Mathematics Curriculum Overview
The Mathematics program at Plaksha University Mohali is designed to provide a balanced mix of theoretical knowledge and practical application. The curriculum spans four years, with each semester building upon the previous one to ensure a comprehensive understanding of mathematical principles and their real-world implications.
Semester-Wise Course Structure
| Semester | Course Code | Course Title | Credit (L-T-P-C) | Prerequisites |
|---|---|---|---|---|
| 1 | MATH-101 | Calculus I | 3-0-2-4 | None |
| 1 | MATH-102 | Linear Algebra | 3-0-2-4 | None |
| 1 | MATH-103 | Introduction to Programming | 2-0-2-4 | None |
| 1 | MATH-104 | Physics for Engineers | 3-0-2-4 | None |
| 1 | MATH-105 | English for Academic Purposes | 2-0-0-2 | None |
| 2 | MATH-201 | Calculus II | 3-0-2-4 | MATH-101 |
| 2 | MATH-202 | Differential Equations | 3-0-2-4 | MATH-101 |
| 2 | MATH-203 | Probability and Statistics | 3-0-2-4 | MATH-101 |
| 2 | MATH-204 | Discrete Mathematics | 3-0-2-4 | MATH-101 |
| 2 | MATH-205 | Computer Science Fundamentals | 3-0-2-4 | MATH-103 |
| 3 | MATH-301 | Real Analysis I | 3-0-2-4 | MATH-201 |
| 3 | MATH-302 | Complex Analysis | 3-0-2-4 | MATH-201 |
| 3 | MATH-303 | Numerical Methods | 3-0-2-4 | MATH-201 |
| 3 | MATH-304 | Abstract Algebra | 3-0-2-4 | MATH-102 |
| 3 | MATH-305 | Operations Research | 3-0-2-4 | MATH-201 |
| 4 | MATH-401 | Real Analysis II | 3-0-2-4 | MATH-301 |
| 4 | MATH-402 | Mathematical Modeling | 3-0-2-4 | MATH-301 |
| 4 | MATH-403 | Stochastic Processes | 3-0-2-4 | MATH-203 |
| 4 | MATH-404 | Advanced Calculus | 3-0-2-4 | MATH-201 |
| 4 | MATH-405 | Capstone Project | 3-0-2-4 | MATH-301, MATH-302, MATH-303 |
Advanced Departmental Electives
These advanced courses are designed to deepen students' understanding of specialized areas within mathematics and prepare them for research or industry applications.
- Mathematical Logic and Foundations: This course explores the logical foundations of mathematics, including propositional and predicate logic, model theory, and proof theory. It emphasizes formal reasoning and the structure of mathematical arguments, preparing students for advanced studies in theoretical mathematics.
- Computational Number Theory: Focused on algorithms and applications of number theory in cryptography and computer science, this course covers topics such as prime factorization, modular arithmetic, and elliptic curves. Students will learn how to implement cryptographic protocols using mathematical principles.
- Advanced Differential Equations: Building upon introductory differential equations, this course delves into partial differential equations, systems of ordinary differential equations, and their applications in physics and engineering. It includes numerical solutions and qualitative analysis techniques.
- Topological Data Analysis: This interdisciplinary course combines topology with data science to analyze complex datasets. Students will learn how topological methods can reveal hidden patterns in data, making it particularly relevant for machine learning and big data analytics.
- Applied Functional Analysis: This course applies functional analysis concepts to solve real-world problems in engineering and physics. Topics include Banach spaces, Hilbert spaces, operator theory, and applications to quantum mechanics and signal processing.
- Financial Derivatives Pricing: Designed for students interested in quantitative finance, this course covers stochastic calculus, Black-Scholes model, Monte Carlo simulations, and pricing models for options and other derivatives. It prepares students for careers in financial institutions and hedge funds.
- Mathematical Methods in Physics: This course explores the mathematical tools used in modern physics, including group theory, differential geometry, tensor calculus, and Lie algebras. Students will apply these methods to physical phenomena such as electromagnetism, quantum mechanics, and general relativity.
- Statistical Inference and Decision Theory: This course covers advanced statistical inference techniques, hypothesis testing, Bayesian methods, and decision theory. It prepares students for careers in data science, policy analysis, and research roles where statistical reasoning is crucial.
- Graph Theory and Network Science: This course focuses on the mathematical properties of graphs and networks, including connectivity, coloring, matching, and optimization problems. Applications include social network analysis, transportation systems, and communication networks.
- Mathematical Biology: This course introduces students to modeling biological processes using mathematical tools such as differential equations, stochastic models, and population dynamics. It explores applications in epidemiology, genetics, and ecological systems.
- Control Theory and Optimization: This course covers control systems design, optimal control theory, and linear programming. Students will learn how to model dynamic systems and optimize performance using mathematical tools and computational methods.
- Geometric Methods in Applied Mathematics: This course explores the application of geometric concepts to real-world problems in physics, engineering, and computer graphics. Topics include manifolds, tensors, differential forms, and their applications in modeling physical systems.
- Algebraic Topology: A rigorous introduction to algebraic topology, this course covers homotopy theory, homology, and cohomology groups. It provides students with tools to study topological spaces and their properties using algebraic methods.
- Advanced Machine Learning Algorithms: This course delves into advanced machine learning techniques such as deep neural networks, reinforcement learning, ensemble methods, and unsupervised learning algorithms. Students will implement these algorithms in practical scenarios using Python and other tools.
- Mathematical Modeling in Industry: This course focuses on developing mathematical models for real-world industrial problems. Students work on projects sponsored by industry partners, applying their knowledge of mathematics to solve actual challenges faced by companies.
Project-Based Learning Philosophy
The Mathematics program at Plaksha University Mohali strongly emphasizes project-based learning as a core component of the educational experience. This approach ensures that students not only understand theoretical concepts but also apply them to real-world situations, fostering innovation and problem-solving skills.
Project-based learning is implemented through two major components:
- Mini-Projects (Year 2 and Year 3): These are smaller-scale projects that allow students to explore specific mathematical concepts or applications. Mini-projects typically involve working in small teams and presenting findings to faculty and peers.
- Final-Year Thesis/Capstone Project: The capstone project is a significant undertaking that requires students to conduct independent research or collaborate on an industry-sponsored initiative. Students select their projects based on interests and career goals, guided by faculty mentors.
The evaluation criteria for these projects include:
- Originality of approach and insights
- Clarity of presentation and documentation
- Mathematical rigor and soundness of reasoning
- Practical applicability and potential impact
- Teamwork and collaboration skills
Students are encouraged to work closely with faculty members who serve as mentors throughout their project journey. The selection process involves a proposal submission, progress reviews, and final presentations. This system ensures that students receive personalized guidance and feedback while developing critical thinking and communication abilities.