We’re excited to expand our ever-growing library of course materials to include our new text, Calculus with Early Transcendentals.
We sat down with authors Dr. Paul Sisson and Dr. Tibor Szarvas, both of whom have many years of experience as professors of mathematics and as university administrators. They described their approach in the classroom and in their textbook as teaching calculus through the use of History, Intuition, Exploration, and Development (HIED).
Calculus is still too often presented as a collection of tools and theorems devoid of human connections and relationships to other topics. This tendency is understandable, given the sheer amount of material many departments try to cram into their calculus sequence, but learning usually suffers as a result.
Our goal was to produce a text that builds on the natural intuition and curiosity of the reader, blending a student-friendly style of exposition with precision and depth. We believe that if done well, the calculus sequence should be a highly enjoyable journey of discovery and growth for the student, reflecting the journeys of discovery experienced by those who originally developed calculus centuries ago.
In other words, we strived to produce a book that is not only instructive, but also enjoyable to read—one that takes its readers from intuitive problem introductions to the rigor of concepts, definitions, and proofs in a natural manner. The text is a linear narrative that builds upon itself, constantly returning to important themes. Students find themselves, to their surprise, actually reading the text.
We really focused on the integration of the human aspect of calculus. The history of the concepts, the motivations of the mathematicians, and the development of the topics from intuitive to rigorous are all woven into the text. The text contains many unique features to consistently incorporate the theme of HIED: History, Intuition, Exploration, and Development.
These features include:
Conceptual & Application Problems: A rich variety of application problems from within and outside of mathematics and the sciences encourage critical thinking, from skill‐building to deep theoretical questions. These practical applications of the fundamentals of calculus engage students and illustrate the importance of these skills in the real world.
Emphasis on Development: Multistep, guided exploratory exercises that allow students to discover certain principles and connections on their own
Opportunities for Exploration: A constant emphasis on modern technology and its potential to enhance teaching and problem solving, as well as being a tool for investigation, reinforcement, and illustration. Instructors are given the flexibility to include graphing calculator or computer algebra system (CAS) instruction as appropriate.
Historical Relevance: Each chapter begins with a brief introduction to the historical context of the calculus concepts that follow. The introductions connect material learned in previous chapters
to upcoming concepts, and illustrate to students the practical and historical importance of the
calculus theories they are about to study.
These four themes allow students to learn calculus by making connections with what they already know, what they suspect to be true, what they discover through the use of technology, and what they logically develop with the guidance of the professor and each other.
In summary, we have aimed for a comprehensive, mathematically rigorous exposition that not only uncovers the inherent beauty and depth of calculus, but also provides insight into the many applications of the subject.
About the Authors
Dr. Paul Sisson
Paul Sisson received his bachelor’s degree in mathematics and physics from New Mexico Tech and his PhD from the University of South Carolina. Since then, he has taught a wide variety of math and computer science courses, including Intermediate Algebra, College Algebra, Calculus, Topology, Mathematical Art, History of Mathematics, Real Analysis, Mathematica Programming, and Network Operating Systems. He is currently Interim Chancellor and Professor of Mathematics at Louisiana State University in Shreveport.
Dr. Tibor Szarvas
Tibor Szarvas received his master’s degree in mathematics from the University of Szeged, Hungary,and his PhD from the University of South Carolina. His teaching experience in mathematics includes courses such as Intermediate Algebra, Liberal Arts Mathematics, Mathematics for Elementary Teachers, Precalculus, Calculus, Advanced Calculus, Discrete Mathematics, Differential Equations, College Geometry, Mathematical Modeling, Linear Algebra, Abstract Algebra, Topology, Real Analysis, Complex Variables, Number Theory, and Mathematical Logic. He is currently serving as Professor and Chair of Mathematics at Louisiana State University in Shreveport.