What you will be able to do at the end

1. Read and reason about Big-O, entropy, and probability without hand-waving.
2. Explain why floating point breaks money math, and how to avoid it.
3. Compute subnet ranges, bandwidth-delay products, and queue depths by hand.
4. Derive gradient descent and backpropagation from the chain rule, not from memory, and explain why attention divides by √d_k and why η < 2/λ_max.
5. Read a formula like an API signature: name every symbol, check the units, and test it on simple numbers and extreme values.
6. Explain why RSA and Diffie-Hellman are secure, using the actual number theory.
7. Quantify password strength, hash collisions, and detection system false-positive rates.
8. Know which branch of math to reach for when a new problem shows up, and where to go deeper.