MA5L002
Masters (Mathematics)
· Generally offered: Autumn
Real Analysis
L 3 T 1 P 0 Credits 4 Hours 4
Real number system and Set theory: Completeness property, Archimedian property, Denseness of rationals and irrationals, Countable and uncountable, Cardinality, Zorn’s lemma, Axiom of choice.
Metric spaces: Open sets, Closed sets, Continuous functions, Completeness, Cantor intersection theorem, Baire category theorem, Compactness, Totally boundedness, Finite intersection property.
Rlemann-Stieitjes integral: Definition and existence of the integral, Properties of the integral, Differentiation and integration.
Sequence and Series of functions: Uniform convergence, Uniform convergence and continuity, Uniform convergence and integration, Uniform convergence and differentiation. Equicontinuity, Ascoli’s Theorem, Weierstrass approximation theorem.
Full syllabus document →
Metric spaces: Open sets, Closed sets, Continuous functions, Completeness, Cantor intersection theorem, Baire category theorem, Compactness, Totally boundedness, Finite intersection property.
Rlemann-Stieitjes integral: Definition and existence of the integral, Properties of the integral, Differentiation and integration.
Sequence and Series of functions: Uniform convergence, Uniform convergence and continuity, Uniform convergence and integration, Uniform convergence and differentiation. Equicontinuity, Ascoli’s Theorem, Weierstrass approximation theorem.
3 questions tagged to this course
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Votes
Range of self-invertible real valued function
Let \( f:\mathbb{R}\longrightarrow\mathbb{R} \) be a function of the form \[ f(x) = \dfrac{ax+b}{cx+d}, \quad\text{where}\quad a,b,c,d \neq 0 \quad\text{and}\quad cx+d \neq 0. \] F…
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Votes
Existance of Null set
What is the general meaning of the word "existence" in broader mathematical context? Does null set exist?