Start: March 19

Abstract Maths 101 Zero to Hero

$$\array{ && im (\phi_n) &&\to&& ker (\phi_{n-1}) \\ & \nearrow && \searrow && \swarrow \\ \Omega_{n+1} &&\stackrel{\phi_n}{\to}&& \Omega_n &&\stackrel{\phi_{n-1}}{\to}&& \Omega_{n-1} }$$

A rigorous foundation. Master Topology, Linear Algebra, and C*-Algebras. Designed for researchers and professionals ready to rebuild their mathematical understanding from first principles.

Early Bird: 60% OFF + Feb "Logic & Proofs" Prep included

Secure Early Bird Price View Syllabus

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 and solve complex problems like a mathematician.

Cohort Schedule

Join early to bridge the gap before the main material begins.

Early Bird Bonus

February Prep Series

Logic & Proofs Bridge: A dedicated series to get you comfortable with mathematical notation, set theory, and proof writing before we dive into Topology.

Included Free with Early Bird
Live Sessions + Recordings

Main Track Kickoff

March 19, 2025

The official start of Abstract Maths 101. Live lectures begin, starting with the fundamentals of Topological Spaces.

Live Times:

1 PM GMT or 8 PM GMT

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

Track C — C*-Algebras (6 lectures)

L1: Banach algebras, involutions, and the C*- Algebras axioms

L2: Spectrum, self-adjoint/normal/unitary elements

L3: Positive elements, order structure, and approximate units

L4: Continuous Functional Calculus for normal elements

L5: States, positive linear functionals, and the GNS construction

L6: Irreducible representations, pure states, & Gelfand-Neumark Theorem

Frequently Asked Questions

What are the prerequisites?

A level of mathematical maturity is expected, but no prior Topology is required. To help you prepare, Early Bird enrollees get access to the February Prep Series, covering Logic and Proof Writing essentials.

What time are the live lectures?

You can join the session that works best for you: 1 PM GMT (Europe & Asia) or 8 PM GMT (Europe & North America).

What if I miss a lecture?

All sessions are recorded and available within 24 hours. You retain lifetime access to these recordings.

Ready for a mathematical transformation?

Join the March 19 cohort. Secure the 60% Early Bird discount and start your prep in February.

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