Mathematical Foundations · Foundation
Mathematics for AI
Linear algebra, calculus, probability, statistics and optimization — taught as the working language of neural networks, not as abstract coursework.
- Level
- Foundation
- Mathematics depth
- Deep
- Engineering depth
- Applied
- Modality
- Cohort-based · problem sessions
- Duration
- Announced per cohort
- Status
- Open for inquiry
Audience
Who this is for
- Developers who want the mathematical layer made explicit
- Students preparing for serious ML coursework
- Practitioners who hit the ceiling of tutorial-level understanding
Career paths
Prerequisites
- — Secondary-school mathematics
- — No prior AI experience required
Outcomes
Skills acquired
- Read model papers and recognize the mathematics underneath
- Derive and implement gradient-based optimization from scratch
- Reason about loss curves, variance and generalization quantitatively
Tools used
Curriculum Architecture
Module progression
Expandable, visual, ordered. Each module is a prerequisite-aware step, not an isolated video.
- 01Linear Algebra for AI
- 02Calculus for Machine Learning
- 03Probability & Randomness
- 04Statistics for Model Reasoning
- 05Optimization & Gradient Descent
- 06Numerical Thinking for Neural Networks
- 07Mathematical Reasoning for Architectures
Projects
- A from-scratch gradient descent library with tests
- A probabilistic analysis of a real dataset with written conclusions
Assessment philosophy
Assessment is engineering review: written error analyses, measured system behavior, defended design decisions. We evaluate whether you can explain and justify what you built — because production will.
Stack position: Mathematics.
FAQ
Frequently asked questions
Do I need a mathematics background?
It depends on the program. Foundation-tier programs start from the mathematics itself; advanced tiers list working linear algebra as a prerequisite. The Mathematics for AI program exists precisely to close that gap.
Is this a bootcamp?
No. CAS Studies is an engineering institute. Programs are built around architectures, derivations and projects with written error analysis — not tutorial replays.
How long does a program take?
The two diploma tracks run on fixed lengths — AI Architectural Engineering spans 18 months, AI Application Engineering spans 1 year. All other program durations are announced per cohort, by modality.
Will I build real systems?
Yes. Every program ends in projects that resemble production work: evaluated models, grounded answer systems, supervised agents — with measurement, not vibes.