Probability and AI for engineers

This unit will introduce fundamental concepts of probability theory applied to engineering problems in a manner that combines intuition and mathematical precision. The treatment of probability includes elementary set operations, sample spaces and probability laws conditional probability, and independence. A discussion of discrete and continuous random variables common distributions, functions, and expectations forms an important part of this unit. You will also learn the law of large numbers and the central limit theorem. In the second half of the unit, the focus shifts to practical machine learning techniques. You will gain hands-on experience in supervised learning methods, ranging from decision trees and random forests to regression analysis. The unit also introduces optimisation theory, crucial for understanding the behaviour of learning algorithms. Furthermore, you will learn about data wrangling and the basics of feedforward neural networks. The unit features application examples from various domains to demonstrate the utility of these mathematical tools in real-world scenarios, including analysing radio telescopy data, images and audio signals.

### 📊 课程难度与压力分析 ECE2191（Probability and AI for engineers）的学习压力通常来自“双重要求”：既要掌握理论模型，又要能在工程语境下完成实现或分析。前几周多是概念框架与基础推导，难点集中在中后段的综合题、实验报告和项目任务。很多同学卡住的原因不是单个公式，而是无法把“模型-参数-结果”串成可解释的完整链路。建议从第 1 周开始就采用固定节奏：每周一次概念整理、一次题目演练、一次结果复盘，把大作业拆成若干可验收的小里程碑。 ### 🎯 备考重点与高分策略 高分关键在于“推导正确 + 过程完整 + 结论可解释”。复习建议分三轮：第一轮补基础概念和高频定理，建立公式适用条件清单；第二轮按题型专项训练（建模题、计算题、设计题、综合分析题），形成固定解题模板；第三轮做限时模拟，重点训练在时间约束下的步骤管理与表达清晰度。工程类课程里，评分往往不只看最终数值，还看你是否说明了假设、边界条件和方案取舍。写答案时建议先给方法框架，再展开关键步骤，最后落到工程含义和改进方向。 ### 📚 学习建议与资源推荐 资料优先级建议为：课程讲义与 tutorial 题 > 实验指导书与评分 rubric > 往年题与补充资料。每周至少保留 45 分钟做“错题画像”：记录错在概念、推导、单位、边界条件还是代码实现，并为每类错误指定一个修正动作。对于实验/编程部分，务必保持“可复现”标准：统一环境、固定输入、记录版本、保存关键中间结果。长期看，这比单纯刷题更能提升成绩稳定性。 ### ⚠️ 作业与考试避坑指南 常见失分点包括：只写结论不写关键步骤、忽略单位与量纲一致性、默认理想条件却未说明、代码能跑但缺测试与解释、图表结论与计算结果不一致。建议采用 D-7 / D-3 / D-1 节奏：D-7 完成主方案与核心验证，D-3 补边界场景与文档表达，D-1 做提交包检查与口径统一。团队任务需尽早明确接口和验收标准，避免最后阶段集成风险。只要持续执行 8-10 周的稳定闭环，ECE2191 的成绩通常会显著提升，并且更容易形成可迁移到后续高阶课程的工程能力。