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#Generating Functions

Showing: 34 courses

Number Theory

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Comprehensive exploration of number theory, covering foundational concepts to advanced topics like quadratic reciprocity, integer partitions, and Ramanujan's congruences.
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34 Lesons
16 hours
On-Demand
Free-Video
Kimberly Brehm

Discrete Math II - Combinatorics

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Explore advanced combinatorics, including permutations, generating functions, recurrence relations, graph theory, and algorithms, enhancing problem-solving skills in discrete mathematics.
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34 Lesons
12 hours
On-Demand
Free-Video
3Blue1Brown

Olympiad Level Counting - How Many Subsets of {1,…,2000} Have a Sum Divisible by 5?

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Explore advanced counting techniques using generating functions and complex numbers to solve a challenging subset sum problem, with applications to Olympiad-level mathematics.
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7 Lesons
35 minutes
On-Demand
Free-Video
Mathologer

Explaining the Bizarre Pattern in Making Change for a Googol Dollars - Infinite Generating Functions

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Explore the fascinating mathematics behind making change for a googol dollars, uncovering surprising patterns and using infinite generating functions to solve this complex problem.
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5 Lesons
31 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Méthodes Automatiques pour la Génération Aléatoire de Structures - Cours 1

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Explorez les méthodes automatiques de génération aléatoire de structures mathématiques dans cette conférence approfondie. Découvrez des techniques avancées pour créer et analyser des structures complexes.
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1 Lesons
1 hour 15 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Functional Equations and Combinatorics

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Explorez les équations fonctionnelles et la combinatoire avec Lucia Di Vizio dans cette conférence mathématique approfondie.
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1 Lesons
1 hour 25 minutes
On-Demand
Free-Video
IPhT-TV

Enumeration of Walks by Winding Angle

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Explore techniques for enumerating walks based on winding angle, delving into mathematical concepts and applications in statistical physics.
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1 Lesons
1 hour
On-Demand
Free-Video
Insights into Mathematics

Combinatorics - Math History - NJ Wildberger

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Explore combinatorics through historical examples, counting problems, graph theory, and generating functions. Delve into partitions, Fibonacci numbers, Catalan sequence, and famous theorems in this engaging mathematical journey.
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8 Lesons
41 minutes
On-Demand
Free-Video
Michael Penn

How Is This Huge Function Useful

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Explore the utility of a complex function through examples, recursion, generating functions, and differential equations in this engaging mathematical analysis.
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5 Lesons
22 minutes
On-Demand
Free-Video
Michael Penn

Some Identities Involving the Riemann-Zeta Function

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Explore the Riemann-Zeta function, its generating function for positive even integers, and derive sum identities in this mathematical deep dive.
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1 Lesons
26 minutes
On-Demand
Free-Video
Michael Penn

Generating Functions and Combinatorial Identities

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Explore techniques for manipulating generating functions to create new combinatorial sum identities, with an application to Fibonacci number sums.
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1 Lesons
24 minutes
On-Demand
Free-Video
Michael Penn

A Series Involving Harmonic Numbers - Featuring the Dilogarithm Function

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Explore generating functions to calculate sums of series with harmonic numbers, featuring the dilogarithm function in advanced mathematical analysis.
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1 Lesons
21 minutes
On-Demand
Free-Video
Michael Penn

What Is It Like to Be a Pure Mathematician?

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Explore the life of a pure mathematician, delving into abstract algebra, group theory, and partitions. Gain insights into the field's challenges, problem-solving approaches, and the beauty of elegant proofs.
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17 Lesons
1 hour 13 minutes
On-Demand
Free-Video
Michael Penn

Difference at Distance 1 - Number Theory

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Explore number theory concepts focusing on difference 2 at distance 1, with examples, proofs, and generating functions to deepen understanding of this mathematical topic.
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6 Lesons
30 minutes
On-Demand
Free-Video
Michael Penn

How to Use Generating Functions with Integer Partitions - Number Theory

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Explore generating functions in integer partitions, including unrestricted and restricted cases, with applications to odd parts and rational functions in number theory.
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10 Lesons
30 minutes
On-Demand
Free-Video
Michael Penn

Generating Functions - Number Theory

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Explore generating functions in number theory, learning their applications and techniques for solving complex mathematical problems.
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1 Lesons
25 minutes
On-Demand
Free-Video
Michael Penn

Catalan Numbers - Generating Function and Closed Form

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Explore generating functions and closed forms for Catalan numbers, building on recursion concepts to derive a comprehensive understanding of this important mathematical sequence.
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1 Lesons
33 minutes
On-Demand
Free-Video
Michael Penn

So Many Factorials

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Explore advanced mathematical techniques to evaluate complex factorial series, utilizing central binomial coefficients, generating functions, and trigonometric integrals for problem-solving.
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1 Lesons
29 minutes
On-Demand
Free-Video
Michael Penn

A Mysterious Chinese Contest Problem

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Explore generating functions for integer partitions to solve a challenging math contest problem, enhancing problem-solving skills and deepening understanding of advanced mathematical concepts.
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1 Lesons
21 minutes
On-Demand
Free-Video
ICTP Mathematics

Invariants of Manifolds from 6 Dimensions

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Explore advanced mathematical concepts in gauge theories and differential invariants, focusing on invariants of manifolds from 6 dimensions and their applications in theoretical physics.
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7 Lesons
1 hour 4 minutes
On-Demand
Free-Video
ICTP Mathematics

Computation of the Vertical Vafa-Witten Invariants II

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Explore advanced algebraic geometry concepts, focusing on vertical Vafa-Witten invariants computation using localization on Hilbert schemes of points for toric surfaces.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
ICTP Mathematics

ICTP-IGAP Algebraic Geometry Seminar on Vertical Vafa-Witten Invariants

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Explore Vafa-Witten invariants, focusing on vertical components. Examine moduli space fixpoint loci, generating functions, and conjectural formulas for both vertical and horizontal invariants.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Fields Institute

Motivic Hochschild Homology Over Algebraically Closed Fields

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Explore Hochschild homology in motivic spectra, uncovering torsion classes and connections to Steenrod algebra. Gain insights into algebraic geometry and homotopy theory applications.
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1 Lesons
33 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Enumeration of Maps via Integrability

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Explore map enumeration techniques, from Tutte's work to KP hierarchy, deriving recurrence formulas for oriented and non-oriented maps using integrability methods in mathematics and physics.
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1 Lesons
46 minutes
On-Demand
Free-Video
Western Hemisphere Virtual Symplectic Seminar

Open/Closed Correspondence and Mirror Symmetry in Gromov-Witten Theory

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Explore open/closed correspondence in Gromov-Witten theory, examining numerical invariants, generating functions, and compatibility with mirror symmetry in toric Calabi-Yau manifolds.
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20 Lesons
52 minutes
On-Demand
Free-Video
NPTEL-NOC IITM

Laguerre Polynomials: Generating Function and Three-Term Recurrence Relation - Lecture 55

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Explore Laguerre polynomials through generating functions and three-term recurrence relations, enhancing your understanding of these important mathematical tools.
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1 Lesons
19 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Hausdorff Moment Problems for Combinatorial Numbers: Heuristics via Meijer Functions

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Explore Hausdorff moment problems for combinatorial sequences, focusing on integral ratios of factorials. Learn techniques to solve these problems and discover patterns in Meijer G-function encodings.
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1 Lesons
45 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Phase Transitions of Composition Schemes and Their Universal Limit Laws

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Explore phase transitions in composition schemes, analyzing critical cases and their impact on asymptotic behavior. Uncover rich limit laws and universal properties in combinatorial structures.
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1 Lesons
47 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Solving Equations from Combinatorics via Computer Algebra

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Explore advanced techniques for solving discrete differential equations in combinatorics using computer algebra, focusing on efficient methods for n=2 cases and recent developments in systems of equations.
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1 Lesons
43 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Counting Partitions by Genus

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Explore set partition counting by genus, focusing on primitive partitions and functional equations to reconstruct all partitions, with emphasis on genus 0-2 cases.
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1 Lesons
49 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Counting Restricted Set Partitions with Hypergeometrics

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Explore advanced set partition counting using hypergeometric functions and generalized Hermite polynomials. Gain insights into restricted Bell numbers and their closed-form expressions.
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1 Lesons
46 minutes
On-Demand
Free-Video
BIMSA

Elliptic Cohomology and Enumerative Geometry

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Explore the intersection of elliptic cohomology and enumerative geometry, focusing on stable envelopes and their role in understanding q-difference equations.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

The Squish Map and the SL_2 Double-Dimer Model

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Explore measure-preserving maps between dimer models on hexagon lattices, connecting single and double-dimer models for insights into partition functions and plane partition enumeration.
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1 Lesons
50 minutes
On-Demand
Free-Video
ACM SIGPLAN

Guaranteed Bounds for Discrete Probabilistic Programs with Loops via Generating Functions - LAFI'24

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Explore a technique for finding guaranteed bounds on posterior distributions in probabilistic programs with loops using probability generating functions and inductive invariants.
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1 Lesons
10 minutes
On-Demand
Free-Video