zeta...

A Guide to the Evaluation of Integrals

Special Integrals of Gradshetyn and Ryzhik: The Proofs provides self-contained proofs of a variety of entries in the frequently used table of integrals by I.S. Gradshteyn and I.M. Ryzhik. The book gives the most elementary arguments possible and uses Mathematica^(r) to verify the formulas. Readers discover the beauty, patterns, and unexpected connections behind the formulas.

Volume I collects 15 papers from Revista Scientia covering logarithmic integrals, the gamma...

This volume presents a selection of papers by Henry P. McKean, which illustrate the various areas in mathematics in which he has made seminal contributions. Topics covered include probability theory, integrable systems, geometry and financial mathematics.