Deconstruct this Calculus 2.5 Journal: sequences and series

This volume in the Deconstruct Series explores powerful mathematical ideas that emerge from a simple question: what happens if we keep going? We'll study sequences, series, and the mathematics of infinity. Rather than treating convergence tests as a long list of rules to memorize, we'll follow in the footsteps of mathematicians who wondered whether an infinite process could produce a finite result. By following the traces of investigation left behind by centuries of thinkers, you'll develop intuition for these ideas before learning the algorithms used to analyze them.

Discover infinite geometric series, Taylor polynomials, power series, and other remarkable tools through activities, visual explorations, challenge problems, and applications that reveal both the beauty and practicality of infinite processes. You'll see how mathematicians approximate complicated functions, model real-world phenomena, and build bridges between algebra, geometry, and calculus. Infinity may seem mysterious at first, but by the end of this journal, you'll understand why it has fascinated mathematicians for generations—and why it remains one of the most useful ideas in all of mathematics.

The Deconstruct Calculus Series of interactive journals teaches calculus in a hands-on way. We have four principles.

First, our books emphasize intuition. You might not have had a book tell you how natural many of the concepts behind the name "Calculus" are. The Deconstruct Series is that book for every student who wants to—or has to—explore this subject we love. You'll learn concepts before calculations and will understand rather than memorize.

Second, Deconstruct books focus on you, the student. We provide answers to every question, examples are personal, and problems are useful.

Third, it's DIY. You'll be doing calculus, not just parroting equations and reciting theorems for a class.

Fourth, the Deconstruct Series emphasizes collaboration. Calculus is better with friends.

From the Publisher

The Deconstruct Calculus Series was developed through more than a decade of educational research, classroom testing, and funded curriculum innovation projects. The project received an Innovation in Teaching Award and has been funded by the Sloan Foundation, the College of Charleston, and the S.C. Space Grant.

Editorial Reviews & Endorsements

Academic Reviews

"I absolutely love the books—they are books that all students taking calculus should use!"
Jo Boaler, Nomellini & Olivier Professor of Education at the Stanford Graduate School of Education and cofounder of youcubed and Struggly

"I am enjoying the calculus books! I wish I had these books when I was taking calculus."
Cathy Williams, Co-Founder and Executive Director of youcubed

"They look beautiful, can't wait to dig in!"
Daniel Egger, Duke University, Pratt School of Engineering

Student Reviews

"The organization of the journal helped me retain information much better than simply reading definitions from a traditional textbook."

"The hands-on approach and study tips helped me discover the learning methods that worked best for me throughout the semester."

"I enjoyed how the journal gradually built my understanding through activities before introducing more challenging problems."

About the Authors

Alex Baham is a data analyst with the University of Texas at Tyler, specializing in healthcare data. For years, she has used her degrees in mathematics and statistics to tutor math-phobic students struggling in calculus.

Dr. Amy N. Langville is a professor of mathematics at the College of Charleston and is passionate about making mathematics more human, creative, and accessible. After years of teaching calculus and authoring internationally recognized books on topics ranging from search engines and ranking systems to mathematically inspired notebooks, Amy became convinced that many students struggle not because calculus is too difficult, but because it is often presented without intuition, context, and opportunities for students to discover mathematics for themselves. She spent more than a decade creating the Deconstruct Calculus Series, the (anti)textbook she always wished her students had.

Dr. Kathryn Pedings-Behling is an instructor of mathematics at the College of Charleston and has taught mathematics at both the secondary and collegiate levels in face-to-face, online, and hybrid classrooms. Her research focuses on improving students' attitudes toward mathematics and broadening participation in STEM. Through years of teaching and curriculum development, she has seen firsthand how confidence and curiosity can transform mathematical learning.