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Foundations of Mathematics
Foundations of Mathematics is
designed to be a self-contained introductory treatment of several
topics that are considered to be fundamental to all of mathematics,
and, consequently, to other disciplines which utilize mathematics.
Foundations of Mathematics is intended for use in a course that
would be beneficial to students who plan to major in mathematics
or other math-related fields; such as, computer science, economics,
one of the natural sciences or pre-engineering, and desire a foundation
for their subsequent studies. Primary emphasis is given to the
development of understanding mathematical concepts rather than
routine problem solving which one finds in many elementary mathematics
books.
Contents:
- Chapter 1 Logic and Mathematical Reasoning
- Chapter 2 Algebra of Sets
- Chapter 3 Functions
- Chapter 4 Relations and Partitions
- Chapter 5 Binary Operations
- Chapter 6 Number Theory
- Chapter 7 Finite and Infinite Sets
- Chapter 8 The Real Number Systems
Chapter 1 is concerned with the study
of logic and will show the student how it facilitates communication.
Chapter 2 presents the notion of an object
and a set which enter into all branches of mathematics.
Chapter 3 expands and formalizes the concept
of a function with which many students are familiar.
Chapters 4 and 5 are devoted to relations
and binary operations.
Chapter 6 deals with some of the more
basic concepts in number theory.
Chapter 7 formalizes the notions of finite
and infinite sets.
Chapter 8 reviews a few of the basic properties
of the real numbers and discusses other facts that should be useful
in subsequent courses in mathematics.
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