

Preface
and table of contents (pdf).
Link
to Wiley's site for the book (order can be placed there).
Videos.
Google
books link. 

Fundamentals
of Mathematics  An Introduction to Proofs, Logic, Sets and
Numbers
This text introduces the reader to the concept of mathematical
proofs by constructing the familiar number systems from the axioms
of set theory. By taking the axiomatic approach, the typical
insecurity what is allowed to be used is avoided: Only what we have
already proved can be used.
Together with this classical approach to introducing proofs, the
text seamlessly integrates current applications, such as digital
circuits and public key encryption, as well as proofs for many
results we recall from high school, such as divisibility tests and
the quadratic formula. Beyond the construction of the number
systems, which ultimately was driven by the desire to solve higher
order equations, the solution methods for third and fourth order
methods are presented, as well as, in a separate chapter, why there
can be no such method for fifth and higher order equations. A
chapter on the Axiom of Choice,
For each section, a video
presentation is
available. 
Preface and table of contents
(pdf).
Link
to Wiley's site for the book (order can be placed there).
Videos.
Google
books link. 

A
Workbook for Differential Equations
A concise introduction to fundamental solution methods for
ordinary differential equations. Topics include first order
equations, constant coefficient equations, Laplace transforms,
partial differential equations, series solutions, systems, and
numerical methods.
The text seamlessly connects to applications (oscillating
systems, circuits, heat equation, hydrogen atom) and is written from
the pointofview that reading is an active task. Introductory and
practice activities are designed to first prepare the reader for a
topic and then to practice after the solution method is understood.
For many of the topics, a video
presentation is
available. 
Instructor's guide (pdf).
Introduction,
Table of Contents, Chapter 1 (locked pdf)
Link
to Birkhäuser's site for the book (order
can be placed there)
Remarks, errata
Google
books link.


Ordered Sets  An
Introduction (Published with Birkhäuser.)
This text introduces the reader to the main constructions and
ideas in the theory of ordered sets. The themebased approach
presents all constructions in a natural context and allows the
reader to confront each new concept in a familiar setting. A
multitude of exercises provides training. Open research problems are
stated at the end of practically every chapter. These problems are
understandable and possibly even solvable with the tools introduced
in the respective chapter.
Since there are few prerequisites,
the text can be used as a focused followup or companion to a first
proof class (set theory and relations) or to a graph theory class.
After covering a comparatively lean core, the text can be used to
concentrate on topics such as, for example, structure theory,
enumeration or algorithmic aspects. In each of these topics the text
lays a solid foundation upon which research in the area can be
started by a mathematically mature reader.
Aside from
introducing open problems that have served and will continue to
serve as inspiration for research in ordered sets, the text covers
some important topics less customary to discrete mathematics/graph
theory. Among these topics are, for example an efficient
introduction of homology for graphs and the presentation of forward
checking as a more efficient alternative to the standard
backtracking algorithm. These topics as well as the many
fundamental results presented give the text lasting value as a
reference. 
