How to use this guide
Ten minutes here will save you many hours later: what this guide is for, the order to read it in, and what is actually worth memorising for 07-280.
The premise
The course slides state results. They tell you that A* is optimal with an admissible heuristic, that mutual information is $H(Y) - H(Y\mid a)$, that the normal equation is $\theta = (X^\top X)^{-1}X^\top y$. They rarely tell you where any of it came from, and a formula you cannot re-derive is a formula you will misapply under exam pressure.
This guide re-teaches the same syllabus from scratch. Every chapter starts from a concrete situation, builds the notation only when the situation demands it, states each definition with every symbol named in words, works a small numeric example by hand, gives the derivation line by line — including the ones the slides skip — and then makes you do it yourself in guided problems. Where the professor's notes pose a question and leave it hanging ("Answer: in poll"), this guide answers it and shows the work.
It is not a summary and it is not a cheat sheet. It is longer than the slides on purpose. There is a cheat sheet, and it is the last thing you should use, not the first.
The dependency map
Chapters build on each other. An arrow means "you will be lost without this first." Click any box to go there.
What the pieces of a page mean
Every chapter is built from the same handful of components. They are not decoration — each one signals how to read what is inside it.
The coloured callouts
Intuition — the mental picture. Skippable if the maths already clicked; the thing to re-read if it did not.
Key idea — the load-bearing sentence. If you remember one line from a section, this is it.
Definition — the formal statement, as the course gives it.
Analogy — a comparison, always with a note on where it breaks.
Proof / derivation — every line justified, no "it can be shown".
Common mistake — an error people actually make, and why it is tempting.
Example — fully worked arithmetic, nothing hand-waved.
Problems, quizzes, figures
Guided problems are the most important thing on any page. Each has a statement, then collapsed steps, then the answer.
Quizzes are single-question checks; the explanation always says why the wrong answers are attractive, so read it even when you were right.
Interactive figures have sliders and buttons. Move them. The caption tells you what to notice, but the understanding comes from watching a quantity move when you change another one.
Opening the reveal before attempting the step. Reading a solution produces the pleasant feeling of understanding without any of the substance — you recognise each line as reasonable and conclude you could have produced it. Under exam conditions you cannot, because recognition and generation are different skills and only one of them is being tested.
The steps are collapsed deliberately. Write something down first — even a wrong attempt, even just "I think I need Bayes here." The failed attempt is what makes the reveal stick: you already have a question, so the answer lands on something instead of washing over you. Attempt, then reveal, then re-do the step yourself from blank paper.
What to memorise, and what to re-derive
This course rewards derivation, not recall. Almost everything can be rebuilt in thirty seconds from a definition, and rebuilt formulas do not get mixed up with each other. Memorise this short list and nothing else:
- The A* optimality conditions — admissible ($h(n) \leq h^*(n)$, never overestimates) for tree search, consistent ($h(n) \leq c(n,n') + h(n')$) for graph search.
- The entropy and mutual information definitions — $H(Y) = \sum_y P(y)\log\frac{1}{P(y)}$ and $I(Y;a) = H(Y) - H(Y\mid a)$.
- The normal equation — $\theta = (X^\top X)^{-1}X^\top y$.
- The gradient descent update — $\theta \leftarrow \theta - \alpha \nabla_\theta \hat R(\theta)$.
- The sigmoid — $\sigma(z) = \dfrac{1}{1+e^{-z}}$, and that $\sigma'(z) = \sigma(z)(1-\sigma(z))$.
Everything else you should be able to re-derive on the spot: why BFS is optimal only with uniform edge costs; why an inconsistent heuristic can make A* re-expand a node; why $\alpha$-$\beta$ pruning cannot change the minimax value; why the minimiser of squared error is the mean; why the normal equation comes from setting a gradient to zero; why zero-one loss cannot be optimised by gradient descent. If you can rebuild those, the memorised five are a convenience rather than a crutch.
A suggested order. Read a chapter in one sitting, doing the guided problems as you meet them rather than saving them for the end. Budget roughly: two sessions for search (Ch. 1–2), one for adversarial search and one for CSPs, one for Chapter 5 — which is short but is the vocabulary for everything after it — then one each for trees, information theory, linear regression and optimization, then one for features and logistic regression, and one each for model selection and neural networks. That is about twelve sittings. Then, and only then, work the problem set cold, without notes, and use the cheat sheet purely to check yourself. If a cheat-sheet line surprises you, go back to the chapter that derived it.
Sources
This guide is a re-teaching of the following course documents. Nothing here is a substitute for them — when the guide and the professor disagree, the professor is right, and please tell us. Cross-check against:
07280_F26_Lec2_Informed_Search(and-runover)07280_F26_Lec3_Adversarial_Search07280_S26_Notes_Adversarial_Search07280_F26_Lec4_CSPs
07280_F26_ML_formulation07280_F26_Notes_ML_Prob_Decision_Trees07280_F26_Lecture_Notes_Decision_Trees07280_F26_Lecture_Notes_Linear_Regression07280_F26_Notes_Optimization_and_Linear_Regression07280_F26_Lecture_Notes_Optimization07280_F26_Notes_Feature_Eng_and_Logistic_Reg
If you only take one habit from this page: after finishing any chapter, close it and write the main result on a blank sheet with its derivation. Whatever you cannot reproduce is exactly what you have not learned yet, and you now know precisely where to go back to.
Start with Chapter 1 — search problems, BFS/DFS/UCS, or jump straight to Chapter 5 — ML problem formulation if machine learning is what is on the exam next.