Semester 1: Mathematical & CS Foundations
Year 1 -- Fundamentals | Phase 1 | Weeks 9-20 | 12 weeks
Semester 1 is learner-ready across all five modules, with a semester project, checkpoint gate, cumulative review, and exam.
Goal
Build mathematical maturity for later algorithms, systems, and rigorous engineering reasoning.
Prerequisites
Complete Semester 0, including the checkpoint gate, cumulative review, and a stable study system.
Semester Structure
The public learner-facing material for Semester 1 covers the full mathematical foundations block:
| # | Module | Status | Focus |
|---|---|---|---|
| 1 | Proof Techniques & Discrete Structures | Learner-ready | Logic, sets, functions, relations, induction, and proof discipline |
| 2 | Combinatorics & Graph Theory | Learner-ready | Counting principles, graph fundamentals, trees |
| 3 | Probability & Statistics | Learner-ready | Probability models, Bayes, random variables, expectation, variance, and statistical reasoning |
| 4 | Linear Algebra for CS | Learner-ready | Systems, spaces, orthogonality, spectra, decompositions, and numerical judgment |
| 5 | Problem-Solving Strategies | Learner-ready | Polya framework, heuristics, debugging |
Why This Semester Matters
Proof-writing and discrete reasoning are where the curriculum stops being slogan-driven and starts demanding rigor. If this layer is weak, later algorithms and systems work become shallow very quickly.
Core Resources
| Book | Role |
|---|---|
| Mathematics for Computer Science | Primary reference for proofs and discrete structures |
| Discrete Mathematics and Its Applications | Secondary source for extra examples |
| Linear Algebra and Its Applications | Primary reference for Module 4 linear algebra |
| How to Solve It | Problem-solving lens for written mathematical reasoning |
Use Rule
Use Semester 1 as the full mathematical foundations path before advancing into algorithm-intensive coursework.
Capstone Throughline
Every semester must leave behind evidence that can survive into the final capstone defense.
- Artifact carried forward: proof notebook and math reasoning log.
- What to preserve: Preserve representative proofs, failed attempts, and repaired reasoning so later design and correctness claims can cite concrete mathematical discipline.
- Module threads: Module 1: Proof Techniques & Discrete Structures, Module 2: Combinatorics & Graph Theory, Module 3: Probability & Statistics, Module 4: Linear Algebra for CS, and Module 5: Problem-Solving Strategies.
- Defense prompt: In Semester 10, explain how this semester's artifact changed a capstone decision, reduced a risk, or made the final system easier to defend.
Model Artifact Calibration
Before submitting proof-heavy work, compare your notebook to the proof notebook model artifact.