BSc Maths Syllabus 2024: Semester & Year Wise Syllabus, Courses & Structure

Have you completed Class 12 Boards or planning to do BSc Mathematics? Check out the comprehensive information related to all the queries that the BSc aspirants are facing before planning to pursue BSc mathematics courses from colleges/ universities across the nation.

Appearing/ Passout students of CLASS 12 board exams are now must be wondering about about the degree that they wanna pursue in their undergraduate course. Students who are from a science stream background or the ones who had opted for Mathematics as one of their subjects in class 12 can choose the BSc Mathematics course to further develop their interest and enhance their critical, analytical and problem-solving skills in order to have successful careers in the domain of Maths.

Also Read: CUET UG Eligibility Criteria for BSc Courses 

Before stepping for the BSc Mathematics Course, aspirants should do a small dig up about the BSc maths syllabus, course structure, eligibility criteria for enrolling in the university/ college, popular colleges and important books. This Shiksha article will provide all the important requirements that a student needs.

The study of BSc Mathematics deals with structure, change and space. Students need to meet the BSc Maths eligibility set-up in order to pursue the course. After completing BSc Mathematics, students have various options they can take up and have a promising career ahead as the scope is bright. Candidates can either build their way up in India or manage to land a dream job abroad as well.

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' 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 65 percent aggregate in their class 12 in order to pursue BSc Mathematics. 

Also Read: How to Prepare for CUET UG BSc Courses 

BSc Maths Course Scheme for Choice-Based Credit System 

Below is the proposed BSc Mathematics course (Semester-wise) system, submitted to 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
				DSE2B
				DSE3B

Also Read: What is BSc course all about? Know the full-form, eligibility & scope 

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

Also Read: Top Colleges of DU for BSc: Total Seats, Expected and Previous Cutoff 

BSc Maths Syllabus 2024

The BSc Mathematics curriculum encompasses six semesters or three years of theoretical study and is organized and diverse. Among the subjects studied in BSc Maths include algebra, integral calculus and trigonometry, advanced calculus, vector analysis and geometry, and mathematical methods. The work breadth and opportunities for those with a BSc in mathematics are highly promising due to the subject's applicability. The BSc Mathematics program includes comprehensive coverage of fields similar to mathematics, such as computer science and statistics. The following topics of BSc Mathematics subjects are covered in brief: 

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.

Also Read: BSc Physics Syllabus: Semester & Year Wise Syllabus, Courses & Structure 

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. 

BSc Maths Entrance Exam 2024

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:

Exam Name	Exam Dates	Exam Details
CUET	Exam Dates are yet to be announced for the 2025 academic cycle	Central University Entrance Test is referred to as CUET. It is a nationwide entrance exam for all participating institutions' UG programmes that are administered by NTA.
UPCATET	Exam Dates are yet to be announced for the 2025 academic cycle	The UP Combined Agriculture and Technology Entrance Test (UPCATET) is an entrance examination held to admit applicants with ties to the state of Uttar Pradesh to various UG and PG programmes provided by various participating universities.
IISER Entrance Exam (BS MS Dual Degree)	Exam Dates are yet to be announced for the 2025 academic cycle	Indian Institutes of Science Education and Research (IISERs) conduct an entrance exam in order to provide admission to candidates in the five-year-long BS-MS dual degree programme offered by them. On the basis of a candidate’s score in the IISER entrance exam (also known as IISER aptitude test), he/she can secure admission at IISER located in Berhampur, Bhopal, Kolkata, Mohali, Pune, Thiruvananthapuram, or Tirupati.

BSc Maths Syllabus of Top Colleges

BSc Mathematics syllabus differ in some subjects of the course from one to college to another college. But all the colleges acroos the nation follows the direct rules and principles mentioned by the University Grants Commission, UGC, New Delhi. Here in this section, canididates will get the BSc Maths syllabus of some famous reputed institutes in order to get the depth comparison between BSc Maths syllabus of dufferent insititutions.

BSc Maths Syllabus- Delhi University

Recognised as an 'Institute of Excellence' by the UGC, the University of Delhi (also known as DU or Delhi University) is listed among the country's most prestigious educational institutions. Established in 1922, Delhi Univerity has grown into one of India's largest universities with more than 6 lakh students under UG, PG, certificate, diploma, PG diploma and distance programmes. It is ranked 11 and 22 under the 'University' and 'Overall' categories by the NIRF 2024 Rankings, respectively. 

Downlaod- BSc Maths Syllabus- Delhi University (DU)

BSc Maths Syllabus- Banaras Hindu University

BHU popular courses include BTech, BSc, BA, MBBS, LLB, MSc and MA among others. These programs are popular for a variety of reasons, including their high academic standards, strong faculty, and excellent placement opportunities. BHU is one of the top universities in India, and these courses are known for their rigorous academic standards. One of the reasons for why BHU programmes are nationally-renowned is its eminent faculty. BHU has a strong faculty of experienced and dedicated professors. This ensures that students receive high-quality instruction from experts in their field.

Downlaod- Bsc Maths Syllabus- Banaras Hindu University (BHU)

BSc Maths Syllabus- Panjab University

Established in 1882 as the University of the Panjab Lahore (in Pakistan now), Panjab University was relocated to Chandigarh in 1947, where the university was split between Pakistan and India. Punjab University (or PUCHD) is a Central and State Government-funded University. The university has been accredited with 3.35 CGPA on a four-point scale with 'A' Grade by the NAAC.

Download- BSc Maths Syllabus- Punjab University

BSc Maths Syllabus- Jamia Milia Islamia, News Delhi

Jamia Milia Islamia, also known as JMI is a central university located in Delhi. It was established in 1920 and is recognised by the UGC. It is a member of the Association of Indian Universities (AIU) and is accredited with an “A” Grade by the National Assessment and Accreditation Council (NAAC). Jamia Milia Islamia has been ranked 3 under the University category with a score of 67.73.

Download- BSc Maths Syllabus- Jamia Milia Islamia, New_Delhi

BSc Maths Syllabus- IGNOU, News Delhi

Indira Gandhi National Open University (popularly known as IGNOU or IGNOU University), established in 1985, is considered one of the prominent names for distance/ part-time education in India. Indira Gandhi National Open University Delhi began by offering two programmes in 1987, with a strength of approximately 4,500 students. Today, the university serves more than three million students in India and abroad through its 21 schools, a network of 67 regional centres, and 29 overseas partner institutions. IGNOU offers more than 200 programmes at certificate, diploma, degree and doctoral levels. 

BSc Subject Code	Name of the subject
MTE - 01	Calculus
MTE - 02	Linear Algebra
MTE - 03	Mathematical Methods
MTE - 04	Elementary Algebra
MTE - 05	Analytical Geometry
MTE - 06	Abstract Algebra
MTE - 07	Advanced Calculus
MTE - 08	Differential Equations
MTE - 09	Real Analysis
MTE - 10	Numerical Analysis
MTE - 11	Probability and Statistics
MTE - 12	Linear Programming
MTE - 13	Discrete Mathematics
MTE - 14	Mathematical Modelling

The study of BSc Mathematics deals with structure, change and space. Students need to meet the BSc Maths eligibility set-up in order to pursue the course. After completing BSc Mathematics, students have various options they can take up and have a promising career ahead as the scope is bright. Candidates can either build their way up in India or manage to land a dream job abroad as well.

BSc Mathematics: Career Opportunities

Candidates who have completed their BSc degree in Mathematics or are in the final year, must be curious and wondering about the career prospectus of BSc Maths. In this section, candidates will be able to understand and get information about the career options available to them after completing their BSc Degree:

Candidates can also check the job opportunities in both the private and government sectors from here: Job Opportunities & Salary Offered After Completing BSc Degree 

Career Options Available after BSc Mathematics
Core (Mathematics) Related Fields	Generic Fields	Higher studies
Data Scientist/Analyst: Analyze large datasets to extract meaningful insights. Statistician: Collect, analyze, interpret, and present data to solve problems. Actuary: Assess financial risk using statistical methods. Operational Researcher: Apply mathematical models to optimize complex systems. Economist: Analyze economic trends and develop policies. Mathematician: Conduct research in pure or applied mathematics	Finance: Investment banking, financial analysis, risk management. Teaching: Become a math teacher at schools, colleges, or universities.  IT: Software development, data engineering, machine learning. Research: Work in research organizations or government labs. Meteorology: Utilize mathematical models to predict weather patterns	Mathematics Statistics Operations Research Applied Mathematics Financial Mathematics

Read More: 

• BSc Maths Syllabus
• Top 10 Universities in India 2024: Check NIRF Ranking
• Job Opportunities & Salary Offered After Completing BSc Degree