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 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.
by Farshid Hajir - University of Massachusetts
Problem Solving, Inductive vs. Deductive Reasoning, An introduction to Proofs; Logic and Sets; Sets and Maps; Counting Principles and Finite Sets; Relations and Partitions; Induction; Number Theory; Counting and Uncountability; Complex Numbers.
by Dave Witte Morris, Joy Morris - University of Lethbridge
This undergraduate textbook provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics. It is designed to be the textbook for a bridge course that introduces undergraduates to abstract mathematics.
by Elias Zakon - The Trillia Group
The book will help students complete the transition from purely manipulative to rigorous mathematics. It covers basic set theory, induction, quantifiers, functions and relations, equivalence relations, properties of the real numbers, fields, etc.