Hi, I’m Dapeng Feng.你好，我是冯大鹏。
I share what I learn about mathematics, physics, and programming here. Through diagrams, interactive experiments, and benchmarks, I try to make abstract ideas easier to understand.我在这里分享数学、物理与编程中的学习和思考，用图解、交互实验和基准测试，把抽象概念讲清楚。
From abstract ideas to visual intuition从抽象公式，到直觉与图形
01 / MATHEMATICSModels that make sense of the world用模型，解释世界如何运转
02 / PHYSICSCloser to the metal. Every cycle counts.走近底层，让每个周期有价值
03 / SYSTEMSLess guessing. More measuring.少一点猜测，多一点测量
04 / EXPERIMENTSFive interactive experiments connect LIF, UltraLIF, BPTT, STDP and EventProp. From dynamics to learning rules, bring the equations to life.用五个交互实验，串起 LIF、UltraLIF、BPTT、STDP 与 EventProp。从动力学到学习规则，让公式真正动起来。
Memory safety, zero-cost abstractions and engineering trade-offs. Explore systems languages through comparisons and code experiments.内存安全、零成本抽象与工程取舍。通过交互对照与代码实验，理解系统语言的选择。
One vector operation, two programming models: interactive indexing, Rust write ownership, C++ boundary checks, and a GPU measurement plan.用同一个向量计算理解 SIMT 与 Tile：交互索引、Rust 写入权限、C++ 边界验证，以及真实 GPU 基准测试的测量方法。
Five interactive experiments connect LIF, UltraLIF, BPTT, STDP and EventProp. From dynamics to learning rules, bring the equations to life.用五个交互实验，串起 LIF、UltraLIF、BPTT、STDP 与 EventProp。从动力学到学习规则，让公式真正动起来。
Memory safety, zero-cost abstractions and engineering trade-offs. Explore systems languages through comparisons and code experiments.内存安全、零成本抽象与工程取舍。通过交互对照与代码实验，理解系统语言的选择。
One vector operation, two programming models: interactive indexing, Rust write ownership, C++ boundary checks, and a GPU measurement plan.用同一个向量计算理解 SIMT 与 Tile：交互索引、Rust 写入权限、C++ 边界验证，以及真实 GPU 基准测试的测量方法。
Warm up, repeat, and verify. Run a small experiment in your browser and examine the conditions behind the numbers.预热、重复测量与结果校验：在你的浏览器里运行一个小实验，理解数字背后的条件。
Change the phase and frequency to see two waves reinforce or cancel. Connect trigonometry with physical intuition.拖动相位与频率，观察两列波如何相长或相消，把三角函数与物理直觉联系起来。
Move entries between a dense matrix and its band storage, then verify a C++ GAXPY implementation.把稠密矩阵元素搬进带状存储，用交互映射与 C++ 校验理解索引、边界和运算成本。
Trace mirrored entries into one packed array and verify both output updates with C++.追踪镜像元素如何共用压缩槽位，用 C++ 校验两路更新，区分存储节省与算术成本。
Explore an eight-point spectrum, unpack the FFT butterfly, and verify C++ FFT results against a direct DFT.从八点频谱看懂蝶形分解，用可运行 C++ 对照直接 DFT，理解 FFT 的速度、误差和适用边界。
See memory strides, compare loop orders and blocking, then compile checked C++ kernels and measure real timings.把访存步长画出来，对比循环顺序与分块，再编译带校验的 C++ 内核并测量真实耗时。
Walk through a constrained optimization path, derive a stopping certificate, and run checked C++ Frank–Wolfe steps.在三角形可行域中逐步观察优化路径，推导停止证书，并运行带校验的 C++ Frank–Wolfe 实现。
Derivations, experiments, and questions worth coming back to.这里存放推导、实验，以及那些值得反复琢磨的问题。