An Introduction to Higher Mathematics
by Patrick Keef, David Guichard, Russ Gordon
Publisher: Whitman College 2010
Number of pages: 144
Contents: Logic (Logical Operations, De Morgan's Laws, Logic and Sets); Proofs (Direct Proofs, Existence proofs, Mathematical Induction, Indirect Proof); Number Theory (The Euclidean Algorithm, The Fundamental Theorem of Arithmetic); Functions (Injections and Surjections, Cardinality and Countability, Uncountability of the Reals).
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by Martin Day - Virginia Tech
The book helps students make the transition from freshman-sophomore calculus to more proof-oriented upper-level mathematics courses. Another goal is to train students to read more involved proofs they may encounter in textbooks and journal articles.
by Alexander Bogomolny - Interactive Mathematics Miscellany and Puzzles
I'll distinguish between two broad categories. The first is characterized by simplicity. In the second group the proofs will be selected mainly for their charm. Most of the proofs in this book should be accessible to a middle grade school student.
by Ted Sundstrom - Pearson Education, Inc.
'Mathematical Reasoning' is designed to be a text for the first course in the college mathematics curriculum that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics.
by Jim Hefferon - Saint Michael's College
Introduction to Proofs is a Free undergraduate text. It is inquiry-based, sometimes called the Moore method or the discovery method. It consists of a sequence of exercises, statements for students to prove, along with a few definitions and remarks.