*Year 1: Core Foundations* 

*Semester 1: * 

- *Calculus: * Limits, Continuity, Differentiation 

- *Algebra: * Matrices, Determinants, Groups 

- *Geometry: * 2D/3D Coordinate Geometry 

- Lab: Python Programming for Math (Optional) 

*Semester 2: * 

- *Real Analysis: * Sequences, Series, Riemann Integration 

- *Linear Algebra: * Vector Spaces, Linear Transformations 

- *Differential Equations: * ODEs (First Order, Linear) 

*Year 2: Advanced Pure & Applied Math* 

*Semester 3:* 

- *Abstract Algebra: * Rings, Fields, Homomorphisms 

- *Complex Analysis: * Analytic Functions, Contour Integration 

- *Probability Theory: * Distributions, Bayes’ Theorem 

*Semester 4:* 

- *Partial Differential Equations: * Wave, Heat, Laplace Equations 

- *Discrete Mathematics:* Graph Theory, Combinatorics 

- *Numerical Methods:* Interpolation, Root-Finding Algorithms 

*Year 3: Specializations & Research* 

*Semester 5:* 

- *Topology:* Metric Spaces, Compactness 

- *Operations Research:* LP, Game Theory 

- *Electives (Choose 1):* 

  - Number Theory 

  - Fluid Dynamics 

  - Cryptography 

*Semester 6: * 

- *Functional Analysis* (Hilbert/Banach Spaces) 

- *Project/Dissertation* (e.g., Modelling with MATLAB) 

- *Optional: * Actuarial Science Basics 

*Key Features: * 

- *Theory-Application Balance: * Proof-based courses + computational math (Python/MATLAB). 

- *Interdisciplinary Links: * Physics (PDEs), CS (Algorithms), Economics (Game Theory). 

- *Labs (where applicable): * Numerical simulations, Data visualization.