B.Sc MPCS Degree Maths Syllabus: Semester Wise Topics
A total of 6 credits are assigned to each Discipline Centric Core theory paper across the program, structured as 5 lecture hours and 1 tutorial hour per week. Below is the details on eligibility, semester-wise subject breakdowns, elective offerings, recommended reference books, and career opportunities post-graduation.
| Parameter | Details |
|---|---|
| Program Duration | 3 Academic Years (6 Semesters) |
| Curriculum Framework | National Education Policy (NEP-2020) |
| Semester I Core Paper | Calculus & Geometry (MAT1101T) – 6 Credits |
| Semester II Core Paper | Differential Equations (MAT1202T) – 6 Credits |
| Semester III Core Paper | Real Analysis (MAT2103T) – 6 Credits |
| Semester IV Core Paper | Abstract & Linear Algebra – 6 Credits |
| Semester V DSE Paper | Vector Calculus & Numerical Analysis – 6 Credits |
| Semester VI DSE Paper | Complex Analysis & Statistics – 6 Credits |
B.Sc MPCS Subjects Year-wise
The first year introduces fundamental concepts in Differential Calculus, Integral Calculus, 3D Geometry, and Differential Equations. Students establish problem-solving foundations through analytical geometry and integration techniques.
| Unit | Core Area | Topics & Modules Covered |
|---|---|---|
| Unit 1 | Differential Calculus & Curves | Derivative of length of arc, Pedal equations, Curvature (Formula, Centre, Chord), Asymptotes, Envelopes & Evolutes, Multiple points, Partial differentiation, Euler’s theorem, Chain rule, Total Differentiation, Jacobian, Maxima/Minima of two variables, Lagrange multipliers, Standard curve tracing (Cartesian & Polar). |
| Unit 2 | Integral Calculus & Multiple Integrals | Beta and Gamma functions, Reduction formulas, Double Integrals in Cartesian and Polar coordinates, Change of order of integration, Triple integrals, Dirichlet’s integral, Liouville’s extension, Quadrature, Rectification, Volumes and Surfaces of solids of revolution. |
| Unit 3 | 3D Analytical Geometry | Sphere: Plane section, Tangent plane, Orthogonality, Radical plane/line/centre. Cone & Cylinder: Enveloping cone/cylinder, Right circular cone/cylinder, Reciprocal cone. Central Conicoids: Standard equation, Tangent planes, Director sphere, Normals, Diametral planes. |
Semester II covers Differential Equations (MAT1202T). Unit 1 includes first-order and first-degree differential equations, exact equations, and equations solvable for x, y, and p. Unit 2 covers higher-order linear differential equations with constant coefficients, simultaneous differential equations, and second-order linear differential equations. Unit 3 deals with first-order partial differential equations (PDEs) using Lagrange’s linear equations, Charpit’s method, and Monge’s method of integration.
In the second year, the focus transitions to rigorous abstract mathematics through Real Analysis in Semester 3 and Abstract & Linear Algebra in Semester 4.
| Unit | Core Area | Topics & Modules Covered |
|---|---|---|
| Unit 1 | Real Numbers & Real Sequences | Set of real numbers as complete ordered field, Incompleteness of Q, Archimedean and Dense properties of R, Absolute value, Intervals, Limit point, Bolzano-Weierstrass theorem, Open and Closed sets. Real Sequences: Bounded/unbounded, Monotonic, Limit of sequence, Convergence, Subsequence, Cauchy sequence, Cauchy’s General principle. |
| Unit 2 | Continuity & Differentiability | Continuity: Cauchy’s and Heine’s definitions, Types of discontinuity, Properties on closed intervals. Differentiability: Darboux theorem, Rolle’s Theorem (Algebraic & Geometric interpretation). Functions of two variables: Limit, continuity, differentiability, Directional derivative, total derivative. |
| Unit 3 | Riemann Integration & Uniform Convergence | Riemann Integration: Partition of interval, Darboux sum, Lower and Upper Riemann Integrals, Fundamental Theorem of Integral calculus, Mean value theorem. Uniform Convergence: Cauchy’s Criterion, Weierstrass M-test, Abel Test, Dirichlet Test, Term-by-term integration/differentiation. |
In the third year (Semesters 5 and 6), students take Level 7 advanced modules. Semester 5 covers Vector Calculus & Numerical Analysis, while Semester 6 addresses Complex Analysis & Statistics.
B.Sc MPCS Electives and Specialisations
Skill Enhancement Courses (SEC) and Discipline Specific Electives (DSE) allow students to focus on applied mathematical tools. During Semester III, students complete Optimization Techniques for 2 credits. In Semester IV, students take Mechanics for 2 credits.
Depending on university structure, additional common complementary or foundation papers in mathematics and statistics include Basic Logic and Number Theory, Probability Theory, and Mathematical Economics.
Books for B.Sc MPCS
Standard reference textbooks recommended for core B.Sc Mathematics papers across Indian universities provide detailed theory and solved problems for term examinations.
| Subject Area | Book Title | Author(s) | Publisher |
|---|---|---|---|
| Differential Calculus | Differential Calculus | J. L. Bansal, S. L. Bhargava, & S. M. Agarwal | Jaipur Publishing House |
| Differential Calculus | Differential Calculus (30th ed.) | S. Narayan & P. K. Mittal | S. Chand Publishing |
| Integral Calculus | Integral Calculus | D. C. Gokhroo & S. R. Saini | Navkar Prakashan |
| Integral Calculus | Integral Calculus (35th ed.) | S. Narayan & P. K. Mittal | S. Chand Publishing |
| 3D Geometry | Analytical 3-D Geometry | D. C. Gokhroo, S. R. Saini, & S. S. Bhati | Navkar Prakashan |
| 3D Geometry | Analytical Solid Geometry (17th ed.) | S. Narayan & P. K. Mittal | S. Chand Publishing |
| Differential Equations | Ordinary and Partial Differential Equations (19th ed.) | M. D. Raisinghania | S. Chand Publishing |
| Partial Differential Equations | Elements of Partial Differential Equations | I. N. Sneddon | McGraw-Hill Education |
| Real Analysis | Real Analysis | A. R. Vasishtha & J. N. Sharma | Krishna Prakashan Media |
How to Apply for B.Sc MPCS Admission in 2026: Step by Step
- Understand the NEP-2020 framework: Review the 6-semester degree framework spanning Level 5 to Level 7 under the National Education Policy.
- Plan First-Year core coursework: Enroll in Discipline Centric Core (DCC) theory papers including Calculus & Geometry (MAT1101T) in Semester I and Differential Equations (MAT1202T) in Semester II.
- Select Skill Enhancement Courses (SEC): Choose 2-credit SEC theory papers such as Optimization Techniques in Semester III and Mechanics in Semester IV.
- Prepare with standard references: Utilize recommended textbooks such as Differential Calculus by J. L. Bansal et al. and Ordinary and Partial Differential Equations by M. D. Raisinghania.
- Identify post-graduation pathways: Prepare for higher education degrees like M.Sc., MCA, or MBA, as well as competitive examinations like UPSC, SSC, and IBPS.
| What to do | Where | Link |
|---|---|---|
| Compare colleges, fees and cutoffs | B.Sc MPCS colleges in India | findmycollege.com |
Students pursuing B.Sc Mathematics under NEP-2020 complete 6 semesters of DCC, SEC, and DSE/GE courses carrying defined credit structures. This curriculum builds strong analytical skills while preparing graduates for technical careers and postgraduate studies.
FAQs
How many semesters are in BSc mathematics?
A standard B.Sc Mathematics program consists of 6 semesters distributed across 3 academic years under the National Education Policy (NEP-2020) framework.
What is the syllabus of B.Sc MPCS Mathematics Semester 1?
Semester 1 focuses on Calculus & Geometry (MAT1101T). Key topics include differential calculus (pedal equations, curvature, partial differentiation), integral calculus (Beta/Gamma functions, double/triple integrals), and 3D geometry (Sphere, Cone, Cylinder, Central Conicoids).
What core topics are studied in Semester 2 Differential Equations?
Semester 2 covers first-order ODEs, higher-order linear differential equations with constant coefficients, simultaneous equations, second-order linear ODEs (variation of parameters), and first/higher-order Partial Differential Equations (Lagrange’s, Charpit’s, and Monge’s methods).
Can I get a job in IT company after BSc maths?
Yes. Students with mathematical and computer science foundations can secure roles such as Software Developers, Web Developers, Data Analysts, System Administrators, Network Engineers, and Technical Support Specialists.
Which standard reference books are recommended for B.Sc Real Analysis and Differential Equations?
Standard references include Ordinary and Partial Differential Equations by M. D. Raisinghania (S. Chand), Elements of Partial Differential Equations by I. N. Sneddon, and Real Analysis by A. R. Vasishtha & J. N. Sharma.
What higher study options are available after completing B.Sc Computer Science / MPCS?
Graduates can pursue postgraduate programs like M.Sc. in Computer Science or Information Technology, MCA, or MBA in IT/Systems Management, as well as specialized certifications in Data Science, AI, and Cybersecurity.
