Functions and coordinate systems
Be able to read and draw a function as a graph, interpret the slope and the y-intercept in y = kx + m, and understand that a function is a rule that gives exactly one output per input.
Practise in Mattegrafen ↗ · Samband och förändringPrerequisites
- BAlgorithmic thinkinghelpful
Intuition
A function is a machine: put a number in, get a number out. f(x) = 2x + 1 gives
f(0) = 1, f(1) = 3, f(2) = 5. The same input always gives the same answer — that is the whole point.
Draw the pairs (x, f(x)) as points in a coordinate system and you get a picture of the
function. For 2x + 1 it comes out as a straight line.
Formal
The straight line y = kx + m:
- k is the slope: how much y goes up when x goes up by 1.
- m is where the line crosses the y-axis (the value when x = 0).
From two points: k = (y₂ − y₁) / (x₂ − x₁). From (1, 3) and (3, 7): k = 4/2 = 2, and m = 3 − 2·1 = 1.
Why does AI care? A model that predicts one number from another is a function, and the simplest model is exactly a straight line. To "train" it means to find k and m.
Mastery means
- Calculates y for a given x in a linear function
- Reads k and m off a graph or a table
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Sources
Leads to
Part of the goals (37)
- The mathematics behind the models
- The language of mathematics in AI texts
- Understand how generative AI works
- Classical machine learning in practice
- The developer's toolbox
- Training neural networks for real
- Build a RAG system you can trust
- Build an NLP system end to end
- Statistics for experiments
- Systems knowledge for AI engineers
- Seeing and hearing with AI
- Image classification with convolutional networks
- Run models more cheaply: quantisation
- Multimodal systems
- Classical ML for real
- Frontier Lab — an independent research project
- AI safety in practice
- Fine-tune a model with LoRA
- AI in production
- Generative models in depth
- Evals in practice
- Language models in practice
- Train an agent with reward
- Build a voice interface
- Build a transformer from scratch
- Interpreting a language model
- Train your first neural network
- Deep reinforcement learning
- Fine-tune and run your own models
- Data: collect, clean, document
- Build a memory system for an agent
- Build an agent you can trust
- Responsible AI in practice
- Build an AI service that survives production
- An AI service in operation
- Reproduce a paper
- AI, ethics and society