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M-SC in Mathematics at Invertis University
Bareilly, Uttar Pradesh
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About the Specialization
What is Mathematics at Invertis University Bareilly?
This M.Sc. Mathematics program at Invertis University focuses on advanced theoretical and applied aspects of mathematics, preparing students for research and diverse analytical careers. In the Indian context, the program emphasizes a robust foundation in pure and applied mathematics, crucial for sectors like data science, finance, and academia, addressing the growing demand for skilled mathematicians. Its interdisciplinary approach aims to make graduates highly adaptable to evolving industry needs.
Who Should Apply?
This program is ideal for mathematics graduates with a B.Sc. in Mathematics or a related field, aspiring to delve deeper into mathematical concepts. It suits fresh graduates seeking entry into academia, R&D, data analytics, or financial modeling roles. Working professionals looking to enhance their quantitative skills for career advancement in analytical domains, as well as career changers aiming to transition into high-demand mathematical fields, will find this program highly beneficial.
Why Choose This Course?
Graduates of this program can expect promising career paths in India, including roles as data scientists, financial analysts, actuarial scientists, researchers, or educators. Entry-level salaries typically range from INR 4-7 LPA, with experienced professionals earning INR 10-20 LPA or more. The strong foundation in analytical and problem-solving skills aligns well with certifications in data science or financial modeling, ensuring growth trajectories in leading Indian companies and startups.
Student Success Practices
Foundation Stage
Master Core Mathematical Concepts- (Semester 1-2)
Dedicate significant time to thoroughly understand foundational subjects like Real Analysis, Abstract Algebra, and Complex Analysis. Engage actively in problem-solving sessions, clarify doubts with faculty, and form study groups to discuss complex theories. This ensures a strong conceptual base.
Tools & Resources
NPTEL lectures, Standard textbooks (e.g., Rudin for Analysis), Online problem-solving platforms like Brilliant.org
Career Connection
A strong grasp of fundamentals is critical for cracking entrance exams for higher studies (PhD) or for advanced roles in quantitative fields and data science requiring rigorous mathematical reasoning.
Develop Programming Proficiency in C- (Semester 1-2)
Actively participate in the C Programming Lab, focusing on implementing mathematical algorithms. Practice coding regularly to build logical thinking and computational skills, which are increasingly vital for applied mathematics careers. Explore additional online coding challenges.
Tools & Resources
HackerRank, LeetCode, GeeksforGeeks, Online C tutorials and documentation
Career Connection
Programming skills, especially in C, are highly valued in scientific computing, quantitative finance, and software development, opening up opportunities in tech companies and financial institutions.
Build Strong Problem-Solving Habits- (Semester 1-2)
Beyond theoretical understanding, practice solving a wide variety of problems from textbooks and previous year papers. Focus on understanding the derivation and application of theorems. Attend workshops on mathematical problem-solving strategies and participate in internal math competitions.
Tools & Resources
University library resources, Faculty office hours, Peer study groups, Competitive math problem sets
Career Connection
Enhanced problem-solving abilities are universally transferable, making graduates effective in any analytical role, consulting, or research position.
Intermediate Stage
Deep Dive into Specialized Electives- (Semester 3)
Carefully choose Elective I based on career interests (e.g., Fuzzy Sets for AI/ML, Cryptography for cybersecurity). Thoroughly explore the chosen subject, going beyond the syllabus with research papers and advanced texts, and consider mini-projects related to the topic.
Tools & Resources
IEEE Xplore, arXiv, Specialized textbooks, MATLAB/Python for simulations
Career Connection
Specialization enhances expertise for niche roles in technology, security, or data science, making you a more attractive candidate for focused industry positions.
Engage in Research Seminars and Presentations- (Semester 3)
Take the Semester 3 Seminar seriously. Choose a relevant topic, conduct thorough literature review, and practice presenting complex mathematical ideas clearly and concisely. Seek feedback from faculty and peers to refine communication skills.
Tools & Resources
LaTeX for document preparation, PowerPoint/Keynote for presentations, University research resources
Career Connection
Strong presentation and research skills are vital for academic careers, R&D roles, and conveying analytical insights effectively in any professional setting.
Explore Practical Applications through Projects- (Semester 3)
Start identifying potential areas for your Semester 4 project. Even in Semester 3, try to connect theoretical knowledge from Functional Analysis or Differential Geometry to real-world problems. Look for opportunities to collaborate on small projects or case studies.
Tools & Resources
Research journals, Industry reports, Faculty expertise, Online datasets
Career Connection
Applying theoretical knowledge practically strengthens your resume and provides tangible examples for interviews, showcasing problem-solving and domain expertise.
Advanced Stage
Undertake an Impactful Major Project- (Semester 4)
Select a challenging project topic that aligns with your career aspirations and allows for in-depth research and application of advanced mathematical concepts. Work closely with your supervisor, document your progress rigorously, and aim for a high-quality report and presentation.
Tools & Resources
Advanced mathematical software (e.g., Mathematica, MATLAB, R, Python libraries), Research databases, University lab facilities
Career Connection
A strong project demonstrates independent research capability, problem-solving skills, and a deep understanding of a specific domain, which is crucial for higher studies and R&D roles.
Network and Prepare for Placements/Higher Studies- (Semester 4)
Attend career workshops, placement drives, and guest lectures. Network with alumni and industry professionals. Prepare your resume, practice technical interviews, and hone your soft skills. If pursuing higher studies, prepare for entrance exams (e.g., NET/GATE/CSIR-JRF).
Tools & Resources
University Career Services, LinkedIn, Mock interview platforms, Relevant competitive exam preparation materials
Career Connection
Proactive career preparation significantly increases chances of securing desired placements in academia, finance, IT, or securing admission to prestigious PhD programs.
Integrate Advanced Electives with Career Goals- (Semester 4)
Leverage Elective II and III choices (e.g., Financial Mathematics for finance, Discrete Mathematics for computing/cryptography) to solidify your professional trajectory. Seek out industry mentors in your chosen field to gain practical insights and align your learning.
Tools & Resources
Industry-specific webinars, Professional associations (e.g., Indian Mathematical Society), Specialized online courses
Career Connection
Strategic elective choices provide a competitive edge, demonstrating specialized knowledge and commitment to a particular career path, making you a more targeted and valuable candidate.
Program Structure and Curriculum
Eligibility:
- B.Sc. in Mathematics/B.Sc. with Mathematics as one of the subjects with a minimum of 50% marks.
Duration: 2 years (4 semesters)
Credits: 76 Credits
Assessment: Internal: 30%, External: 70%
Semester-wise Curriculum Table
Semester 1
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| M.Sc. M-101 | Real Analysis | Core | 4 | Metric Spaces, Compactness and Connectedness, Riemann-Stieltjes Integral, Sequences and Series of Functions, Functions of Several Variables |
| M.Sc. M-102 | Abstract Algebra | Core | 4 | Groups and Subgroups, Sylow’s Theorems, Rings and Fields, Ideals and Factor Rings, Polynomial Rings |
| M.Sc. M-103 | Differential Equations | Core | 4 | Existence and Uniqueness of Solutions, Linear Differential Equations, Boundary Value Problems, Green’s Function, Partial Differential Equations of First Order |
| M.Sc. M-104 | Topology | Core | 4 | Topological Spaces, Continuous Functions, Connectedness, Compactness, Countability and Separation Axioms |
| M.Sc. M-105 | Programming in C (Lab) | Lab | 2 | Introduction to C, Operators and Expressions, Control Statements, Functions and Arrays, Pointers and Structures |
Semester 2
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| M.Sc. M-201 | Complex Analysis | Core | 4 | Complex Numbers and Functions, Analytic Functions, Complex Integration (Cauchy''''s Theorem), Series Expansions (Taylor, Laurent), Conformal Mappings |
| M.Sc. M-202 | Advanced Abstract Algebra | Core | 4 | Field Extensions, Galois Theory, Solvability by Radicals, Modules and Vector Spaces, Noetherian and Artinian Rings |
| M.Sc. M-203 | Measure Theory and Integration | Core | 4 | Lebesgue Measure, Measurable Functions, Lebesgue Integral, Modes of Convergence, Product Measures |
| M.Sc. M-204 | Classical Mechanics | Core | 4 | Newtonian Mechanics, Lagrangian Mechanics, Hamiltonian Mechanics, Canonical Transformations, Hamilton-Jacobi Theory |
| M.Sc. M-205 | Numerical Methods (Lab) | Lab | 2 | Error Analysis, Solution of Algebraic & Transcendental Equations, Interpolation, Numerical Differentiation & Integration, Solution of Ordinary Differential Equations |
Semester 3
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| M.Sc. M-301 | Functional Analysis | Core | 4 | Normed Linear Spaces, Banach Spaces, Hilbert Spaces, Bounded Linear Operators, Dual Spaces |
| M.Sc. M-302 | Integral Equations & Calculus of Variations | Core | 4 | Integral Equations (Fredholm, Volterra), Resolvent Kernel, Calculus of Variations, Euler-Lagrange Equation, Hamilton''''s Principle |
| M.Sc. M-303 | Differential Geometry | Core | 4 | Curves in R3, Surfaces (First & Second Fundamental Forms), Weingarten Map, Gaussian and Mean Curvature, Geodesics |
| M.Sc. M-304(A) | Fuzzy Sets & Their Applications | Elective | 4 | Fuzzy Sets and Operations, Fuzzy Relations, Fuzzy Arithmetic, Fuzzy Logic, Fuzzy Control Systems |
| M.Sc. M-304(B) | Cryptography | Elective | 4 | Classical Ciphers, Symmetric Key Cryptography (DES, AES), Asymmetric Key Cryptography (RSA), Hash Functions, Digital Signatures |
| M.Sc. M-305 | Seminar | Project | 2 | Research Topic Selection, Literature Review, Presentation Skills, Academic Writing, Q&A and Discussion |
Semester 4
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| M.Sc. M-401 | Operations Research | Core | 4 | Linear Programming (Simplex Method), Duality Theory, Transportation and Assignment Problems, Queuing Theory, Inventory Control Models |
| M.Sc. M-402 | Fluid Dynamics | Core | 4 | Fluid Kinematics, Equation of Motion, Inviscid Flow, Viscous Flow (Navier-Stokes), Boundary Layer Theory |
| M.Sc. M-403(A) | Financial Mathematics | Elective | 4 | Interest Rates and Discounting, Derivatives (Futures, Options), Option Pricing Models (Black-Scholes), Portfolio Theory, Risk Management |
| M.Sc. M-403(B) | Mathematical Modelling | Elective | 4 | Introduction to Modelling, Compartmental Models, Dynamical Systems, Numerical Methods for Models, Case Studies |
| M.Sc. M-404(A) | Discrete Mathematics | Elective | 4 | Logic and Proofs, Set Theory and Relations, Functions and Sequences, Graph Theory, Combinatorics |
| M.Sc. M-404(B) | Number Theory | Elective | 4 | Divisibility and Euclidean Algorithm, Congruences, Prime Numbers and Factorization, Quadratic Residues, Diophantine Equations |
| M.Sc. M-405 | Project Work & Viva-Voce | Project | 6 | Independent Research, Project Report Writing, Data Analysis and Interpretation, Presentation Skills, Viva-Voce Examination |
