Learning log / Field notes
Small steps, documented honestly.
Notes from mathematics, computer science, and AI. These are working records, not polished claims of expertise.
October 17, 2026
Analysis Homework: Sequence Properties and the Stolz Theorem
Separating convergence, boundedness and growth in absolute value, then unpacking telescoping sums and the vanishing initial contribution in the Stolz theorem.
October 6, 2026
Sequence-Limit Practice: Bounds, Squeezing, and Counterexamples
Notes from my recent practice with sequence limits: controlling oscillating factors, rewriting radicals, and using counterexamples to distinguish convergence from divergence.
September 22, 2026
From Suprema to Sequence Limits: Reviewing My Bernoulli Inequality Project
Connecting my recent work on completeness with the epsilon-N definition and reviewing a Bernoulli-inequality proof that qⁿ→0 when |q|<1.
September 20, 2026
From Dedekind Cuts to Suprema: Organizing the Real Number Story
Connecting Dedekind lower sets, decimal expansions, the Archimedean property, density of the rationals, and the supremum principle.
September 18, 2026
From the Rationals to the Reals: Three Viewpoints
Revisiting Dedekind cuts, Cauchy sequences, and the Archimedean property while recording what I still do not fully understand.
September 13, 2026
From Python Conditionals to s×n Matrices
Reviewing f-strings, conditional branches, pass, and nested statements while beginning n-variable linear systems and their matrix representation.
September 11, 2026
Uniqueness of a Dedekind Boundary and Python Modulo
Getting stuck on the boundary-number proof behind Dedekind continuity, then clarifying modulo, equality, and inequality in Python.
September 8, 2026
Starting with 0.4 − 0.3: Python Basics and a Study Strategy Reset
Reviewing Python operators, conditionals, and floating-point approximation in the library, then clarifying the roles of my university text, Understanding Analysis, Python, and English.
September 2, 2026
One Hour After Training: Python Escape Sequences and Induction
An hour in the library revisiting Python type checks and escape sequences, then tracing the logic of mathematical induction in an English-language textbook.
August 30, 2026
Two Hours in the Library: Proof Strategies and Temporary Variables
Distinguishing direct proof, contradiction, and contraposition in Understanding Analysis, then reviewing temporary variables in Python.
August 29, 2026
Three Hours in the Library: Revisiting Python Basics
A review of Python types and triple-quoted strings, alongside continued work on my Chinese–English analysis glossary.
August 29, 2026
August Notes: Python Foundations and a First Look at Analysis
Early work on Python and real analysis, the gaps that became visible after a break, and a plan to revisit the foundations.
July 31, 2026
Day Zero: Why I am learning in public
The starting point of a four-year experiment in mathematics, AI, and honest documentation.