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M-SC in Mathematics at The National College, Jayanagar, Bengaluru
Bengaluru, Karnataka
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About the Specialization
What is Mathematics at The National College, Jayanagar, Bengaluru Bengaluru?
This M.Sc Mathematics program at The National Degree College focuses on advanced theoretical concepts and their applications, equipping students with a strong foundation in pure and applied mathematics. It is highly relevant in the Indian context for careers in research, data science, actuarial science, and various STEM fields, meeting the growing demand for skilled analytical minds.
Who Should Apply?
This program is ideal for fresh science graduates with a strong undergraduate background in Mathematics, aspiring to pursue higher studies or research. It also suits working professionals from related fields seeking to deepen their mathematical expertise for roles in quantitative analysis, academic teaching, or advanced computational problem-solving.
Why Choose This Course?
Graduates of this program can expect diverse career paths in India, including roles as data scientists (INR 6-12 LPA), research analysts (INR 5-10 LPA), actuaries (entry-level INR 4-8 LPA), or educators. The strong analytical and problem-solving skills developed are highly valued across IT, finance, and defense sectors in Indian companies, leading to robust growth trajectories.
Student Success Practices
Foundation Stage
Deep Dive into Core Theories- (Semester 1-2)
Focus on mastering fundamental concepts in Algebra, Real, and Complex Analysis by solving a wide range of problems beyond textbooks. Collaborate with peers on complex proofs and participate in departmental tutorial sessions to solidify understanding.
Tools & Resources
NPTEL courses for advanced concepts, Mathematics Stack Exchange for challenging problems, departmental study groups
Career Connection
Builds robust problem-solving skills crucial for competitive exams (NET/SET) and research, essential for careers in academia or quantitative analysis.
Cultivate Computational Fluency- (Semester 1-2)
Actively engage with practical sessions involving mathematical software like Python with NumPy/SciPy, MATLAB, or R. Apply theoretical knowledge to computational problems and try to automate routine mathematical tasks to gain practical experience.
Tools & Resources
Online platforms like HackerRank for coding challenges, Kaggle for data manipulation practice, free academic licenses for MATLAB/Mathematica
Career Connection
Develops critical computational skills highly sought after in data science, scientific computing, and algorithmic development roles in Indian tech firms.
Participate in Math Olympiads/Competitions- (Semester 1-2)
Join university or inter-college mathematics competitions. This helps in understanding diverse problem-solving approaches and boosts confidence in high-pressure environments. Form a team to practice for contests regularly to enhance competitive spirit.
Tools & Resources
Previous year question papers, problem books like ''''Problem-Solving Strategies'''' by Engel, local university math clubs
Career Connection
Enhances critical thinking, competitive spirit, and quick problem-solving, which are vital for competitive job interviews and analytical roles in finance and tech.
Intermediate Stage
Explore Specialization & Electives- (Semester 3)
Carefully select hard-core electives based on career interests, such as Fluid Dynamics for engineering or Graph Theory for computer science. Conduct preliminary literature reviews on topics related to chosen electives to gain deeper insights and focus.
Tools & Resources
Research papers on arXiv, Scopus, Google Scholar, discussions with faculty mentors specializing in these areas
Career Connection
Allows for early career specialization, making graduates more attractive to specific industry segments like quantitative finance, cybersecurity, or research and development roles.
Undertake Mini-Projects/Research Internships- (Semester 3)
Seek out opportunities for mini-projects under faculty guidance or apply for short-term research internships at reputed research institutions during semester breaks. Focus on applying theoretical knowledge to real-world problems to gain practical experience.
Tools & Resources
Departmental notice boards for project announcements, online portals for internships like Internshala, faculty network for referrals
Career Connection
Provides practical research experience, strengthens resume, builds professional network, and is a strong differentiator for higher studies or R&D jobs in India.
Build a Professional Network- (Semester 3)
Attend seminars, workshops, and guest lectures organized by the department or university. Connect with visiting professors, industry experts, and alumni on platforms like LinkedIn to gain insights into career paths and opportunities in mathematics.
Tools & Resources
LinkedIn professional profile, professional networking events, university alumni association, departmental newsletters
Career Connection
Opens doors to mentorship, internship leads, and potential job opportunities in various sectors, from academia to industry, leveraging the ''''who you know'''' factor in the Indian job market.
Advanced Stage
Intensive Project Work and Dissertation- (Semester 4)
Dedicate significant effort to the M.Sc project, treating it as a stepping stone to real-world problem-solving or research. Focus on novel contributions, rigorous methodology, and excellent documentation. Seek regular feedback from the supervisor.
Tools & Resources
LaTeX for professional report writing, statistical software like R or SPSS for data analysis, academic databases for literature review
Career Connection
A strong project demonstrates independent research capability, analytical rigor, and project management skills, highly valued for R&D, data scientist, or PhD applications.
Placement & Career Preparation- (Semester 4)
Actively participate in campus placement drives. Prepare a targeted resume highlighting mathematical and computational skills. Practice technical interviews, aptitude tests, and group discussions focusing on quantitative and logical reasoning.
Tools & Resources
Placement cell resources, mock interview sessions, online aptitude test platforms like Indiabix, company-specific interview guides
Career Connection
Directly leads to securing entry-level positions in prominent Indian and multinational companies recruiting from campuses, ensuring a smooth transition into the professional world.
Explore Higher Education/Research Avenues- (Semester 4)
For those inclined towards academia or advanced research, prepare for national-level entrance exams like CSIR NET or GATE Mathematics, or PhD entrance exams for top Indian universities. Begin identifying potential research areas and supervisors.
Tools & Resources
Previous year question papers, standard reference books, university admission portals, discussions with senior researchers/professors
Career Connection
Essential for pursuing M.Phil/PhD degrees, becoming a lecturer or professor, or joining research organizations in India and abroad, contributing to the nation''''s scientific advancement.
Program Structure and Curriculum
Eligibility:
- B.Sc. degree with Mathematics as a major/optional subject, securing a minimum aggregate percentage as per Bangalore City University norms.
Duration: 2 years / 4 semesters
Credits: 96 Credits
Assessment: Internal: 30%, External: 70%
Semester-wise Curriculum Table
Semester 1
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| PGMM101T | Algebra I | Core | 4 | Groups and Subgroups, Homomorphisms and Isomorphisms, Rings, Ideals and Quotient Rings, Integral Domains and Fields, Polynomial Rings |
| PGMM102T | Real Analysis I | Core | 4 | Metric Spaces, Completeness and Compactness, Connectedness, Riemann-Stieltjes Integral, Sequences and Series of Functions |
| PGMM103T | Complex Analysis I | Core | 4 | Complex Numbers and Functions, Analytic Functions, Cauchy-Riemann Equations, Complex Integration, Cauchy''''s Theorem and Formula |
| PGMM104T | Ordinary Differential Equations | Core | 4 | First Order Equations, Higher Order Linear Equations, Power Series Solutions, Sturm-Liouville Theory, Green''''s Function |
| PGMM105P | Mathematics Practical I | Lab | 4 | Numerical Methods Implementation, Differential Equations Solving using Software, Complex Variable Computations, Linear Algebra Problems with Tools, Mathematical Data Visualization |
| PGMM106OE | Open Elective I (Basic Mathematics for Science) | Elective | 4 | Sets, Relations and Functions, Matrices and Determinants, Basic Calculus, Permutations and Combinations, Probability and Statistics |
Semester 2
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| PGMM201T | Algebra II | Core | 4 | Vector Spaces, Linear Transformations, Eigenvalues and Eigenvectors, Cayley-Hamilton Theorem, Canonical Forms |
| PGMM202T | Real Analysis II | Core | 4 | Functions of Several Variables, Inverse Function Theorem, Implicit Function Theorem, Lebesgue Measure, Lebesgue Integral |
| PGMM203T | Complex Analysis II | Core | 4 | Residue Theorem Applications, Conformal Mappings, Mobius Transformations, Analytic Continuation, Riemann Mapping Theorem |
| PGMM204T | Partial Differential Equations | Core | 4 | First Order PDEs, Charpit''''s Method, Classification of Second Order PDEs, Wave and Heat Equations, Laplace Equation and Boundary Value Problems |
| PGMM205P | Mathematics Practical II | Lab | 4 | Numerical Solutions to PDEs, Algebraic Structures Analysis, Real Analysis Computations, Complex Analysis Visualizations, Programming for Mathematical Models |
| PGMM206OE | Open Elective II (Quantitative Aptitude) | Elective | 4 | Percentages, Ratios and Proportions, Time and Work, Speed and Distance, Data Interpretation, Number Systems, Logical Reasoning |
Semester 3
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| PGMM301T | Topology | Core | 4 | Topological Spaces, Open and Closed Sets, Continuity and Homeomorphisms, Connectedness and Compactness, Product Spaces |
| PGMM302T | Functional Analysis | Core | 4 | Normed Linear Spaces, Banach Spaces, Hilbert Spaces, Linear Operators, Hahn-Banach Theorem |
| PGMM303T | Differential Geometry | Core | 4 | Curves in Space, Surfaces and Tangent Planes, First and Second Fundamental Forms, Gaussian Curvature, Geodesics |
| PGMM304E | Hard Core Elective I (Fluid Dynamics) | Elective | 4 | Kinematics of Fluids, Equations of Motion, Viscous Flows, Boundary Layer Theory, Potential Flow |
| PGMM305E | Hard Core Elective II (Graph Theory) | Elective | 4 | Basic Graph Concepts, Paths and Cycles, Trees and Spanning Trees, Connectivity and Planar Graphs, Matching and Coverings |
| PGMM306P | Mathematics Practical III | Lab | 4 | Topological Space Visualization, Functional Analysis Computations, Differential Geometry Simulations, Elective Subject Implementations, Advanced Mathematical Software Applications |
Semester 4
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| PGMM401T | Measure Theory and Integration | Core | 4 | Sigma Algebras and Measures, Lebesgue Measure, Measurable Functions, Lebesgue Integral, Convergence Theorems |
| PGMM402T | Operations Research | Core | 4 | Linear Programming, Simplex Method, Duality Theory, Transportation and Assignment Problems, Game Theory |
| PGMM403E | Hard Core Elective III (Wavelets) | Elective | 4 | Fourier Analysis Review, Continuous Wavelet Transform, Discrete Wavelet Transform, Multiresolution Analysis, Wavelet Applications in Signal Processing |
| PGMM404E | Hard Core Elective IV (Financial Mathematics) | Elective | 4 | Interest Rates and Discounting, Pricing of Securities, Options and Futures, Black-Scholes Model, Risk Management and Portfolio Theory |
| PGMM405PW | Project Work / Dissertation | Project | 4 | Research Problem Identification, Literature Review, Methodology Design, Data Analysis and Interpretation, Report Writing and Presentation |
| PGMM406VV | Viva-Voce | Assessment | 4 | Overall Course Comprehension, Understanding of Project Work, Ability to Defend Research, General Mathematical Aptitude, Communication Skills |
