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B-SC in Mathematics at T.S. Paul Manipur Women's College
Imphal West, Manipur
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About the Specialization
What is Mathematics at T.S. Paul Manipur Women's College Imphal West?
This B.Sc. Mathematics program at T.S. Paul Manipur Women''''s College, affiliated with Manipur University, focuses on developing strong analytical and problem-solving skills through a rigorous curriculum in core mathematical disciplines. With its roots in theoretical foundations, the program prepares students for diverse applications in science, technology, and finance, meeting the growing demand for quantitative experts in the Indian market.
Who Should Apply?
This program is ideal for high school graduates with a strong aptitude for mathematics, seeking a foundational degree to pursue higher studies or careers in analytical fields. It suits those interested in research, data science, actuarial science, and teaching, providing the rigorous academic background required for these demanding professions within India. Students aiming for competitive exams benefit significantly.
Why Choose This Course?
Graduates of this program can expect to pursue various India-centric career paths such as data analyst (entry-level INR 3-5 LPA), research assistant, or a career in teaching. With further specialization, roles in actuarial science, quantitative finance, or academic research are accessible, offering significant growth trajectories in Indian companies, educational institutions, and public sector organizations.
Student Success Practices
Foundation Stage
Build Strong Analytical Foundations- (Semester 1-2)
Focus on understanding fundamental concepts in Calculus and Algebra deeply. Utilize online platforms like Khan Academy or NPTEL for supplementary learning and problem-solving. This strong base is crucial for excelling in advanced subjects and analytical roles.
Tools & Resources
Khan Academy, NPTEL, Textbook exercises
Career Connection
A solid foundation is essential for higher studies, competitive exams, and careers requiring strong mathematical reasoning like data analytics and research.
Cultivate Problem-Solving Aptitude- (Semester 1-2)
Regularly practice solving a wide range of problems from textbooks, past papers, and challenge sets. Join peer study groups to discuss challenging problems, developing critical thinking essential for competitive exams and technical interviews.
Tools & Resources
Previous Year Question Papers, Maths Olympiad problems
Career Connection
Enhances logical reasoning and critical thinking, key skills for problem-solving roles in IT, finance, and engineering sectors.
Enhance Communication Skills- (Semester 1-2)
Actively participate in AECC courses to improve English or MIL communication. Practice explaining complex mathematical concepts clearly, both verbally and in writing. Strong communication is vital for presentations and professional interactions.
Tools & Resources
Public speaking clubs, Writing workshops, Grammar resources
Career Connection
Effective communication is crucial for academic success, presentations, and any professional role requiring clear articulation of ideas.
Intermediate Stage
Apply Theoretical Knowledge to Practical Problems- (Semester 3-5)
Engage with Skill Enhancement Courses like R Programming or LaTeX to apply mathematical concepts practically. Work on small data analysis projects using R to bridge theory with real-world applications, preparing for data-driven roles.
Tools & Resources
R Studio, Overleaf for LaTeX, Kaggle for datasets
Career Connection
Develops practical skills highly sought after in data science, quantitative finance, and research, improving internship and job prospects.
Seek Early Exposure to Specialized Fields- (Semester 3-5)
Explore different DSE options to identify areas of interest like Numerical Analysis or Probability & Statistics. Consider attending workshops or online courses in these domains to gain an edge for future specialization or internships.
Tools & Resources
Coursera, edX, NPTEL courses on specific topics
Career Connection
Helps in making informed career choices and building a specialized skill set that aligns with industry demands, leading to better career opportunities.
Develop Research and Presentation Skills- (Semester 3-5)
For projects or assignments, learn to use LaTeX for professional document presentation. Practice presenting findings effectively to peers and faculty, sharpening skills important for academic pursuits and conveying complex ideas in a professional setting.
Tools & Resources
LaTeX templates, Presentation software (PowerPoint, Google Slides)
Career Connection
Crucial for higher studies (M.Sc., PhD), academic roles, and any profession requiring report writing and effective communication of technical information.
Advanced Stage
Intensive Placement and Higher Study Preparation- (Semester 6)
Focus on mastering advanced topics like Linear Algebra and Metric Spaces. Prepare for competitive exams (e.g., JAM for M.Sc., NET for research) or job interviews by solving mock tests, practicing aptitude questions, and revising core concepts.
Tools & Resources
Online test series, Interview preparation guides, GATE/JAM study materials
Career Connection
Directly prepares students for postgraduate admissions in top universities and for challenging technical interviews in various industries.
Undertake Project-Based Learning- (Semester 6)
Identify a research problem or an application area for a final year project under faculty guidance. Collaborate with faculty or peers to develop a comprehensive project, which can serve as a strong portfolio piece for job applications or higher education.
Tools & Resources
Research papers, Academic databases, Mentorship from faculty
Career Connection
Showcases practical application skills, critical thinking, and problem-solving abilities, highly valued by employers and admissions committees.
Network and Professional Development- (Semester 6)
Attend webinars, seminars, and career fairs related to mathematics and its applications, locally or online. Connect with alumni and industry professionals on platforms like LinkedIn to gain insights into career opportunities and build professional relationships.
Tools & Resources
LinkedIn, Professional conferences (online/offline), Alumni network
Career Connection
Opens doors to internships, job opportunities, mentorship, and helps in understanding industry trends, which is vital for career planning.
Program Structure and Curriculum
Eligibility:
- No eligibility criteria specified
Duration: 6 semesters / 3 years
Credits: 140 Credits
Assessment: Internal: 25%, External: 75%
Semester-wise Curriculum Table
Semester 1
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| CC1 | Calculus | Core | 6 | Real numbers, Sequences, Series, Limits, Continuity, Differentiability, Rolle''''s Theorem, Mean Value Theorem, Maxima/Minima, Partial Differentiation, Riemann Sums, Definite Integrals |
| CC2 | Algebra | Core | 6 | Integers, Divisibility, Congruence, Groups, Subgroups, Cyclic groups, Permutation groups, Isomorphism, Homomorphism, Rings, Integral Domains |
| AECC1 | Environmental Studies | Ability Enhancement Compulsory | 2 | Multidisciplinary Nature of Environmental Studies, Natural Resources and Ecosystems, Biodiversity and Conservation, Environmental Pollution, Social Issues and the Environment |
Semester 2
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| CC3 | Real Analysis | Core | 6 | Metric Spaces, Open and Closed sets, Compact sets, Connected sets, Sequences and series of real numbers, Limits, Continuity, Uniform continuity, Differentiability of functions |
| CC4 | Differential Equations | Core | 6 | First order Ordinary Differential Equations, Exact equations, Integrating factors, Higher order linear ODEs, Cauchy-Euler equation, Power series solutions, Laplace transforms |
| AECC2 | English/MIL Communication | Ability Enhancement Compulsory | 2 | Language and Communication, Reading skills, Note making, Writing skills, Essay writing, Grammar, Vocabulary building, Formal and Informal communication |
Semester 3
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| CC5 | Theory of Real Functions | Core | 6 | Limits and Continuity of functions, Uniform Continuity, Differentiability, Mean Value Theorems, Taylor''''s Theorem, Riemann Integration, Improper Integrals |
| CC6 | Group Theory II | Core | 6 | Isomorphism theorems, Automorphisms, Inner Automorphisms, Cayley''''s Theorem, Normalizers, Permutation groups, Sylow''''s Theorems, Solvable groups, Nilpotent groups |
| CC7 | Partial Differential Equations | Core | 6 | First order linear PDEs, Lagrange''''s method, First order non-linear PDEs, Charpit''''s method, Classification of second order PDEs, Wave Equation, Heat Equation, Laplace Equation |
| SEC1 | LaTeX and HTML (Example) | Skill Enhancement | 2 | Introduction to LaTeX, Document Structure and Formatting, Mathematical Typesetting, Tables, Figures, Beamer Presentation, HTML Basics, Web Page Design |
| GE1 | Generic Elective from other disciplines (Choice) | Generic Elective | 6 | Subjects from other faculties or departments as per choice |
Semester 4
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| CC8 | Riemann Integration and Series of Functions | Core | 6 | Riemann integrability, Mean Value Theorems, Improper integrals, Convergence tests, Pointwise and Uniform Convergence, Power series, Radius of convergence, Fourier series, Half-range series |
| CC9 | Ring Theory and Linear Algebra I | Core | 6 | Rings, Subrings, Ideals, Homomorphisms, Quotient rings, Vector spaces, Subspaces, Basis and Dimension, Sum and Direct sum, Linear Transformations, Rank-Nullity Theorem |
| CC10 | Complex Analysis | Core | 6 | Complex numbers, Functions of complex variable, Analytic functions, Cauchy-Riemann equations, Complex Integration, Cauchy''''s Integral Theorem, Taylor and Laurent series expansions, Residue Theorem, Evaluation of definite integrals |
| SEC2 | R Programming (Example) | Skill Enhancement | 2 | Introduction to R, R Environment, Data types, Vectors, Matrices, Lists, Data Frames, Control Flow, Functions, Data Visualization with R, Basic Statistical Analysis using R |
| GE2 | Generic Elective from other disciplines (Choice) | Generic Elective | 6 | Subjects from other faculties or departments as per choice |
Semester 5
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| CC11 | Multivariable Calculus | Core | 6 | Functions of several variables, Limits and Continuity, Partial Derivatives, Directional Derivatives, Maxima/Minima, Lagrange multipliers, Multiple Integrals (Double and Triple), Green''''s, Stokes'''' and Gauss Divergence Theorems |
| CC12 | Ring Theory and Linear Algebra II | Core | 6 | Integral Domains, Fields, Characteristic of a Ring, Polynomial Rings, Eisenstein''''s Criterion, Unique Factorization Domains (UFD), Principal Ideal Domains (PID), Euclidean Domains (ED), Modules, Submodules |
| DSE1 | Numerical Analysis (Example) | Discipline Specific Elective | 6 | Errors, Iterative methods for roots of equations, Bisection, Newton-Raphson, Secant Method, Interpolation: Lagrange, Newton''''s formulae, Numerical differentiation, Numerical integration: Trapezoidal, Simpson''''s rules |
| DSE2 | Probability and Statistics (Example) | Discipline Specific Elective | 6 | Basic concepts of probability, Conditional probability, Bayes'''' theorem, Random variables, Probability distributions (Binomial, Poisson, Normal), Expectation, Variance, Covariance, Bivariate distribution, Correlation, Regression |
| GE3 | Generic Elective from other disciplines (Choice) | Generic Elective | 6 | Subjects from other faculties or departments as per choice |
Semester 6
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| CC13 | Metric Spaces and Topology | Core | 6 | Metric spaces, Open and Closed balls, Neighbourhoods, Open and Closed sets, Convergence of sequences, Cauchy sequences, Continuity, Compactness, Connectedness, Topological spaces, Bases and Subbases |
| CC14 | Linear Algebra II | Core | 6 | Linear transformations, Null space, Range space, Matrix representations of linear transformations, Eigenvalues and Eigenvectors, Diagonalization, Inner product spaces, Orthogonality, Gram-Schmidt process, Orthogonal projections |
| DSE3 | Discrete Mathematics (Example) | Discipline Specific Elective | 6 | Logic and Proofs, Set theory, Relations and Functions, Partially ordered sets, Lattices and Boolean algebra, Graph theory: Basic definitions, Paths, Cycles, Trees, Spanning trees |
| DSE4 | Mathematical Modelling (Example) | Discipline Specific Elective | 6 | Simple models, Compartmental models, Population dynamics models, Traffic flow models, Pollution models, Differential equation models, Difference equation models, Simulation |
| GE4 | Generic Elective from other disciplines (Choice) | Generic Elective | 6 | Subjects from other faculties or departments as per choice |
