Teaching

Mathematics is often viewed as a subject of abstraction and complexity, but at its core, it is a language of clarity, logic, and profound beauty. As an educator, my mission is to make this beauty accessible and inspiring for every student. Over the years, I have designed and delivered undergraduate and postgraduate courses that not only build technical proficiency but also nurture an appreciation for mathematics as a powerful tool for innovation and problem-solving. My approach to teaching blends conceptual clarity with practical problem-solving, fostering a classroom environment where students are encouraged to question, explore, and connect mathematical ideas to real-world applications.

Amity University

Business Mathematics (click here)

This foundational and application-oriented course equips students with the essential mathematical tools for quantitative business analysis and financial problem-solving. Covering core topics in linear algebra, financial mathematics, and calculus, the course bridges theory and practice. Through structured problem-solving, formula application, and real-world business scenarios, students learn to model, analyze, and solve key managerial and financial challenges.

What You’ll Learn

• Matrices and Determinants: Performing matrix algebra, calculating inverses, and applying Cramer's Rule and matrix methods to solve systems of equations for multi-variable business problems.

• Mathematics of Finance: Mastering time value of money concepts by calculating present and future values under different compounding rates, and evaluating annuities, loans, leases, and sinking funds for investment and capital budgeting decisions.

• Differential Calculus: Understanding functions, limits, and derivatives to analyze rates of change, and applying optimization techniques to find maxima and minima for single-variable business scenarios like cost, revenue, and profit.

• Integral Calculus: Learning the principles of indefinite integration and its methods to solve business applications related to areas under curves and accumulation functions.

Research Methodology (click here)

This comprehensive course provides students with a systematic framework for conducting scientific inquiry in biological sciences. It bridges the gap between theoretical research concepts and practical application, guiding students through the entire research lifecycle—from problem formulation and literature review to data analysis and paper writing. Through structured learning, students will develop the skills to design robust experiments, apply appropriate statistical tests, and ethically communicate their findings.

What You’ll Learn

• Research Fundamentals: Defining research problems, conducting literature reviews using databases like PubMed, and formulating testable hypotheses.

• Research Design: Classifying research types (experimental, descriptive, etc.) and developing sound experimental and sampling designs.

• Biostatistics: Applying descriptive and inferential statistics, including t-tests, ANOVA, correlation, and regression, to analyze biological data.

• Scientific Writing: Interpreting data, structuring a research paper, understanding journal metrics (impact factor), and navigating ethical issues like plagiarism.

IT Workshop (click here)

This practical and application-oriented course introduces the core computational environment of MATLAB, bridging the gap between programming theory and technical problem-solving in engineering. From basic script writing to leveraging advanced toolboxes, students gain hands-on experience with a powerful platform for simulation, analysis, and visualization. Through hands-on exercises, function creation, and data manipulation, the course emphasizes building practical scripts to automate calculations, process data, and model systems.

What You’ll Learn

• MATLAB Fundamentals: Navigating the MATLAB environment, declaring and using variables, and working with its various in-built functions and additional data types.

• Programming & Logic: Implementing program control flow using branching (conditional) and looping statements to create efficient and dynamic scripts.

• Function & Data Management: Creating user-defined functions for modular code and effectively utilizing arrays for data storage and manipulation, including input/output operations.

• Visualization & Analysis: Generating various types of plots to visualize data and gaining an introduction to the advanced analysis capabilities of MATLAB.

• Toolbox Exploration: Discovering specialized MATLAB toolboxes for applied fields such as Image Processing, Neural Networks, and Fuzzy Logic, providing insight into advanced engineering applications.

Business Statistics (click here)

This applied and data-driven course introduces the core concepts of statistics for effective business decision-making. From summarizing and visualizing data to modeling uncertainty and forecasting trends, students gain both theoretical understanding and practical skills. Through numerical exercises, Excel-based labs, and real-world case applications, the course emphasizes interpreting statistical results for managerial insights.

What You’ll Learn

• Descriptive statistics: data types, measures of central tendency, dispersion, skewness, and kurtosis

• Probability theory and business applications: conditional probability, Bayes’ theorem, and probability distributions (Binomial, Poisson, Normal)

• Correlation and regression: measuring relationships, estimating trends, and interpreting coefficients

• Index numbers and time-series analysis: constructing price indices, trend fitting, seasonal variations, and forecasting

• Practical application of statistical tools using Excel for visualization and interpretation

Essentials of Mathematics & Statistics in Forensic Science (click here)

This foundational and interdisciplinary course introduces the essential mathematical and statistical tools used in forensic science. From measurement systems and algebraic functions to probability models and statistical inference, students learn how quantitative methods enhance evidence analysis and crime investigation. With applications ranging from bloodstain pattern analysis to fingerprint matching and ballistic trajectories, the course emphasizes analytical rigor, data interpretation, and scientific reporting. Case studies, assignments, and presentations help bridge theory with real-world forensic practice.

What You’ll Learn

• Core concepts: number systems, measurement units, uncertainty, and basic chemical calculations

• Descriptive statistics: frequency distributions, central tendency, dispersion, correlation, and regression

• Mathematical functions: polynomial, exponential, logarithmic, and trigonometric functions with forensic applications (e.g., pH analysis, ricochet, bloodstain patterns)

• Probability theory: conditional probability, Bayes’ theorem, discrete and continuous distributions (binomial, normal, hypergeometric) in forensic contexts

• Graph theory and data visualization: linearization, calibration, and interpretation in ballistic and biological evidence

• Statistical inference: hypothesis testing (t-test, chi-square, F-test), evaluation of evidence, likelihood ratios, and weight of evidence

Plaksha University

Computational Linear Algebra (click here)

This foundational and hands-on course explores the core concepts of linear algebra with a computational lens. From solving systems of equations to matrix decompositions and eigenvalue analysis, students learn to apply abstract linear algebra ideas to real-world scenarios using Python. With labs, worksheets, and engineering case studies—including applications in search engines and large language models—this course builds both mathematical intuition and coding fluency.

What You'll Learn

• Matrix operations, vector spaces, and subspace geometry

• Solving linear systems using direct (Gauss elimination) and iterative methods

• Matrix decompositions: LU, QR, Cholesky, and Gram-Schmidt orthonormalization

• Eigenvalues and eigenvectors: theory, computation, and interpretation

• Applications in dynamical systems, stochastic processes, and modern AI 

Computational Methods and Optimization (click here)

This application-focused course introduces students to computational strategies for solving real-world optimization problems using numerical methods and vector calculus. With a balance of theory, coding, and problem-solving, students learn to design and implement optimization algorithms in Python and apply them across engineering and operations research domains. From root-finding and integration to dynamic programming and linear optimization, this course is a comprehensive toolkit for aspiring problem solvers.

What You'll Learn

• Root-finding methods and numerical integration techniques

• Multivariable calculus for optimization: gradients, Hessians, and Taylor expansion

• Unconstrained and constrained optimization using gradient descent and Lagrange multiplier

• Linear programming and integer programming with real-world case studies

• Dynamic programming applications including the Travelling Salesman Problem

Math of Uncertainty (click here)

This experiential, simulation-rich course introduces students to the foundational and advanced principles of probability, statistics, and stochastic processes as applied to real-world engineering and decision-making problems. With a strong emphasis on hands-on learning, students engage in weekly coding labs using MATLAB and Python, and complete five thematic mini-projects that model randomness in natural and engineered systems—from predicting insurance claims to simulating aircraft control paths.

What You'll Learn

• Axiomatic probability, random variables, and conditional probability

• Bayesian reasoning, expectation laws, and central limit theorems

• Discrete and continuous probability distributions, joint/marginal distributions

• Modelling dynamic systems with discrete and continuous time Markov chains

• Queuing theory, birth-death processes, and detailed balance in stochastic systems

• Statistical inference, multivariate analysis, regression, and principal component analysis (PCA)

Engineering Math In Action (click here)

This hands-on, application-driven course introduces students to foundational and advanced concepts in linear algebra and differential equations through the lens of real-world engineering problems. Blending theory with computational tools like Python and MATLAB, students will explore the mathematical language behind modern engineering systems—from Google’s PageRank algorithm to chemical reaction networks and circuit design.

What You'll Learn

• Vector spaces, linear transformations, and matrix factorizations

• Solving systems of linear equations using direct and iterative methods

• Eigenvalues, eigenvectors, and their applications in data science and modeling

• Analytical and numerical solutions of ordinary differential equations (ODEs)

• Modeling and simulation of dynamic systems using first-order and higher-order ODEs

Akal University

Calculus

This course provides a rigorous introduction to the fundamental concepts of calculus, including limits, continuity, differentiation, and integration, with emphasis on both theory and applications. Students will study the formal ε–δ definition of limits, properties of continuous functions, techniques of differentiation and successive derivatives, reduction formulae for integrals, and methods for curve sketching using curvature, asymptotes, and concavity. The course builds a solid foundation for advanced mathematical analysis and its applications in science and engineering.

What You’ll Learn

• Limits, continuity, and ε–δ definition

• L’Hospital’s Rule and hyperbolic functions

• Differentiability, higher-order derivatives, and Leibniz’s Rule

• Integral reduction formulae for standard functions

• Curvature in Cartesian, parametric, and polar coordinates

• Concavity, convexity, double points, and asymptotes

• General rules for tracing curves

Logic & Sets

This course introduces the fundamental concepts of discrete mathematics through the study of propositional and predicate logic, truth tables, quantifiers, and logical equivalences. Students will explore the structure of sets, operations on sets, partitions, and principles of counting, along with important results such as the Inclusion–Exclusion Principle. The course also develops an understanding of relations, including equivalence and partial order relations, providing a rigorous foundation for higher studies in mathematics and computer science.

What You’ll Learn

• Propositions, connectives, implications, and truth tables

• Propositional equivalence, predicates, and quantifiers

• Set operations, laws of set theory, Venn diagrams, and counting principles

• Power sets, partitions, symmetric difference, and set identities

• Inclusion–Exclusion Principle and applications

• Relations: product sets, composition, equivalence, and partial order relations

Theory of Differential Equations

This course develops the theory and methods of solving ordinary and partial differential equations, with emphasis on existence and uniqueness results, boundary value problems, and applications. Students will study linear systems of ODEs, higher-order differential equations, Sturm–Liouville problems, and orthogonal expansions, along with an introduction to PDEs and their classification. Fundamental equations of mathematical physics, such as the heat, wave, and Laplace equations, are also explored, providing a strong foundation for advanced studies in applied mathematics and engineering.

What You’ll Learn

• Existence and uniqueness of solutions, dependence on initial conditions

• Boundary value problems and Sturm–Liouville theory

• Linear systems of ODEs, fundamental solutions, Wronskian, and Abel–Liouville formula

• Higher-order linear differential equations and reduction of order

• Adjoint and self-adjoint systems, Floquet theory, Sturm’s theorems

• First- and higher-order PDEs with constant coefficients

• Classification of second-order PDEs and solutions of heat, wave, and Laplace equations

Discrete Mathematics

This course introduces fundamental concepts of discrete mathematics with emphasis on combinatorics and graph theory. Students will explore counting principles, recurrence relations, generating functions, and foundational graph theoretic concepts, all of which form the backbone of computer science, optimization, and modern mathematics.

What you will learn:

• Fundamental principles of counting: permutations, combinations, pigeonhole principle.

• Binomial theorem, inclusion–exclusion principle, and recurrence relations.

• Generating functions and their applications in combinatorics.

• Basics of graph theory: graphs, subgraphs, degree, connectivity, paths, cycles.

• Special classes of graphs: trees, bipartite graphs, planar graphs.

• Graph coloring, matchings, and applications.

• Introduction to network flows and combinatorial optimization.

General Mathematics-I

This course introduces the fundamentals of set theory, relations, counting principles, and binomial expansions. It equips students with mathematical tools useful for problem solving in higher mathematics and related fields.

What you will learn

• Sets, Venn diagrams, laws of set algebra, inclusion–exclusion principle

• Relations: types, partitions, equivalence, adjacency matrices, closures

• Fundamental principle of counting, permutations and combinations

• Binomial theorem, general and middle terms, binomial coefficients and their applications

General Mathematics-II

This course introduces matrices, systems of linear equations, functions, and probability theory. The focus is on problem-solving skills and applications, particularly in contexts relevant to science.

What you will learn

• Matrices: operations, determinants, adjoint, inverse, elementary transformations

• Rank of matrices, echelon forms, consistency of systems, Cramer’s rule

• Functions: domain, range, types, composition, inverse, cardinality

• Probability: events, axioms, conditional probability, independence, Bayes’ theorem, total probability

Group Theory

This course provides a rigorous introduction to the fundamental concepts of group theory, a central area of abstract algebra with wide applications in mathematics and science. Students will study the structure and properties of groups, subgroups, cyclic groups, and permutation groups, along with key results such as Lagrange’s Theorem and Cauchy’s Theorem. The course further develops the theory of group homomorphisms, isomorphisms, and the fundamental isomorphism theorems, laying the foundation for advanced algebraic study.

What You’ll Learn

• Definition and elementary properties of groups with examples

• Subgroups, centralizer, normalizer, and product of subgroups

• Cyclic groups, cosets, Lagrange’s Theorem, and Fermat’s Little Theorem

• Normal subgroups, factor groups, and Cauchy’s Theorem for finite abelian groups

• Permutations, cycle notation, alternating group, and simplicity of 𝐴_𝑛 for 𝑛≥5

• Group homomorphisms, Cayley’s Theorem, and First, Second, and Third Isomorphism Theorems

Linear Algebra

This course introduces the fundamental structures and methods of linear algebra, emphasizing both theoretical understanding and practical applications. Students will learn how linear algebra provides tools for mathematics, computer science, physics, and engineering, with focus on vector spaces, transformations, eigenvalues, and canonical forms. This course develops the algebraic foundations necessary for advanced mathematics and provides powerful tools widely used in applied sciences.

What you will learn:

• Vector spaces over arbitrary fields: subspaces, linear dependence and independence, basis, and dimension.

• Linear transformations: kernel, image, rank–nullity theorem, matrix representations, and change of basis.

• Dual spaces, linear functionals, transpose mappings, quotient spaces, and invariant subspaces.

• Eigenvalues and eigenvectors, minimal polynomial, Cayley–Hamilton theorem, diagonalization, and primary decomposition.

• Canonical forms: nilpotent operators, Jordan canonical form, rational canonical form, cyclic decomposition theorem.

• Inner product spaces: orthogonality, Gram–Schmidt process, adjoint and self-adjoint operators, normal operators.

Numerical Analysis

This course introduces fundamental numerical techniques for solving mathematical problems where analytical solutions are difficult or impossible. It emphasizes error analysis, iterative and direct methods for equations, interpolation, numerical differentiation and integration, and numerical solutions of differential and partial differential equations. This course provides a foundation for advanced studies in numerical methods, scientific computing, and applied mathematics.

What you will learn:

• Sources of error and error analysis in numerical computations.

• Iterative methods for solving nonlinear equations: bisection, false position, Newton–Raphson, and systems of equations.

• Direct and iterative methods for linear systems: Gauss elimination, LU decomposition, Jacobi and Gauss–Seidel methods.

• Interpolation techniques: Newton, Lagrange, Hermite, and finite difference methods.

• Numerical differentiation and integration: trapezoidal rule, Simpson’s rules, Gaussian quadrature, and Romberg integration.

• Numerical solutions of initial and boundary value problems: Taylor series, Picard’s method, Runge–Kutta methods, predictor–corrector schemes.

• Finite difference methods for solving partial differential equations: Laplace, heat, and related problems.

Mechanics

This course introduces the theoretical foundations of mechanics, focusing on the principles of statics and dynamics and their mathematical formulation. Students will study force systems, conditions of equilibrium, moments and couples, and the motion of particles under various constraints. The course further develops concepts of work, power, energy, and momentum, including conservation laws and the impact of elastic bodies, equipping students with the analytical tools to model and solve physical problems mathematically.

What You’ll Learn

• Force systems: coplanar, concurrent, parallel, and conditions of equilibrium

• Moments, Varignon’s Theorem, couples, and the equilibrium of rigid bodies

• Dynamics of particles: Newton’s laws, motion under gravity, Atwood’s machine, and motion on inclined planes

• Work, power, conservative forces, kinetic and potential energy, and energy conservation

• Linear and angular momentum, impulse, collisions, and energy loss in impact

Numerical Methods for ODEs

This course develops techniques for approximating solutions of differential equations when exact analytic solutions are difficult or impossible to obtain. It covers single-step and multi-step methods, Runge-Kutta methods, and stability, consistency, and convergence analysis. Students also explore boundary value problems and shooting methods, gaining practical skills in the numerical treatment of both initial value and boundary value problems. Emphasis is placed on error analysis and stability considerations that guide the design of effective algorithms, providing a foundation for advanced studies in mathematics and its applications.

What you will learn:

• Principles of numerical approximation for ODEs.

• Implementation of single-step and multi-step methods.

• Runge-Kutta methods and their applications.

• Concepts of stability, consistency, and convergence.

• Numerical approaches to boundary value problems.

• Error analysis and its role in designing reliable algorithms.

Algebraic Coding Theory

This course introduces the mathematical foundations of error detection and correction through algebraic coding theory. It covers Hamming distance, linear codes, parity-check matrices, syndrome decoding, and weight enumerators, along with perfect codes such as Hamming and Golay codes. Students will also study cyclic codes, BCH codes, and Reed-Solomon codes, while exploring the role of finite fields in encoding and decoding processes. Emphasis is placed on both theoretical concepts and their practical applications in communication and data transmission systems, providing a foundation for advanced studies in mathematics and its applications.

What you will learn:

• Mathematical principles of error detection and correction.

• Hamming distance, error bounds, and decoding strategies.

• Linear codes, dual codes, and syndrome decoding.

• Perfect codes including Hamming and Golay codes.

• Weight enumerators and their significance in coding theory.

• Structure and decoding of cyclic, BCH, and Reed-Solomon codes.

• Applications of finite field theory in coding and decoding.

Methods in Applied Mathematics

This course introduces essential mathematical methods widely used in applied mathematics, focusing on integral equations and Fourier analysis. Topics include Fredholm and Volterra integral equations, methods of successive approximations, Fourier series expansions, and Fourier transforms. Emphasis is placed on both theory and applications, particularly in solving boundary value problems and simulating problems in science and engineering. The course provides students with tools necessary for advanced research and computational applications.

What you will learn:

• Formulation and solution techniques for Fredholm and Volterra integral equations.

• Successive approximation methods and Neumann series.

• Application of resolvent kernels in solving integral equations.

• Fourier series expansions for periodic and discontinuous functions.

• Half-range expansions, Parseval’s theorem, and harmonic analysis.

• Fourier integrals, transforms, and their inversion formulas.

• Applications of Fourier transforms to boundary value problems.

Topics in Algebra

This course explores advanced concepts in Group Theory and Ring Theory, two central areas of algebra. Students will study group actions, Sylow theorems, solvable and nilpotent groups, as well as ideals, quotient rings, and factorization theory. The course emphasizes both abstract theory and its applications in algebraic structures, preparing students for deeper study in modern algebra and related fields.

What you will learn:

• Structure and properties of dihedral and symmetric groups.

• Group actions, stabilizers, orbits, and applications of Sylow theorems.

• Direct products and classification of finite abelian groups.

• Composition series, Jordan–Hölder theorem, solvable and nilpotent groups.

• Ideals, quotient rings, maximal and prime ideals, and Zorn’s lemma.

• Divisibility, irreducibility, and factorization of polynomials.

• Unique Factorization Domains (UFDs), Principal Ideal Domains (PIDs), and Euclidean domains.

Graph Theory and Discrete Mathematics

This course introduces the fundamental concepts of discrete mathematics and graph theory, focusing on structures essential for mathematical reasoning and computer science applications. Students will study partially ordered sets, lattices, generating functions, and recurrence relations, along with the theory of graphs and their properties. Topics such as Eulerian and Hamiltonian graphs, shortest path algorithms, and the Traveling Salesman Problem highlight the interplay between discrete structures and problem-solving in computational settings.

What You’ll Learn

• Mathematical induction, posets, Hasse diagrams, and lattices

• Generating functions and recurrence relations with applications

• Graphs, subgraphs, isomorphism, degree sequences, and matrix representation

• Bipartite, planar, Eulerian, and Hamiltonian graphs

• Shortest path algorithms and the Travelling Salesman Problem