DIPS Academy offers the UPPSC Assistant Professor Test Series for Mathematics with detailed explanations. This online test series is designed to match the exact exam pattern and difficulty level, offering complete coverage of the UPPSC Assistant Professor syllabus. It also includes an in-depth analysis of previous years’ question papers based on the UPPSC Assistant Professor exam pattern. This test series is a perfect tool for aspirants aiming to succeed in the Uttar Pradesh Assistant Professor Mathematics exam with confidence.
Module-Wise Tests covering complete syllabus.
Detailed module-wise coverage.
Tests with real exam simulation.
Based on Exact Preliminary Exam Pattern.
Detailed insight into strengths & weaknesses.
Get the Answer key for self-assessment.
UPPSC ASSISTANT PROFESSOR TEST SERIES SCHEDULE |
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Note: The Test Paper will go live at 5:00 PM on the scheduled date. |
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| Test Dates | Unit | Tests | Topics Covered |
|---|---|---|---|
| 01 Apr 2026 11 Apr 2026 21 Apr 2026 | Unit 1 | 3 |
Real Analysis & Set Theory
Elementary set theory, finite/countable/uncountable sets, real number system as a complete ordered field, Archimedean property, supremum, infimum. Sequences & series, convergence, limsup, liminf, uniform convergence. Bolzano–Weierstrass theorem, Heine–Borel theorem.
Metric Spaces
Completeness, connectedness.
Integration Theory
Riemann integration, Lebesgue measure, Lebesgue integration.
Functional Analysis
Normed linear spaces, Banach spaces, spaces of continuous functions, open mapping theorem, closed graph theorem, Hahn–Banach theorem, Hilbert spaces.
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| 03 Apr 2026 13 Apr 2026 23 Apr 2026 | Unit 2 | 3 |
Calculus
Continuity, types of discontinuity, uniform continuity, differentiability, monotonic functions, functions of bounded variation, mean value theorems. Sequences & series of functions, multivariable calculus (directional/partial/total derivatives), maxima/minima, saddle points, Lagrange multipliers, double & triple integrals, improper integrals.
Vector Calculus
Gradient, divergence and curl; Green's theorem, Stokes' theorem, Gauss divergence theorem.
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| 05 Apr 2026 15 Apr 2026 25 Apr 2026 09 May 2026 | Unit 3 | 4 |
Group Theory & Number Theory
Divisibility in ℤ, fundamental theorem of arithmetic, congruences, Chinese remainder theorem, Euler's φ-function, Fermat's theorem. Groups, subgroups, normal subgroups, quotient groups, homomorphisms, cyclic groups, permutation groups, Cayley's theorem, class equation, Sylow's theorems.
Ring Theory & Field Theory
Rings, ideals, prime & maximal ideals, quotient rings, UFD, PID, Euclidean domain, polynomial rings, irreducibility. Fields, finite fields, field extensions, Galois theory.
Module Theory
Submodules, cyclic modules, free modules, Noetherian & Artinian modules, Hilbert basis theorem.
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| 07 Apr 2026 17 Apr 2026 27 Apr 2026 | Unit 4 | 3 |
Linear Algebra
Vector spaces, subspaces, linear dependence/independence, basis, dimension, algebra of linear transformations. Rank-nullity theorem, matrix representations, change of basis, systems of linear equations. Eigenvalues & eigenvectors, Cayley–Hamilton theorem, diagonal/triangular/rational/Jordan canonical forms. Inner product spaces, orthonormal basis. Quadratic forms, reduction and classification.
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| 09 Apr 2026 19 Apr 2026 | Unit 5 | 2 |
Complex Analysis
Limit, continuity & differentiability of complex functions, analytic functions, Cauchy–Riemann equations. Complex integration, Cauchy's theorem & integral formula, Liouville's theorem, maximum modulus principle, Schwarz lemma, Taylor & Laurent series, calculus of residues, contour integrals, conformal mappings, Möbius transformations.
Topology
Basic concepts, basis, dense sets, topological subspaces, first & second countable spaces, separation axioms, connected spaces & components, locally connected spaces, compactness, sequential & countable compactness.
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| 29 Apr 2026 11 May 2026 | Unit 6 | 2 |
Ordinary Differential Equations
Existence & uniqueness of solutions, singular solutions of first order ODEs, systems of ODEs. Homogeneous & non-homogeneous linear ODEs, Sturm–Liouville BVP, Green's function. Second order linear ODEs: change of variables, variation of parameters.
Partial Differential Equations
Linear PDE of first order (Lagrange's method), nonlinear PDE (Charpit's method), higher order PDEs with constant coefficients, classification of second order PDEs, separation of variables, Laplace equation, wave equation, heat equation.
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| 01 May 2026 13 May 2026 | Unit 7 | 2 |
Numerical Analysis
Numerical solutions of algebraic equations, iteration & Newton–Raphson method, rate of convergence. Gauss elimination & Gauss–Seidel methods. Finite differences, Gregory–Newton & Lagrange interpolation, divided difference. Numerical differentiation & integration, Newton–Cotes formulae. ODEs: Picard, Euler, modified Euler & Runge–Kutta methods.
Calculus of Variations
Functional variation, Euler–Lagrange equation, fixed & variable end-point problems, variational problems with subsidiary conditions.
Linear Integral Equations
Fredholm & Volterra equations of first & second kind, successive approximations, conversion of differential equations, separable kernels, eigenvalues & eigenfunctions, resolvent kernel.
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| 03 May 2026 15 May 2026 | Unit 8 | 2 |
Geometry
Polar equation of a conic, Cartesian & polar coordinates in 3D, plane, straight lines, shortest distance between skew lines; sphere, cone, cylinder, central conicoid, paraboloid.
Tensors
Contravariant & covariant tensors, transformation formulae, (r,s)-type tensors, symmetric & skew-symmetric properties, contraction, inner product, quotient law.
Differential Geometry
Curves in space, curvature & torsion, Serret–Frenet formulae, helix, first & second fundamental forms of a surface.
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| 05 May 2026 18 May 2026 | Unit 9 | 2 |
Operations Research
LPP, basic feasible solution, graphical method, simplex method, duality, transportation & assignment problems, travelling salesman problem, convex optimization, gradient descent, stochastic gradient descent.
Statistics & Probability
Variance, standard deviation, curve fitting, correlation & regression, logistic regression, SVR, LDA. Sample space, laws of probability, independent events, expectation, Bayes' theorem. Random variables; Binomial, Poisson & Normal distributions.
Graph Theory
Graphs, isomorphism, subgraphs, matrix representations, degree of vertex, connected graphs, shortest path algorithms. Trees, minimum spanning trees, bipartite graphs, Hamilton graphs, planar graphs, Euler's formula, Eulerian directed graphs.
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| 07 May 2026 20 May 2026 | Unit 10 | 2 |
Mechanics
Moment of inertia, rigid body motion about an axis, 2D motion of rigid bodies, generalized coordinates & momentum, Lagrange's equations, Hamilton's canonical equations, Hamilton's principle of least action, contact transformations, Poisson bracket.
Fluid Dynamics
Equation of continuity, Euler's equation for inviscid flow, streamlines, boundary surface, 2D motion: sources & sinks, method of images, flow past a cylinder and sphere.
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Total: 25 Tests across 10 Units
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