Everything about Real analysis
Mathematics of real numbers and real functions
Real analysis is the part of mathematical analysis, especially as taught in undergraduate and graduate courses, that develops calculus rigorously over the real numbers and Euclidean spaces. Introductory real analysis is sometimes called advanced calculus, and studies limits, continuity, compactness, differentiation, integration, and series. More advanced courses often include measure theory, Lebesgue integration, and function spaces. Real analysis is also known, especially in older books, as the theory of functions of a real variable, in contrast to the theory of complex variables. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Real analysisA 5-minute orientation
- Skim a recent paper: Large-Scale Analysis on Anti-Analysis Techniques in Real-World MalwareInfluential work since 2022
- Pick up a classic book: Problems and theorems in analysisThe most-reprinted book on the subject
- Read the landmark paper: Analysis of Relative Gene Expression Data Using Real-Time Quantitative PCR and the 2−ΔΔCT MethodCited 168,064 times
- Go sideways: Lebesgue integralA closely related topic
- Go sideways: Glossary of real and complex analysisA closely related topic
📖 Definitions
Noun The branch of mathematics dealing with the real numbers and related structures.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Analysis of Relative Gene Expression Data Using Real-Time Quantitative PCR and the 2−ΔΔCT Method
Getting Real in Analysis
Set Theoretic Real Analysis
Real Analysis in Reverse
Mechanizing Nonstandard Real Analysis
Algebraic real analysis
Real and Complex Analysis.
Finitistic real analysis
🆕 Influential since 2022
📚 Books worth reading
Problems and theorems in analysisGeorge Pólya, Gábor Szegő · 1925
Real AnalysisH. L. Royden, Patrick Fitzpatrick · 1963
Introduction to real analysisManfred Stoll · 1997
Income Approach to Property ValuationAndrew Baum, David Mackmin · 1989
Understanding AnalysisStephen Abbott · 2001
CalculusHarley Flanders · 1970
Matematicheskiĭ analizG. E. Shilov · 1960
Introduction to AnalysisCorey M. Dunn · 2017
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Lebesgue integral In mathematics, the integral of a non-negative function of a single variable can be regarded, in the simplest case, as the area between the graph of that…
- Glossary of real and complex analysis This is a glossary of concepts and results in real analysis and complex analysis in mathematics. In particular, it includes those in measure theory (as…
- Lebesgue differentiation theorem In mathematics, the Lebesgue differentiation theorem is a theorem of real analysis, which states that for almost every point, the value of an integrable…
- Mathematical analysis Mathematical analysis is the branch of mathematics that studies functions, spaces, and operators through methods of approximation and convergence. It grew…
- List of real analysis topics This is a list of articles that are considered real analysis topics. See also: glossary of real and complex analysis. Limit of a sequence Subsequential…
- Integral In mathematics, an integral is the continuous analog of a sum, and is used to calculate areas, volumes, and their generalizations. The process of computing…
- Uniform convergence In the mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence. A sequence of functions…
- Radon measure In mathematics, specifically measure theory), a Radon measure, named after Johann Radon, is a measure on the σ-algebra of Borel sets of a Hausdorff space…