Syllabus

B.Sc Mathematics Syllabus 2025: Detailed Curriculum & Key Subjects

Get the latest 2025 B.Sc Mathematics syllabus covering core subjects like Calculus, Linear Algebra, Real & Complex Analysis, Probability & Statistics, Numerical Methods, and more—structured semester by semester for easy reference.

Bachelor of Science in Mathematics (B.Sc Mathematics) is a 3-year undergraduate program designed for students with a keen interest in analytical reasoning, quantitative techniques, and mathematical principles. It lays a strong foundation for careers in research, data analysis, education, actuarial science, and various competitive exams like UPSC, GATE, and more.

This article covers the complete B.Sc Mathematics syllabus with semester-wise breakdown, full topic details, descriptions, marks distribution, recommended books, preparation tips, specialization paths, and a syllabus PDF download link.

B.Sc Mathematics Exam Overview

Feature Details
Course Duration 3 Years (6 Semesters)
Examination Type Semester-wise
Eligibility 10+2 with Mathematics
Core Subjects Algebra, Calculus, Geometry, Real Analysis, Statistics
Career Pathways Teaching, Research, Data Science, Banking, Actuarial Science

Semester-Wise B.Sc Mathematics Syllabus (Full Topics & Descriptions)

Semester 1

Subject Topics Description
Calculus – I Functions, Limits, Continuity, Differentiability, Mean Value Theorem, Taylor & Maclaurin Series, Asymptotes, Curvature Basics of single-variable calculus and limit behavior with curve analysis.
Algebra – I Sets, Relations, Modular Arithmetic, Groups, Subgroups, Cyclic Groups, Symmetric Groups Introduction to abstract algebra and foundational algebraic structures.
Geometry Lines, Circles, Conics, Plane, Sphere, Cone, Cylinder Analytical and coordinate geometry in 2D and 3D space.

Semester 2

Subject Topics Description
Calculus – II Partial Derivatives, Double/Triple Integrals, Beta-Gamma Functions, Improper Integrals Advanced integration and multivariable calculus.
Algebra – II Matrices, Rank, Vector Spaces, Basis, Dimension Focus on matrix algebra and vector systems.
Differential Equations – I First-order ODEs, Exact Equations, Orthogonal Trajectories Foundations of solving basic differential equations.

Semester 3

Subject Topics Description
Real Analysis – I Real Numbers, Sequences, Series, Convergence Tests Mathematical rigor and real number theory fundamentals.
Vector Calculus Gradient, Divergence, Curl, Green’s Theorem, Gauss & Stokes Theorems Application of calculus in vector fields.
Differential Equations – II Higher-order ODEs, Power Series, Legendre & Bessel Equations Advanced methods and special differential equations.

Semester 4

Subject Topics Description
Real Analysis – II Continuity, Differentiability, Riemann Integration, Mean Value Theorem Advanced study of functions and integrability.
Mechanics Newton’s Laws, Work, Energy, Motion, Equilibrium Application of math in classical physics.
Abstract Algebra Quotient Groups, Homomorphisms, Isomorphisms, Lagrange’s Theorem Explores abstract mathematical structures and symmetry.

Semester 5

Subject Topics Description
Complex Analysis Analytic Functions, Cauchy-Riemann, Residues, Conformal Mapping Study of complex variable functions and their behavior.
Numerical Methods Root Finding, Interpolation, Numerical Integration, Error Analysis Solving equations using numerical approximations.
Linear Algebra Eigenvalues, Diagonalization, Inner Product, Gram-Schmidt Process Core linear transformations and orthogonalization techniques.

Semester 6

Subject Topics Description
Topology Open/Closed Sets, Continuity, Compactness, Metric Spaces Study of geometric properties preserved under deformation.
Mathematical Modelling Population, Epidemics, Traffic, Economics, Newton’s Law, Drug Dosage Applying math to simulate real-world systems and behaviors.
Project/Elective Graph Theory, Fluid Mechanics, Number Theory, Game Theory Specialization or research work in advanced mathematical fields.

B.Sc Mathematics Syllabus PDF Download

Click here to download the full B.Sc Mathematics syllabus PDF

Recommended Books for B.Sc Mathematics

Subject Book Title Author
Calculus Calculus Thomas & Finney
Algebra Elements of Modern Algebra Linda Gilbert
Real Analysis Principles of Mathematical Analysis Walter Rudin
ODEs Ordinary Differential Equations M.D. Raisinghania
Mechanics Introduction to Classical Mechanics David Morin
Complex Analysis Complex Variables and Applications Churchill & Brown
Numerical Methods Numerical Methods S.S. Sastry
Topology Topology James Munkres

B.Sc Mathematics Preparation Tips

  • Revise NCERT and 12th-grade fundamentals first.
  • Solve previous years’ question papers regularly.
  • Use quality textbooks instead of shortcut guides.
  • Create personal formula charts and proof notes.
  • Watch NPTEL, YouTube, or MIT lectures for better clarity.
  • Practice time-bound mock tests weekly.
  • Group study helps with theorem-based understanding.

Specializations After B.Sc Mathematics

Specialization Area Career Opportunities
Pure Mathematics Researcher, Professor, Mathematician
Applied Mathematics Data Scientist, OR Analyst, Analyst in R&D
Statistics Statistician, Market Analyst
Actuarial Science Actuary, Insurance Consultant
Mathematical Physics Research Physicist, Scientist
Computer Applications Developer, Data Analyst

Conclusion

The B.Sc Mathematics syllabus builds a strong theoretical and applied foundation over six semesters. Students gain expertise in abstract reasoning, analytical thinking, and mathematical modeling. With the right strategy, books, and practice, B.Sc Mathematics opens doors to postgraduate studies, competitive exams, and high-paying jobs in analytics, research, and academia.

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