Category: mathPage 1 of 2

How far is Three from Two?

I am logging what I witnessed in different fields, the example and potential contributing factors for two – three crevice. Exploring the intractability boundary, I theorized two is…

Stochastic quotes

Quotes I invented for myself and for teaching. Will be continuously updated. Rate becomes probability for time customer (s/s) dBt: Denstined to be created By part and killed…

Dictionary of Induction and Contradiction

The most memorable comment from Daniel Bienstock’s first optimization lecture was “we use induction when there is a structure”. But upon my question “how about contradiction” instead of…

Approach via its Dual and Negative form

두 수학과 교수님께서 수학기본정신으로 강조하신 내용 체용 (or 음양)의 쌍대론 수학적 귀납법과 귀류법이 전부 을 제 언어로 풀어봤습니다: 귀납법은 용적 명제를 체로 접근 (용-체) 귀류법은 체적 명제를 이체로…

fixed point algorithm

How would you find the solution to the following equation? First, evaluate x in the first equation with y = 1 on the left, call this x_1. Then…

Clever Lifting

My question began from how and where could the idea of lifting or augmentation be used cleverly like HMC? Adding the momentum variable helps structured sampling in HMC….

Ten great ideas about chance

– How chance is solidified as probability and applied to mathematics, statistics, economics, and finance to physics and computer science – Starting from Cardano and Ramsey who thought…

Structure-based Transport: how Bayes meets Geometry

Optimal exploration of model+algorithm space is my research interest. We, modelers, face this problem every day as we add, subtract, and transform the predictors to our time-series, linear…

MathLog

Model+Algorithm space aka. mathematical formulation + computational tool trying to reproduce the real world and posterior space. As the figure suggests, a combination of two mathematical formulations, prior…

Review on Math without numbers

(tbc) contents topology: shape, manifold, dimension analysis: infinity, continuum, maps algebra: abstraction, structure, inference foundation modeling: model, automata, science Theory proved in the book there are infinite number…