Maths Syllabus 2025: Check Semester-wise Subjects & Syllabus

Calculus

Calculus comprises of derivatives for graphics, sketching and tracing curves, calculation of volume and area and the application of vector calculus.

Algebra

It introduces candidates to the theory of complex numbers, the equivalence relations and the basic number theory. It also explains the Row Echelon Form of Matrices.

Real Analysis

The course defines the real number system, its properties, sequences and the application of infinite series.

Differential Equations

Students learn about the basics of differential equations, their application in population growth models and their analysis.

Theory of Real Functions

It deals with the concepts of limits of functions, properties of continuous functions, application of derivability and Taylor’s theorem.

Group Theory

The course explains the elementary properties of groups and subgroups, cyclic and permutation groups and the derivation of Lagrange’s theorem.

Ring Theory and Linear Algebra

The course introduces learners to the ring theory, ring homomorphism, vector spaces and linear transformations.  

Metric Spaces

Metric Spaces deals with its topology, uniform continuity, automorphism, group action, connectedness and compactness of groups.

Multivariate Calculus

The subject deals with the calculus of functions with multi-variables, double and triple integrals and the theorems of Green, Stokes and Gauss.

Functional Analysis

This course deals with the concepts of Banach Contracton Principle, Hilbert Spaces, Pythagorean Law, Monotone Functions and Lebesgue Outer Measure.

Linear Algebra

Linear Algebra consists of principles of vector spaces, Eigen vectors, Cayley-Hamilton theorem, homomorphism of group and commutative rings.

Elements of General Topology

The course deals with the topological spaces and application of Kuratowski closure operators in complex analysis.

Operations Research

This is an introductory course on Operations Research and preparation of mathematical formulation of any assignment problem.

Differential Geometry

The course deals with the integral of any partial differential equation and application of Gauss Formula in differential geometry.

Set Theory

An interesting module which introduces the Zorn’s Lemma and Hausdorff Maximality principle and the Cartesian product of sets.

Mathematical Logic

The course deals with the statement calculus and arguments to for proving validity and consequences.

Numerical Analysis

The course introduces methods to solve algebraic, linear and transcendental equations. It also deals with interpolation and numerical differentiation and integration.

Mathematical Modelling and Graph Theory

Students learn about the power series solutions, Laplace Transforms, Monte Carlo Simulations and the application of Graph Theory.

C++ Programming for Mathematics

The course deals with the basics of C++, working with containers, templates, structured data and usage of mathematical libraries and packages.

Probability Theory and Statistics

Learners understand the probability functions, univariate discrete and continuous distributions, bivariate distributions and the application of central limit theorem.

Discrete Mathematics

The course deals with ordered sets, lattices, graph theory and the application of Boolean Algebra.

Mathematical Finance

Mathematical Finance deals with the application of mathematics in financial systems, types of interest rates and trading strategies.

Biomathematics

It is an interesting course which introduces the concept of bio-mathematical models and modelling of molecular evolution and genetics.

Number Theory

The course deals with the concepts of distribution of primes, primitive roots and the quadratic reciprocity law.

Differential Geometry of Manifolds

It introduces to the principles of topological groups, tangent spaces and exterior algebra.

Advanced Functional Analysis

The course deals with hyperplanes, types of sets and vector spaces.

Advanced Real Analysis

It deals with the upper and lower limits of a real function, the properties and functions of differential equations and various types of functions.

Lattice Theory

Lattice theory enumerates the Fourier series, Fejer’s Theorem, Dirichlet’s and Fatou’s theorem and their applicability.

Harmonic Analysis

The course deals with the conjugate function series and the approximate identities.

Advanced Operations Research

It is an advanced course in Operations Research which explains non-linear, constrained and unconstrained optimization.

Measure and Integration

The course deals with the algebra pf sets, types of measurable functions, process of approximation and the properties of integrals.

Calculus

Howard Anton, Stephen Davis

The authors write on the polynomials, logarithms, rational functionals with the help of examples and exercises.

Linear Algebra and its Applications

David Lay, R Steven, Judi McDonald

The book comprehensively deals with the concepts of spanning, vector space, eigenvalues and least squares.  

Introduction to Real Analysis

Robert G Bartle, Donald R Sherbet

It delves into the concept of real analysis and its application to engineering, computer science and other physical sciences.

Differential Equations

Shepley Ross

Differential Equations deals is a treatise on the methods of solving differential equations and analyses of various differential models.

An Introduction to the Theory of Groups

Joseph Rotman

A celebrated work on linear and abstract algebra and other structures such as vector spaces and rings.

Basic Multivariate Calculus

Marsden, Weinstein

It delves into the equations having various variables, double and triple integrals with the help of comprehensive examples.  

Elementary Number Theory

David Burton

It is a popular book prescribed for Mathematics and Computer Science students providing information on the classical number theory.