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2024 Spring / 2024.05.21.

수학적 모델링과 미분방정식

연사: 김태훈 (성균관대학교)

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Mathematical Modeling and Differential Equation

Presentation Material

Slide deck: Mathematical Modeling and Differential Equation

SEMINARS

Denoising Diffusion Probabilistic Models(DDPM)
Invariant of Knot
Random Walks on Sₙ
Why Precise Definitions Matter in Mathematics: Bertrand's Paradox
Functor of Points in AG
Continuum Hypothesis and Descriptive Set-theorical Approaches
Dimension in Mathematics
Regression and Its Applications
Do You Know All About π?
Derivation of the Black-Scholes PDE
The Shortest Proofs in Math
Cybenko’s Universal Approximation Theorem and Why It Is Not Enough
Categorical Classical Physics via Commutative and Boolean Algebras
The Four Color Theorem
S¹, S², S³
Uniqueness of the Sudoku Solution
Counting with Symmetry
Simple Homotopy and Whitehead Group

1+1=0
Course Registration and Game Theory
Tessellations of H²
Randomness and Infinity
Dual Number and Split-Complex Number
Basic Convex Optimization II - Second-Order Methods
Peter-Weyl Theorem
Root System of Semisimple Lie Algebra and Its Classification
Antipodes and Involutions
Understanding Surfaces with Curvatures
Introducing Mapping Class Group, Teichmuller Space and Moduli Space
Introduction to CNN and RNN
What Makes a Good Rhythm?
Alternative Way to Estimate Our Test Rank, Bayesian Statistics
The Mathematics of Uncertainty: An Introduction to Fuzzy Sets
Duality in Mathematics
From 0 to Complex Numbers

Euclid’s 5th Postulate and Non-Euclidean Geometry
A Novel Approach to Math, Combinatorics
Mystery of Infinite Series
Euler-Lagrange Equation
Functions Defined on Rational Numbers
Is Mathematics Complete?
Two Perspectives on Satisfaction: Topology and Economics
Thinking About the Collatz Conjecture
A Linear Convergence Result for the Jacobi-Proximal Alternating Direction Method of Multipliers
Continuity and Differentiability of Weierstrass Function
Basic Convex Optimization (Algorithm and Duality)
Introduction to Gradient Descent
Integration Techniques and Feynman’s Trick
Chord Progressions and Math
Game Is Math: Mathematical Strategies and Algorithms in the Mini Metro Game
Computer and Simulation
Introduction and Construction of Polar Code
P-adic Number and Hasse-Minkowski Theorem

Introduction of Gamma Function
Winning Strategies for Party Games
The German Tank Problem
What Is Distance?
Elementary Proof of the Insolvability of the Quintic
Integrals in Euclidean and Banach Spaces
Poset Matrices Structure, Enumeration, and Application
Electromagnetic Properties Interpreted in Elementary Calculus
Fourier Series and Transformation
Matrix Norm: Condition Number and Eigenvalue Problem
Riemann-Roch Theorem
Intuition and Construction of Differential Form
How to Define Tensor Product
Introduction to Hypothesis Testing and Statistics
QuantGANs Using GANs for Financial Forecasting
Is a Donut the Same as Coffee Mug? Using First Homotopy and Simplicial Homology
On Analysis of Desire

What Is Counting?
Fundamental Theorem of Algebra
0.999... ≠ 1
Supervised Learning VS Reinforcement Learning
P-adic Number
What is Knot Theory
Maxwell Equation Using Differential Forms
Number of Straw Holes
An Introduction to the Gromov-Hausdorff Distance Between Spheres
An Introduction to Operator Theory
What Is Scissors Congruence?
Introduction to Zeta Functions of Algebraic Structures and Their Applications
Find a Rabid Dog!
Mathematical Modeling and Differential Equation
Introduction to Riordan Poset and Its Application
Parity: Even and Odd Number
Introduction to Knots and Fundamental Groups
Mathematics of Fools: Farey Sequence

100 Prisoners Problem

History of Mathematics : A Journey to Find the Foundation of Mathematics

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