7 titles · free · PDF
Monographs, full courses, worked commentaries and short notes. Everything is free to read, free to download and free to pass on to a student. No account, no email, no paywall.
Pure Mathematics
Part I builds the grammar of counting from the ground to JEE Advanced. Part II turns to structure and symmetry for ISI, CMI, IAT, CSIR–NET, NBHM and olympiad work.
A self-contained course in the mathematics of combining ordered lists — from Borda and Condorcet through Arrow’s theorem to the fusion rules used in modern retrieval.
The notation f⁻¹ is overloaded: it names two entirely different objects depending on context, and conflating them leads to real errors. A few pages to fix it permanently.
Applied Mathematics
A complete course in sequential decision making: dynamic programming, temporal-difference learning, policy gradients, deep RL, offline methods, and policy optimisation for large language models.
From first pictures to the research frontier: weak solutions, finite elements, operator semigroups, stochastic calculus, Gaussian measures and SPDE discretisation. Prepared as a self-study spine.
Examination material
All one hundred and twenty items, treated from first principles. Every concept developed in full — no step assumed, no result quoted without its reason.
What the practice exam returns when you finish it: score, subject and topic breakdown, and a full worked solution for every one of the 125 questions.
Brand & source files
The house identity, for anyone printing or reproducing Manifold material. The lockup exists in all five palettes — click a swatch in the header to see the site itself change.
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Mathematics
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