A Concise Introduction to Pure Mathematics 4th Edition by Martin Liebeck (PDF)

Description

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 EditionTwo new chapters that serve as an introduction to abstract algebra via the theory of groups, covering abstract reasoning as well as many examples and applicationsNew material on inequalities, counting methods, the inclusion-exclusion principle, and Euler’s phi function Numerous new exercises, with solutions to the odd-numbered onesThrough 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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I ordered from a third party and it took forever to get to me so if you can get it from amazon directly do that. The binding is awful and pages are falling out after just a few months of moderate use. Ink is smeared across the pages like a bad photocopy. The content isn’t the best although it does explain surprisingly well. The author is lazy about the solutions so don’t expect much from the answer key. I am not a fan of the weird notation that isn’t commonly used in the US or anywhere else except for the UK probably. When it says it’s concise it really means it. If you’re expecting a high quality text you will be disappointed.

⭐Has challenging exercises and introduces a variety of topics to get one interesting in proof based mathematics while also introducing the student to different methods of proof. Used this as the textbook for my class and it was enjoyable.

⭐Clear exposition for the nine professional.

⭐Clear, concise, systematic and readable introduction to Pure Mathematics.The Preface states it is appropriate for self-study. However, there are no worked solutions to the even-numbered problems, or a link to an online resource containing same. If I could offer one suggestion, it would be to rectify this.Excellent book otherwise, though, and definitely recommended.

⭐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.

⭐My son is the mathematician and he thinks it’s a great book. Might as well be written in Martian speak for all I understand in it!

⭐Amazing to learn from and goes into great detail!

⭐How non-mathematicians should start. Love it

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