[
    {"title":"人工智能的本质是数学：从神经网络到深度学习","module":"数人","sub_category":"计算机与AI","discipline":"人工智能","discipline_icon":"🤖","video_url":"https://www.bilibili.com/video/BV1example004","cover_url":"","description":"AI最底层的三个数学基石：线性代数、微积分、概率论。它们是怎么组合成ChatGPT的？","author":"计算机科学与工程学院·陈同学","duration_min":8},
    {"title":"深度学习中的矩阵运算","module":"数人","sub_category":"AI核心","discipline":"人工智能","discipline_icon":"🤖","video_url":"","cover_url":"","description":"为什么GPU比CPU快？矩阵乘法在神经网络推理中的决定性作用。","author":"人工智能学院·周同学","duration_min":6},
    {"title":"强化学习与博弈论","module":"数人","sub_category":"AI算法","discipline":"人工智能","discipline_icon":"🤖","video_url":"","cover_url":"","description":"AlphaGo背后的数学：蒙特卡洛树搜索与强化学习入门。","author":"人工智能学院·吴同学","duration_min":7},
    {"title":"计算机视觉中的几何变换","module":"数人","sub_category":"AI应用","discipline":"人工智能","discipline_icon":"🤖","video_url":"","cover_url":"","description":"手机扫码、人脸识别——背后的射影几何与矩阵变换。","author":"人工智能学院·郑同学","duration_min":5},

    {"title":"芯片里的数学：集成电路与布尔代数","module":"数人","sub_category":"微电子","discipline":"微电子","discipline_icon":"🔌","video_url":"https://www.bilibili.com/video/BV1example012","cover_url":"","description":"芯片设计的底层是布尔逻辑——0和1的世界。从非门到CPU，本质是一个巨大的数学逻辑电路。","author":"微电子学院·孙同学","duration_min":6},
    {"title":"光刻机中的光学数学","module":"数人","sub_category":"半导体工艺","discipline":"微电子","discipline_icon":"🔌","video_url":"","cover_url":"","description":"衍射极限与傅里叶光学：如何用光刻出纳米级的电路？","author":"微电子学院·林同学","duration_min":8},
    {"title":"半导体物理中的薛定谔方程","module":"数人","sub_category":"器件物理","discipline":"微电子","discipline_icon":"🔌","video_url":"","cover_url":"","description":"量子力学是微电子的根基。能带理论是如何通过波动方程推导出来的？","author":"微电子学院·张同学","duration_min":7},
    {"title":"集成电路布局布线中的图论","module":"数人","sub_category":"EDA技术","discipline":"微电子","discipline_icon":"🔌","video_url":"","cover_url":"","description":"在指甲盖大小的芯片上排布数亿个晶体管：最短路径算法的应用。","author":"微电子学院·王同学","duration_min":5},

    {"title":"手机信号背后的傅里叶变换","module":"数人","sub_category":"通信工程","discipline":"电子信息","discipline_icon":"📡","video_url":"https://www.bilibili.com/video/BV1example007","cover_url":"","description":"4G/5G信号传输的核心是傅里叶变换，一个把波形变成频率的数学魔术。","author":"电子工程与光电技术学院·赵同学","duration_min":5},
    {"title":"天线设计中的麦克斯韦方程组","module":"数人","sub_category":"射频技术","discipline":"电子信息","discipline_icon":"📡","video_url":"","cover_url":"","description":"看不见的电磁波是如何被精确控制的？矢量分析在天线工程中的应用。","author":"电光学院·李同学","duration_min":7},
    {"title":"数字信号处理中的采样定理","module":"数人","sub_category":"信号处理","discipline":"电子信息","discipline_icon":"📡","video_url":"","cover_url":"","description":"奈奎斯特采样定理：为什么CD的采样率是44.1kHz？","author":"电光学院·陈同学","duration_min":6},
    {"title":"雷达测距与多普勒效应","module":"数人","sub_category":"雷达工程","discipline":"电子信息","discipline_icon":"📡","video_url":"","cover_url":"","description":"通过频率变化计算目标速度：多普勒频移公式的直观解读。","author":"电光学院·刘同学","duration_min":5},

    {"title":"你的自行车为什么不会倒：机械里的数学原理","module":"数人","sub_category":"机械工程","discipline":"机械工程","discipline_icon":"⚙️","video_url":"https://www.bilibili.com/video/BV1example003","cover_url":"","description":"从陀螺效应到有限元分析，机械工程的核心是偏微分方程和数值计算。","author":"机械工程学院·张同学","duration_min":7},
    {"title":"齿轮啮合中的渐开线几何","module":"数人","sub_category":"机械设计","discipline":"机械工程","discipline_icon":"⚙️","video_url":"","cover_url":"","description":"为什么齿轮的齿形是这个形状？微分几何在机械传动中的应用。","author":"机械学院·王同学","duration_min":5},
    {"title":"有限元分析入门","module":"数人","sub_category":"结构仿真","discipline":"机械工程","discipline_icon":"⚙️","video_url":"","cover_url":"","description":"把复杂的零件拆成数百万个小方块：线性代数方程组在强度分析中的作用。","author":"机械学院·李同学","duration_min":8},
    {"title":"振动分析与动力学建模","module":"数人","sub_category":"机械动力学","discipline":"机械工程","discipline_icon":"⚙️","video_url":"","cover_url":"","description":"消除噪音与振动：常微分方程在机械避震系统中的应用。","author":"机械学院·赵同学","duration_min":6},

    {"title":"CT扫描背后的数学：拉东变换入门","module":"数人","sub_category":"生物医学工程","discipline":"生物医学","discipline_icon":"🧬","video_url":"https://www.bilibili.com/video/BV1example001","cover_url":"","description":"CT是怎么把人切片成图像的？背后的拉东变换是如何让医生看穿人体的？","author":"生物医学工程系·李同学","duration_min":6},
    {"title":"心电图(ECG)的波形分析","module":"数人","sub_category":"医学仪器","discipline":"生物医学","discipline_icon":"🧬","video_url":"","cover_url":"","description":"如何通过数学滤波器从微弱的电压中提取心跳信息？","author":"生医系·王同学","duration_min":5},
    {"title":"DNA序列分析中的信息论","module":"数人","sub_category":"生物信息学","discipline":"生物医学","discipline_icon":"🧬","video_url":"","cover_url":"","description":"生命是一串代码。哈夫曼编码与熵在基因组比对中的应用。","author":"生医系·陈同学","duration_min":7},
    {"title":"医学影像分割中的水平集方法","module":"数人","sub_category":"影像处理","discipline":"生物医学","discipline_icon":"🧬","video_url":"","cover_url":"","description":"如何用偏微分方程让电脑自动画出肿瘤的轮廓？","author":"生医系·张同学","duration_min":8},

    {"title":"金融里的数学：为什么风险可以算出来","module":"数人","sub_category":"经济管理","discipline":"经济管理","discipline_icon":"📊","video_url":"https://www.bilibili.com/video/BV1example005","cover_url":"","description":"Black-Scholes方程、VaR风险模型——金融的核心不是猜涨跌，而是随机微积分。","author":"经济管理学院·周同学","duration_min":6},
    {"title":"博弈论与市场竞争","module":"数人","sub_category":"微观经济","discipline":"经济管理","discipline_icon":"📊","video_url":"","cover_url":"","description":"纳什均衡：为什么两家奶茶店总是开在隔壁？","author":"经管学院·吴同学","duration_min":5},
    {"title":"供应链优化中的线性规划","module":"数人","sub_category":"物流管理","discipline":"经济管理","discipline_icon":"📊","video_url":"","cover_url":"","description":"运费最低、路径最短。单纯形法如何解决复杂的物流调度问题？","author":"经管学院·郑同学","duration_min":7},
    {"title":"消费者行为预测的回归分析","module":"数人","sub_category":"市场营销","discipline":"经济管理","discipline_icon":"📊","video_url":"","cover_url":"","description":"如何通过历史数据预测下个月的销量？最小二乘法入门。","author":"经管学院·孙同学","duration_min":6},

    {"title":"化学反应的数学语言：反应动力学方程","module":"数人","sub_category":"化学工程","discipline":"化工材料","discipline_icon":"🧪","video_url":"https://www.bilibili.com/video/BV1example008","cover_url":"","description":"一个化学反应的速度、产率、平衡——全都可以用微分方程精确描述。化工专业学姐带你入门。","author":"化学与化工学院·刘同学","duration_min":6},
    {"title":"晶体结构中的空间群与对称性","module":"数人","sub_category":"材料科学","discipline":"化工材料","discipline_icon":"🧪","video_url":"","cover_url":"","description":"群论在化学中的应用：为什么钻石比石墨硬？","author":"材料学院·林同学","duration_min":7},
    {"title":"传质传热过程中的数学模型","module":"数人","sub_category":"单元操作","discipline":"化工材料","discipline_icon":"🧪","video_url":"","cover_url":"","description":"化工厂里的巨型塔器如何设计？热传导方程的工程应用。","author":"化工学院·赵同学","duration_min":8},
    {"title":"计算材料学：从头算起","module":"数人","sub_category":"材料模拟","discipline":"化工材料","discipline_icon":"🧪","video_url":"","cover_url":"","description":"通过薛定谔方程预测新材料的超导性。","author":"材料学院·杨同学","duration_min":9},

    {"title":"机器人控制的数学基石","module":"数人","sub_category":"自动化","discipline":"自动化","discipline_icon":"🦾","video_url":"https://www.bilibili.com/video/BV1example010","cover_url":"","description":"想让机械臂精准抓取一个杯子？你需要矩阵变换、PID控制、运动学正逆解。","author":"自动化学院·吴同学","duration_min":7},
    {"title":"无人机飞控系统中的卡尔曼滤波","module":"数人","sub_category":"控制理论","discipline":"自动化","discipline_icon":"🦾","video_url":"","cover_url":"","description":"在噪声中寻找真相：如何实时估算飞行器的姿态？","author":"自动化学院·李同学","duration_min":6},
    {"title":"PLC逻辑控制与梯形图","module":"数人","sub_category":"工业自动化","discipline":"自动化","discipline_icon":"🦾","video_url":"","cover_url":"","description":"离散数学在工厂流水线控制中的应用。","author":"自动化学院·张同学","duration_min":5},
    {"title":"最优控制理论入门","module":"数人","sub_category":"现代控制","discipline":"自动化","discipline_icon":"🦾","video_url":"","cover_url":"","description":"变分法在轨迹规划中的应用：让导弹飞得最准。","author":"自动化学院·王同学","duration_min":8},

    {"title":"气候变化模型：环境科学中的偏微分方程","module":"数人","sub_category":"环境科学","discipline":"环境工程","discipline_icon":"🌱","video_url":"https://www.bilibili.com/video/BV1example009","cover_url":"","description":"天气预报和气候预测的背后，是Navier-Stokes方程——一组还没被完全解开的数学方程。","author":"环境与生物工程学院·杨同学","duration_min":6},
    {"title":"污水处理中的质量平衡模型","module":"数人","sub_category":"环保工艺","discipline":"环境工程","discipline_icon":"🌱","video_url":"","cover_url":"","description":"输入等于输出加积累。一阶线性微分方程在反应池设计中的应用。","author":"环境学院·周同学","duration_min":5},
    {"title":"生态网络中的种群动力学","module":"数人","sub_category":"生态模拟","discipline":"环境工程","discipline_icon":"🌱","video_url":"","cover_url":"","description":"食肉动物与食草动物的平衡：Lotka-Volterra方程解析。","author":"环境学院·陈同学","duration_min":7},
    {"title":"大气污染扩散的高斯模型","module":"数人","sub_category":"空气治理","discipline":"环境工程","discipline_icon":"🌱","video_url":"","cover_url":"","description":"烟囱里的废气会飘向哪里？概率密度函数在环境监测中的应用。","author":"环境学院·刘同学","duration_min":6},

    {"title":"核能发电中的中子扩散方程","module":"数人","sub_category":"能源工程","discipline":"能源动力","discipline_icon":"🔥","video_url":"","cover_url":"","description":"如何控制核裂变反应？二阶偏微分方程在核反应堆中的应用。","author":"能源学院·孙同学","duration_min":8},
    {"title":"工程热力学中的熵增原理","module":"数人","sub_category":"动力机械","discipline":"能源动力","discipline_icon":"🔥","video_url":"","cover_url":"","description":"为什么永动机不可能存在？热力学定律的数学表达。","author":"能动学院·王同学","duration_min":5},
    {"title":"流体力学中的边界层理论","module":"数人","sub_category":"流体机械","discipline":"能源动力","discipline_icon":"🔥","video_url":"","cover_url":"","description":"飞机机翼为什么会产生升力？空气动力学的数学奥秘。","author":"能动学院·李同学","duration_min":7},
    {"title":"太阳能电池效率的理论极限","module":"数人","sub_category":"新能源","discipline":"能源动力","discipline_icon":"🔥","video_url":"","cover_url":"","description":"半导体光电转换中的统计力学模型。","author":"能动学院·张同学","duration_min":6},

    {"title":"全国大学生数学建模竞赛(CUMCM)历年题目解析","module":"数人","sub_category":"数模入门","discipline":"数学建模","discipline_icon":"📐","video_url":"","cover_url":"","description":"从碎纸机拼接、月球着陆到共享单车调度。数模到底在比什么？","author":"数学与统计学院·赵同学","duration_min":10},
    {"title":"Matlab与Python在数模中的应用","module":"数人","sub_category":"编程实现","discipline":"数学建模","discipline_icon":"📐","video_url":"","cover_url":"","description":"如何用代码实现遗传算法、模拟退火和神经网络。","author":"数统学院·陈同学","duration_min":8},
    {"title":"数模论文写作：如何讲好数学故事","module":"数人","sub_category":"写作技巧","discipline":"数学建模","discipline_icon":"📐","video_url":"","cover_url":"","description":"模型建立、灵敏度分析与误差分析：一份优秀论文的结构。","author":"理学院·李同学","duration_min":7},
    {"title":"综合评价模型：层次分析法(AHP)","module":"数人","sub_category":"常用算法","discipline":"数学建模","discipline_icon":"📐","video_url":"","cover_url":"","description":"如何量化主观评价？特征值与特征向量在决策中的妙用。","author":"数统学院·吴同学","duration_min":6},

    {"title":"密码学与网络安全：从凯撒密码到RSA","module":"数人","sub_category":"网络安全","discipline":"计算机","discipline_icon":"💻","video_url":"https://www.bilibili.com/video/BV1example011","cover_url":"","description":"你的微信聊天为什么别人看不到？数论——尤其是大质数分解——是现代密码学的基础。","author":"网络空间安全学院·郑同学","duration_min":5},
    {"title":"操作系统调度算法中的队列论","module":"数人","sub_category":"系统结构","discipline":"计算机","discipline_icon":"💻","video_url":"","cover_url":"","description":"为什么电脑开多了会卡？随机过程在多任务调度中的应用。","author":"计算机学院·张同学","duration_min":6},
    {"title":"编译原理与形式语言","module":"数人","sub_category":"理论计算机","discipline":"计算机","discipline_icon":"💻","video_url":"","cover_url":"","description":"自动机理论：如何让计算机理解你写的代码？","author":"计算机学院·王同学","duration_min":8},
    {"title":"数据库索引中的B+树","module":"数人","sub_category":"数据存储","discipline":"计算机","discipline_icon":"💻","video_url":"","cover_url":"","description":"在大数据中瞬间找到你要的信息：树形数据结构的数学美感。","author":"计算机学院·刘同学","duration_min":7},

    {"title":"你被平均数骗过吗？","module":"数说","sub_category":"统计思维","discipline":"数学建模","video_url":"https://www.bilibili.com/video/BV1example101","cover_url":"","description":"我和马云平均一下，人均身价几百亿——平均数、中位数、众数到底该信哪个？","author":"数学与统计学院","duration_min":5},
    {"title":"为什么彩票不值得买——概率入门","module":"数说","sub_category":"概率思维","discipline":"数学建模","video_url":"https://www.bilibili.com/video/BV1example102","cover_url":"","description":"2元博500万？你中头奖的概率比你连续被雷劈三次还低。一个有趣的概率入门故事。","author":"数学与统计学院","duration_min":5},
    {"title":"地图为什么永远画不准？","module":"数说","sub_category":"几何直觉","discipline":"数学建模","video_url":"https://www.bilibili.com/video/BV1example103","cover_url":"","description":"把球面摊平一定会变形——这就是高斯绝妙定理。世界地图上的格陵兰为什么比非洲还大？","author":"理学院","duration_min":5},
    {"title":"费米问题：估算钢琴调音师的数量","module":"数思","sub_category":"逻辑推演","discipline":"数学建模","video_url":"https://www.bilibili.com/video/BV1example201","cover_url":"","description":"没有手机查，怎么估算一个城市有多少个钢琴调音师？谷歌面试题背后的数量级估算思维。","author":"理学院","duration_min":6},
    {"title":"二进制与AI：计算机为什么只认识0和1","module":"数思","sub_category":"计算思维","discipline":"计算机","video_url":"https://www.bilibili.com/video/BV1example202","cover_url":"","description":"从莱布尼茨的二进制到现代AI芯片，最底层的逻辑竟然是小学数学。","author":"计算机科学与工程学院","duration_min":5},
    {"title":"图论与社交网络：六度分隔是真的吗","module":"数思","sub_category":"网络思维","discipline":"数学建模","video_url":"https://www.bilibili.com/video/BV1example203","cover_url":"","description":"你认识奥巴马吗？理论上通过最多6个人就能联系到他。图论研究点和线之间关系的数学分支。","author":"理学院","duration_min":5}
]
