# Not Just Calculus: First-Year Introduction to Upper-Level Mathematics

## About the Textbook

This free, online text is designed to be used as 1-semester or
2-semester course for first-year mathematical sciences students.

The purpose of this text is to provide a first-year introduction to
upper-level mathematics in the undergraduate curriculum. *Not just
calculus* acknowledges that a single course on proof
writing in the second year is too little, too late. Using topics that will be useful
in later courses, this book accelerates the process of "mathematical
maturity" through active reading, reasoning, problem solving, and writing.

This text can be used for a one-semester course, or for two
half-credit courses spread over two semesters in the first year. This
text is *not* intended to replace a formal introduction to
proof writing. It *is* intended to widen student's perspectives
beyond high school mathematics and introductory calculus courses.

The exposition is overtly designed for active reading. There are almost
no examples, and almost no illustrating figures. Embedded reading
exercises ("Checkpoints") require the reader to construct examples and
make drawings. End-of-section problems ("Exercises") guide students in constructing
short arguments to prove if-then propositions. An overall theme is that
a few carefully chosen, powerful abstractions (such as: sets and
functions, modular arithmetic, linear transformations of the plane, to
name a few) form the basis for widely various applications.

## About the Author

David W. Lyons is a professor of mathematics at Lebanon
Valley College in Annville, Pennsylvania, USA, where he has
taught and conducted research since 2000. Lyons works in
mathematical physics, leading a student-faculty research program
in quantum information science since 2002. For more information,
visit his academic website at the URL below.

quantum.lvc.edu/lyons