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Big-O notationAlgorithms · Count the steps in real loops, then compare n, n log n, n² and 2ⁿ on a live chart.RecursionAlgorithms · Watch frames push and pop on the call stack for factorial and Fibonacci.BFS vs DFSAlgorithms · A queue against a stack: draw a graph and see which order each search visits it in.Sorting algorithmsAlgorithms · Seven sorts on the same input, with comparison, swap and write counts side by side.Binary searchAlgorithms · Halve the range, probe the middle, repeat: with lo, mid and hi drawn on the array.Sets, relations and functionsDiscrete maths · Shade any set expression on a Venn diagram and test a relation for its properties.Proof by inductionDiscrete maths · Four worked proofs revealed one step at a time, and a broken one to diagnose.CombinatoricsDiscrete maths · An exact nPr and nCr calculator, and a Pascal’s triangle that shows its own addition rule.Boolean algebraDiscrete maths · The laws, De Morgan, and normal forms, with a truth-table generator built in.Finite-state machinesTheory · Build a DFA in a table, see it drawn, and run strings through it one symbol at a time.Domain theoryTheory · Why recursion needs least fixed points, and how CPOs, Scott continuity and powerdomains supply them.Truth table generatorTools · Expression in, truth table out: with DNF, CNF, a minimal form and LaTeX.Graph traversal visualiserTools · Draw a graph, then animate BFS, DFS and Dijkstra with the frontier shown.Recursion tree visualiserTools · Paste a recursive function or a recurrence and see its call tree and call count.Gradient descentML maths · Drag the starting point, set the learning rate, and watch it converge or blow up.Vectors and embeddingsML maths · Bend the plane with a 2×2 matrix and measure how close toy word vectors are.Softmax and cross-entropyML maths · Edit the logits and watch the probabilities, the loss and the gradient update live.AttentionML maths · Q, K and V for three tokens, a live score heatmap, and the weighted sum of values.Formatting a CS paper in LaTeXLaTeX · Page limits, \documentclass, front matter, theorem environments and the bibliography.Camera-ready checklistLaTeX · Fonts embedded, PDF/A, copyright form, source bundle, and why final versions get rejected.LaTeX templatesLaTeX · Where the official classes live, plus a minimal article template you can copy.AlgorithmsSection · Step-through visualisations of sorting, searching, recursion, graph traversal and Big-O growth, each with pseudocode that highlights the line being run.Discrete mathsSection · Sets, relations and functions, proof by induction, counting, and Boolean algebra, explained with worked examples and small interactive checkers.TheorySection · Finite-state machines, automata and the mathematical semantics of programming languages, explained from first principles.ML mathsSection · Gradient descent, vectors and embeddings, softmax and cross-entropy, and attention, each with a formula, a worked numeric example and a live version.ToolsSection · A truth-table generator with CNF, DNF and LaTeX output, a graph-traversal visualiser for BFS, DFS and Dijkstra, and a recursion-tree visualiser.LaTeXSection · How to format a CS conference or workshop paper in LaTeX, a camera-ready checklist, and a minimal template you can adapt.
Theory

Theory of computation and semantics

What can a machine compute, and what does a program mean? Start with finite automata you can build and test, then move on to domain theory.

Two questions

The theory of computation asks what machines can do at all, given limited resources. Finite-state machines are the simplest interesting answer: machines with a fixed, finite memory. They are enough for searching text and recognising tokens, and the proof that they cannot count without bound is the first real impossibility result most students meet.

The semantics of programming languages asks what a program means, as a mathematical object, so that we can prove programs equivalent or correct. Domain theory is the mathematics that makes this work for recursive programs, by ordering partial results by information and taking least fixed points.