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.
Reviews (5)
5 reviews for A Concise Introduction to Pure Mathematics
jack
Rated 5 out of 5
December 3, 2018
Amazing to learn from and goes into great detail!
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Y.
Rated 5 out of 5
January 19, 2018
How non-mathematicians should start. Love it
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LW
Rated 5 out of 5
December 6, 2017
Great book
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MC
Rated 5 out of 5
March 24, 2016
This book is indeed a concise introduction to a bunch of important topics in mathematics. As a post-grad that studied computer science and is now stud...More
This book is indeed a concise introduction to a bunch of important topics in mathematics. As a post-grad that studied computer science and is now studying in a mathematics-based department, I needed to catch up on even the most basic of notation that I did not require to get me through my undergraduate. This book moves at a nice pace, flows naturally but most importantly, doesn't skip the explanation of notation and formulation of proofs. Sometimes when you haven't studied maths, the hardest part of approaching a new topic is the lack of understanding of some of the basic notation used to represent the concepts and ideas. Thankfully, this book discusses them as they appear and continues to encourage you to ask questions about the topics, rather than just bury you with proofs. The chapters are pretty self-contained also, and the author suggests some good groupings of chapters for teaching/self-learning of certain subjects. Definitely recommended for self-study or an introductory course on (discrete) mathematics.
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mjo763
Rated 5 out of 5
March 3, 2016
My BA in math dates from 1978 and I have four grandsons who are collectively beginning to study algebra, entering university, or launching into demand...More
My BA in math dates from 1978 and I have four grandsons who are collectively beginning to study algebra, entering university, or launching into demanding studies and work. Thinking about what I might do for the boys I realised I couldn't remember, for example, how to integrate by partial fractions. This book has been invaluable in dusting off old skills and bringing to mind old knowledge. Heartily recommended.
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Sometimes when you haven't studied maths, the hardest part of approaching a new topic is the lack of understanding of some of the basic notation used to represent the concepts and ideas. Thankfully, this book discusses them as they appear and continues to encourage you to ask questions about the topics, rather than just bury you with proofs. The chapters are pretty self-contained also, and the author suggests some good groupings of chapters for teaching/self-learning of certain subjects. Definitely recommended for self-study or an introductory course on (discrete) mathematics.