Subjects & Chapters

Calculus

4 chapters

Limits and ContinuityDerivatives and ApplicationsIntegration TechniquesPolar Coordinates and Parametric Equations
Explore Subject Details

Algebra

4 chapters

Complex Numbers and De Moivre's TheoremEquivalence Relations and PartitionsSystems of Linear EquationsEigenvalues and Eigenvectors
Explore Subject Details

Real Analysis

5 chapters

Real Number System and CompletenessSequences of Real NumbersInfinite Series and Convergence TestsLimit and Continuity of FunctionsUniform Continuity and Differentiability
Explore Subject Details

Differential Equations

5 chapters

First Order Exact Differential EquationsLinear Differential Equations of Higher OrderSystems of Linear Differential EquationsLaplace Transforms and ApplicationsPower Series Solutions
Explore Subject Details

Theory of Real Functions

4 chapters

Limits of Functions and Sequential CriterionContinuous Functions and PropertiesDifferentiability and Taylor's TheoremConvex Functions and Inequalities
Explore Subject Details

Group Theory

5 chapters

Symmetries and Dihedral GroupsSubgroups and Cyclic GroupsPermutation Groups and Alternating GroupsCosets and Lagrange's TheoremNormal Subgroups and Isomorphism Theorems
Explore Subject Details

Multivariate Calculus

4 chapters

Functions of Several VariablesPartial Derivatives and DifferentiabilityMultiple Integrals (Double and Triple)Vector Calculus (Gradient, Divergence, Curl)
Explore Subject Details

Partial Differential Equations

4 chapters

First Order Partial Differential EquationsClassification of Second Order PDEsWave equation and Heat equationLaplace Equation and Boundary Value Problems
Explore Subject Details

Riemann Integration and Series of Functions

4 chapters

Riemann Integrability and Darboux SumsFundamental Theorem of CalculusSequences and Series of FunctionsPower Series and Radius of Convergence
Explore Subject Details

Ring Theory and Linear Algebra I

5 chapters

Rings and SubringsIdeals and Quotient RingsVector Spaces and SubspacesBasis and DimensionLinear Transformations and Matrices
Explore Subject Details

Metric Spaces and Complex Analysis

6 chapters

Definition and Examples of Metric SpacesOpen, Closed Sets, and ConvergenceCompleteness and CompactnessComplex Numbers and Analytic FunctionsCauchy-Riemann EquationsContour Integration and Cauchy's Theorem
Explore Subject Details

Ring Theory and Linear Algebra II

4 chapters

Polynomial Rings and IrreducibilityPrincipal Ideal Domains and Unique Factorization DomainsDual Spaces and AnnihilatorsInner Product Spaces and Orthogonality
Explore Subject Details

Probability and Statistics

5 chapters

Probability Spaces and Random VariablesDiscrete and Continuous DistributionsJoint Distributions and CovarianceLimit Theorems (Law of Large Numbers, CLT)Estimation and Hypothesis Testing
Explore Subject Details

Numerical Methods

5 chapters

Solutions of Algebraic and Transcendental EquationsInterpolation TechniquesNumerical DifferentiationNumerical Integration (Simpson's and Trapezoidal rules)Numerical Solutions of ODEs (Euler and Runge-Kutta)
Explore Subject Details

Preparation Tip

Focus on high-weightage subjects first. Cover all chapters systematically using our structured learning path.

Quick Stats

Total Subjects14
Total Chapters64
AccessAlways Free

Unlock full learning — topics, practice questions, and mock tests.

Browse Courses