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Subject · Mathematics

Mathematics Courses

Move from mathematical language to structure, geometry, uncertainty and calculus.
Course map

Choose one coherent pathway

Each Course will open into Volumes, Chapters, six-Concept Arcs and numbered Questions.

01IISER mapped

Mathematical Language and Algebra

Learn the objects and operations used by every later mathematical course.

  1. Sets and logic
  2. Relations and functions
  3. Complex numbers
  4. Quadratic equations
  5. Linear inequalities
Curriculum mapped
02IISER mapped

Counting, Binomial Ideas and Sequences

Count structured possibilities and recognise finite and infinite patterns.

  1. Permutations and combinations
  2. Binomial theorem
  3. Arithmetic progressions
  4. Geometric progressions
  5. Special series
Curriculum mapped
03IISER mapped

Trigonometry

Build circular, graphical and inverse-function meaning before using identities.

  1. Angle measure
  2. Trigonometric functions
  3. Identities and equations
  4. Inverse trigonometric functions
  5. Graphs
Curriculum mapped
04IISER mapped

Vectors and 3D Geometry

Describe direction, projection, lines and planes using geometric and algebraic evidence.

  1. Vector language
  2. Components and section formula
  3. Dot and cross products
  4. Lines in space
  5. Planes and distances
Curriculum mapped
05IISER mapped

Matrices and Determinants

Represent linked quantities and solve transformations and systems systematically.

  1. Matrix types and operations
  2. Row and column operations
  3. Inverse matrices
  4. Determinants
  5. Minors, cofactors and applications
Curriculum mapped
06IISER mapped

Coordinate and Analytical Geometry

Translate geometric conditions into equations and recover geometry from those equations.

  1. Cartesian coordinates
  2. Straight lines
  3. Circles
  4. Parabola
  5. Ellipse and hyperbola
Curriculum mapped
07Priority pathway

Single-Variable Calculus

Understand changing quantities, local rate, accumulation and mathematical models.

  1. Functions
  2. Limits and continuity
  3. Differentiation
  4. Integration
  5. Differential equations
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08IISER mapped

Probability and Statistics

Reason about variation, uncertainty and evidence without confusing them with guesswork.

  1. Measures of dispersion
  2. Events and sample spaces
  3. Conditional probability
  4. Total probability
  5. Bayes' theorem
Curriculum mapped
Mathematics references
book

Calculus: Single and Multivariable — Hughes-Hallett et al.

Multiple representations, interpretation, modelling and units.

attached
book

Problems in Calculus of One Variable — I. A. Maron

Technical progression, structural recognition and advanced problem-solving practice.

attached
book

Counterexamples in Calculus — Sergiy Klymchuk

Misconception diagnosis, theorem-hypothesis checking and proof-by-counterexample.

local-bank
official course

AP Calculus AB and BC

Written conceptual reasoning, interpretation and evidence-based free response.

Open official source ↗
exam archive

IISER IAT previous-year questions

Indian exam transfer, multi-concept selection and time-aware practice.

local-bank
exam archive

NEST previous-year questions

Deep conceptual transfer across mathematics and science.

local-bank
exam archive

KVPY SA and SX previous-year questions

Concept-first Indian science aptitude practice and prerequisite diagnosis.

local-bank