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Real analysis - an introduction : mathematical arguments and elementary proof techniques / Michael Cullinane.
- Format:
- Book
- Author/Creator:
- Cullinane, Michael J., author.
- Series:
- De Gruyter graduate
- Language:
- English
- Subjects (All):
- Functions of real variables.
- Mathematical analysis.
- Physical Description:
- 1 online resource.
- Place of Publication:
- Berlin : De Gruyter, [2025]
- Summary:
- Designed for a broad spectrum of mathematics majors, not only those pursuing graduate school, this book also provides a thorough explanation of undergraduate Real Analysis. Through a developmentally appropriate narrative that integrates informal discussion, motivation, and basic proof writing approaches with mathematical rigor and clarity, the aim is to assist all students in learning more about the real number system and calculus theory.
- Contents:
- Frontmatter
- VPreface
- VIIContents
- Algebraic and order properties of the real numbers
- Absolute value and distance
- The natural numbers, the integers, and the rational numbers
- The completeness of the real numbers
- Finite sets and infinite sets
- The nested intervals property
- Limit points, closed sets, and open sets
- Connected sets and compact sets
- An introduction to sequences and sequential convergence
- More about sequences and convergence
- Subsequences
- Limits of functions
- An introduction to continuous functions
- More about continuity
- The derivative
- The mean value theorem
- Taylor polynomials
- The Riemann integral
- Criteria for integrability
- The fundamental theorem of calculus
- Approximating the value of an integral
- Infinite series
- Absolute convergence and conditional convergence
- Regroupings and rearrangements of series
- Sequences and series of functions
- Uniform convergence
- More about power series and Taylor series
- The trigonometric functions
- Two remarkable results of Weierstrass
- Sets, relations, and functions
- Fundamentals of logic
- Essential proof strategies
- A geometric approach to the cosine and sine functions
- 573Index
- Notes:
- Includes bibliographical references and indexes.
- Online resource; title from PDF title page (De Gruyter Brill, viewed May 8, 2026).
- Other Format:
- Print version: Cullinane, Michael J. Real analysis - an introduction.
- ISBN:
- 9783111429946
- 3111429946
- 9783111429564
- 3111429563
- OCLC:
- 1530778255
- Publisher Number:
- CIPO000260330
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