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.
Univariate and Multivariate Calculus, Summer 2024, July 2024 - Dec 2024.
Fractal Geometry, 7th semester, Elective course, July 2024 - November 2024.
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.
Current Semester: I am teaching the following course: Discrete Mathematical Structures (DMS) to BTech 2nd-sem students and Linear Algebra (Lecture notes).
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
Fractal Geometry (Elective Course)
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.
Tutorials and Practicals: Tut-1 Tut-2 Tut-3 Tut-4 Tut-5 Tut-6 Practicals Lab Assignment-1 Lab Assignment-2