Discrete Math & Proofs for Computer Science
Logic, sets, combinatorics, and basic proof techniques aimed at CS and security students.
What you’ll learn
- Turn word problems into clear mathematical models
- Use the right theorem or method without guessing
- Blend analytic techniques with numerical intuition
- Check your own work with simple sanity checks and visuals
Curriculum
M1
Getting set up — 2 lessons
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Propositional logic: truth tables & operatorsLesson outline – video coming soon.14m
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Logical equivalence & lawsLesson outline – video coming soon.14m
M2
Language basics, fast — 2 lessons
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Predicates, quantifiers & domainsLesson outline – video coming soon.16m
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Nested quantifiers & translationLesson outline – video coming soon.14m
M3
Data structures & iteration — 2 lessons
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Direct proof strategiesLesson outline – video coming soon.14m
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Proof by contrapositive & contradictionLesson outline – video coming soon.16m
M4
Functions & modules — 2 lessons
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Set operations & Venn diagramsLesson outline – video coming soon.14m
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Set identities & proofsLesson outline – video coming soon.12m
M5
Files, serialization & pathlib — 2 lessons
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Functions: injective, surjective, bijectiveLesson outline – video coming soon.16m
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Composition & inverse functionsLesson outline – video coming soon.14m
M6
Errors, testing & logging — 2 lessons
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Relations: reflexive, symmetric, transitiveLesson outline – video coming soon.14m
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Equivalence relations & partitionsLesson outline – video coming soon.14m
M7
OOP, dataclasses & typing — 2 lessons
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Counting principles: sum & product rulesLesson outline – video coming soon.14m
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Permutations & combinationsLesson outline – video coming soon.16m
M8
CLI apps & automation — 2 lessons
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Binomial theorem & combinatorial identitiesLesson outline – video coming soon.14m
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Pigeonhole principle & applicationsLesson outline – video coming soon.12m
M9
Web APIs — 2 lessons
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Recurrence relations & solving techniquesLesson outline – video coming soon.16m
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Generating functions (intro)Lesson outline – video coming soon.14m
M10
Data wrangling — 2 lessons
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Graphs: definitions, paths & connectivityLesson outline – video coming soon.16m
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Euler & Hamiltonian pathsLesson outline – video coming soon.14m
M11
Packaging & deployment — 2 lessons
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Trees & spanning treesLesson outline – video coming soon.14m
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Graph coloring & planar graphsLesson outline – video coming soon.14m
M12
Capstone project — 2 lessons
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Mathematical induction: base & stepLesson outline – video coming soon.16m
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Strong induction & well-orderingLesson outline – video coming soon.16m
Projects
- Model a real-world system (growth, decay, motion, or heat flow) or dataset
- Write a short report comparing analytic and numerical solutions
- Create study notes and formula sheets you can reuse in exams
Prerequisites
- Prior exposure to high-school algebra and functions
- For ODE/PDE: at least Calculus I (or concurrent)
- Willingness to pause and re-watch explanations until they click
Who is this for?
- Students currently in a university math course who want a second pass
- STEM majors building a stronger analysis foundation
- Self-taught learners filling in gaps before ML/AI or physics
Outcomes
- Less “formula hunting”, more structured problem-solving
- A reusable set of notes, diagrams, and checklists
- More confidence walking into problem sets and exams
Resources
- Starter project / template (ZIP)
- Setup & study checklists (PDF)
- Core formulas / syntax cheatsheet (PDF)
Tip: Right-click → “Save link as…” if your browser opens the file.
FAQ
Is this beginner-friendly?
Yes. We start from mental models and build up with guided practice and plenty of worked examples.
Will I need extra software?
We stick to free or standard tools. Any optional extras are clearly marked and have alternatives.
Do I get updates?
Yes—lifetime access with updates as the field, tools, and exam expectations evolve.