Editor: "Seymour B. Elk"

Calculus: The Logical Extension of Arithmetic

eBook: US $29 Special Offer (PDF + Printed Copy): US $155
Printed Copy: US $141
Library License: US $116
ISBN: 978-1-68108-204-2 (Print)
ISBN: 978-1-68108-203-5 (Online)
Year of Publication: 2016
DOI: 10.2174/97816810820351160101


Digital or ‘virtual’ currencies pose significant challenges for government, financial and legal institutions because of their non-physical nature and their relative anonymity to physical currency. These attributes make this form of exchange extremely volatile and, at the same time, attractive to criminals. Many countries around the world have, therefore issued warnings against the use of digital currencies and have enacted laws to regulate and in some cases, restrict their use among members under their respective jurisdictions.

Calculus: The Logical Extension of Arithmetic re-examines the calculus paradigm by expanding the set of ‘indeterminate forms’ espoused by l’Hôpital 320 years ago. Starting from the 54 possible binary combinations of the foundational numbers (zero, one and infinity), a replacement for the function theory formulated earlier by Newton and Leibniz, is presented. A logical extension of the three concepts of differentiation, integration and the Naperian base number e follows this introduction, which is interpreted as ‘zero divided by zero’, ‘infinity times zero’ and ‘one raised to the infinite power’, respectively. The concept that a number postulated as representing ‘nothing’ is reinforced a useful connection to calculus theory. This treatise proposes a ‘similar’ number to denote and quantify ‘all’, in order to understand the concept of infinity. Other topics covered in this text include analytical geometry, infinite sequences and infinite series.

Calculus: The Logical Extension of Arithmetic is a useful reference on advanced calculus theory for mathematics students and researchers.


Review 1

“ …One does find in the book, presentations that well cater to the wide ambit of students, for elements of calculus. The sequence of topics is well adhered to, going back necessarily to prerequisites. So, it can fit well in with the requirements of not only fresh learners but also, teachers.”

Dilip Kumar Sinha
Guest Faculty, Department of Marine Sciences,
University of Calcutta,
Kolkata, India

Review 2

“In this thought-provoking book, Dr. Elk presents a novel approach to teaching calculus embodying an overarching algebraic theme. Among the unique aspects are early use of ∞ as a number, division by zero is allowed if properly defined and this, for example, can be used to give a priori definitions of l’Hospital’s rules andintegration as ∞-0 interpreted in a “constrained way”. This book might lead to a healthy reexamination of traditional calculus pedagogy.” -

Denis Blackmore, New Jersey Institute of Technology


.Advanced Mathematical Applications in Data Science.
.Markov Chain Process (Theory and Cases).
.Advances in Special Functions of Fractional Calculus: Special Functions in Fractional Calculus and Their Applications in Engineering.
.On Generalized Growth rates of Integer Translated Entire and Meromorphic Functions.