For B.Tech
Discrete Mathematical Structures, 2nd-semester course in 2021, 2022,2023, 2024, Summer 2024, 2025.
Linear Algebra, 1st-semester course in 2021, 2022, 2023, 2024, January - May 2025, August -December 2025.
Univariate and Multivariate Calculus, Summer 2024, July - December 2024.
Fractal Geometry, 7th semester, Open Elective course, July - November 2024, July - November 2025.
Professional Ethics, 1st sem, August-Dec 2025, Jan-May 2026.
Operation Research, 4th semester, Jan- May 2026.
Measure Theory, 6th semester, Minor course, Jan-May 2026.
For M.Tech/Ph.D:
Mathematical Foundation for Data Science, January 2022 - May 2022.
Fundamentals of Discrete Mathematics, September 2021-December 2021.
Mathematical Analysis, September 2021- December 2021, August 2022 - December 2022, January 2023 - May 2023, July 2024 - December 2024.
Fractal Geometry, August 2023 - November 2023.
Discrete Mathematical Structures (DMS)
Course Outcomes:
Students will be able to:
Understand logic and proof techniques.
Apply the above techniques in counting and solving recurrence relations.
Analyze real-world models using graph theory.
Extend their usefulness in succeeding courses in algorithm design and analysis, computing theory, software engineering, and computer systems.
Course Content:
Proof by contradiction, Proof by induction-weak and strong induction, Structural induction, Proof by proving the contrapositive, Proof by cases, and Proof by counter-example.
Introduction to Logic, Truth tables, Predicates and Quantifiers, Finite and Infinite sets, Power sets, Cartesian Product, well-ordering, Countable and Uncountable sets, Cantor's diagonalization, Relations, Equivalence Relations, Functions, Bijections, Binary relations, Posets and Lattices, Hasse Diagrams, Boolean Algebra.
Counting, Sum and product rule, Principle of Inclusion-Exclusion, Pigeon Hole Principle, Counting by Bijections, Double Counting, Linear Recurrence relations - methods of solutions, Generating Functions, Permutations and counting.
Graphs and Trees (Basics), Euler graph, Hamiltonian graph, Planar graph, Structured sets with respect to binary operations, Groups, Semigroups, Monoids, Rings, and Fields.
Text/Reference Books:
Discrete Mathematics and its Applications, Kenneth H. Rosen, 7th Edition -Tata McGraw Hill Publishers, 2011.
Mathematics for Computer Science, Eric Lehman; F Thomson Leighton; Albert R Meyer, 2010.
Logic in Computer Science, Huth and Ryan, Cambridge University Press, 2014.
Attendance Policy: Attendance is compulsory in lecture and tutorial classes. At least 75% attendance (including medical reasons) is mandatory in lecture and tutorial classes per the institute norms. Strict action will be taken in case of proxy attendance. You are requested to consult your course instructor for any attendance-related issues.
Evaluation Policy:
Formative Assessment (Part-1): 35 marks will be as follows: one Quiz: 15 marks (6:45 PM -7:15 PM on Feb 07), two Computational Projects/Assignments: 15 (=8+7) marks (tentatively, Feb 24- March 03 and April 03-09), and Attendance: 5 marks.
Formative Assessment (Part-2) - Mid-semester Exam: 25 marks (will be announced by AAA section, possible dates March 04--12)
Summative Assessment- End-semester Exam: 40 marks (will be announced by AAA section, possible dates May 05--15)
Tutorials: Tut-1 Tut-2 Tut-3 Tut-4 Tut-5 Tut-6 Computational Project-1 Computational Project-2
Tentative Marking Scheme_DMS_End_Sem Seating Plan for copy-showing
Lectures: Lect-1 Lect-2 Lect-3 Lect-11 Lect-15-16 Lect-17 Lect-18
Linear Algebra (AS1002):
Syllabus and Text/Reference Books
Attendance Policy: Attendance is compulsory in lecture and tutorial classes. At least 75% attendance (including medical reasons) is mandatory in lecture and tutorial classes per the institute norms. Strict action will be taken in case of proxy attendance. You are requested to consult your course instructor for any attendance-related issues.
Evaluation Policy:
Formative Assessment (Part-1): 35% will be as follows: one Quiz: 15 marks (25th September, 6:30 - 7:00 PM), two Computational Projects/Assignments: 10+10 marks (November).
Formative Assessment (Part-2) - Mid-semester Exam: 25% (will be announced by AAA section, possible dates Oct 13--16)
Summative Assessment- End-semester Exam: 40% (will be announced by AAA section, possible dates Dec 22--27)
Note: 1. We hope every student knows the minimum percentage marks required to pass each of the above assessments.
2. We encourage every student especially PwD students to consult the coordinator, instructors and associated TAs for any academic or non-academic issues related to the course/understanding the concepts.
Lecture notes and tutorials: Here
Marking scheme for quiz-exam Seating plan_quiz for copy-showing
Computational Project 1 Computational project 2 Marking_scheme for Mid-sem End-sem
Professional Ethics (MS1004): 1st sem
Attendance Policy: as per the institute norms.
Evaluation Policy:
Formative Assessment (Part-1): 35% will be as follows: two quizzes (20+15=35 marks); Quiz 1 on 29th September (6:30 PM - 7:00 PM) and Quiz 2 on 20th November (6:30 PM - 7:00 PM).
Formative Assessment (Part-2) - Mid-semester Exam: 25% (16th October 2025, possible dates Oct 13--16).
Summative Assessment- End-semester Exam: 40% (20th December 2025, possible dates Dec15-20).
Lecture Notes: Note-1 Note-2 Note-3 Note-4 Note-5
Fractal Geometry (AS5516):
Course outcomes: Students will be able to:
Estimate/compute the Hausdorff and Box-counting dimensions
Use the Iterated function systems and fractal interpolation in approximation
Create effective computer codes for generating fractal sets and estimating dimensions.
Course content: Basic set theory, functions and limits, measures and mass distributions, Euclidean distance, Hausdorff distance
Box-counting dimensions, properties of box-counting dimensions, Hausdorff measure, Hausdorff dimension, calculation of Hausdorff dimension, relationship between these dimensions
Fractals constructed by iteration, Iterated function systems, self-similar sets, self-affine sets, continued fraction examples, dimensions of graphs, the Weierstrass function and self-affine graphs
Chaos game algorithm, fractal interpolation and its applications, MATLAB/Python/ any other computer codes for estimation/computation of dimensions.
Text Books/References:
K. J. Falconer, Fractal Geometry: Mathematical Foundations and Applications, Third Edition, Wiley, 2014.
G. Edgar, Measure, Topology and Fractal Geometry, Second Edition, Springer, 2008.
M. F. Barnsley, Fractals Everywhere, Dover Publications, 2012.
Attendance Policy: as per the institute norms.
Evaluation Policy:
Formative Assessment (Part-1): 35% will be as follows: two open-book Quizzes: 10+10 marks (20 minutes each), Computational Project-1: 7 marks (Handwritten project submitted by 14th August), Computational Project-2: 8 marks.
Formative Assessment (Part-2) - Mid-semester Exam: 25% (will be announced by AAA section, possible dates 15 Sept - 23rd Sept).
Summative Assessment- End-semester Exam: 40% (will be announced by AAA section, possible dates 24th Nov - 4th Dec).
Tutorials and Practicals: Tut-1 Tut-2 Tut-3 Tut-4 Tut-5 Tut-6 Practicals Lab Assignment-1 Lab Assignment-2
Note-1 Note-2
Marking scheme for Mid-sem Marking scheme for end-sem
Current Semester: I am teaching the following courses: Operation Research, Professional Ethics, and Measure Theory.
Professional Ethics (MS1004): 2nd sem
Attendance Policy: as per the institute norms.
Evaluation Policy:
Formative Assessment (Part-1): 35% will be as follows: two quizzes (20+15=35 marks); Quiz 1 on 18th February (6:30 PM - 7:00 PM) and Quiz 2 on 16th April (6:30 PM - 7:00 PM).
Formative Assessment (Part-2) - Mid-semester Exam: 25% (possible dates 11-17 March 2026).
Summative Assessment- End-semester Exam: 40% (possible dates 11-20 May 2026).
Lecture Notes: Note-1 Note-2 Note-3 Note-4 Note-5
Operation Research: 4th sem
Foundational Concepts: Introduction to Operations Research, Formulation of Linear Programming Problem, Graphical Method, Simplex Method, Sensitivity Analysis and Duality, Integer Programming, Dynamic Programming.
Logistics Optimization and Project Management: Transportation and Assignment Problems, North West Corner Rule (NCWR), Least Cost Method (LCM), Vogel’s Approximation Problem (VAM), Travelling Salesman Problem, Game Theory, Minimax, Maximin Criteria and Optimal Strategies, Critical Path Method (CPM), Program Evaluation and Review Technique (PERT).
Applications: AI in Operations Research, Operations Research in Machine Learning, Financial Portfolio Optimization, Risk Management Models, IT Service Management, Business Process Optimization.
Texts/Reference Books
1. Introduction to Operations Research by H. A. Taha.
2. Introduction to Operations Research by Hillier and Lieberman
Attendance Policy: as per the institute norms.
Evaluation Policy:
Formative Assessment (Part-1): 35% will be as follows: two quizzes (10+10=20 marks); Quiz 1 on 29th Jan (6:30 PM - 7:00 PM) and Quiz 2 on 28th April (6:30 PM - 7:00 PM), and three Computational Projects (5+5+5=15 marks).
Formative Assessment (Part-2) - Mid-semester Exam: 25% (possible dates 11-17 March 2026).
Summative Assessment- End-semester Exam: 40% (possible dates 11-20 May 2026).
Lecture Notes: Note-1 Note-2 Note-3
Measure Theory: 6th sem (with Dr. Abdullah Bin Abu Baker)
Course Outcomes:
Students will be able to:
Deal with Lebesgue measure, fractal measures, and measurable sets
Compute Lebesgue integration, which is more general than Riemann integration
Analyze and apply convergence theorems and some inequalities taught
Apply Lebesuge spaces and Lebesgue integration to study various problems
Course Contents:
Lebesgue outer measure, Measurable Set, regularity, Measurable functions, Borel and Lebesgue measurability, fractal measures on the real line, nonmeasurable subsets of real line, Littlewood’s three principles
Integration of nonnegative simple measurable functions, Integration of nonnegative measurable functions, integrable functions, Riemann and Lebesgue integrals
Monotone convergence theorem, Fatou’s lemma, dominated convergence theorem, The Lebesgue spaces L_p, Holder’s inequality, Minkowski’s inequality, the completeness theorem
Text books and references:
E. M. Stein and R. Shakarchi, Real Analysis: Measure Theory, Integration, and Hilbert Spaces, Princeton University Press, 2005.
H. L. Royden and P. M. Fitzpatrick, Real Analysis, 4th edition, 2010.
G. D. Barra, Measure theory and integration, 2000.
Inder K. Rana, An introduction to Measure and integration, 2nd edition, American Mathematical Society, 2002.
Attendance Policy: as per the institute norms.
Evaluation Policy: For more details visit https://profile.iiita.ac.in/abdullah/Teaching.php
Lecture Notes: Note-1 Note 2 Note 3