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BSC-HONOURS in Mathematics at City College
Kolkata, West Bengal
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About the Specialization
What is Mathematics at City College Kolkata?
This Mathematics Honours program at City College, Kolkata, offers a comprehensive exploration of fundamental and advanced mathematical concepts. It nurtures analytical reasoning, problem-solving abilities, and abstract thinking, which are invaluable across diverse professional landscapes. The curriculum aligns with the escalating demand for mathematically astute professionals in India''''s rapidly growing technology, finance, and research sectors, equipping students for intellectual leadership.
Who Should Apply?
This program is ideally suited for ambitious high school graduates who demonstrate a profound interest and strong aptitude for mathematics. It appeals to individuals aspiring for rigorous academic pursuits like Master''''s or Doctoral degrees, and those aiming for careers in quantitative finance, data science, actuarial science, or academia. Professionals seeking to enhance their analytical capabilities for career transitions into STEM fields will also find this program beneficial.
Why Choose This Course?
Graduates of this program are well-positioned for rewarding careers in India as data scientists, financial analysts, actuaries, academic researchers, and educators. Entry-level compensation typically ranges from INR 3 to 6 LPA, with significant growth potential for experienced professionals. The robust analytical training also provides an excellent foundation for competitive examinations such as UPSC, banking sector tests, and GATE, facilitating entry into government services and diverse engineering roles.
Student Success Practices
Foundation Stage
Master Core Mathematical Fundamentals- (Semester 1-2)
Dedicate extensive effort to understanding foundational concepts in Calculus, Algebra, and Real Analysis. Utilize prescribed textbooks thoroughly, supplement with online resources like NPTEL or MIT OpenCourseWare, and actively participate in peer-learning groups. Consistent practice with diverse problem sets, focusing on proofs and conceptual derivations, is crucial for building a strong base for all subsequent advanced mathematics courses.
Tools & Resources
University prescribed textbooks, NPTEL videos on core mathematics, Khan Academy, Dedicated study groups with peers
Career Connection
A solid conceptual foundation is indispensable for excelling in competitive postgraduate entrance exams and quantitative roles that demand strong theoretical understanding.
Develop Early Computational & Programming Proficiency- (Semester 1-3)
Engage enthusiastically with practical components of courses, particularly those involving scientific software (e.g., Mathematica, MATLAB, R) and introductory programming languages like C. Practice implementing numerical methods and mathematical algorithms. Participating in basic coding contests or building small computational projects helps bridge theoretical math with practical application, a highly valued skill in technology-driven industries.
Tools & Resources
Software tutorials for Mathematica/MATLAB/R, Online coding platforms (e.g., GeeksforGeeks, HackerRank), Departmental computer labs
Career Connection
Acquiring these practical skills early enhances employability in rapidly growing fields such as data science, quantitative analysis, and software development.
Cultivate Advanced Problem-Solving Strategies- (Semester 1-2)
Beyond routine coursework, challenge yourself by attempting complex problems from advanced mathematics texts or past competitive examinations. Join college mathematics clubs or participate in inter-collegiate math challenges. This fosters creative problem-solving and critical thinking, which are essential for research, innovation, and tackling unstructured problems in professional environments.
Tools & Resources
Problem-solving books for math enthusiasts, College Math Society activities, Mentorship from senior students or faculty
Career Connection
Sharpens analytical prowess, a key differentiator in interview processes and crucial for navigating complex challenges in any analytical career.
Intermediate Stage
Strategically Choose Specialization Electives- (Semester 3-5)
Actively explore and select Skill Enhancement Courses (SECs) and Discipline Specific Electives (DSEs) that align with your long-term career aspirations. For instance, opt for ''''Computer Fundamentals'''' if aiming for data science, or ''''Linear Programming'''' for operational research. Deepen your knowledge in these chosen areas by exploring supplementary materials, advanced texts, or relevant online courses to gain an early specialization edge.
Tools & Resources
University syllabus for elective options, Faculty counselors for guidance, Coursera/edX for specialized topics
Career Connection
Provides a tailored skillset, making you a more attractive candidate for specific industry roles or for specialized postgraduate programs.
Actively Pursue Internships and Research Projects- (Semester 4-5)
Proactively seek summer internships in fields relevant to mathematics, such as data analytics, actuarial science, or financial modeling, offered by Indian companies. Engage in small research projects under faculty guidance within the department. These practical experiences offer invaluable real-world exposure, opportunities to apply theoretical knowledge, and critical networking avenues within the Indian professional landscape.
Tools & Resources
College placement cell, Internshala, LinkedIn for internship listings, Departmental faculty for research mentorship
Career Connection
Practical experience significantly bolsters your resume, provides industry insights, and can often lead to pre-placement offers or strong professional recommendations.
Build a Robust Professional Network- (Semester 3-5)
Attend academic seminars, workshops, and guest lectures hosted by City College or other reputable institutions in Kolkata. Connect with alumni who have successfully transitioned into desired career fields, and foster relationships with professors. Leverage platforms like LinkedIn to network with professionals in mathematics-intensive industries. A strong network provides mentorship, job leads, and collaborative opportunities within India.
Tools & Resources
College alumni network events, LinkedIn professional networking platform, Local and online industry webinars/conferences
Career Connection
Essential for uncovering hidden job market opportunities, gaining industry-specific insights, and securing referrals for placements or higher studies.
Advanced Stage
Intensify Placement and Higher Education Preparation- (Semester 6)
During the final year, dedicate focused time to preparing for campus placements or advanced postgraduate entrance exams (e.g., GATE, JAM, GRE). Systematically revise all core and elective subjects, practice quantitative aptitude tests, and prepare for technical interviews. For research-inclined students, refine research proposals and identify target universities for Master''''s or PhD programs, both in India and abroad.
Tools & Resources
College placement resources, Mock interview sessions, Previous years'''' question papers for entrance exams, Online aptitude test platforms
Career Connection
Directly impacts securing positions in top Indian and multinational companies or admission to prestigious higher education institutions.
Undertake a Comprehensive Capstone Project/Dissertation- (Semester 6)
If chosen as a Discipline Specific Elective, dedicate substantial effort to your project work, aiming for a significant contribution or a robust application of mathematical principles. Even if not formally opted, consider an independent research paper or a complex mathematical modeling project. This demonstrates advanced problem-solving, research aptitude, and the ability to work autonomously, highly valued by both employers and academic institutions.
Tools & Resources
Faculty mentors for guidance, Academic databases (JSTOR, MathSciNet), Specialized mathematical software
Career Connection
Showcases in-depth expertise and research capabilities, critical for roles requiring advanced analytics, R&D, or for admission to doctoral programs.
Refine Communication and Presentation Skills- (Semester 5-6)
Regularly practice articulating complex mathematical concepts clearly and concisely, both in written reports and oral presentations. Participate in departmental seminars, college cultural festivals, or public speaking competitions. Effective communication of technical information is a universally sought-after skill across all professional domains, from academic research to corporate leadership roles.
Tools & Resources
College debate/public speaking societies, Presentation software (PowerPoint, LaTeX Beamer), Peer feedback sessions
Career Connection
Enhances employability by enabling effective communication with colleagues, clients, and stakeholders, crucial for leadership and project management positions in India.
Program Structure and Curriculum
Eligibility:
- Passed Higher Secondary (10+2) or equivalent Examination with minimum 50% marks in aggregate and 45% marks in Mathematics OR 55% marks in Mathematics. (As per University of Calcutta general eligibility criteria)
Duration: 3 years (6 semesters)
Credits: 140 Credits
Assessment: Internal: Approximately 16% (derived from 10 marks Internal Assessment for a 125-mark paper which includes theory and practical), External: Approximately 84% (derived from 105 marks End-Semester Examination for a 125-mark paper which includes theory and practical)
Semester-wise Curriculum Table
Semester 1
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| CEMA-CC-1-1-TH | Calculus | Core Theory | 4 | Real Numbers and Functions, Limits, Continuity and Uniform Continuity, Differentiability, Mean Value Theorems, Partial Differentiation, Euler''''s Theorem, Integration, Reduction Formulae, Quadrature |
| CEMA-CC-1-1-P | Calculus Practical | Core Practical | 2 | Programming with Scientific Software (e.g., Mathematica/MATLAB/R), Plotting Functions and Curves, Numerical Limits, Derivatives, Integrals, Series Expansion and Approximation, Maxima and Minima of Functions, Surface Plotting |
| CEMA-CC-1-2-TH | Algebra | Core Theory | 6 | Set Theory, Relations, Functions, Group Theory (groups, subgroups, normal subgroups, homomorphisms), Ring Theory (rings, subrings, ideals, integral domains, fields), Polynomials (roots, fundamental theorem of algebra), Vector Spaces (linear dependence, basis, dimension) |
| AECC-1 | Environmental Studies | Ability Enhancement Compulsory Course | 2 | Multidisciplinary Nature of Environmental Studies, Natural Resources and Associated Problems, Ecosystems and Biodiversity, Environmental Pollution and Management, Human Population and Sustainable Development |
| GE-1 | Generic Elective - I | Generic Elective (from other disciplines) | 6 | Subject to be chosen by student from unrelated disciplines (e.g., Physics, Chemistry, Computer Science, Economics), Content not specific to Mathematics specialization |
Semester 2
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| CEMA-CC-2-3-TH | Real Analysis | Core Theory | 4 | Real Number System (axioms, completeness, Archimedean property), Sequences (convergence, Cauchy criteria, monotonic sequences), Series of Real Numbers (convergence tests, absolute convergence), Continuity of Functions (properties, uniform continuity), Differentiability (Roll''''s, Lagrange''''s, Cauchy''''s MVT), Riemann Integral |
| CEMA-CC-2-3-P | Real Analysis Practical | Core Practical | 2 | Programming with Scientific Software, Numerical Sequences and Series, Limits and Continuity Visualization, Numerical Differentiation and Integration, Testing Riemann Integrability of Functions |
| CEMA-CC-2-4-TH | Differential Equations | Core Theory | 6 | First Order Ordinary Differential Equations (exact, integrating factors, orthogonal trajectories), Higher Order Linear ODEs (constant coefficients, variation of parameters), Cauchy-Euler Equation, Power Series Solutions, Laplace Transforms and Inverse Transforms, Partial Differential Equations (first order, Lagrange''''s method, Charpit''''s method) |
| AECC-2 | Communicative English/MIL | Ability Enhancement Compulsory Course | 2 | Reading Comprehension and Critical Reading, Grammar, Punctuation and Sentence Structure, Writing Skills (essays, reports, summaries), Listening and Speaking Skills, Oral Presentations, Vocabulary Building and Communication Strategies |
| GE-2 | Generic Elective - II | Generic Elective (from other disciplines) | 6 | Subject to be chosen by student from unrelated disciplines, Content not specific to Mathematics specialization |
Semester 3
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| CEMA-CC-3-5-TH | Theory of Real Functions and Introduction to Metric Spaces | Core Theory | 6 | Point Set Topology (open/closed sets, limit points, compact sets), Sequences and Series of Functions (pointwise and uniform convergence), Power Series, Taylor and Maclaurin Series, Fourier Series and its Convergence, Metric Spaces (definitions, examples, topological properties, completeness) |
| CEMA-CC-3-6-TH | Group Theory and Ring Theory | Core Theory | 6 | Groups (Isomorphism Theorems, Cayley''''s Theorem, Automorphisms), Sylow''''s Theorems and Applications, Solvable and Nilpotent Groups, Rings (prime/maximal ideals, integral domains, fields), Euclidean Domains, Principal Ideal Domains, Unique Factorization Domains |
| CEMA-CC-3-7-TH | Ordinary Differential Equations and Special Functions | Core Theory | 4 | Series Solutions of ODEs (Frobenius Method), Legendre Polynomials (properties, recurrence relations), Bessel Functions (properties, generating function), Sturm-Liouville Problem, Orthogonality of Eigenfunctions, Green''''s Function for Boundary Value Problems |
| CEMA-CC-3-7-P | Ordinary Differential Equations and Special Functions Practical | Core Practical | 2 | Numerical Methods for ODEs (Euler, Runge-Kutta methods), Plotting Legendre Polynomials and Bessel Functions, Computing Orthogonality Properties, Solving Boundary Value Problems Numerically |
| CEMA-SEC-A-3-1-TH | Computer Fundamentals and Programming in C | Skill Enhancement Course (Option) | 2 | Basic Computer Organization, Hardware and Software, Operating Systems Concepts, Introduction to Networks, Number Systems and Data Representation, C Programming (variables, operators, control structures, functions), Arrays, Pointers, Structures, File I/O in C |
| GE-3 | Generic Elective - III | Generic Elective (from other disciplines) | 6 | Subject to be chosen by student from unrelated disciplines, Content not specific to Mathematics specialization |
Semester 4
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| CEMA-CC-4-8-TH | Partial Differential Equations and Vector Analysis | Core Theory | 4 | First-Order PDEs (Charpit''''s method, Jacobi''''s method), Classification of Second-Order PDEs, Wave Equation, Heat Equation, Laplace Equation (separation of variables), Vector Calculus (gradient, divergence, curl, vector identities), Green''''s, Stoke''''s, Gauss''''s Divergence Theorems |
| CEMA-CC-4-8-P | Partial Differential Equations and Vector Analysis Practical | Core Practical | 2 | Plotting Vector Fields and Scalar Potentials, Numerical Solutions for Simple PDEs, Verification of Vector Identities, Visualization of Line and Surface Integrals, Applications of Green''''s, Stoke''''s, Gauss''''s Theorems |
| CEMA-CC-4-9-TH | Complex Analysis | Core Theory | 6 | Complex Numbers and Functions of Complex Variables, Analytic Functions, Cauchy-Riemann Equations, Complex Integration, Cauchy''''s Integral Theorems and Formulas, Taylor and Laurent Series Expansions, Singularities, Residue Theorem, Conformal Mappings |
| CEMA-CC-4-10-TH | Numerical Methods | Core Theory | 4 | Error Analysis, Sources of Errors, Root Finding Methods (Bisection, Newton-Raphson, Secant), Interpolation (Lagrange, Newton''''s Divided Difference Formula), Numerical Differentiation and Integration (Trapezoidal, Simpson''''s Rules), Solution of Linear Systems (Gauss Elimination, Iterative Methods) |
| CEMA-CC-4-10-P | Numerical Methods Practical | Core Practical | 2 | Implementation of Numerical Algorithms (in C/C++/Python/R), Solving Algebraic and Transcendental Equations, Numerical Integration of Functions, Solving Systems of Linear Equations, Error Analysis in Numerical Computations |
| CEMA-SEC-B-4-1-TH | Graph Theory | Skill Enhancement Course (Option) | 2 | Introduction to Graphs, Basic Definitions, Paths, Cycles, Trees and Forests, Planar Graphs, Euler''''s Formula, Graph Coloring, Connectivity and Traversal Algorithms (BFS, DFS), Matching and Coverings in Graphs |
| GE-4 | Generic Elective - IV | Generic Elective (from other disciplines) | 6 | Subject to be chosen by student from unrelated disciplines, Content not specific to Mathematics specialization |
Semester 5
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| CEMA-CC-5-11-TH | Mechanics | Core Theory | 6 | Statics (forces, moments, couples, friction, equilibrium), Kinematics of Particles and Rigid Bodies, Dynamics (Newton''''s Laws, D''''Alembert''''s Principle, work-energy), Impulse-Momentum Principle, Conservative Forces, Motion of Rigid Bodies (rotation, centrodes, moments of inertia) |
| CEMA-CC-5-12-TH | Linear Algebra | Core Theory | 6 | Vector Spaces and Subspaces, Linear Span, Basis, Dimension, Direct Sums, Linear Transformations, Rank-Nullity Theorem, Eigenvalues, Eigenvectors, Diagonalization, Inner Product Spaces, Orthogonal Transformations |
| CEMA-DSE-A-5-1-TH | Advanced Algebra | Discipline Specific Elective (Option) | 6 | Further Group Theory (free groups, group actions, classification of finite abelian groups), Further Ring Theory (localization, polynomial rings, Gauss''''s Lemma), Modules and Vector Spaces over Fields, Galois Theory (fundamental theorem, solvability by radicals), Field Extensions and Algebraic Closures |
| CEMA-DSE-A-5-2-TH | Linear Programming | Discipline Specific Elective (Option) | 6 | Linear Programming Problem Formulation, Graphical Method, Simplex Method (Big M, Two-Phase), Duality Theory and Dual Simplex Method, Transportation Problems and Assignment Problems, Game Theory (two-person zero-sum games, graphical solution) |
Semester 6
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| CEMA-CC-6-13-TH | Numerical Analysis and Operational Research | Core Theory | 4 | Numerical Solutions of Ordinary Differential Equations (Picard, Euler, Runge-Kutta), Numerical Solution of Systems of Non-Linear Equations, Constrained and Unconstrained Optimization, Inventory Control Models (EOQ models), Queuing Theory (M/M/1, M/M/C models) |
| CEMA-CC-6-13-P | Numerical Analysis and Operational Research Practical | Core Practical | 2 | Implementation of Numerical Optimization Algorithms, Solving Inventory and Queuing Problems Using Software, Simulation of Operational Research Models, Data Analysis for Operational Research Applications, Use of Software for Numerical and OR Solutions |
| CEMA-CC-6-14-TH | Mathematical Modelling | Core Theory | 6 | Introduction to Mathematical Modelling Process and Types of Models, Modelling with Ordinary Differential Equations (population dynamics, epidemiology), Modelling with Difference Equations, Applications in Finance and Economics, Case Studies in Biological, Physical, and Social Sciences |
| CEMA-DSE-B-6-1-TH | Point Set Topology | Discipline Specific Elective (Option) | 6 | Topological Spaces (definitions, examples, basis for a topology), Open and Closed Sets, Neighborhoods, Limit Points, Continuous Functions, Homeomorphisms, Compactness (Heine-Borel theorem, product of compact spaces), Connectedness (components), Separation Axioms (T0, T1, T2, T3, T4) |
| CEMA-DSE-B-6-3-TH | Project Work/Dissertation | Discipline Specific Elective (Option) | 6 | Independent Research on a Mathematical Topic, Literature Review and Problem Formulation, Methodology and Data Analysis/Proof Development, Report Writing and Presentation of Findings, Critical Evaluation and Future Scope of Research |
