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MPPSC Assistant Professor Mathematics Syllabus 2026, Exam Pattern
MPPSC Assistant Professor Mathematics Syllabus 2026, Exam Pattern, Exam Date 2026
Detail Information about MPPSC has published notification 2026 for the recruitment of Assistant Professor (Mathematics) vacancies. Those Candidates who are Interested to the following vacancy and completed all Eligibility Criteria can read the Notification & Apply Online. In this page we provide the Complete Syllabus of this Recruitment with Latest Update Exam Pattern and the Exam.
MPPSC Assistant Professor Syllabus 2026 - Overview
MPPSC Assistant Professor Syllabus 2026 - Overview
| Name of the Organization | Madhya Pradesh Public Service Commission |
| Name of the Posts | Assistant Professor (Mathematics) |
| Total Post | 107 |
| Exam Date 2026 | 04th October 2026 |
| Job Location | Madhya Pradesh |
| Category | Syllabus and Exam Pattern |
| Official Website | www.mppsc.nic.in |
MPPSC Assistant Profesor (Mathematics) Syllabus 2026
Paper 1 : Syllabus :
General knowledge of Madhya Pradesh, National and International level and basic knowledge of computer
1. History culture and literature of M.P. :
1. Important Historical events and Major dynasties of M.P.
2. Contribution of Madhya Pradesh in the Independence movements
3. Art, Architecture and culture of M.P.
4. Main Tribes and Dialects of M.P.
5. Main festivals, folk music and folk art of M.P.
6. Important literary figures of M.P. and their literature
7. Main Tourist places of M.P.
8. Important personalities of M.P.
2. Geography of the Madhya Pradesh :
1. Forest, Mountain and Rivers of M.P.
2. Climate of M.P.
3. Natural and mineral resources of M.P.
4. Energy Resources: Conventional and Non- conventional
5. Main irrigation and Power projects of M.P.
3. Politics and Economy of M.P. :
1. Political system of M.P. (Governor, Cabinet, Legislative Assembly)
2. Panchayati Raj in M.P.
3. Social system of M.P.
4. Demography and census of M.P.
5. Economic development of M.P.
6. Main industries of M.P.
7. Agriculture and Agri based industries in M.P.
4. Current events of International, National and M.P.
Important Contemporaneous events
Famous sports competitions; awards and sports institution of the State and country
Welfare schemes of M.P. state
Famous personalities and Places
5. Information and Communication Technology :
1. Electronics, computers, information and communication technology
2. Robotics, artificial intelligence and cyber security
3. E- Governance
4. Internet and Social networking site
5. E- Commerce
Paper 2: Concerned Subjects :-
Mathematics :
UNIT-I: Calculus and Advanced calculus :
a. Successive differentiation, Leibnitz's theorem, Maclaurin's and Taylor's expansions, Asymptotes, Curvature, Concavity and convexity, Point of inflexion, Multiple points, Tracing of curves.
b. Integration, Definite integral, Reduction formulae, Quadrature and Rectification.
c. Sequence, Limit and convergence of a sequence, Bounded and monotonic sequences, Cauchy's convergence criterion, Series of non-negative terms, Various convergence tests. Alternating series, Absolute and conditional convergence.
d. Limit and continuity of functions of single variable and two variables, Change of variables, Uniform continuity, Mean value theorem, Chain rules.
e. Maxima and minima of functions of two variables, Beta and Gamma functions, Double and triple integrals, Volume and surface of solids of revolution, Change of order of integration in double integrals.
UNIT-II: Ordinary and Partial differential equations :
a. Linear and reducible to linear differential equations, Exact differential equation, First order and higher degree equations solvable for x,y and
p, Claiurat equations, Singular solutions, Orthogonal trajectories.
b. Linear equations with constant coefficients, Linear equations of second order, Method of variation of parameters.
c. Series solution of differential equations, Bessel's and Legender's equations and functions, Orthogonality of functions, Laplace
transformation, Inverse Laplace transformations, Convolution theorem and their applications.
d. Partial differential equations of first order, Charpit's general method.
e. Partial differential equations of second and higher order, Classification, Homogeneous and non-homogeneous equations with constant coefficients, Heat equation, Wave equation, Laplace equation.
UNIT-III: Discrete Mathematics, logic, Algebra and Trigonometry :
a. Contribution of Indian mathematicians: Baudhayan and Madhavan, Bhashkaracharya II and Shridharacharya, Aryabhata, Brahm gupta, Varalmihira. Srinivasa Iyengar Ramanujan, Bharti Krishna Tirtha and thematic analysis on Vedic mathematics and its importance.
b. Boolean function, Partial order relation, Totally order set, Hasse diagrams- Maximal- Minimal- First and last elements. Lattice, Graph, Path and Circuits, Trees, Matrix representation of graphs, Planer graphs.
c. Rank of matrix, Eigen values, Eigen vectors, Linear independence of row and column matrix, Cavley's Hamilton theorem, Adjoint and inverse of matrix, Applications of matrix to solve a system of Linear equutions.
d. Logic: Logical connectiveness, Truth tables, Tautology, Contradiction, Algebra of prepositions, Logic gates and circuits.
e. Relation between roots and coefficients of a general polynomial equation in one variable, Decart's sign rule, Demoiver's theorem and its applications, Hyperbolic and inverse hyperbolic functions, Expansion of trigonometric functions
UNIT-IV: Vector analysis, Geometry and Analytic geometry :
a. Product of vectors, Vector differentiation, Gradient, Divergence and Curl, Vector identities and Vector equations.
b. Vector integration, Gauss's, Green's and Stock's theorems and their applications.
c. General equation of second degree, Tracing of conics, Polar equation of conics.
d. Equation of cone, Generators, Condition for three mutually perpendicular generators, Right circular cone, Cylinder with properties.
e. Central conicoid, Paraboloid, Ellipsoid, Hyperboloid and their properties.
UNIT-V: Abstract Algebra :
a. Sets, Algebra of sets, Subset, Power set, Relation, Equivalence relation mapping, Congruence module-m relation, Permutation, Combination, Pigeon hole principle, Inclusion- exclusion principle, Primitive roots, Divisibility in z, Remainder theorem,
b. Group, Subgroup, Normal subgroup, Order of an element, Lagarange's theorem, Cyclic group Homomorphism and isomorphism, Kernel of homomorphism, Quotient group, Permutation group, Cayley's theorem.
c. Class equation, Counting principle, Cauchy's theorems, Double coset Sylow's theorems.
d. Ring, Subring, Ideals, Quotient ring, Unique Factorization domain, Principal ideal domain, Euclidian domain, Integral domain, field, Subfield.
e. Polynomial rings, Reducibility and irreducibility of polynomials, Finite fields, Field extension.
UNIT-VI: Linear algebra:
a. Vector spaces, Vector subspaces and their algebra, Linear dependence and independence, Basis and dimension.
b. Linear transformations and their matrix representation, Change of basis Canonical forms, Diagonalization, Triangular forms, Jordan form.
c. Algebra of matrices, Rank and nullity, Sylvester's theorem, Eigen values, Eigen vectors.
d. Inner Product, Inner Product spaces, Orthonormal basis.
e. Quadratic forms, Reduction and classification of quadratie forms
UNIT-VII: Real Analysis :
a. The real numbers, R as a complete ordered field, Intervals, Bounded and unbounded sets in R, Archimedean property, Absolute value, Open and closed sets in R, Countability of sets.
b. Real sequences, Subsequences, Infinite series, Various tests for convergence of infinite series, Alternating series, Absolute and conditionally convergent series, Power series, Rearrangements of terms of a series.
c. Real funtions, Limit & continuity of functions, Uniform continuity, Differentiability, Mean value theorem, Higher derivatives, Intermediate forms.
d. Riemann integrability, Riemann- Stieljes integrability, Uniform convergence of sequences and series of functions, Improper integrals.
e. Metric spaces, Subspaces, Complete metric space, Contraction principle Bolzano Weirstrass Property (BWP). Sequentially compact metric space, Connected metric space
UNIT-VIII: Complex Analysis :
a. Algebra of complex numbers, Complex plane, Polynomials, Power series.
b. Analytic function, Cauchy-Riemann equations, Contour integral, Cauchy's theorem, Cauchy's Integral formula.
c. Liouville's theorem, Maximum modulus principle, Schwarz's lemma, Taylor's series, Laurent Series.
d. Fixed points, Cross ratio, Bilinear transformation.
e. Residue Theory- Residue at a pole, Residue at infinity, Cauchy's residues theorem, Computation of residue at a finite pole
UNIT-IX: Statistics and Numerical Analysis :
a. Central Tendency- Mean, Median, Mode, Measures of dispersion- range, Interquartile range, Mean deviation.
b. Sampling Sampling of large samples, Null and alternating hypothesis, Test of significance based on x² (chi-square), t, F and Z- statistics.
c. Probability- Events, Sample space, Probability of an event, Addition and multiplication theorem, Baye's theorem.
d. Numerical solution of algebraic equations, Method of iteration and Newton-Raphson method, Solution of system of linear algebraic equations using Guass elimination and Guass - Scidal methods.
e. Numerical differentiation and integration, Numerical solutions of ordinary differential equations using Picard, Euler, Modified Euler and Runge-kutta method.
UNIT-X: Functional Analysis :
a. Normed Linear Spaces, Banach Spaces, Finite dimension normed linear spaces, Normed linear subspaces, Equivalent norms, Riesz lemma and compactness, Quotient spaces.
b. Linear operators, Bounded Linear operators, Continuous and Non- linear operators, Linear and bounded linear functional, Dual space.
c. Hilbert space, Orthogonal complements sets and sequences Orthonoral sets, Bessel's inequality, Complete orthonormal sets, Hilbert adjoint operators, Self adjoint operators, Adjoint operators.
d. Unitary and normal operators, Positive operators, Hahn-Banach theorem, Adjoint operators on norlaed spaces, Reflexive spaces.
e. Category theorem, Bair's Category theorem, Uniform boundedness theorem, Open mapping theorem, Closed graph theorem, Strong and weak convergence in normed spaces.
| Paper | Subject | No.of Question | Marks | Duration |
| Paper 1 | General knowledge of Madhya Pradesh, National and International level and basic knowledge of computer | 50 | 200 | 1 Hour |
| Paper 2 | Concerned Subjects (Mathematics) | 150 | 600 | 3 Hour |
| Total | 200 | 800 |
Exam Date 2026 : 04th October 2026
Starting Date of Application Form : 28th July 2026
Last Date of Application Form : 15th August 2026
Total Post : 107
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