Basic Concepts of Mathematics
by Elias Zakon
Publisher: The Trillia Group 2007
Number of pages: 208
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, and basic properties of n-dimensional Euclidean spaces.
Home page url
Download or read it online for free here:
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 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 Patrick Keef, David Guichard, Russ Gordon - Whitman College
Contents: Logic (Logical Operations, De Morgan's Laws, Logic and Sets); Proofs (Direct Proofs, Existence proofs, Mathematical Induction); Number Theory (The Euclidean Algorithm); Functions (Injections and Surjections, Cardinality and Countability).
by James Franklin, Albert Daoud - Kew Books
This is a small (98 page) textbook designed to teach mathematics and computer science students the basics of how to read and construct proofs. The book takes a straightforward, no nonsense approach to explaining the core technique of mathematics.