01Differential Equations
ODEs and PDEs: the language in which physical law is written, classical through weak solutions.
- ODEs & dynamical systems
- Classical PDEs
- Weak solutions
- Operator semigroups
- Stochastic PDEs
Structure put to work
Applied Mathematics
Applied mathematics is not diluted mathematics. Modelling a diffusion, discretising an operator or proving a policy converges demands the same rigour — with the added burden that the answer must survive contact with data.
Areas
What the branch covers
02Numerical Analysis
Turning a theorem into an algorithm that terminates, and knowing the error you paid for it.
- Numerical linear algebra
- Finite elements
- Quadrature
- Stability & convergence
- Scientific computing
03Probability & Stochastics
Randomness with a σ-algebra under it: martingales, Itô calculus, Feynman–Kac.
- Measure-theoretic probability
- Markov processes
- Stochastic calculus
- Feynman–Kac
- Gaussian measures
04Optimisation & Decision
Best, subject to constraints — and what happens when the constraints move.
- Linear programming
- Convex optimisation
- Dynamic programming
- Rank aggregation
- Game & choice theory
05Machine Learning Theory
The mathematics underneath the models: Bellman equations, gradients of expectations, policy optimisation.
- Reinforcement learning
- Temporal-difference learning
- Policy gradients
- Offline methods
- LLM policy optimisation
06Mathematical Physics
The equations physics hands to mathematics, and what mathematics hands back.
- Classical mechanics
- Wave & heat equations
- Variational principles
- Statistical mechanics
- Quantum formalism
Reading
Applied Mathematics in the library
4 titles from the library sit on this branch.
CSIR–UGC NET 2026 — Worked Commentary
Paper of 17 July 2026
All one hundred and twenty items, treated from first principles. Every concept developed in full — no step assumed, no result quoted without its reason.
- CSIR-NET
- Solutions
- All areas
Reinforcement Learning
From the Bellman Equation to Language Models
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.
- Dynamic programming
- Policy gradients
- Offline RL
Bridge Monograph — Numerics of SPDEs
The road to the stochastic heat equation
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.
- Weak solutions
- Finite elements
- Itô calculus
Sample Solutions Report
MM-20260721 · Sets · Units & Dimensions · Mole Concept
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.
- CUET
- Report
- Worked solutions