BSc Mathematics Syllabus: Year-wise Syllabus & Course Structure

Students who have completed or are about to complete their Class 12 can opt for the BSc Mathematics. If you're planning to pursue it, then you must check this Shiksha Article for the brief information about the BSc Mathematics courses from different colleges and universities across the country.

Students who have recently passed their Class 12 exams are now confused about the degree they want to pursue and the jobs they wish to pursue. Students who have completed their 10 + 2 in the science stream with maths as their core subjects and have a minimum score of 50% to 60% marks from a recognised board can pursue BSc mathematics.

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Students should note that each college has its own specific eligibility and admission criteria, so it is very important for the students to check the requirements for the college or university they want admission.

BSc Mathematics Eligibility Criteria

Before submitting an application for admission to the course, students must be eligible for a BSc in mathematics. To be eligible for admission, an applicant must absolutely satisfy the BSc Mathematics's established eligibility requirements. From university to university, the eligibility requirements may vary. The following basic eligibility requirements for BSc Mathematics are listed:

The candidate should have completed their Class 12 in PCM (Physics, Chemistry, and Mathematics) from a recognised board.
Students need to secure a minimum of 50% to 60% percent aggregate in their class 12 to pursue BSc Mathematics.

BSc Mathematics Education Criteria

Minimum aggregate marks required in 12th Class is 50 per cent. This requirement may keep changing for various colleges. It would be better to read the admission criteria of the institute in which the candidate wishes to apply:

Institution Type	Minimum Aggregate Marks (General)	Minimum Aggregate Marks (Reserved Categories)
Colleges/Universities	50-60%	5% relaxation (e.g., 45-55%)
Distance Education (e.g., IMTS)	50%	45% for reserved categories

Reserved Categories Criteria

Reserved category candidates have more relaxed norms for admission. Candidates who hold a certificate to prove that they belong to Scheduled Castes (SC), the Scheduled Tribes (ST), and the Other Backward Classes (OBC) then a minimum of 5% relaxation will be granted to them as per the policies.

College-based Eligibility Criteria

For every college, the eligibility to seek admission depends on the minimum marks scored by the candidate. For example:

Colleges affiliated with central universities may have stricter mark requirements (closer to 60%)

State-affiliated colleges may have lower thresholds (closer to 50%).

Programs offered through distance education generally have no age restrictions and grant merit-based admission. However, they would still require a candidates to have passed the Mathematics subject in class 12.

BSc Maths for Choice-Based Credit System

Read on to find out BSc Mathematics course (Semester-wise) system requirements suggested by the University Grants Commission under the Choice Based Credit System:

Semester	Core Course (12)	Ability Enhancement Compulsory Course (AECC) (2)	Skill Enhancement Course (SEC) (2)	Discipline Specific Elective (DSE) (6)
1	Differential Calculus	AECC1
	C2A
	C3A
2	Differential Equations	AECC2
	C2B
	C3B
3	Real Analysis		SEC1
	C2C
	C3C
4	Algebra		SEC2
	C2D
	C3D
5			SEC3	DSE1A
				DSE2A
				DSE3A
6			SEC4	DSE1B
6			SEC4	DSE2B
				DSE3B

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Discipline Specific Electives (DSE)
DSE 1A (choose one)
1. Matrices
2. Mechanics
3. Linear Algebra
DSE 1B (choose one)
1. Numerical Methods
2. Complex Analysis
3. Linear Programming

Skill Enhancement Course (SEC)
SEC 1 (choose one)
1. Logic and Sets
2. Analytical Geometry
3. Integral Calculus
SEC 2 (choose one)
1. Vector Calculus
2. Theory of Equations
3. Number Theory
SEC 3 (choose one)
1. Probability and Statistics
2. Mathematical Finance
3. Mathematical Modeling
SEC 4 (choose one)
1. Boolean Algebra
2. Transportation and Game Theory

3. Graph Theory

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BSc Maths Syllabus 2026

BSc Mathematics is a three-year course that has six semesters in it. Here we'll provide a semester-wise BSc Maths syllabus for the students:

BSc Maths Syllabus: Semester Wise

The below mentioned is the BSc Maths Syllabus Semester Wise:-

BSc Maths Syllabus: First Year
BSc Maths First Semester Syllabus	BSc Maths Second Semester Syllabus
Algebra Differential Calculus & Vector Calculus Vector Analysis & Geometry Integral Calculus & Trigonometry	Advanced Calculus Mathematical Methods Differential Equations Mechanics
BSc Maths Third Semester Syllabus	BSc Maths Fourth Semester Syllabus
Mechanics II Differential Equations II Analysis I	Vector Analysis Differential Equations III Analysis II
BSc Maths Fifth Semester Syllabus	BSc Maths Sixth Semester Syllabus
Numerical Methods Numerical Methods Practical using C Algebra III Analysis III	Probability Theory Linear Programming and Optimization Algebra IV Analysis IV

BSc Maths Syllabus: Year - Wise

The BSc Maths Course is of 3 years. Read the complete section in order to know about year wise Mathematics syllabus.

BSc Maths First Year Syllabus

Candidates can find the list of subjects which are included in the BSc Maths first year syllabus below:

BSc Maths First Year Syllabus
Calculus	Limit and Continuity (ε and δ definition), Types of discontinuities, Differentiability of functions, Successive differentiation, Leibnitz’s theorem, Partial differentiation, Euler’s theorem on homogeneous functions. Tangents and normals, Curvature, Asymptotes, Singular points, Tracing of curves. Parametric representation of curves and tracing of parametric curves, Polar coordinates and tracing of curves in polar coordinates. Rolle’s theorem, Mean Value theorems, Taylor’s theorem with Lagrange’s and Cauchy’s forms of remainder, Taylor’s series, Maclaurin’s series of sin x, cos x, ex , log(l+x), (l+x)m, Maxima and Minima, Indeterminate forms.
Algebra	Definition and examples of groups, examples of abelian and non-abelian groups, the group Zn of integers under addition modulo n and the group U(n) of units under multiplication modulo n. Cyclic groups from number systems, complex roots of unity, circle group, the general linear group GLn (n,R), groups of symmetries of (i) an isosceles triangle, (ii) an equilateral triangle, (iii) a rectangle, and (iv) a square, the permutation group Sym (n), Group of quaternions. Subgroups, cyclic subgroups, the concept of a subgroup generated by a subset and the commutator subgroup of group, examples of subgroups including the center of a group. Cosets, Index of subgroup, Lagrange’s theorem, order of an element, Normal subgroups: their definition, examples, and characterizations, Quotient groups. Definition and examples of rings, examples of commutative and non-commutative rings: rings from number systems, Zn the ring of integers modulo n, ring of real quaternions, rings of matrices, polynomial rings, and rings of continuous functions. Subrings and ideals, Integral domains and fields, examples of fields: Zp, Q, R, and C. Field of rational functions.
Real Analysis	Finite and infinite sets, examples of countable and uncountable sets. Real line, bounded sets, suprema and infima, completeness property of R, Archimedean property of R, intervals. Concept of cluster points and statement of Bolzano-Weierstrass theorem. Real Sequence, Bounded sequence, Cauchy convergence criterion for sequences. Cauchy’s theorem on limits, order preservation and squeeze theorem, monotone sequences and their convergence (monotone convergence theorem without proof). Infinite series. Cauchy convergence criterion for series, positive term series, geometric series, comparison test, convergence of p-series, Root test, Ratio test, alternating series, Leibnitz’s test (Tests of Convergence without proof). Definition and examples of absolute and conditional convergence. Sequences and series of functions, Pointwise and uniform convergence. Mn-test, M-test, Statements of the results about uniform convergence and integrability and differentiability of functions, Power series and radius of convergence.
Differential Equations	First order exact differential equations. Integrating factors, rules to find an integrating factor. First order higher degree equations solvable for x, y, p. Methods for solving higher-order differential equations. Basic theory of linear differential equations, Wronskian, and its properties. Solving a differential equation by reducing its order. Linear homogenous equations with constant coefficients, Linear non-homogenous equations, The method of variation of parameters, The Cauchy-Euler equation, Simultaneous differential equations, Total differential equations. Order and degree of partial differential equations, Concept of linear and non-linear partial differential equations, Formation of first order partial differential equations, Linear partial differential equation of first order, Lagrange’s method, Charpit’s method. Classification of second order partial differential equations into elliptic, parabolic and hyperbolic through illustrations only.

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BSc Maths Second Year Syllabus

Candidates can find the list of subjects which are included in the BSc Maths second year syllabus below:

BSc Maths Second Year Syllabus
Theory of Real Functions	Continuous Functions and their Properties Limits of Functions Taylor's Theorem and its Applications Derivability and its Applications
Graph Theory	Definition, examples and basic properties of graphs, pseudographs, complete graphs, bi‐partite graphs, isomorphism of graphs, paths and circuits, Eulerian circuits, Hamiltonian cycles, the adjacency matrix, weighted graph, travelling salesman’s problem, shortest path, Dijkstra’s algorithm, Floyd‐Warshall algorithm.
Multivariate Calculus	Integration by Partial fractions, integration of rational and irrational functions. Properties of definite integrals. Reduction formulae for integrals of rational, trigonometric, exponential and logarithmic functions and of their combinations. Areas and lengths of curves in the plane, volumes and surfaces of solids of revolution. Double and Triple integrals. Differentiation and partial differentiation of a vector function. Derivative of sum, dot product and cross product of two vectors. Gradient, divergence and curl.
Partial Differential Equations	First Order PDE and Method of Characteristics The Cauchy Problem and Wave Equations Mathematical Models and Classification of 2nd Order Linear PDE Method of Separation of Variables

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BSc Maths Third Year Syllabus

Candidates can find the list of subjects which are included in the BSc Maths third year syllabus below:

BSc Maths Third Year Syllabus
Metric Spaces	Topology and Metric Spaces Basic Concepts Connectedness and Compactness Continuity & Uniform Continuity in Metric Spaces
Group Theory	Automorphism and Properties Group Action Sylow Theorems and Applications External and Internal Direct Products of Groups
Probability and Statistics	Sample space, probability axioms, real random variables (discrete and continuous), cumulative distribution function, probability mass/density functions, mathematical expectation, moments, moment generating function, characteristic function, discrete distributions: uniform, binomial, Poisson, continuous distributions: uniform, normal, exponential. Joint cumulative distribution function and its properties, joint probability density functions, marginal and conditional distributions, expectation of function of two random variables, conditional expectations, independent random variables.
Boolean Algebra	Definition, examples and basic properties of ordered sets, maps between ordered sets, duality principle, maximal and minimal elements, lattices as ordered sets, complete lattices, lattices as algebraic structures, sublattices, products and homomorphisms. Definition, examples and properties of modular and distributive lattices, Boolean algebras, Boolean polynomials, minimal forms of Boolean polynomials, Quinn-McCluskey method, Karnaugh diagrams, switching circuits and applications of switching circuits.

NOTE: Candidates must note that the syllbus mentioned below is General BSc Maths. The syllabus may differ from university to univerity, but the topics mentioned below comprises the major content of BSc Mathematics syllabus.

BSc Maths: List of Important Books (Topic Wise)

Here are the list of some important books which are recommended for the candidates to take reference while studying the BSc Maths in their undergraduate course:

List of Important Books
Differential Calculus	1. H. Anton, I. Birens and S. Davis, Calculus, John Wiley and Sons, Inc., 2002. 2. G.B. Thomas and R.L. Finney, Calculus, Pearson Education, 2007.
Differential Equations	1. Shepley L. Ross, Differential Equations, 3rd Ed., John Wiley and Sons, 1984. 2. I. Sneddon, Elements of Partial Differential Equations, McGraw-Hill, International Edition, 1967.
Real Analysis	1. T. M. Apostol, Calculus (Vol. I), John Wiley and Sons (Asia) P. Ltd., 2002. 2. R.G. Bartle and D. R Sherbert, Introduction to Real Analysis, John Wiley and Sons (Asia) P. Ltd., 2000. 3. E. Fischer, Intermediate Real Analysis, Springer Verlag, 1983. 4. K.A. Ross, Elementary Analysis- The Theory of Calculus Series- Undergraduate Texts in Mathematics, Springer Verlag, 2003.
Algebra	1. John B. Fraleigh, A First Course in Abstract Algebra, 7th Ed., Pearson, 2002. 2. M. Artin, Abstract Algebra, 2nd Ed., Pearson, 2011. 3. Joseph A Gallian, Contemporary Abstract Algebra, 4th Ed., Narosa, 1999. 4. George E Andrews, Number Theory, Hindustan Publishing Corporation, 1984.
Matrices	1. A.I. Kostrikin, Introduction to Algebra, Springer Verlag, 1984. 2. S. H. Friedberg, A. L. Insel and L. E. Spence, Linear Algebra, Prentice Hall of India Pvt. Ltd., New Delhi, 2004. 3. Richard Bronson, Theory and Problems of Matrix Operations, Tata McGraw Hill, 1989.
Linear Algebra	1. Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence, Linear Algebra, 4th Ed., PrenticeHall of India Pvt. Ltd., New Delhi, 2004. 2. David C. Lay, Linear Algebra and its Applications, 3rd Ed., Pearson Education Asia, Indian Reprint, 2007. 3. S. Lang, Introduction to Linear Algebra, 2nd Ed., Springer, 2005. 4. Gilbert Strang, Linear Algebra and its Applications, Thomson, 2007.
Complex Analyisis	1. James Ward Brown and Ruel V. Churchill, Complex Variables and Applications, 8th Ed., McGraw – Hill International Edition, 2009. 2. Joseph Bak and Donald J. Newman, Complex analysis, 2nd Ed., Undergraduate Texts in Mathematics, Springer-Verlag New York, Inc., New York, 1997.
Logics and Sets	1. R.P. Grimaldi, Discrete Mathematics and Combinatorial Mathematics, Pearson Education, 1998. 2. P.R. Halmos, Naive Set Theory, Springer, 1974. 3. E. Kamke, Theory of Sets, Dover Publishers, 1950.
Integral Calculus	1. G.B. Thomas and R.L. Finney, Calculus, 9th Ed., Pearson Education, Delhi, 2005. 2. H. Anton, I. Bivens and S. Davis, Calculus, John Wiley and Sons (Asia) P. Ltd., 2002.
Vector Calculus	1. G.B. Thomas and R.L. Finney, Calculus, 9th Ed., Pearson Education, Delhi, 2005. 2. H. Anton, I. Bivens and S. Davis, Calculus, John Wiley and Sons (Asia) P. Ltd. 2002. 3. P.C. Matthew’s, Vector Calculus, Springer Verlag London Limited, 1998.
Probability and Statistics	1. Robert V. Hogg, Joseph W. McKean and Allen T. Craig, Introduction to Mathematical Statistics, Pearson Education, Asia, 2007. 2. Irwin Miller and Marylees Miller, John E. Freund, Mathematical Statistics with Application, 7th Ed., Pearson Education, Asia, 2006. 3. Sheldon Ross, Introduction to Probability Model, 9th Ed., Academic Press, Indian Reprint, 2007.

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Top Colleges for BSc Mathematics

After completing a BSc in Mathematics at a reputable university, candidates can apply for entry-level positions that are plentifully available across a variety of industries. The chances of landing a lucrative career can increase if candidates enrol in a professional programme or a master's degree in specialisation. The top BSc Mathematics colleges are given in the table below.

Top Government Colleges for BSc Mathematics

Candidates can check the top popular BSc government colleges that offer BSc Mathematics in the table below. Candidates can also check out BSc Mathematics fees for every popular college mentioned below:

College Name	Total Fees (in INR)
Banaras Hindu University	17 K
Delhi University	11 K
Jamia Millia Islamia	23 K
Panjab University	41 K - 96 K
Cochin University of Science and Technology, Kochi	54 K
Guru Nanak Dev University	3 L

Top Private Colleges for BSc Mathematics

Candidates can check the top popular BSc private colleges that offer BSc Mathematics in the table below. Candidates can also check out BSc Mathematics fees for every popular college mentioned below:

Particulars	Details
VIT Vellore	4 L
Amity University, Noida	4 L - 5 L
Chandigarh University	2 L
SRM Institute of Science and Technology, Chennai	2 L
BITS Pilani	20 L
SASTRA (Deemed to be University)	2 L
Kalasalingam Academy of Research and Education	90 K
LPU - Lovely Professional University	5 L
Srinivasa Ramanujan Center, Shanmugha Arts, Science, Technology and Research Academy	1 L

Note: The fee given above is a range of all levels of Mathematics courses such as UG, PG, PhD and Diploma.

Top World BSc Maths Colleges

Here's a table listing some of the top colleges/universities in the world for pursuing a BSc in Mathematics or equivalent undergraduate mathematics programs, based on global reputation and academic excellence:

University	Country	Program Highlights	World Ranking (QS 2024 - Math)
Massachusetts Institute of Technology (MIT)	USA	Strong focus on pure & applied math, research-driven	1
Harvard University	USA	Theoretical and interdisciplinary math focus	2
Stanford University	USA	Emphasis on innovation, tech integration	3
University of Cambridge	UK	Famous Mathematical Tripos program	4
University of Oxford	UK	Rigorous mathematical curriculum, long tradition	5
Princeton University	USA	Theoretical math, home of many Fields Medalists	6
University of California, Berkeley (UC Berkeley)	USA	Strong research opportunities, applied and pure math	7
ETH Zurich	Switzerland	Technical focus, strong in applied mathematics	8
University of Chicago	USA	Theoretical foundation with interdisciplinary options	9
Imperial College London	UK	Emphasis on mathematical sciences and computing	10

These universities are highly competitive, and admissions generally require exceptional academic performance, strong math background, standardized test scores (SAT/ACT, or equivalent), and sometimes interviews or subject tests.

BSc Maths Entrance Exam 2026

The admission test requirements for BSc Mathematics are fully dependent on the conducting body and vary as well. To be admitted to the BSc Maths, candidates must take the entrance tests listed below and pass them. Candidates should be aware that each college may have a different admissions and entrance exam method. But applicants must follow the regulations and pass these entrance tests in order to enroll in the BSc Mathematics program. The table below lists a few of the well-known admission tests for BSc Mathematics:

Entrance Exam Name	Exam Tentative Dates
CUET	May 2026
UPCATET	June 2026
IISER Entrance Exam (BS MS Dual Degree)	Third week May 2026
CMI Entrance Exam	May 2026
ISI Admission Test 2026	May 2026

BSc Maths Syllabus: Semester & Year Wise Syllabus, Courses & Structure