This unique and contemporary text not only offers an introduction
to proofs with a view towards algebra and analysis, a standard fare
for a transition course, but also presents practical skills for
upper-level mathematics coursework and exposes undergraduate
students to the context and culture of contemporary mathematics.
The authors implement the practice recommended by the Committee on
the Undergraduate Program in Mathematics (CUPM) curriculum guide,
that a modern mathematics program should include cognitive goals
and offer a broad perspective of the discipline. Part I offers: An
introduction to logic and set theory. Proof methods as a vehicle
leading to topics useful for analysis, topology, algebra, and
probability. Many illustrated examples, often drawing on what
students already know, that minimize conversation about "doing
proofs." An appendix that provides an annotated rubric with
feedback codes for assessing proof writing. Part II presents the
context and culture aspects of the transition experience,
including: 21st century mathematics, including the current
mathematical culture, vocations, and careers. History and
philosophical issues in mathematics. Approaching, reading, and
learning from journal articles and other primary sources.
Mathematical writing and typesetting in LaTeX. Together, these
Parts provide a complete introduction to modern mathematics, both
in content and practice. Table of Contents Part I - Introduction to
Proofs Logic and Sets Arguments and Proofs Functions Properties of
the Integers Counting and Combinatorial Arguments Relations Part II
- Culture, History, Reading, and Writing Mathematical Culture,
Vocation, and Careers History and Philosophy of Mathematics Reading
and Researching Mathematics Writing and Presenting Mathematics
Appendix A. Rubric for Assessing Proofs Appendix B. Index of
Theorems and Definitions from Calculus and Linear Algebra
Bibliography Index Biographies Danilo R. Diedrichs is an Associate
Professor of Mathematics at Wheaton College in Illinois. Raised and
educated in Switzerland, he holds a PhD in applied mathematical and
computational sciences from the University of Iowa, as well as a
master's degree in civil engineering from the Ecole Polytechnique
Federale in Lausanne, Switzerland. His research interests are in
dynamical systems modeling applied to biology, ecology, and
epidemiology. Stephen Lovett is a Professor of Mathematics at
Wheaton College in Illinois. He holds a PhD in representation
theory from Northeastern University. His other books include
Abstract Algebra: Structures and Applications (2015), Differential
Geometry of Curves and Surfaces, with Tom Banchoff (2016), and
Differential Geometry of Manifolds (2019).
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