Accessible to all students with a sound background in high school
mathematics, A Concise Introduction to Pure Mathematics, Fourth
Edition presents some of the most fundamental and beautiful ideas
in pure mathematics. It covers not only standard material but also
many interesting topics not usually encountered at this level, such
as the theory of solving cubic equations; Euler's formula for the
numbers of corners, edges, and faces of a solid object and the five
Platonic solids; the use of prime numbers to encode and decode
secret information; the theory of how to compare the sizes of two
infinite sets; and the rigorous theory of limits and continuous
functions. New to the Fourth Edition Two new chapters that serve as
an introduction to abstract algebra via the theory of groups,
covering abstract reasoning as well as many examples and
applications New material on inequalities, counting methods, the
inclusion-exclusion principle, and Euler's phi function Numerous
new exercises, with solutions to the odd-numbered ones Through
careful explanations and examples, this popular textbook
illustrates the power and beauty of basic mathematical concepts in
number theory, discrete mathematics, analysis, and abstract
algebra. Written in a rigorous yet accessible style, it continues
to provide a robust bridge between high school and higher-level
mathematics, enabling students to study more advanced courses in
abstract algebra and analysis.
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