Abstract Maths 101: From Zero to Hero
Finish the year with a mathematical transformation. A combined, bi‑weekly live programme on Topology and Linear Algebra designed for ambitious professionals in fundamental science and emerging technologies.
$$\array{ && im (\phi_n) &&\to&& ker (\phi_{n-1}) \\ & \nearrow && \searrow && \swarrow \\ \Omega_{n+1} &&\stackrel{\phi_n}{\to}&& \Omega_n &&\stackrel{\phi_{n-1}}{\to}&& \Omega_{n-1} \\ & && \swarrow && \searrow && \nearrow \\ && coker (\phi_n) &&\stackrel{}{\to}&& im (\phi_{n-1}) }$$Master the Fundamentals
Go beyond recipes and build a rigorous, proof-based understanding of topology and linear algebra from the ground up.
Become AI & Quantum Ready
Grasp the mathematical language behind ML generalisation, quantum computing, and modern algorithms.
Develop Problem-Solving Skills
With bi-weekly homework and fully worked solutions, you'll learn to think like a mathematician and solve complex problems like a mathematician.
Syllabus at a Glance
Track A — Topology 101 (6 lectures)
L1: Topological spaces, bases & subbases
L2: Continuity, homeomorphisms, product/subspace
L3: Separation axioms; Hausdorff & uniqueness of limits
L4: Connectedness & path‑connectedness
L5: Compactness (Heine–Borel, metric spaces)
L6: Quotients & glimpses of algebraic topology
Track B — Linear Algebra (6 lectures)
L1: Vector spaces, subspaces, span, basis, dimension
L2: Linear maps, matrices, rank–nullity
L3: Inner products, norms, orthogonality, projections
L4: Eigenvalues/eigenvectors, diagonalisation, SVD
L5: Normal, self‑adjoint, unitary/orthogonal; spectral theorem
L6: Groups of matrices; applications to ML & quantum
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Frequently Asked Questions
What time are the live lectures?
To accommodate learners from around the world, live lectures are now held three times. You can join the session that works best for you: 6pm GMT (for Europe), 6pm EST (for US East Coast), or 6pm PT (for US West Coast).
What are the prerequisites for this programme?
A good grasp of basic set theory and a level of mathematical maturity is expected. Nice to be comfortable with basic proof techniques such as induction and contradiction. No prior exposure to topology or linear algebra is required.
What if I miss a live lecture?
No problem. All live lectures are recorded and will be available to paid Substack subscribers within 24 hours, along with the corresponding homework assignment.
Is this course theoretical or applied?
Both. The programme is rigorously proof-based to build a solid theoretical foundation. However, the content is specifically chosen for its relevance and application to machine learning and quantum computing.
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