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Welcome to Jiahao's Academic Space

"The theory of probability as mathematical discipline can and should be developed from axioms in exactly the same way as Geometry and Algebra." โ€” Andrey Kolmogorov (ๅฎ‰ๅพท้›ทยท็ง‘ๅฐ”่Žซๅ“ฅๆด›ๅคซ)

"All models are wrong, but some are useful." โ€” George E.P. Box (ไน”ๆฒปยทๅšๅ…‹ๆ–ฏ)

๐Ÿ‘จโ€๐Ÿ’ป About Me

Welcome to my academic notes homepage! I am an undergraduate student majoring in Statistics at the School of Mathematical Sciences, Zhejiang University (ZJU). Prior to this, I was a student in the Physics program of the Qiushi Science Class at Chu Kochen Honors College. I later transferred to the School of Mathematical Sciences driven by personal interest and long-term career goals.

Currently, my research interests focus on the following fields:

  • High-Dimensional Statistical Inference (e.g., Knockoff Filter algorithms)

  • Conformal Prediction

  • Probability Theory and Stochastic Processes (Personal pursuit)

  • Quantitative Finance (Personal interest)

๐Ÿ’ก Philosophy

The purpose of this website is twofold. First, it serves as a platform to organize my scattered handwritten derivations from scratch paper and my iPad into systematic notes for future review. Second, I firmly believe in the power of open-source and knowledge sharing, hoping that these notes might provide some value to others in the community.

๐Ÿ“– Selected Coursework

Below are the mathematics and statistics courses I have completed or am currently taking at ZJU:

๐Ÿ“ˆ Probability & Statistics

  • Stochastic Differential Equations

  • Asymptotic Statistical Theory

  • Stochastic Processes

  • Mathematical Statistics

  • Probability Theory

  • Multivariate Statistical Analysis

  • Regression Analysis

  • Statistical Learning

  • Statistical Computing

  • Mathematical Practice

๐Ÿงฎ Advanced Pure Mathematics

  • Functions of Real Variables

  • Functional Analysis

  • Point-Set Topology

  • Ordinary Differential Equations

  • Honors Mathematical Analysis I & II

  • Advanced Algebra & Analytic Geometry I & II

  • Mathematical Analysis III

๐ŸŒŒ Applied Mathematics & Computation

  • Mathematical Software

  • Discrete Mathematics

  • Practical Optimization Algorithms

  • Data Structures and Algorithms

  • Intro to Uncertainty Quantification

๐Ÿ“ฌ Contact & Contribution

All mathematical derivations on this website originate from my personal course-taking (including on-campus courses and recorded lectures from ZJU) and self-study manuscripts. The progress and difficulty are matched to the undergraduate and graduate curricula of the School of Mathematical Sciences at Zhejiang University.

To improve efficiency, the Markdown formatting, LaTeX typesetting, and the translation of the English version were completed with the assistance of Large Language Models (primarily Gemini 3.1 Pro).

Mathematical derivations inevitably contain typos or blind spots. If you find any errors while reading, or if you share a mutual interest in statistical inference, conformal prediction, probability theory, stochastic processes, or quantitative finance, I would be more than happy to connect!

๐ŸŒ Beyond Math

Beyond probability measures and statistical methods, I am a passionate football fan (Visca el Barรงa!). One of my bucket list items is to attend a World Cup knockout match involving Spain or Argentina, or a UEFA Champions League match featuring FC Barcelona at the Camp Nou.

๐Ÿ“š Quick Navigation

  • Stochastic Differential Equations Enter

  • Asymptotic Statistics Enter

  • Email: jiahaot1122@gmail.com

  • GitHub: @jhao1122

Stay rigorous, and keep computing.

๐Ÿ’ฌ Comments