The Master of Arts (MA) and Master of Science (M.Sc.) in Mathematics programs at Tribhuvan University (TU) share an identical academic curriculum and exam structure. The degree title simply depends on whether your undergraduate background was in Arts (BA) or Science (B.Sc.).

Managed by the Central Department of Mathematics, it is a 2-year, 4-semester program requiring a total of 100 credit hours (25 credits per semester). The curriculum emphasizes high-level rigor in both pure and applied mathematics.

Core Areas of the Curriculum

Rather than tracking a rigid semester-by-semester layout (since elective availability changes based on specialized professors at campuses), the courses are structurally split across four core dimensions over your 2 years:

1. Pure Mathematics (Foundational)

• Topology I & II: Metric spaces, topological spaces, compactness, connectedness, and separation axioms.

• Algebra I & II: Advanced group theory, ring theory, modules, field extensions, and Galois theory.

• Linear Algebra & Its Applications: Vector spaces, inner product spaces, canonical forms, and spectral theorems.

• Measure Theory and Integration I & II: Lebesgue measure, measurable functions, integration theory, and $L^p$ spaces.

• Functional Analysis I & II: Banach spaces, Hilbert spaces, bounded linear operators, and open mapping theorems.

2. Mathematical Analysis & Geometry

• Complex Analysis and Applications I & II: Analytic functions, Cauchy’s theorem, residue calculus, and conformal mappings.

• Differential Geometry: Curves and surfaces in three-dimensional space, tensor analysis, and Riemannian geometry.

• Theory of Functions / Functions of Several Variables

3. Applied & Computational Mathematics

• Differential Equations: Advanced ordinary and partial differential equations (ODEs & PDEs).

• Mechanics: Analytical dynamics, Lagrangian and Hamiltonian mechanics.

• Numerical Analysis / Scientific Computing: Numerical optimization, error analysis, and finite difference schemes.

• Introduction to C Programming: Foundations of coding mathematical algorithms.

4. Optimization & Operations Research (Popular Electives)

• Mathematical Programming / Linear & Integer Programming

• Combinatorial Optimization & Network Optimization

• Scheduling Theory / Graph Theory

5. Research Component (Final Year)

• Math 589: Seminar (2 Credits)

• Math 590: Thesis / Dissertation Writing (5 Credits - Optional baseline, taken in place of an elective paper in the 4th semester).

Marks & Evaluation System

• The 40/60 Split: Each 100-mark course is split into an Internal Assessment (40%) conducted by the campus department and an External Board Exam (60%) conducted centrally by TU (Institute of Science and Technology for M.Sc. / Faculty of Humanities for MA).

• High Pass Boundary: The minimum passing grade is 50% separately in both internal and external evaluations.

• Exam Style: Question papers heavily focus on rigorous proofs, theorem validations, and presenting conceptual examples rather than basic calculations.

Admission Requirements

• Eligibility: A 3-year or 4-year B.Sc. or BA degree with a major in Mathematics (having completed at least 600 full marks or 80 credit hours of math courses at the undergraduate level).

• Entrance Exam: Admission is based on a competitive 2-hour centralized entrance exam containing multiple-choice questions (MCQs) based on the Bachelor-level math syllabus.

• Merit Formula: Final admission ranking is calculated via:

  $$\text{Merit Score} = 80\% \text{ (Entrance Exam Score)} + 20\% \text{ (Bachelor\'s Aggregate Mark)}$$