BHU BSc Mathematics Syllabus 2026-27: Semester-wise Subjects & Topics

The BHU BSc Mathematics Syllabus provides a comprehensive undergraduate curriculum covering core areas of mathematics such as algebra, calculus, differential equations, analysis, geometry, linear algebra and numerical methods. 

The programme is offered by the Department of Mathematics, Faculty of Science, Banaras Hindu University (BHU).

BHU BSc Mathematics Syllabus

The BSc (Hons.) Mathematics programme is structured across six semesters. Students study core mathematics papers along with elective courses, programming, computational mathematics and a final project. The syllabus has a total of 64 credits.

The curriculum gradually moves from foundational concepts such as algebra and calculus to advanced topics including abstract algebra, mathematical analysis, differential geometry, numerical analysis, probability and operations research.

BHU BSc Mathematics Semester-Wise Syllabus

Semester I

The first semester consists of two core papers:

• MTB 101 – Algebra: Covers matrix algebra, elementary matrix operations, inverse and rank of matrices, systems of linear equations, groups, subgroups, cyclic groups, cosets, Lagrange's theorem, homomorphism, isomorphism and permutation groups.

• MTB 102 – Calculus: Includes successive differentiation, Leibnitz theorem, limits, continuity, differentiability, mean value theorems, Taylor and Maclaurin theorems, curve sketching and definite integrals.

Each paper carries 3 credits, giving the semester a total of 6 credits.

Semester II

Semester II includes:

• MTB 201 – Statics & Dynamics

• MTB 202 – Multivariable Calculus

Statics and Dynamics covers equilibrium of coplanar forces, virtual work, velocity and acceleration, central orbit, Kepler's laws, simple harmonic motion, Coriolis force and centrifugal force. Multivariable Calculus includes functions of two variables, partial differentiation, maxima and minima, double and triple integrals, Beta and Gamma functions, gradient, divergence, curl, and Green's, Stokes' and Gauss' theorems.

Semester III and IV

Semester III

The third semester introduces:

• MTB 301 – Differential Equations

• MTB 302 – Tensor & Geometry

Differential Equations covers first-order ordinary differential equations, linear differential equations, series solutions, and Bessel and Legendre equations. Tensor & Geometry includes contravariant and covariant vectors, tensor transformations, contraction, conics, spheres, cones, cylinders, paraboloids and central conicoids.

Semester IV

The fourth semester consists of:

• MTB 401 – Partial Differential Equations

• MTB 402 – Mathematical Methods

The Partial Differential Equations paper covers first-order linear and nonlinear PDEs, Charpit's method, higher-order PDEs, Monge's method and solutions of heat and wave equations. Mathematical Methods includes Laplace transformations, Fourier series and calculus of variations.

Semester V Syllabus

Semester V expands into advanced mathematics and applied areas. The core papers include:

• Analysis-I

• Abstract Algebra

• Programming in C

• Differential Geometry

• Discrete Mathematics

Analysis-I includes Riemann integration, improper integrals, sequences and infinite series. Abstract Algebra covers automorphisms, group actions, rings, integral domains, fields, ideals and polynomial rings. Programming in C introduces fundamentals, data types, operators, loops, arrays, functions, structures, pointers and file handling.

Differential Geometry covers space curves, Serret-Frenet formulae, surfaces, fundamental forms, curvatures and developables. Discrete Mathematics includes logic, lattices, Boolean algebra, graphs and planar graphs.

Students also choose one Elective-I paper from options including Combinatorial Mathematics, Business Mathematics, Special Theory of Relativity-I and Computational Mathematics Lab-I.

Semester VI Syllabus

Semester VI includes:

• Analysis-II

• Linear Algebra

• Numerical Analysis

• Mechanics

• Operations Research

• Elective-II

• Project

Analysis-II covers complex analysis and metric spaces, while Linear Algebra includes vector spaces, linear transformations, rank and nullity, eigenvalues, eigenvectors, diagonalization and inner product spaces. Numerical Analysis includes numerical solutions of equations, interpolation, numerical differentiation, quadrature and eigenvalue computation.

Operations Research introduces linear programming, simplex algorithms, duality, transportation and assignment problems, travelling salesman problems and portfolio theory.

For Elective-II, students can choose from Number Theory, Probability, Advanced Differential Geometry, Special Theory of Relativity-II and Computational Mathematics Lab-II.

BHU BSc Mathematics Syllabus PDF

The BHU BSc Mathematics Syllabus PDF is provided below for students to download and refer to during their academic preparation. 

The PDF contains the prescribed syllabus and topics, helping students understand the course structure and plan their studies. Candidates can download the PDF below and use it as a reference for tracking subjects, organising study plans and preparing effectively for the BHU BSc Mathematics programme. 

BHU BSc Mathematics Syllabus PDF

BHU BSc Mathematics Project

The programme also includes MTB 611 – Project, carrying 4 credits. The project allows students to undertake innovative written work related to mathematics or applications of mathematics using knowledge gained during the undergraduate course.

How to Prepare for BHU BSc Mathematics

A focused study strategy can help students understand the concepts covered across the six-semester BHU BSc Mathematics curriculum and build a strong foundation for advanced mathematical topics.

• Build Strong Fundamentals: Start with core areas such as Algebra, Calculus and mathematical reasoning, as these concepts support several advanced subjects in later semesters.

• Practise Mathematics Regularly: Solve mathematical problems consistently to strengthen conceptual understanding and improve accuracy, especially in subjects such as Analysis, Differential Equations and Linear Algebra.

• Maintain Semester-Wise Notes: Prepare organised notes for every subject and regularly revise important definitions, formulas, theorems and problem-solving methods.

• Use Recommended Books: Refer to the books recommended for individual courses in the BHU syllabus to supplement classroom learning and develop a deeper understanding of mathematical concepts.

• Practise Programming and Computational Topics: For Programming in C and Computational Mathematics, combine theoretical study with practical programming and numerical problem-solving practice.

The BHU BSc Mathematics Syllabus offers a broad combination of pure and applied mathematics. From Algebra and Calculus in the first semester to Analysis, Linear Algebra, Probability, Number Theory, Operations Research and computational subjects in later semesters, the curriculum provides students with a strong mathematical foundation and opportunities to explore specialised areas through electives and project work.