Concept

Combinatorics

Related lectures (30)

Ergodic properties of low complexity symbolic systems

Explores the influence of complexity on ergodic properties of symbolic systems, presenting the Curtis-Hedlund-Lyndon Theorem and constructions of minimal subshifts.

Applications of Ergodic Theory to Combinatorics

Explores the applications of ergodic theory to combinatorics and number theory, including Szemerédi's Theorem and the Erdős-Kac Theorem.

Metric Spaces and Isometric Embeddings

Covers metric spaces, isometric embeddings, and equilateral spaces with examples and proofs.

Probability and Statistics

Introduces probability, statistics, distributions, inference, likelihood, and combinatorics for studying random events and network modeling.

Correlation Functions in Loop Models: Structural Assumptions

Covers correlation functions in loop models and the role of degenerate fields in conformal field theory.

Algebraic Structures: Groups and Rings

Introduces algebraic structures essential for understanding mathematical objects used in science and engineering.

Carpan Collector Problem

Explores the Carpan collector problem, analyzing expected completion times and waiting times for collecting different objects uniformly at random.

Combinatorial Principles: Factorials and Probabilities

Introduces combinatorial principles, factorials, probabilities, harmonic series convergence, and strategic decision-making in a romantic scenario.

Combinatorics: Counting Methods

Introduces combinatorics and counting methods for determining possible outcomes in various scenarios, illustrated with examples.

Probability Theory: Properties and Combinatorial Principles

Explores probability properties, inclusion-exclusion principle, combinatorial rules, and birthday coincidence probability calculation.

Algebraic Structures: Groups and Rings

Covers groups, rings, number theory, atomic bonds, and materials structure, setting the foundation for further exploration.

Combinatorial Group Theory

Introduces combinatorial group theory, emphasizing group presentations, normal subgroups, and group quotients.

Binomial coefficients

Explores binomial coefficients, Pascal's triangle, binomial theorem, and object distribution among persons.

Probabilistic Methods in Combinatorics

Covers the Erdős-Ko-Rado problem, intersecting set families, and selecting valid winners.

Determinants: Alternate Forms and Symmetrization

Explores alternate forms, symmetric forms, and determinants in linear algebra.

Group Theory: Combinatorial Approach

Covers group theory with a focus on group presentations and subgroup generation.

Counting, Recording: Summary

Summarizes counting principles, rules, and theorems in combinatorics with examples.

Permutation of In: Simplified Notation

Covers the simplified notation for expressing permutations and their applications in mathematics.

Combinatorial Logic Circuits

Covers the basics of logical systems, Boolean algebra, logic gates, and coding in digital circuits.

Tactical Configurations: Rödl Nibble

Explores tactical configurations, covering the minimal size of subsets needed to cover element sets and the concept of K-sets and base points.

Related lectures (30)

Ergodic properties of low complexity symbolic systems

Explores the influence of complexity on ergodic properties of symbolic systems, presenting the Curtis-Hedlund-Lyndon Theorem and constructions of minimal subshifts.

Applications of Ergodic Theory to Combinatorics

Explores the applications of ergodic theory to combinatorics and number theory, including Szemerédi's Theorem and the Erdős-Kac Theorem.

Metric Spaces and Isometric Embeddings

Covers metric spaces, isometric embeddings, and equilateral spaces with examples and proofs.

Probability and Statistics

Introduces probability, statistics, distributions, inference, likelihood, and combinatorics for studying random events and network modeling.

Correlation Functions in Loop Models: Structural Assumptions

Covers correlation functions in loop models and the role of degenerate fields in conformal field theory.

Algebraic Structures: Groups and Rings

Introduces algebraic structures essential for understanding mathematical objects used in science and engineering.

Carpan Collector Problem

Explores the Carpan collector problem, analyzing expected completion times and waiting times for collecting different objects uniformly at random.

Combinatorial Principles: Factorials and Probabilities

Introduces combinatorial principles, factorials, probabilities, harmonic series convergence, and strategic decision-making in a romantic scenario.

Combinatorics: Counting Methods

Introduces combinatorics and counting methods for determining possible outcomes in various scenarios, illustrated with examples.

Probability Theory: Properties and Combinatorial Principles

Explores probability properties, inclusion-exclusion principle, combinatorial rules, and birthday coincidence probability calculation.

Algebraic Structures: Groups and Rings

Covers groups, rings, number theory, atomic bonds, and materials structure, setting the foundation for further exploration.

Combinatorial Group Theory

Introduces combinatorial group theory, emphasizing group presentations, normal subgroups, and group quotients.

Binomial coefficients

Explores binomial coefficients, Pascal's triangle, binomial theorem, and object distribution among persons.

Probabilistic Methods in Combinatorics

Covers the Erdős-Ko-Rado problem, intersecting set families, and selecting valid winners.

Determinants: Alternate Forms and Symmetrization

Explores alternate forms, symmetric forms, and determinants in linear algebra.

Group Theory: Combinatorial Approach

Covers group theory with a focus on group presentations and subgroup generation.

Counting, Recording: Summary

Summarizes counting principles, rules, and theorems in combinatorics with examples.

Permutation of In: Simplified Notation

Covers the simplified notation for expressing permutations and their applications in mathematics.

Combinatorial Logic Circuits

Covers the basics of logical systems, Boolean algebra, logic gates, and coding in digital circuits.

Tactical Configurations: Rödl Nibble

Explores tactical configurations, covering the minimal size of subsets needed to cover element sets and the concept of K-sets and base points.