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
“Mathematics, in its many forms.”
School · Intermediate · Undergraduate · Postgraduate · PhD
A pure education project: one continuous road through mathematics, from school arithmetic to the research frontier. Nothing here is sold and nothing is gated: the monographs, worked commentaries and study tools below are free to read, download and pass on.
The two branches
Pure and Applied
Mathematics divides, roughly and imperfectly, into the study of structure and the use of it. Both are taught here, and neither is treated as the junior partner.
∀
Pure Mathematics
Pure mathematics asks what is true, and why, with no obligation to be useful. Every applied technique on the other branch of this site was once somebody’s pure curiosity.
- Algebra
- Analysis
- Topology & Geometry
- Combinatorics & Discrete
- Number Theory
- Logic & Foundations
Explore the pure branch →
∂
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.
- Differential Equations
- Numerical Analysis
- Probability & Stochastics
- Optimisation & Decision
- Machine Learning Theory
- Mathematical Physics
Explore the applied branch →
The pathway
From school to PhD, and beyond
Six stages, one road. Most syllabi break at the joins — school to Intermediate, coursework to research. The material here is written to cross those joins without a gap.
Stage 1
School
Class 8 – 10
Where the habit of proof begins.
Number, ratio, mensuration, elementary geometry and the first real algebra. The aim at this stage is not speed but the discovery that a mathematical claim can be argued, not merely asserted.
- Arithmetic & number sense
- Ratio, proportion, percentage
- Elementary algebra
- Euclidean geometry
- Mensuration
- Introductory statistics
Stage 2
Intermediate
IPE · EAMCET · JEE
The five pillars of the senior-secondary syllabus.
The classical Intermediate course, taught the way it is actually used later: calculus as a theory of change rather than a table of rules, vectors as geometry rather than bookkeeping, probability as measure-in-miniature.
- Algebra
- Calculus
- Vectors
- Trigonometry
- Probability
- Coordinate geometry
Stage 3
Entrance
CUET · IISER IAT · ISI · CMI
Selection papers, treated as mathematics.
Competitive papers reward structure, not tricks. The material here works each question from first principles and names the principle used, so that practice compounds into understanding instead of pattern-matching.
- CUET UG mathematics
- IISER IAT
- ISI / CMI entrance
- Olympiad-style counting
- Timed problem craft
Stage 4
Undergraduate
B.Sc. · B.Tech · B.Stat
The first encounter with rigour.
Epsilons and deltas, groups and rings, linear maps and their canonical forms. This is where mathematics stops being computation with symbols and becomes the study of structure.
- Real analysis
- Linear algebra
- Abstract algebra
- Ordinary differential equations
- Probability theory
- Numerical methods
Stage 5
Postgraduate
CSIR-NET · GATE MA · JAM MA · NBHM
Breadth, at speed, with proof.
The national qualifying papers span the whole of the M.Sc. syllabus. The Manifold approach is to build a spine — one worked commentary per paper, every item developed from first principles — rather than a bank of shortcuts.
- Complex analysis
- Functional analysis
- Topology
- Measure theory
- Partial differential equations
- Optimisation & linear programming
Stage 6
PhD & beyond
Research
Where the syllabus runs out.
Past coursework there is no list to finish. The bridge monographs are written for exactly this crossing: they start at a picture a second-year student can hold and end at the discretisation schemes of a current research paper, without a gap in between.
- Stochastic analysis
- Numerics of SPDEs
- Operator semigroups
- Differential geometry
- Reinforcement learning theory
- Mathematical physics
Selected reading
From the library
7 monographs, courses, worked commentaries and short notes — all free, all PDF.
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
Permutations & Combinations
The theory and craft of counting, in two parts
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.
- Counting
- Symmetry
- EAMCET → NBHM
Practice
Interactive tools
Single-file applications that run entirely in your browser. Nothing is uploaded; your progress stays on your own machine.
CSIR NET · GATE MA · JAM MA
Study App
A working desk for postgraduate revision: topic-by-topic study state, spaced revisits and progress across the three national papers.
CSIR NET · GATE MA · JAM MA
Syllabus Tracker
The full syllabus of all three papers as a single checkable tree, so you can see coverage rather than guess at it.
Mathematical Sciences
CSIR NET Planner
Turns the CSIR NET Mathematical Sciences syllabus into a dated plan — what to study, in what order, against the calendar you actually have.
125 questions · 150 minutes · MM-20260721
CUET Practice Exam
A full mock in exam conditions: 75 mathematics, 25 physics, 25 chemistry, live timer, question navigator, and a step-by-step worked solution for every item afterwards.
Entrance preparation
CUET UG + IISER IAT Tracker
Coverage tracking across both papers at once, since their syllabi overlap far more than the coaching material admits.