Discrete Calculus

Carlo Mariconda was born in 1964. In 1991 he received his PhD in Functional Analysis from the International School for Advanced Studies (SISSA-ISAS), Trieste, Italy. Since 1992 he has been a member of the Department of Mathematics at the University of Padova, where he is now Professor in Mathematical Analysis. His scientific interests mainly focus on the Calculus of Variations and Functional Analysis. Alberto Tonolo was born in 1962. In 1993 he received his PhD in Algebra from the University of Florence, Italy. Since 1992 he has been a member of the Department of Mathematics at the University of Padova, where he is now Professor in Algebra. His scientific interests mainly focus on Module and Ring Theory and Homological Algebra.

• 1 Let’s Learn to Count.- 2 Counting Sequences and Collections.- 3 Occupancy Constraints.- 4 Inclusion/Exclusion.- 5 Stirling Numbers and Eulerian Numbers.- 6 Manipulation of Sums.- 7 Formal Power Series.- 8 Generating Formal Series and Applications.- 9 Recurrence Relations.- 10 Linear Recurrence Relations.- 11 Symbolic Calculus.- 12 The Euler-Maclaurin Formulas of Order 1 and 2.- 13 The Euler-Maclaurin Formula of Arbitrary Order.- 14 Cauchy and Riemann Sums, Factorials, Ramanujan Numbers and their Approximations.- 15 Tables and Formulas.- 16 Appendix A.

“Discrete Calculus is an introductory text to combinatorics and finite calculus. … the work is well organized, and its massive size is also a strength since an interested reader will be  able to find any related topic with the assistance of its comprehensive index including symbols, helpful appendixes, and markers indicating what information is most and least important. … Summing Up: Recommended. Graduate students, researchers, and faculty.” (A. Misseldine, Choice, Vol. 54 (11), July, 2017)