# abstract algebra (blogs) — RSS Amplifier Recent posts from the 2 feeds in the RSS Amplifier directory that cover abstract algebra. Page: Feed: --- ## [Analyzing the narrative of \Kittens Game\](https://ulysseszh.github.io/literature/2026/06/25/kittens-analysis.html) _2026-06-25 · UlyssesZhan · Ulysses’ trip_ Kittens Game is an incremental game that has very few narrative sentences presented in the game. However, it tells a very rich story in its own unique way through the interaction with the player. ## [AI makes learning feel too easy](https://blog.danielyj.com/blog/ai-makes-learning-feel-easy) _2026-06-08 · djeong@colgate.edu (Daniel Jeong) · Daniel Jeong's Blog_ An hour with an AI tutor feels like the best teaching you've ever had, and then nothing sticks. I don't think that's laziness. I think AI is the first tool that can max out the feeling of understanding while starving the fact of it. ## [Text-based visual art in LaTeX](https://ulysseszh.github.io/programming/2026/06/06/tex-text-art.html) _2026-06-07 · UlyssesZhan · Ulysses’ trip_ Using the verbatimbox package, one can include a text-based visual art in a figure in a document generated by LaTeX. ## [macOS Sleep Prevention Cheat Sheet](https://blog.danielyj.com/blog/prevent_sleep) _2026-06-07 · djeong@colgate.edu (Daniel Jeong) · Daniel Jeong's Blog_ caffeinate blocks idle sleep. pmset disablesleep blocks lid-close sleep. ## [Claude doesn't know what time it is](https://blog.danielyj.com/blog/please-give-it-a-clock) _2026-05-23 · djeong@colgate.edu (Daniel Jeong) · Daniel Jeong's Blog_ Gemini has a clock. ChatGPT has the date. Claude has neither, and the obvious fix isn't as obvious as it looks. ## [Democracy's Missing Quarter](https://blog.danielyj.com/blog/demeny-voting) _2026-04-30 · djeong@colgate.edu (Daniel Jeong) · Daniel Jeong's Blog_ A quarter of citizens cannot vote. There is already a proposal for this, called Demeny voting, and it deserves more attention than it gets. ## [Ways of reducing mass rebuilds in Nix without changing Nix](https://ulysseszh.github.io/programming/2026/04/16/reduce-nix-rebuild.html) _2026-04-16 · UlyssesZhan · Ulysses’ trip_ One serious problem with Nix is the amount of mass rebuilds happening in Nixpkgs every time some package with many dependents gets an update. I thought about three ideas to reduce mass rebuilds: store path replacements, separating compiling and linking, and ditching check phases. Each of them has some degree of impracticality. ## [There is but one truly serious philosophical problem, and that is suicide](https://blog.danielyj.com/blog/suicide) _2026-02-27 · djeong@colgate.edu (Daniel Jeong) · Daniel Jeong's Blog_ Contemplating Camus ## [Determining the stabilizability of the abelian sandpile model](https://ulysseszh.github.io/math/2026/01/03/sandpile-stabilizable.html) _2026-01-03 · UlyssesZhan · Ulysses’ trip_ The abelian sandpile model is a cellular automaton where each cell is a sandpile that can topple to put grains on neighboring cells when having enough grains. It is stable if none of the sandpiles can topple. A natural question to ask is whether it can become stable eventually. In this article, I will show that one can determine the stabilizibility usiung integer linear programming for the abelian… ## [From Picard iteration to Feynman path integral](https://ulysseszh.github.io/physics/2025/11/13/picard-path-integral.html) _2025-11-14 · UlyssesZhan · Ulysses’ trip_ The Schrödinger equation is an ODE, so we can approach its solution through Picard iteration. This approach leads to a sum over walks on the graph formed by an orthonormal basis as vertices and the Hamiltonian matrix elements as edge weights. This sum is exactly the Feynman path integral if we choose the position basis and take the continuum limit. ## [Trade Smarter With IBKR (Sponsored)](https://crawlproof.com/a/PFFoD7WTP9At) _2025-11-14 · **Sponsored**_ Join Interactive Brokers through a referral and start investing with low-cost global access. ## [Imperative programming in Nix language](https://ulysseszh.github.io/programming/2025/11/06/nix-imperative.html) _2025-11-07 · UlyssesZhan · Ulysses’ trip_ Nix is a functional programming language primarily used for package management and system configuration. However, it may be interesting to emulate imperative programming constructs within Nix. This post explores how to achieve imperative-style programming in Nix, ipmlementing control flow, exception handling, and interactive IO. ## [Abstract Algebra](https://blog.danielyj.com/blog/class/math-375) _2025-09-08 · djeong@colgate.edu (Daniel Jeong) · Daniel Jeong's Blog_ Note from 2025 Fall Abstract Algebra Course ## [Multi-pass Gaussian blur filter](https://ulysseszh.github.io/programming/2025/07/17/blur-filter.html) _2025-07-17 · UlyssesZhan · Ulysses’ trip_ According to the central limit theorem, the sum of some i.i.d. samples is normally distributed in the limit of large sample size. This fact can be used to implement a multi-pass Gaussian blur filter, where the total number of passes is equal to the number of samples used in the averaging. Through this, we can also see a nice relation to the heat equation, which is not surprising since the heat… ## [The buildup kickroll in \Time to beat the odds\](https://ulysseszh.github.io/music/2025/06/22/beat-the-odds-kickroll.html) _2025-06-22 · UlyssesZhan · Ulysses’ trip_ There is a gradually-accelerating buildup kickroll at 1:18 in the song Time to beat the odds by 影虎。. In order to know the details of this rhythm, I have to analyze the sample using Python. The main method is to do a short-time Fourier transform and to find the peaks in the high-frequency region of the spectrogram. A linear regression shows that the time intervals decay geometrically. ## [Eigenfunctions of the Laplacian on an annulus with homogeneous Neumann boundary condition](https://ulysseszh.github.io/math/2025/04/11/laplacian-annulus.html) _2025-04-11 · UlyssesZhan · Ulysses’ trip_ Several features of the eigenfunctions of the Laplacian on an annulus with homogeneous Neumann boundary condition are discussed. The distribution of the eigenvalues is discussed in detail, making use of a phase angle function called θ \\tht . The limiting cases of a disk and a circle are discussed. ## [The role of particle indistinguishability in statistical mechanics](https://ulysseszh.github.io/physics/2025/03/03/indistinguishability.html) _2025-03-04 · UlyssesZhan · Ulysses’ trip_ Indistinguishability plays an important role in enumerative problems in combinatorics. This article explains the concept and significance of particle indistinguishability in statistical mechanics. ## [Why it is a bad idea to use GitHub for submiting school homework](https://ulysseszh.github.io/misc/2025/01/09/github-homework.html) _2025-01-10 · UlyssesZhan · Ulysses’ trip_ It is common for school courses to require students to submit their homework using GitHub. However, this is usually a bad idea for several reasons, potentially including TOS violation, community degradation, and reliability. ## [How to use JavaScript in GitHub Actions without committing \node\_modules\](https://ulysseszh.github.io/guide/2024/11/15/gh-action-modules.html) _2024-11-16 · UlyssesZhan · Ulysses’ trip_ I was creating my first GitHub Action. According to the official documentation, I should commit the node\_modules to the repo or generate a script that bundles the whole node\_modules if I want to create a JavaScript action. I think this is not good practice, so I try to find another way: manually managing the caches for the dependencies in node\_modules . ## [Some understanding of Grassmann numbers out of intuition](https://ulysseszh.github.io/math/2024/10/10/grassmann-num.html) _2024-10-11 · UlyssesZhan · Ulysses’ trip_ I was briefly introduced to Grassmann numbers when I studied quantum field theory. I then had the natural question of how we can formally define them. In this article, I went with my intuition and tried to answer this question. ## [MATH354 Data Analysis I](https://blog.danielyj.com/blog/class/data-analysis) _2024-10-05 · djeong@colgate.edu (Daniel Jeong) · Daniel Jeong's Blog_ Notes for MATH354A - Data Analysis I from Fall 2024, taught by Dr. William Cipolli. ## [Stop CI/CD & Supply-Chain Attacks (Sponsored)](https://crawlproof.com/a/aG8CulCw4Iu3) _2024-10-05 · **Sponsored**_ Per-PR: 17 CI/CD checks and package malware scans with inline Check Run findings. ## [Number Theroy & Mathematical Reasoning](https://blog.danielyj.com/blog/class/num-theo) _2024-10-04 · djeong@colgate.edu (Daniel Jeong) · Daniel Jeong's Blog_ Note from 2024 Fall Number Theory & Mathematical Reasoning Course ## [The notational convenience of imaginary time in the derivation of the metric in Poincaré coordinates](https://ulysseszh.github.io/physics/2024/09/10/poincare-coord-imag.html) _2024-09-10 · UlyssesZhan · Ulysses’ trip_ In general relativity, people usually choose one of the two major metric signatures. However, in certain cases, the imaginary time convention can be more convenient. Here is one of such cases: the derivation of the metric in Poincaré coordinates for the anti-de Sitter space.