01Algebra
Groups, rings, fields, modules — and the canonical forms that classify a linear map up to similarity.
- Group theory
- Ring & field theory
- Linear algebra
- Canonical forms
- Galois theory
Structure for its own sake
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.
Areas
What the branch covers
02Analysis
Limits made honest. From the completeness of the reals to Lebesgue measure and functional analysis.
- Real analysis
- Complex analysis
- Measure theory
- Functional analysis
- Fourier analysis
03Topology & Geometry
What survives bending. Open sets, compactness, manifolds — including the torus in our own mark.
- Point-set topology
- Algebraic topology
- Differential geometry
- Manifolds
- Riemannian geometry
04Combinatorics & Discrete
Counting as a theory. Bijections, symmetry, graphs, and the arithmetic of orderings.
- Enumeration
- Permutations & combinations
- Graph theory
- Order & lattice theory
- Social choice
05Number Theory
The oldest questions, and the ones still open.
- Divisibility & congruences
- Arithmetic functions
- Diophantine equations
- Analytic number theory
06Logic & Foundations
What a proof is, what a set is, and what mathematics can decide about itself.
- Set theory
- Mathematical logic
- Proof technique
- Computability
Reading
Pure Mathematics in the library
5 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
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
The Arithmetic of Disagreement
Monograph Series, Volume 14
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.
- Social choice
- Order theory
- Arrow’s theorem
Inverse Map vs Inverse Function
Monograph Series — Short Note 1
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.
- Set theory
- Notation
- Foundations
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