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University of Oxford

Multidimensional Analysis and Geometry - Introduction to the Derivative in Higher Dimensions - Lecture 1

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Explore the derivative in higher dimensions, extending single-variable concepts to multidimensional functions and introducing the derivative as a linear map for best approximation.
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1 Lesons
53 minutes
On-Demand
Free-Video
University of Oxford

The Banach Contraction Mapping Theorem - Oxford Mathematics 1st Year Lecture

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Explore the Banach contraction mapping theorem in this Oxford Mathematics lecture, focusing on guaranteeing convergence of fixed point iterations in one dimension.
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1 Lesons
55 minutes
On-Demand
Free-Video
University of Oxford

Analysis III: Basic Properties of Riemann Integration - Lecture 1

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Explore the fundamental properties of Riemann integration in this first-year Oxford Mathematics student lecture. Delve into the intricacies of proving familiar concepts, such as how the integral of a sum of two functions equals the sum of their individua…
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1 Lesons
47 minutes
On-Demand
Free-Video
Wrath of Math

Uniform Continuity Explained - Real Analysis

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Dive into uniform continuity in real analysis, exploring its definition, examples, proofs, and related theorems. Gain insights into its distinction from standard continuity and its application to compact sets.
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6 Lesons
13 minutes
On-Demand
Free-Video

Sequences

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Explore fundamental concepts of sequences, including limits, convergence, and advanced topics like limsup and the Bolzano Weierstraß Theorem. Gain a deep understanding of mathematical analysis.
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48 Lesons
10 hours
On-Demand
Free-Video

Real Analysis

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Explore fundamental concepts of real analysis, including supremum, completeness, sequences, series, continuity, differentiability, and integration, with a focus on rigorous mathematical proofs and theorems.
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60 Lesons
15 hours
On-Demand
Free-Video
statisticsmatt

Sequences and Series of Real Numbers and Functions

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Comprehensive exploration of real number sequences and series, covering convergence, limits, and advanced mathematical concepts for a deep understanding of analysis fundamentals.
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32 Lesons
4 hours 30 minutes
On-Demand
Free-Video
The Bright Side of Mathematics

Real Analysis

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Comprehensive exploration of real analysis, covering sequences, limits, series, functions, continuity, differentiation, integration, and fundamental theorems of calculus.
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64 Lesons
10 hours
On-Demand
Free-Video
The Bright Side of Mathematics

Functional Analysis

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Comprehensive exploration of functional analysis, covering metric spaces, Banach spaces, Hilbert spaces, operators, and spectral theory, with detailed examples and key theorems.
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32 Lesons
4 hours 30 minutes
On-Demand
Free-Video
NIOS

A Basic Course in Real Analysis

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Explore fundamental concepts of real analysis, including limits, continuity, sets, sequences, series, and theorems. Develop a strong foundation in mathematical reasoning and proof techniques.
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34 Lesons
1 day 7 hours
On-Demand
Free-Video
Wrath of Math

Proving All the Sequence Limit Laws - Real Analysis

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Comprehensive proof of five fundamental sequence limit laws in real analysis, covering sum, difference, constant multiple, product, and quotient of convergent sequences with practical applications.
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7 Lesons
54 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

L1 Full Groups of Flows in Measured Group Theory

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Explore probability measure-preserving actions of reals, associated Polish groups, and their properties. Investigate L1 full groups, their abelianization, and topological rank.
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1 Lesons
33 minutes
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Free-Video
Centre de recherches mathématiques - CRM

Mathematical Tools for the Detection and Analysis of Local Singularities - Lecture 3

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Explorez les outils mathématiques pour détecter et analyser les singularités locales dans divers domaines, en utilisant des bases d'ondelettes et de Wilson pour la classification et l'analyse multifractale.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Local Singularities of Functions: Cusps, Chirps, and Oscillating Singularities - Part II

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Explorez les singularités locales des fonctions, leurs types et applications. Apprenez les méthodes d'analyse harmonique pour détecter et caractériser ces comportements dans divers domaines scientifiques.
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1 Lesons
1 hour 1 minute
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Free-Video
Centre International de Rencontres Mathématiques

Space of Actions of Groups on the Real Line

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Explore group actions on the real line, delving into mathematical concepts and theories presented by Bertrand Deroin in this insightful conference talk.
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1 Lesons
1 hour
On-Demand
Free-Video
Fields Institute

Tame Phenomena Over the Real Field - Lecture 6

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Explore control theory concepts including flows, log spirals, limit cycles, and restricted analytic functions in this advanced graduate-level lecture on tame phenomena.
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11 Lesons
56 minutes
On-Demand
Free-Video
Fields Institute

Tame Phenomena Over the Real Field - Graduate Course Lecture 1

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Explore fundamental concepts of tame control theory, focusing on real field applications and advanced mathematical principles in this graduate-level lecture.
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1 Lesons
46 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

On the Dani Correspondence and Its Applications - Lecture 3

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Delve into ergodic theory and dynamics applications in Diophantine approximation, exploring Dani's correspondence and its impact on understanding rational number density patterns.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

The Dani Correspondence and Its Applications in Diophantine Approximation - Lecture 1

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Explore the dynamic connection between ergodic theory and Diophantine approximation, focusing on Dirichlet's Theorem and its interpretation through orbital behavior in mathematical systems.
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1 Lesons
55 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Noncommutative Maximal Inequality and Ergodic Theorem for Actions of Amenable Groups

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Delve into noncommutative maximal inequality and ergodic theorem, exploring measure-preserving transformations and actions of amenable groups in advanced mathematical theory.
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16 Lesons
58 minutes
On-Demand
Free-Video
Insights into Mathematics

Problems with Limits and Cauchy Sequences - Real Numbers and Limits Math Foundations

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Explores challenges in defining real numbers using Cauchy sequences, discussing convergence concepts and visualizing sequences in the plane. Highlights issues in establishing arithmetic for real numbers.
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8 Lesons
29 minutes
On-Demand
Free-Video
Michael Penn

Real Analysis - Continuity

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Explore the precise definition of continuity in real analysis, its equivalence to sequential continuity, and its connection to Calculus 1 limits. Gain a deeper understanding of this fundamental concept.
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1 Lesons
22 minutes
On-Demand
Free-Video
Michael Penn

Real Analysis - Subsequences

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Explore subsequences in Real Analysis, including the Bolzano-Weirstrass Theorem. Learn key concepts and proofs to deepen your understanding of this fundamental mathematical topic.
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1 Lesons
22 minutes
On-Demand
Free-Video
Michael Penn

Real Analysis - Algebraic Properties of Limits

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Explore algebraic properties of limits in real analysis, proving classic theorems and enhancing understanding of fundamental mathematical concepts.
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5 Lesons
21 minutes
On-Demand
Free-Video
Michael Penn

Real Analysis - The Countability of the Rational Numbers

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Explore a rigorous proof demonstrating the countability of rational numbers using a unique approach of representing them as a countable union of disjoint finite sets in real analysis.
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5 Lesons
21 minutes
On-Demand
Free-Video
Michael Penn

Real Analysis - The Fundamental Theorem of Calculus

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Comprehensive proof of both parts of the Fundamental Theorem of Calculus, demonstrating the relationship between differentiation and integration in real analysis.
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1 Lesons
23 minutes
On-Demand
Free-Video
Michael Penn

Real Analysis - L'Hospital's Rule - Infinity-Infinity Case

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Rigorous proof of L'Hospital's rule for infinity/infinity case, demonstrating its application in calculating limits of indeterminate forms in real analysis.
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7 Lesons
20 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Sam Sanders - Uniformity in Mathematics

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Explore uniformity in mathematics, from historical examples to modern applications. Examine how uniform theorems challenge traditional logical systems and impact proof methods across various mathematical domains.
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13 Lesons
34 minutes
On-Demand
Free-Video
Insights into Mathematics

Real Numbers as Cauchy Sequences - Limitations and Challenges - Math Foundations 114

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Explores logical weaknesses in using Cauchy sequences to define real numbers, challenging traditional approaches and highlighting ambiguities in fundamental mathematical concepts.
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13 Lesons
52 minutes
On-Demand
Free-Video
Insights into Mathematics

Real Numbers and Cauchy Sequences of Rationals - Math Foundations 113

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Explore Archimedean real numbers and Cauchy sequences, examining their definitions, properties, and applications in mathematical analysis and approximation theory.
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6 Lesons
30 minutes
On-Demand
Free-Video
Insights into Mathematics

Real Numbers and Cauchy Sequences of Rationals - Math Foundations 112

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Explores the concept of real numbers, challenging their existence and examining how quantities like length, area, and function values are inherently approximate rather than exact 'real' values.
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8 Lesons
36 minutes
On-Demand
Free-Video
Insights into Mathematics

Real Numbers and Cauchy Sequences of Rationals - Math Foundations 111

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Explores Cauchy sequences of rational numbers as a foundation for real numbers, discussing limits, equivalence classes, and the logical challenges in this approach to constructing the real number system.
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7 Lesons
21 minutes
On-Demand
Free-Video
Insights into Mathematics

Limits to Infinity - Real Numbers and Limits

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Exploring limits of sequences approaching infinity, focusing on rational polynomials and functions. Introduces a simplified definition for verifying limits as finite tasks.
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1 Lesons
38 minutes
On-Demand
Free-Video
Insights into Mathematics

Dedekind Cuts and Computational Difficulties with Real Numbers - Famous Math Problems 19

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Explores the challenges and misconceptions surrounding 'real numbers', examining various approaches like infinite decimals, Dedekind cuts, and Cauchy sequences, while emphasizing the importance of concrete computations in mathematics.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
Insights into Mathematics

Inequalities and Limits in Real Numbers - Math Foundations 107

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Simplified epsilon-delta limit definition for rational polynumbers, with visual interpretation and practical examples. Comprehensive review of inequalities for natural numbers, integers, and rational numbers.
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10 Lesons
35 minutes
On-Demand
Free-Video
Insights into Mathematics

Understanding Limits in Real Numbers - Math Foundations

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Simplified definition of limits for rational polynumber sequences, challenging traditional epsilon-delta approach. Introduces scale and start numbers for bounding differences, offering a more intuitive understanding of limits.
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9 Lesons
35 minutes
On-Demand
Free-Video
Institute for Mathematical Sciences

How to Check When a System of Real Quadratic Equations Has a Solution - Part 2

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Explore advanced techniques for determining solvability of real quadratic equation systems, building on previous concepts and delving into more complex mathematical analysis.
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1 Lesons
38 minutes
On-Demand
Free-Video
NCCR SwissMAP

Factorization of the Calderón Problem Through the Born Approximation

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Explore analytic techniques in dynamics and geometry, focusing on the Calderón problem and its factorization through the Born approximation.
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21 Lesons
58 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Limits and Continuity - Lecture 3

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Explore limits and continuity concepts in calculus, enhancing mathematical understanding and problem-solving skills.
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1 Lesons
19 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

The Heine-Borel Theorem for Metric Spaces

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Explore the Heine-Borel Theorem's application in metric spaces, understanding its significance and implications for compact sets and open covers.
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1 Lesons
17 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

The Bolzano-Weierstrass Property

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Explore the Bolzano-Weierstrass Property, a fundamental concept in mathematical analysis, and its implications for understanding convergence in real number sequences.
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1 Lesons
10 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

The Stone-Weierstrass Theorem

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Explore the Stone-Weierstrass theorem, a fundamental result in functional analysis and approximation theory.
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1 Lesons
31 minutes
On-Demand
Free-Video
BIMSA

Analysis from a Boldface Recursion Theory Point of View

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Explore real analysis through recursion theory, applying results and techniques to gain new insights and perspectives.
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1 Lesons
50 minutes
On-Demand
Free-Video
Banach Center

The 1950s: A Golden Age of Harmonic Analysis - Connections with Calderón-Zygmund Theory - Part 4

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Explore connections between harmonic analysis and Calderón-Zygmund theory in the 1950s, focusing on groundbreaking developments and their lasting impact.
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1 Lesons
1 hour
On-Demand
Free-Video
Banach Center

The 1950s: A Golden Age of Harmonic Analysis - Connections with Calderón-Zygmund Theory - Part 3

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Explore connections between harmonic analysis and Calderón-Zygmund theory in the 1950s, focusing on groundbreaking developments and their lasting impact.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Banach Center

The 1950's: A Golden Age of Harmonic Analysis - Connections with Calderón-Zygmund Theory - Part 1

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Explore connections between harmonic analysis and Calderón-Zygmund theory in the 1950s, focusing on key developments and their impact on modern mathematics.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
Banach Center

The 1950's: A Golden Age of Harmonic Analysis - Connections with Calderón-Zygmund Theory - Part 2

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Explore connections between harmonic analysis and Calderón-Zygmund theory in the 1950s, focusing on groundbreaking developments and their lasting impact on mathematics.
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1 Lesons
1 hour 19 minutes
On-Demand
Free-Video
Banach Center

Maximal Singular Averages - Part 3

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Explore advanced concepts in maximal singular averages, delving into complex mathematical theories and applications in functional analysis.
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1 Lesons
1 hour 17 minutes
On-Demand
Free-Video
Banach Center

Maximal Singular Averages - Part 4

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Explore advanced concepts in maximal singular averages, delving into complex mathematical theories and applications in functional analysis.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Banach Center

Maximal Singular Averages - Part 2

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Explore advanced concepts in maximal singular averages, building on previous knowledge and delving into complex mathematical theories and applications.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Banach Center

Maximal Singular Averages - Part 1

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Explore maximal singular averages with David Beltran from University of Valencia, delving into advanced mathematical concepts and their applications.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
Banach Center

Bourgain's Proof of the Circular Maximal Function Theorem - Part 3

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Explore Bourgain's groundbreaking proof of the circular maximal function theorem, delving into advanced mathematical concepts and techniques.
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1 Lesons
48 minutes
On-Demand
Free-Video
Banach Center

Bourgain's Proof of the Circular Maximal Function Theorem - Part 4

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Explore Bourgain's groundbreaking proof of the circular maximal function theorem in this advanced mathematical lecture by Jonathan Hickman.
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1 Lesons
53 minutes
On-Demand
Free-Video
Banach Center

Bourgain's Proof of the Circular Maximal Function Theorem - Part 1

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Explore Bourgain's groundbreaking proof of the circular maximal function theorem, delving into its mathematical intricacies and significance in harmonic analysis.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
HyperComplex Seminar

The Grad Div Operator in Symmetric Tensors on Riemannian Manifolds

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Explore the grad div operator in symmetric tensors on Riemannian manifolds, focusing on gradient and divergence definitions and their composition in differential geometry.
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1 Lesons
16 minutes
On-Demand
Free-Video