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GATE Mathematics Syllabus
Graduate Aptitude Test in Engineering. The full GATE Mathematics syllabus: 14 subjects, 84 chapters, 110 topics and 41 sub-topics, with 713 flashcards written against it.
GATE Mathematics subjects
GATE Mathematics has 14 subjects. Each one is listed below with its chapters in syllabus order; open a subject for every topic and sub-topic inside them.
Calculus
- Functions of two or more variables · 7 topics
- Double and Triple integrals · 3 topics
- Vector Calculus · 8 topics
Linear Algebra
- Finite Dimensional Vector Spaces · 1 topic
- Linear Transformations and Matrix Representations · 1 topic
- Systems of Linear Equations
- Characteristic Polynomial, Eigen Values, and Eigen Vectors · 1 topic
- Cayley-Hamilton Theorem
- Finite Dimensional Inner Product Spaces · 1 topic
- Symmetric, Skew-Symmetric, Hermitian, Skew-Hermitian, Normal, Orthogonal, and Unitary Matrices · 1 topic
- Jordan Canonical Form
- Bilinear and Quadratic Forms
Real Analysis
- Metric spaces
- Connectedness
- Compactness
- Completeness
- Sequences and series of functions · 2 topics
- Weierstrass approximation theorem
- Contraction mapping principle
- Power series
- Differentiation of functions of several variables
- Inverse and Implicit function theorems
- Lebesgue measure on the real line
- Measurable functions
- Lebesgue integral · 3 topics
Complex Analysis
- Functions of a Complex Variable · 3 topics
- Complex Integration · 5 topics
- Zeros and Singularities
- Power Series · 3 topics
- Residue Theorem and Applications · 1 topic
- Rouche’s Theorem
- Argument Principle
- Schwarz Lemma
- Conformal Mappings
- Mobius Transformations
Ordinary Differential Equations
- First Order Ordinary Differential Equations · 1 topic
- Linear Ordinary Differential Equations of Higher Order with Constant Coefficients
- Second Order Linear Ordinary Differential Equations with Variable Coefficients
- Cauchy-Euler Equation
- Method of Laplace Transforms for Solving Ordinary Differential Equations
- Series Solutions · 2 topics
- Legendre and Bessel Functions and Their Orthogonal Properties
- Systems of Linear First Order Ordinary Differential Equations
- Sturm's Oscillation and Separation Theorems
- Sturm-Liouville Eigenvalue Problems
- Planar Autonomous Systems of Ordinary Differential Equations · 3 topics
Algebra
- Groups · 8 topics
- Rings · 8 topics
- Fields · 4 topics
Functional Analysis
- Normed Linear Spaces · 4 topics
- Inner-Product Spaces · 1 topic
Numerical Analysis
- Systems of linear equations · 3 topics
- Numerical solutions of nonlinear equations · 4 topics
Interpolation
- Lagrange and Newton forms of interpolating polynomial · 1 topic
- Error in polynomial interpolation of a function · 1 topic
Partial Differential Equations
- Method of Characteristics for First Order Linear and Quasilinear Partial Differential Equations · 1 topic
- Second Order Partial Differential Equations in Two Independent Variables: Classification and Canonical Forms · 1 topic
- Method of Separation of Variables for Laplace Equation in Cartesian and Polar Coordinates · 2 topics
- Heat and Wave Equations in One Space Variable · 2 topics
Wave equation
- Cauchy problem and d'Alembert formula
- Domains of dependence and influence
- Non-homogeneous wave equation
Topology
- Basic concepts of topology · 11 topics
Linear Programming
- Linear programming models
- Convex sets
- Extreme points
- Basic feasible solution
- Graphical method
- Simplex method
- Two phase methods
- Revised simplex method
- Infeasible and unbounded linear programming models
- Alternate optima
- Duality theory
- Weak duality and strong duality
- Balanced and unbalanced transportation problems
- Initial basic feasible solution of balanced transportation problems · 3 topics
- Optimal solution
- Modified distribution method
- Solving assignment problems · 1 topic
General Aptitude
- Verbal Aptitude · 3 topics
- Quantitative Aptitude · 3 topics
- Analytical Aptitude · 1 topic
- Spatial Aptitude · 2 topics
GATE Mathematics flashcards
713 question-and-answer cards across 14 subject decks, each shown in full on its subject page.
- Calculus — 51 cards
- Linear Algebra — 50 cards
- Real Analysis — 50 cards
- Complex Analysis — 50 cards
- Ordinary Differential Equations — 50 cards
- Algebra — 57 cards
- Functional Analysis — 50 cards
- Numerical Analysis — 51 cards
- Interpolation — 51 cards
- Partial Differential Equations — 51 cards
- Wave equation — 51 cards
- Topology — 50 cards
- Linear Programming — 51 cards
- General Aptitude — 50 cards
GATE Mathematics syllabus FAQ
What subjects are in the GATE Mathematics syllabus?
GATE Mathematics covers 14 subjects: Calculus, Linear Algebra, Real Analysis, Complex Analysis, Ordinary Differential Equations, Algebra, Functional Analysis, Numerical Analysis, Interpolation, Partial Differential Equations, Wave equation, Topology, Linear Programming and General Aptitude.
How many chapters and topics are in the GATE Mathematics syllabus?
84 chapters and 110 topics, broken down further into 41 sub-topics, across 14 subjects. Algebra is the largest subject, with 20 topics in 3 chapters.
Are there GATE Mathematics flashcards?
Yes — 713 question-and-answer flashcards in 14 subject decks. Each deck is printed in full on its subject page here, and the same cards are in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.
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