B.Sc. in 4 years Mathematics Honours/ Honours with Research (NEP): Vidyasagar University

B.Sc. Mathematics Honours at Vidyasagar University: A 4-Year Journey Under NEP

Pursuing a B.Sc. Mathematics Honours Vidyasagar University offers students a comprehensive understanding of advanced mathematical concepts through a structured 4-year course. In alignment with the National Education Policy (NEP), this program has evolved to provide an enhanced learning experience with opportunities for research, critical thinking, and interdisciplinary learning. Students enrolled in this course will explore a diverse Mathematics Honours syllabus, which prepares them for a wide range of careers in academia, research, and industry.

Structure of the B.Sc. Mathematics Honours Program

The B.Sc Mathematics Honours NEP program at Vidyasagar University is designed to offer a robust curriculum, which includes theoretical courses, practicals, and research opportunities. The Vidyasagar University Mathematics syllabus covers core subjects such as algebra, calculus, real analysis, and differential equations, while also offering interdisciplinary options. This allows students to choose from courses that align with their specific interests, including computational mathematics, statistics, and applied mathematics.

Moreover, the 4 years B.Sc Honours Research component under NEP encourages students to engage in research, providing them with the tools to conduct scientific investigations and contribute to the field. The curriculum is structured to ensure that students are prepared not only for exams but also for real-world problem-solving scenarios in their future careers.

Key Highlights of the NEP B.Sc Mathematics Syllabus

The NEP B.Sc Mathematics syllabus at Vidyasagar University is specially curated to meet the educational standards set by the National Education Policy. It integrates a balance of theory and practice, allowing students to delve deep into their chosen topics. With a strong emphasis on research, students can pursue Mathematics Honours Research courses, gaining hands-on experience in data analysis, theoretical modeling, and more.

For the B.Sc Mathematics Honours degree, students will also be required to complete practical and project-based work. This ensures that they are well-prepared for both academic challenges and the job market, with skills in data-driven analysis, problem-solving, and critical thinking.

Conclusion

Vidyasagar University’s B.Sc Mathematics Honours Vidyasagar University program offers an enriching experience under the new National Education Policy, equipping students with the skills and knowledge required to excel in the field of mathematics. With an innovative curriculum, diverse specializations, and strong research opportunities, this course provides a gateway for students to embark on successful academic and professional journeys.

Semester-1
MJ-1 (Calculus, Geometry & Ordinary Differential Equation)
Unit-1:
– Hyperbolic functions, higher order derivatives, Leibnitz rule and its applications to problems of type \( \pmb{e^{ax}+b \sin x }\), \(\pmb{e^{ax}+b \cos x}\), \(\pmb{(ax+b)^{n} \sin x}\), \(\pmb{(ax+b)^{n} \cos x}\), concavity and inflection points, curvature, envelopes, asymptotes, curve tracing in cartesian coordinates, tracing in polar coordinates of standard curves, L’Hospital’s rule, applications in business, economics and life sciences.
Unit-2:
– Reduction formulae, derivations and illustrations of reduction formulae of the type \(\pmb{\int \sin nx dx}\), \(\pmb{\int \cos nx dx}\), \(\pmb{\int \tan nx dx}\), \(\pmb{\int \sec nx dx}\), \(\pmb{\int (\log x)^{n} dx}\), \(\pmb{\int \sin nx \sin mx dx}\), parametric equations, parameterizing a curve, arc length of a curve, arc length of parametric curves, area under a curve, area and volume of surface of revolution, techniques of sketching conics.
Unit-3:
– Reflection properties of conics, rotation of axes and second degree equations, classification of conics using the discriminant, polar equations of conics.
-Spheres, Cylindrical surfaces, Central conicoids, paraboloids, plane sections of conicoids, generating lines, classification of quadrics, illustrations of graphing standard quadric surfaces like cone, ellipsoid.
Unit-4:
– General, particular, explicit, implicit and singular solutions of a differential equation, First order but not first degree. Exact differential equations and integrating factors, and equations reducible to this form, linear equation, Bernoulli equation and special integrating factors and transformations
MI-1 (Calculus, Geometry & Ordinary Differential Equation)
Unit-1:
– Hyperbolic functions, higher order derivatives, Leibnitz rule and its applications to problems of type \( \pmb{e^{ax}+b \sin x }\), \(\pmb{e^{ax}+b \cos x}\), \(\pmb{(ax+b)^{n} \sin x}\), \(\pmb{(ax+b)^{n} \cos x}\), concavity and inflection points, curvature, envelopes, asymptotes, curve tracing in cartesian coordinates, tracing in polar coordinates of standard curves, L’Hospital’s rule, applications in business, economics and life sciences.
Unit-2:
– Reduction formulae, derivations and illustrations of reduction formulae of the type \(\pmb{\int \sin nx dx}\), \(\pmb{\int \cos nx dx}\), \(\pmb{\int \tan nx dx}\), \(\pmb{\int \sec nx dx}\), \(\pmb{\int (\log x)^{n} dx}\), \(\pmb{\int \sin nx \sin mx dx}\), parametric equations, parameterizing a curve, arc length of a curve, arc length of parametric curves, area under a curve, area and volume of surface of revolution, techniques of sketching conics.
Unit-3:
– Reflection properties of conics, rotation of axes and second degree equations, classification of conics using the discriminant, polar equations of conics.
-Spheres, Cylindrical surfaces, Central conicoids, paraboloids, plane sections of conicoids, generating lines, classification of quadrics, illustrations of graphing standard quadric surfaces like cone, ellipsoid.
Unit-4:
– General, particular, explicit, implicit and singular solutions of a differential equation, First order but not first degree. Exact differential equations and integrating factors, and equations reducible to this form, linear equation, Bernoulli equation and special integrating factors and transformations
SEC-1 (MATLAB-1)
Unit:
– MATLAB interface, data types, variables, Flow control statements, arrays: creating, indexing, operations, Matrix creating, indexing, operations, Input and output function, Mathematical library functions, userdefined function: anonymous function.
– Plotting of two dimensional functions: Graph plotting, Graph formatting (title, axis, line styles, colors, etc.), multiple plots, matrix plots, polar plots, 3D plotting (line, surface, mesh, and contour) of three
dimensional functions.
  1. Find the sum, product, max, min of a list of number in an array, in a sub-array without library function.
  2. Find a sub-matrix of the given matrix
  3. Find the column sum, product, max, min of the given matrix without library function.
  4. Find the row sum, product, max, min of the given matrix without library function.
  5. Define any transcendental function and then find and show the table of its functional values.
  6. TeaPlotting of graph of functions \(\pmb{e^{ax+b}}\), \(\pmb{\log (ax + b)}\), \(\pmb{\log \frac{1}{ax + b}}\), \(\pmb{\sin (ax + b)}\), \(\pmb{\cos (ax + b)}\), \(\pmb{|ax+b|}\) and to illustrate the effect of a and b on the graph.
  7. Plotting the graphs of polynomial of degree 4 and 5, the derivative graph, the second derivative graph and comparing them.
  8. Sketching parametric curves (eg. trochoid, cycloid, epicycloids, hypocycloid).
  9. Tracing of conics in cartesian coordinates/ polar coordinates.
  10. Sketching ellipsoid, hyperboloid of one and two sheets, elliptic cone, elliptic, paraboloid, and hyperbolic paraboloid using cartesian coordinates.
VAC-1 (ENVS)
Unit-1: Introduction to environmental studies
  1. Multidisciplinary nature of environmental studies
  2. Scope and importance; Concept of sustainability and sustainable development.
Unit-2: Ecosystems
  1. What is an ecosystem? Structure and function of ecosystem; Energy flow in an ecosystem: food chains, food webs and ecological succession. Case studies of the following ecosystems: a) Forest ecosystem; b) Grassland ecosystem c) Desert ecosystem d) Aquatic ecosystems (ponds, streams, lakes, rivers, oceans, estuaries)
Unit-3: Natural Resources: Renewable and Non-renewable Resources
  1. Land resources and land use change; Land degradation, soil erosion and desertification
  2. Deforestation: Causes and impacts due to mining, dam building on environment, forests, biodiversity and tribal populations. Joint forest management.
  3. Water: Use and over–exploitation of surface and ground water, floods, droughts, conflicts over water (international and interstate).
  4. Energy resources: Renewable and non renewable energy sources, use of alternate energy sources, growing energy needs, case studies.
Unit-4: Biodiversity and Conservation
  1. Levels of biological diversity: genetic, species and ecosystem diversity; Bio- geographic zones of India; Biodiversity patterns and global biodiversity hot spots
  2. India as a mega–‐biodiversity nation; Endangered and endemic species of India
  3. Threats to biodiversity: Habitat loss, poaching of wildlife, man–wildlife conflicts, biological invasions; Conservation of biodiversity: In-situ and Ex-situ conservation of biodiversity
  4. Ecosystem and biodiversity services: Ecological, economic, social, ethical, aesthetic and Informational value
Unit-5: Environmental Pollution
  1. Environmental pollution: types, causes, effects and controls; Air, water, soil and noise pollution
  2. Nuclear hazards and human health risks
  3. Solid waste management: Control measures of urban and industrial waste.
  4. Pollution case studies.
  5. Noise pollution.
Unit-6: Environmental Policies and Practices
  1. Climate change, global warming, ozone layer depletion, acid rain and impacts on human communities and agriculture
  2. Environment Laws: Environment Protection Act; Air (Prevention and Control of Pollution) Act; Water (Prevention and control of Pollution) Act; Wildlife Protection Act; Forest Conservation Act. International agreements: Montreal and Kyoto protocols and Convention on Biological Diversity (CBD).
  3. Nature reserves, tribal populations and rights, and human wildlife conflicts in Indian context.
  4. Environmental policy and gender issues
Unit-7: Human Communities and the Environment
  1. Human population growth: Impacts on environment, human health and welfare.
  2. Resettlement and rehabilitation of project affected persons; case studies.
  3. Disaster management: floods, earthquake, cyclones and landslides.
  4. Environmental movements: Chipko, Silent valley, Bishnois of Rajasthan.
  5. Environmental ethics: Role of Indian and other religions and cultures in environmental conservation.
  6. Environmental communication and public awareness, case studies (e.g. CNG vehicles in Delhi)
Unit-8: Field work
  1. Visit to an area to document environmental assets: river/ forest/ flora/fauna, etc.
  2. Visit to a local polluted site- Urban/ Rural/ Industrial/ Agricultural
  3. Study of common plants, insects, birds and basic principles of identification.
  4. Study of simple ecosystems–pond, river, Delhi Ridge, etc.
  5. Disaster management.
  6. Coastal ecosystem
AEC-1 (Communicative English-1)
1. Communication Skills:
  1. Types and Models of Communication
  2. Verbal and Non-verbal Communication
  3. Barriers and Strategies
  4. Inter-personal Communication
2. Listening Skills:
  1. Active and Passive Listening
3. Speaking Skills:
  1. Different forms of Speaking – Formal/Informal
  2. Group Discussion
  3. English in Situations: Greeting and Leave Taking, Making and Granting/ Refusing Requests, Queries and Giving Information/ Direction, Describing objects/ process, Narrating events and Commentary, Persuasion and Motivation, Complaints and Apologies, Expressing disapproval, Alerting and Warning
4. Reading Skills:
  1. Different types of Reading
  2. Comprehension
MDC-1 (Multidisciplinary Course-1) (Optional: Indian Constitution)
Unit-1:
Historical Background – Constituent Assembly of India – Philosophical Foundations Of The Indian Constitution – Preamble – Fundamental Rights – Directive Principles Of State Policy – Fundamental Duties – Citizenship – Constitutional Remedies For Citizens.
Unit-2:
Union Government – Structures of the Union Government and Functions – President – Vice President – Prime Minister – Cabinet – Parliament – Lok Sabha – Composition and Powers – Rajya Sabha – Composition and Powers – Supreme Court of India – Judicial Review
Unit-3:
State Government – Structure and Functions – Governor – Chief Minister – Cabinet – State Legislature – Judicial System in States – High Courts and other Subordinate Courts.
MDC-1 (Multidisciplinary Course-1) (Optional: Social Value and Ethics)
Unit-1: Philosophy of Life and Individual Qualities
Human Life on Earth – Purpose of Life, Meaning and Philosophy of Life. The Law of Nature – Protecting Nature /Universe. Basic Culture – Thought Analysis – Regulating desire – Guarding against anger – To get rid of Anxiety – The Rewards of Blessing – Benevolence of Friendship – Love and Charity – Self – tranquility/Peace.
Unit-2: Social Values (Individual and Social Welfare)
Family – Peace in Family, Society, The Law of Life Brotherhood – The Pride of Womanhood – Five responsibilities/duties of Man : – a) to himself, b) to his family, c) to his environment, d) to his society, e) to the Universe in his lives, Thriftiness (Thrift)/Economics. Health – Education – Governance – People’s Responsibility / duties of the community, World peace.
Unit-3: Mind Culture and Tending Personal Health
Mind Culture – Life and Mind – Bio – magnetism, Universal Magnetism (God –Realization and Self Realization) – Genetic Centre – Thought Action – Short term Memory – Expansiveness – Thought – Waves, Channelizing the Mind, Stages – Meditation, Spiritual Value. Structure of the body – the three forces of the body- life body relation, natural causes and unnatural causes for diseases, Methods in Curing diseases.
MDC-1 (Multidisciplinary Course-1) (Optional: Basics of information technology (IT))
Unit-1: Introduction to Computers
Introduction, Definition, Characteristics of computer, Evolution of Computer, Block Diagram of a computer, Generations of Computer, Classification Of Computers, Applications of Computer, Capabilities and limitations of computer.
Unit-2: Basic Computer Organization
Role of I/O devices in a computer system. Input Units: Keyboard, Terminals and its types. Pointing Devices, Scanners and its types, Voice Recognition Systems, Vision Input System, Touch Screen, Output Units: Monitors and its types. Printers: Impact Printers and its types. Non Impact Printers and its types, Plotters, types of plotters, Sound cards, Speakers.
Unit-3: Software
Software and its needs, Types of S/W. System Software: Operating System, Utility Programs Programming Language: Machine Language, Assembly Language, High Level Language their advantages and disadvantages. Application S/W and its types: Word Processing, Spread Sheets Presentation, Graphics, DBMS s/w.
Unit-4: Operating System
Functions, Measuring System Performance, Assemblers, Compilers and Interpreters. Batch Processing, Multiprogramming, Multi Tasking, Multiprocessing, Time Sharing, DOS, Windows, Unix/Linux.
Unit-5: Data Communication
Communication Process, Data Transmission speed, Communication Types (modes), Data Transmission Medias, Modem and its working, characteristics, Types of Networks, LAN Topologies, Computer Protocols, Concepts relating to networking.
Unit-6: Business Data Processing
Introduction, data storage hierarchy, Method of organizing data, File Types, File Organization, File Utilities.
MDC-1 (Multidisciplinary Course-1) (Optional: Basics of Accounting)
Unit-1: Introduction to Financial Accounting
Meaning, Importance and objectives of Accounting; Concepts and Convention of Accounting. Meaning, Users, Sources of accounting information; Some Basic Terms –Transaction, Account, Asset, Liability, Capital, Expenditure, Income, Revenue, Profit, Loss, Concept of revenue and capital transactions, Accounting Year, Financial Year; Features of recordable transactions and events; Recording of Transactions; Types of Accounts – Personal account, Real Account and Nominal Account; Golden Rules and American Approach of Accounting-Rules for Debit and Credit; Double Entry System, Accounting Equation, Process of accounting – Business transactions – Journal entries – Ledger posting, Trial Balance
Unit-2: Accounting for Depreciation
Concept; Causes of Depreciation; Objectives of Providing Depreciation; Methods of providing depreciation: Fixed Instalment Method and Reducing Balance Method.
Unit-3: Accounting for Joint Venture
Meaning and features; Distinction between Partnership and Joint Venture; Accounting Treatment of Joint venture
Unit-4: Single entry System of Book keeping and Conversion of Single Entry to Double Entry system of Book Keeping
Unit-5: Final accounts of Non-Profit Organizations
Meaning and Features of Non-Profit Organization; Preparation of Receipt and Payment Account; Income and Expenditure Account and Balance Sheet.
Unit-6: Final Accounts of Sole Trading Concern
Preparation of Trading and Profit and Loss account and Balance sheet.
MDC-1 (Multidisciplinary Course-1) (Optional: NGO and its Operations)
Unit-1: Introduction to Financial Accounting
Meaning, Importance and objectives of Accounting; Concepts and Convention of Accounting. Meaning, Users, Sources of accounting information; Some Basic Terms –Transaction, Account, Asset, Liability, Capital, Expenditure, Income, Revenue, Profit, Loss, Concept of revenue and capital transactions, Accounting Year, Financial Year; Features of recordable transactions and events; Recording of Transactions; Types of Accounts – Personal account, Real Account and Nominal Account; Golden Rules and American Approach of Accounting-Rules for Debit and Credit; Double Entry System, Accounting Equation, Process of accounting – Business transactions – Journal entries – Ledger posting, Trial Balance
Unit-2: Accounting for Depreciation
Concept; Causes of Depreciation; Objectives of Providing Depreciation; Methods of providing depreciation: Fixed Instalment Method and Reducing Balance Method.
Unit-3: Accounting for Joint Venture
Meaning and features; Distinction between Partnership and Joint Venture; Accounting Treatment of Joint venture
Unit-4: Single entry System of Book keeping and Conversion of Single Entry to Double Entry system of Book Keeping
Unit-5: Final accounts of Non-Profit Organizations
Meaning and Features of Non-Profit Organization; Preparation of Receipt and Payment Account; Income and Expenditure Account and Balance Sheet.
Unit-6: Final Accounts of Sole Trading Concern
Preparation of Trading and Profit and Loss account and Balance sheet.
MDC-1 (Multidisciplinary Course-1) (Optional: Business Organisation)
Unit-1: Introduction: Concept and Functions of NGOs
  1. Concept of NGOs: Definition and meaning of NGOs, Historical evolution of NGOs, Role and significance of NGOs in society
  2. Functions of NGOs: Social welfare and development activities, Advocacy and awareness campaigns, Empowerment and capacity-building initiatives
Unit-2: Types and Characteristics of NGOs
  1. Types of NGOs: Charitable NGOs, Service NGOs, Advocacy NGOs, Operational NGOs, Networking NGOs International NGOs (INGOs), Community-Based Organizations (CBOs)
  2. NGO Characteristics: Non-profit nature, Voluntary participation, Private initiative, Independence and autonomy, Social objectives
  3. Strengths and Weaknesses of NGOs Advantages of NGOs in development work, Challenges and limitations faced by NGOs
Unit-3: Strategic Planning and Leadership in NGOs
  1. Planning and Leading a Team: Importance of strategic planning in NGOs, Setting goals and objectives, Formulating action plans, Effective team leadership and management
  2. Conflict Resolution: Understanding conflicts in NGO settings, Conflict resolution techniques, Promoting harmonious work environments
Unit-4: Issues Related to NGO Operations
  1. Concentration of Power, Staff, and Accountability: Power dynamics within NGOs, Ensuring transparency and accountability, Staff management and motivation
  2. Fundraising: Importance of fundraising for NGO sustainability, Fundraising strategies and techniques, Ethical considerations in fundraising activities
Unit-5: Funding Agencies and Schemes
  1. National Bank for Agriculture and Rural Development (NABARD): Overview of NABARD and its role, funding opportunities for rural development projects
  2. National Human Rights Commission (NHRC): Understanding the role of NHRC in protecting human rights, Collaboration opportunities for NGOs
  3. Schemes for NGOs under the Government of India: Introduction to various government schemes and programs, Eligibility criteria and application procedures for NGO participation
MDC-1 (Multidisciplinary Course-1) (Optional: Sports and fitness)
Unit-1: Introduction to Sports
  1. Concept of Play, Games and Sports.
  2. Objectives and importance of Play, Games and Sports
  3. Fundamental movements of Sports in relation to joints.
  4. Warming up and Limbering down
    1. General warm up exercises
    2. Specific warm up exercises
Unit-2: Health and Performance Related Physical Fitness
  1. Meaning and Definition of Fitness and Physical Fitness
  2. Components of Health and Performance Related Physical Fitness
  3. Importance of Physical Fitness in present society
  4. Assessment of Health and Performance Related Physical Fitness
Course Structure
Semester-1
  1. MJ-1
    Credit: 4
    L-T-P: 3-1-0
    Marks: 75
    CA-15, ESE-60
  2. MI-1
    Credit: 4
    L-T-P: 3-1-0
    Marks: 75
    CA-15, ESE-60
  3. SEC-1
    Credit: 3
    L-T-P: 0-0-3
    Marks: 50
    CA-10, ESE-40
  4. AEC-1
    Credit: 2
    L-T-P: 2-0-0
    Marks: 50
    CA-10, ESE-40
  5. VAC-1
    Credit: 4
    L-T-P: 2-0-2
    Marks: 100
    CA-50, ESE-50
  6. MDC-1
    Credit: 3
    L-T-P: 3-0-0
    Marks: 50
    CA-10, ESE-40
Semester-2
  1. MJ-2
    Credit: 4
    L-T-P: 3-1-0
    Marks: 75
    CA-15, ESE-60
  2. MI-2
    Credit: 4
    L-T-P: 3-1-0
    Marks: 75
    CA-15, ESE-60
  3. SEC-2
    Credit: 3
    L-T-P: 0-0-3
    Marks: 50
    CA-10, ESE-40
  4. AEC-2
    Credit: 2
    L-T-P: 2-0-0
    Marks: 50
    CA-10, ESE-40
  5. VAC-2
    Credit: 4
    L-T-P: 2-0-2
    Marks: 50
    CA-10, ESE-40
  6. MDC-2
    Credit: 3
    L-T-P: 3-0-0
    Marks: 50
    CA-10, ESE-40
  7. CS
    Credit: 4
    L-T-P: 0-0-4
    Marks: 50
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