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Advanced Mathematics Mastery — Integration, Linear Algebra, Probability & Game Theory
Verified Curriculum
Mathematics & STEM / Competitive Exam Prep Global Enrollment Open

Advanced Mathematics Mastery — Integration, Linear Algebra, Probability & Game Theory

Integral Cup 2026 Official Preparation Program

Advanced Mathematics Mastery

Integration · Linear Algebra · Probability · Game Theory

🇺🇸 United States 🇬🇧 United Kingdom 🇮🇳 India
38
Curriculum units
4
Expert tracks
200+
Practice problems
Self-paced
Learn anywhere

Who is this course for?

🎓
Undergrad & Grad Students
MIT, Oxford, IIT, UCL, Stanford, IISc — build the rigorous math foundations your programme expects.
🏆
Competition Participants
Integral Cup, Putnam, IMO, CMI entrance, USAMO — get structured prep aligned to real competition syllabi.
🤖
ML & AI Engineers
Understand the maths behind transformers, diffusion models, GPs, and optimisation — not just the APIs.
📈
Quant & Finance Professionals
SDEs, optimal transport, game theory, Bayesian inference — the quantitative toolkit for modern finance.

What you will master

✓Single & multivariable integration, Fourier & Laplace transforms
✓Gradient descent, KKT conditions & convex optimisation
✓Eigenvalues, SVD, tensor decomposition & optimal transport
✓Probability, measure theory & Brownian motion
✓PAC learning, Rademacher complexity & generalisation bounds
✓MCMC, variational inference & Gaussian processes
✓Diffusion models, score matching & SDEs
✓Nash equilibria, Sprague-Grundy & backward induction

4-track curriculum — 38 units

Every topic is sequenced so prerequisites always come first. Official Integral Cup 2026 content highlighted.

Track 1 Integration & Analysis 16 units
Basic integrals & substitution Infinite series & summation Limits & continuity MVT & differentiability Riemann–Lebesgue sums ODEs & Laplace transforms Fourier transforms ★ Multivariable calculus ★ Gradient descent & optimisation ★ Autodiff & backpropagation ★ Variational calculus & Euler–Lagrange ★ Riemannian optimisation ★ Neural ODEs & Hamiltonian dynamics ★ SDEs & score matching
Track 2 Linear Algebra & Optimisation 13 units
Matrices & determinants Vector spaces & linear maps Eigenvalues & SVD Convex optimisation & KKT Linear programming & simplex ★ Spectral graph theory ★ Kernel methods & RKHS ★ Tensor decomposition (CP, Tucker) ★ Random matrix theory ★ Optimal transport ★ Attention & positional embeddings ★ Neural tangent kernel ★ Manifold learning & PCA
Track 3 Probability & Statistics 19 units
Random variables & distributions Joint distributions & CLT Statistical inference & testing Markov chains Bayesian statistics & queuing ★ Measure theory ★ Information theory & KL divergence ★ Concentration inequalities ★ PAC learning & VC dimension ★ Variational inference & ELBO ★ MCMC & Gibbs sampling ★ Gaussian processes ★ Brownian motion & Itô calculus ★ Diffusion probabilistic models ★ Causal inference & high-dim stats
Track 4 Game Theory 6 units
Strategic & extensive form games Nash equilibria Rationalizable strategies Zero-sum & impartial games Sprague–Grundy theorem Backward & forward induction

⬛ Standard = official Integral Cup 2026 syllabus  |  ★ Extended = advanced AI/ML mathematics layer

Trusted by serious learners worldwide

3,800+
Active students
4.9 / 5
Average rating
28
Countries enrolled
94%
Completion rate

What students say

★★★★★

"The curriculum sequencing is genius — everything builds perfectly on what came before. I finally understand the maths behind transformers."

Priya S.
IIT Bombay, India
★★★★★

"Placed top 50 in the Integral Cup after three weeks of study. The sample-problem alignment to curriculum units is something no other course offers."

James T.
University of Cambridge, UK
★★★★★

"As an ML engineer at a top US lab, I needed the real math — not tutorials. This course gave me Itô calculus, NTK, and optimal transport in one place."

Marcus R.
Senior ML Engineer, San Francisco

Frequently asked questions

Do I need prior university-level maths?
A solid A-Level / AP Calculus / Class 12 CBSE foundation is enough. The curriculum is sequenced from first principles — Units 1A through 1D cover everything from scratch before advancing.
Is this course good for Integral Cup 2026 prep?
Yes — the official Integral Cup 2026 Grand Prix syllabus is the backbone of this curriculum. Every sample problem is mapped to specific units in the course.
How long does the course take to complete?
Most students complete the full 38-unit programme in 12–16 weeks studying 8–10 hours per week. You can also pick individual tracks (roughly 3–4 weeks each at the same pace).
Is there a certificate?
Yes — a verified digital certificate is awarded on completing all 38 units and passing the final assessments. Recognised by STEMvibe and shareable on LinkedIn.

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