Computer Science Fundamentals

Apply Discrete Mathematics Through Formal Proofs

Required foundation. Discrete mathematics is the formal proof language underpinning all of CS — logic, induction, graph theory, and combinatorics appear in algorithm analysis, cryptography, and systems reasoning. Every subsequent step on this path (and on the Algorithms path) depends on being able to construct and evaluate formal arguments.

Understand Computer Architecture by Building Below the Language

Required. You cannot reason about what an OS does without understanding what the hardware does beneath it. This step requires building something that operates at the hardware/software boundary — assembler, CPU emulator, or cache simulator — and explaining it to a reviewer who will trace your execution.

Implement an OS Component to Prove Systems Understanding

Elective. Implement a scheduler, memory allocator, or file system component and analyse trade-offs against alternatives. The OS is where architectural decisions become concrete — understanding it changes how you write application code.

Demonstrate Network Understanding Through Traffic Analysis and Implementation

Elective. Capture and analyse your own network traffic, implement a TCP client/server from raw sockets, and write a report mapping your captures to the protocol stack. Network understanding is foundational for security, distributed systems, and cloud architecture.

Implement Core Data Structures From Scratch with Complexity Analysis

Elective bridge to the Algorithms & Data Structures path. Implementing data structures from scratch here proves you understand what a 'list' or 'map' actually is — the prerequisite for analysing algorithm complexity meaningfully.

Free MIT course covering all the discrete mathematics on this path: logic, proofs, induction, graph theory, and combinatorics. Lecture notes, problem sets, and solutions all freely available.

Free, self-paced course that builds a complete computer system from NAND gates up to a working OS and application. The most direct path to understanding computer architecture through building — not just reading about it.

The standard CS systems textbook at CMU, MIT, and Stanford. Covers architecture, assembly, memory hierarchy, OS interfaces, and networking — all the foundations in one book. Draft chapters available free on the author's site.

Berkeley's free computer architecture course. Lecture videos, labs, and projects covering RISC-V assembly, digital logic, pipelining, and memory systems. Strong complement to Nand to Tetris for depth.