B.Tech. in Mathematics and Computing
The department offers a four-year B.Tech. program in Mathematics and Computing, which commenced in the academic year 2019–2020 and currently has a total student strength of 145. Admission to the program is through JEE (Advanced), ensuring a highly competitive and talented student cohort.
This program is designed to build a strong foundation in mathematics, statistics, and computer science, with an emphasis on analytical thinking and algorithmic problem-solving. A distinctive focus is placed on artificial intelligence, and data science, approached through the rigorous lenses of mathematical modeling, statistical inference, and computational methods.
From the initial semesters, students are immersed in core subjects such as calculus, linear algebra, probability and statistics, optimization, programming, machine learning etc, which form the backbone of modern AI and data-driven technologies. A wide range of industry-relevant electives is offered in advanced topics like deep learning, mathematical image processing, data mining, computer architecture, and more, enabling students to specialize and stay aligned with current technological trends.
Graduates of this program are equipped not only with strong engineering and technical expertise, but also with a solid mathematical foundation, making them uniquely positioned for careers in research, data-driven industries, software development, and advanced studies.
Semester-I
| Sr. | Course Code | Course Name | Credits |
|---|---|---|---|
| 1. | MA101 | Calculus | 3 |
| 2. | HS103 or HS102 | Professional English Communication (HS103) or English Language Skill (HS 102) | 3 |
| 3. | NC101 | NCC I | 1 |
| 4. | CY101 | Chemistry for Engineers | 4 |
| 5. | GE103 | Introduction to Computer Programming & Data Structure | 4.5 |
| 6. | GE105 | Engineering Drawing | 1.5 |
| 7. | HS101 | History of Technology | 1.5 |
| Total Credits: | 18.5 | ||
Semester-II
| Sr. | Course Code | Course Name | Credits |
|---|---|---|---|
| 1. | MA102 | Linear Algebra, Integral Transforms and Special Functions | 3 |
| 2. | MAXXY or MAXXZ | Program Core (3 ) or Program-Specific General Engineering | 3 |
| 3. | NC102 or NO102 or NS102 | NCC II or NSO II or NSS II | 1 |
| 4. | PH101 | Physics for Engineers | 5 |
| 5. | GE104 | Introduction to Electrical Engineering | 3 |
| 6. | GE102 | Workshop Practice | 2 |
| 7. | GE101 | Technology Museum Lab | 1 |
| Total Credits: | 18 | ||
Semester-III
| Sr. | Course Code | Course Name | Credits |
|---|---|---|---|
| 1. | CS201 | Data Structures | 4 |
| 2. | MA411 | Real Analysis | 3 |
| 3. | MA201 | Differential Equations | 3 |
| 4. | EE201 | Signals and Systems | 3 |
| 5. | NCIII/ NOIII/ NSIII | Introduction to Electrical Engineering | 1 |
| 6. | HS201/ GE108 | Economics/ Basic Electronics | 3/3 |
| 7. | GE107/ GE109 | Tinkering Lab / Introduction to Engineering Products | 1.5/1 |
| Total Credits: | 18/18.5 | ||
Semester-IV
| Sr. | Course Code | Course Name | Credits |
|---|---|---|---|
| 1. | MA204 | Introduction to Numerical Analysis | 3 |
| 2. | MA426 | Theory of Computation | 3 |
| 3. | MA205 | Computing Lab | 2 |
| 4. | MA202 | Probability and Statics | 3 |
| 5. | HS202/ BM101 | Human Geography and Societal Needs / Biology for Engineers | 3/3 |
| 6. | NCIV / NOIV / NSIV | NCC / NSO / NSS | 1 |
| 7. | HS201 / GE108 | Economics/ Basic Electronics | 3/3 |
| 8. | GE107 / GE109 | Tinkering Lab / Introduction to Engineering Products | 1.5/1 |
| Total Credits: | 19/19.5 | ||
Semester-V
| Sr. | Course Code | Course Name | Credits |
|---|---|---|---|
| 1. | MA514 | Analysis & Design of Algorithms | 3 |
| 2. | MA515 | Foundation of Data Science | 4 |
| 3. | MA301 | Computational Algebra | 3 |
| 4. | HS202/ BM101 | Human Geography and Societal Needs / Biology for Engineers | 3/3 |
| 5. | HS301/ GE111 | Industrial Management / Introduction to Environmental Science & Engineering | 3 |
| 6. | HS104 | Professional Ethics [about 50% students] | 1.5 |
| Total Credits: | 17.5 | ||
Semester-VI
| Sr. | Course Code | Course Name | Credits |
|---|---|---|---|
| 1. | MA302 | Optimization Techniques | 3 |
| 2. | MA303 | Computing Lab-II | 2 |
| 3. | CS503 | Machine Learning | 4 |
| 4. | CP301 | Development Engineering Project | 3 |
| 5. | HS301 / GE111 | Industrial Management / Introduction to Environmental Science & Engineering | 3 |
| 6. | HS104 | Professional Ethics [about 50% students] | 1.5 |
| Total Credits: | 16.5 | ||
| Summer Vacation Course following Semester 6 | |||
| Sr. | Course Code | Course Name | Credits |
| 1. | II301 | Industrial Internship and Comprehensive Viva Voce (70% weightage for 8-week full internship and 30% for comprehensive viva on program fundamentals) | 3.5 | Credits: | 3.5 |
Semester-VII
| Sr. | Course Code | Course Name | Credits |
|---|---|---|---|
| 1. | CP302 | Capstone Project I | 3 |
| ELECTIVE COURSES | |||
| 2. | HSXXX | An English Language/Literature elective course in either 7th or 8th sem for students who had “English Language Skills” in 1st Semester | 3 |
| 3. | BMXXX /MAXXX /CYXXX /PHXXX | Science Maths Elective I | 3 |
| 4. | MAXXX | Program Elective I | 3 |
| 5. | XXXXX | Any extra credits taken under HS Elective /Program Elective/Science Maths Elective | 3 |
| Total Credits: | 15 | ||
Semester-VIII
| Sr. | Course Code | Course Name | Credits |
|---|---|---|---|
| 1. | CP303 | Capstone Project II | 3 |
| ELECTIVE COURSES | |||
| 2. | HSXXX | An English Language/Literature elective course in either 7th or 8th sem for students who had “English Language Skills” in 1st Semester | 3 |
| 3. | BMXXX /MAXXX /CYXXX /PHXXX | Science Maths Elective II | 3 |
| 4. | MAXXX | Program Elective II | 3 |
| 5. | XXXXX | Any extra credits taken under HS Elective /Program Elective/Science Maths Elective | 3 |
| Total Credits: | 15 | ||
B.Tech. Courses
MA101 Calculus: 3
Single Variable Calculus: Limits and continuity of single variable functions, differentiation and applications of derivatives, Definite integrals, fundamental theorem of calculus, Applications to length, moments and center of mass, surfaces of revolutions, improper integrals, Sequences, series and their convergence, absolute and conditional convergence, power series. Taylor’s and Maclaurin’s series.
Multi Variable Calculus: Functions of several variables-limits and continuity, partial derivatives, chain rule, gradient, directional derivatives, tangent planes, normals, extreme values, saddle points, Lagrange multipliers, Taylor’s formula, Double and triple integrals with applications, Jacobians, change of variables, line integrals, divergence, curl, conservative fields, Green’s theorem, surface integrals, Stokes’s Gauss Divergence theorem.
MA102 Linear Algebra, Integral Transforms and Special Functions: 3
Linear Algebra: Vector spaces over R and C, Subspaces, Basis and Dimension, Matrices and determinants, Rank of a matrix, System of linear equations, Gauss, elimination method, Linear transformations, Rank-nullity theorem, Change of basis, Eigen values, Eigen vectors, Diagonalization of a linear operator, Inner product spaces. Spectral theorem, for real symmetric matrices, application to quadratic forms.
Integral Transforms: Laplace transforms of elementary functions, Inverse Laplace transforms and applications, Fourier series, Fourier transforms, Fourier cosine and sine integrals, Dirichlet integral, Inverse Fourier transforms. Special Functions: Gamma and Beta functions, Error’ functions.
MA201 Differential Equations: 3
Ordinary Differential Equations: First Order Equation, Exact equations, integrating factors and Bernoulli equations. Lipschitz condition, examples on non-uniqueness. Second order differential equations with constant coefficients: homogeneous and non-homogeneous differential equations. Wronskian and linear independence of solutions, method of variation of parameters. Cauchy-Euler equations, method to second order equations with variable coefficients, Some applications, Solution of IVP using Laplace Transform and Euler’s Method. Series solutions, Frobenius method, Legendere and Bessel equations, orthogonal properties of Legendre polynomials.
Partial Differential Equations: Linear second order partial differential equations and their classification, heat equation, vibrating string, Laplace equation; method of separation of variables.
MA202 Probability and Statistics: 3
Probability: Axioms of probability, conditional probability, independence of two or more events, Bayes’ theorem. Random variable, distribution functions, standard probability distributions and their properties, Simulation. Multiple random variables, marginal and conditional probability distribution, independence of random variables, bivariate normal and multinomial distributions. Functions of random variables, covariance and correlation. Conditional expectation, sum of random number of independent random variables. Convergence in probability, laws of large numbers and central limit theorem.
Statistics: Sample, population, sampling techniques, descriptive statistics, popular sampling distributions. Point estimation, parameter estimation with MLE, interval estimation, hypothesis testing. Ordinary least Squares (OLS) regression, assumptions and limitations of OLS, inference concerning regression parameters, other regressions. Analysis of variance.
MA204 Introduction to Numerical Analysis: 3
Module 1: Definition of errors, Solutions of nonlinear equation, Bisection method, Newton’s method and its variants, fixed point iterations, convergence analysis.
Module 2: Solutions of Linear system of equations, LU Decomposition, Newton’s method and fixed point method for Non-linear systems; Finite differences.
Module 3: Interpolation; Numerical Differentiation, Numerical integration – Trapezoidal and Simpson’s rules, Gaussian quadrature.
Module 4: Numerical Solutions of Ordinary differential equations and Initial value problems – Taylor series method, Euler and modified Euler methods, Runge¬Kutta methods, multistep methods and stability.
MA205 Computing Lab: 2
Module 1: Introduction to MATLAB/Mathematica, Solutions of nonlinear equation, Bisection method, Newton’s method and its variants, fixed point iterations.
Module 2: Newton’s method and fixed point method for Non-linear systems; Finite differences, polynomial interpolation.
Module 3: Interpolation; Numerical Differentiation, Numerical integration – Trapezoidal and Simpson’s rules, Gaussian quadrature.
Module 4: Numerical Solutions of Ordinary differential equations and Initial value problems – Taylor series method, Euler and modified Euler methods, Runge¬Kutta methods, multistep methods and stability; Boundary value problems -finite difference method, collocation method.
MA301 Computational Algebra: 3
Introduction to Group Theory: Groups, Subgroups, Symmetric groups, cyclic group, Homomorphism, Sylow Theorem (Without Proof).
Ring Theory: Rings, Ideals, Maximal ideal, Prime ideal, Euclidean domain, PID, Factorization of polynomials.
Field theory: Finite field, Existence and uniqueness of finite field, Split extension, Factorization of multivariate polynomial.
Application: Primality testing, Application of algebra in coding theory and decoding.
MA302 Optimization Techniques: 3
Introduction to Optimization and Modeling Real World Optimization Problems as LPP: Introduction to optimization, Formulation of linear Optimization problems, Convex set.
Methods to Solve Linear Programming Problem: Linear Programming model, Graphical method, Simplex method, Finding a feasible basis – Big M and two phase Simplex method, revised simplex method.
Duality: Duality in Linear Program. Primal-dual relationship & economic interpretation of Duality, Dual Simplex Algorithm, Sensitivity analysis.
Transportation Model: Transportation & Assignment problem. Network Analysis.
Integer Linear Programming Problem: Integer programming problem: Formulation, Branch & Bound and Cutting Plane methods.Dynamic Programming (DP).
Non-linear Programming: Non-linear Programming: Lagrange multipliers and Kuhn – Tucker conditions, convex optimization. Numerical optimization techniques.
MA303 Computing Lab-II: 2
Introduction to MATLAB: Learning MATRIX Operations.
Formulating Problems as Linear Programming Problems: Formulating Real World Optimization Problems as Linear programming Problems.
MATLAB code for Simplex and Dual Simplex Method: MATLAB code to implement Simplex Method and Dual Simplex Method to Solve Linear Programming Problem.
MATLAB code for Hungarian Method: MATLAB code to solve Assignment Problem using Hungarian Method.
MATLAB code for Branch and Bound Method: MATLAB code for Branch and Bound Method to solve Integer Linear Programming Problem.
Brief Introduction to CPLEX/LINGO: To learn Optimization Modeling Software for Linear, Nonlinear, and Integer Programming Problems.
MA426 Theory of computation: 3
Finite Automata: Deterministic Finite Automata, Non deterministic finite Automata, Equivalence to DFA, NDFA.
Regular Languages: Regular Languages and its properties, Pumping Lemma, Minimization of DFA.
Push Down Automata: Context Free Grammars and Context Free Languages, Pushdown Automata, Equivalence of CFG and PDA.
Context Free Languages: Properties of Context Free Languages, Pumping Lemma for CFG, Chomsky Normal Form.
Turing Machines and Undecidability: Turing Machines, Recursive Languages, Recursive Enumerable Languages, Undecidability, Halting Problem, Post Correspondence Problem.
MA514 Analysis & Design of Algorithms: 3
Introduction to Algorithms: Analyzing Algorithms, Asymptotic notations.
Divide-and-Conquer, Sorting Algorithms: Sorting and Searching; Matrix Multiplication and application of technique in other problems.
Dynamic Programming and Greedy Algorithms: Principles of Dynamic Programming; Knapsack problem; Longest Common Sequence and application of technique in other problems. Greedy Algorithms: Interval Scheduling; Finding Closest Pair of Points; Huffman Codes; Matroids and application of technique in other problems.
Graph Algorithms: Graph Traversals: Breadth First Search, Depth First Search; Topological Sort; Minimum spanning trees; Shortest path problems; Network flows: Ford-Fulkerson Algorithm; Bipartite Matching.
NP-completeness, Approximation Algorithms and Fixed Parameter Algorithms: Complexity Classes: NP, NP-hard and NP-complete; Polynomial-time reductions; Approximation techniques: Greedy, Linear programming and rounding. Introduction to Parameterized Algorithms, Kernelization, Bounded Search Tree.
MA515 Foundations of Data Science: 4
Overview of probability and statistics, multivariate Gaussian, MLE, MAP, expectation maximization; statistical learning: definition, principles and different types of statistical learning, assessing model accuracy, bias-variance tradeoff; regression models: simple linear and multiple linear and non-linear; resampling methods: assessing model prediction quality, cross validation, bootstrap; model selection and regularization: dimensionality reduction, ridge and lasso; unsupervised learning: clustering approaches, K-means and hierarchical clustering; supervised learning: classification problem, classification using logistic regression, naive Bayes, classification with Support Vector Machines, neural networks.