Maths Syllabus & Subjects 2023: Semester-wise List, Top Colleges Syllabus PDF
Akansha BishtContent Writer
Mathematics is a branch of pure science which deals with the study of numbers, shapes, formulas, equations, theorems, quantities and their applications in branches such as Physics and Engineering. Mathematics emerged from the fundamental practices of counting numbers, measuring quantities and drawing and depicting shapes of various objects around us. It consists of other sub-branches such as Algebra, Geometry, Number theory, Real analysis, Set theory etc. It dates back to 300BC, when Greek scholars such as Aristotle, Euclid, Pythagoras described the concepts of number system and geometry.
Mathematics is a popular course which finds its applications across all fields of science. Therefore, it is offered as a core subject in almost all engineering and science disciplines such as Physics, Geology, Chemistry etc. Mathematics is also applied in the science of Statistics which finds usage in fields such as finance, investment, chartered accountancy, management etc. The major application of Mathematics is also seen in computing or computer science and information theory. It is applied in preparing models for pollution control, climate change assessment and population growth predictions. The beauty of this subject can be seen from the fact that it also finds its application in social science such as Economics, Psychology, Sociology as well as Earth Sciences.
Therefore, Mathematics is a widely chosen subject across the country with many top institutes offering courses in undergraduate, postgraduate and doctoral levels.
Mathematics- Important Facts
- Course Duration- Undergraduate courses or B.Sc in Mathematics is a three-year course, M.Sc or postgraduate course in Mathematics is a two-year course and Doctoral course in Mathematics of Ph.D in Mathematics is a three-year course. Candidates must meet the required eligibility criteria to be eligible to pursue the above courses.
- Eligibility Criteria- To pursue undergraduate course, candidate must have completed Class 12th from recognised board and must have studied Mathematics as a compulsory subject. For postgraduate courses, candidate should have completed graduation in Mathematics/Statistics from a recognised board. For pursuing doctoral programme, candidate must have completed Master’s in Mathematics and have an inclination towards research.
- Course Fees- The course fee for Sc Mathematics ranges from INR 3,000 to 1 lakh per annum, fees for M.Sc ranges from INR 3,000 to 50,000 per annum.
- Scope in India- Mathematics is a popular choice amongst candidates providing wide range of job opportunities in the field of school and university teaching, engineering, banking and finance, securities and investment, insurance and industrial sector. Graduates can work as teachers and professors after completing or can pursue higher education for a career in academics or research.
- Research in Mathematics- Many top institutes in country promote research in the field of Mathematics on areas such as Bio-Mathematics, Pure Mathematics, Applied and Computational Mathematics and Operations Research. Candidates can either pursue Ph.D or conduct independent research in these fields. Some of the top research institutes include Tata Institute of Fundamental Research, Chennai Mathematical Institute, Indian Statistical Institute, Indian Institute of Science etc.
Read More: Mathematics Overview
Mathematics Syllabus
Core Subjects
| UG Program |
|
|---|---|
| Subject |
Details |
| Calculus |
Calculus comprises of derivatives for graphics, sketching and tracing curves, calculation of volume and area and the application of vector calculus. |
| Algebra |
It introduces candidates to the theory of complex numbers, the equivalence relations and the basic number theory. It also explains the Row Echelon Form of Matrices. |
| Real Analysis |
The course defines the real number system, its properties, sequences and the application of infinite series. |
| Differential Equations |
Students learn about the basics of differential equations, their application in population growth models and their analysis. |
| Theory of Real Functions |
It deals with the concepts of limits of functions, properties of continuous functions, application of derivability and Taylor’s theorem. |
| Group Theory |
The course explains the elementary properties of groups and subgroups, cyclic and permutation groups and the derivation of Lagrange’s theorem. |
| Ring Theory and Linear Algebra |
The course introduces learners to the ring theory, ring homomorphism, vector spaces and linear transformations. |
| Metric Spaces |
Metric Spaces deals with its topology, uniform continuity, automorphism, group action, connectedness and compactness of groups. |
| Multivariate Calculus |
The subject deals with the calculus of functions with multi-variables, double and triple integrals and the theorems of Green, Stokes and Gauss. |
| PG Program |
|
|---|---|
| Subject |
Details |
| Functional Analysis |
This course deals with the concepts of Banach Contracton Principle, Hilbert Spaces, Pythagorean Law, Monotone Functions and Lebesgue Outer Measure. |
| Linear Algebra |
Linear Algebra consists of principles of vector spaces, Eigen vectors, Cayley-Hamilton theorem, homomorphism of group and commutative rings. |
| Elements of General Topology |
The course deals with the topological spaces and application of Kuratowski closure operators in complex analysis. |
| Operations Research |
This is an introductory course on Operations Research and preparation of mathematical formulation of any assignment problem. |
| Differential Geometry |
The course deals with the integral of any partial differential equation and application of Gauss Formula in differential geometry. |
| Set Theory |
An interesting module which introduces the Zorn’s Lemma and Hausdorff Maximality principle and the Cartesian product of sets. |
| Mathematical Logic |
The course deals with the statement calculus and arguments to for proving validity and consequences. |
Elective Subjects
| UG Program | |
|---|---|
| Subject |
Details |
| Numerical Analysis |
The course introduces methods to solve algebraic, linear and transcendental equations. It also deals with interpolation and numerical differentiation and integration. |
| Mathematical Modelling and Graph Theory |
Students learn about the power series solutions, Laplace Transforms, Monte Carlo Simulations and the application of Graph Theory. |
| C++ Programming for Mathematics |
The course deals with the basics of C++, working with containers, templates, structured data and usage of mathematical libraries and packages. |
| Probability Theory and Statistics |
Learners understand the probability functions, univariate discrete and continuous distributions, bivariate distributions and the application of central limit theorem. |
| Discrete Mathematics |
The course deals with ordered sets, lattices, graph theory and the application of Boolean Algebra. |
| Mathematical Finance |
Mathematical Finance deals with the application of mathematics in financial systems, types of interest rates and trading strategies. |
| Biomathematics |
It is an interesting course which introduces the concept of bio-mathematical models and modelling of molecular evolution and genetics. |
| Number Theory |
The course deals with the concepts of distribution of primes, primitive roots and the quadratic reciprocity law. |
| PG Program | |
|---|---|
| Subject | Description |
| Differential Geometry of Manifolds |
It introduces to the principles of topological groups, tangent spaces and exterior algebra. |
|
Advanced Functional Analysis |
The course deals with hyperplanes, types of sets and vector spaces. |
| Advanced Real Analysis |
It deals with the upper and lower limits of a real function, the properties and functions of differential equations and various types of functions. |
| Lattice Theory |
Lattice theory enumerates the Fourier series, Fejer’s Theorem, Dirichlet’s and Fatou’s theorem and their applicability. |
| Harmonic Analysis |
The course deals with the conjugate function series and the approximate identities. |
| Advanced Operations Research |
It is an advanced course in Operations Research which explains non-linear, constrained and unconstrained optimization. |
| Measure and Integration |
The course deals with the algebra pf sets, types of measurable functions, process of approximation and the properties of integrals. |
Popular Books and Authors for Mathematics
The popular books prescribed across universities for Mathematics courses are as follows:
| Book |
Authors |
Description |
|---|---|---|
| Calculus |
Howard Anton, Stephen Davis |
The authors write on the polynomials, logarithms, rational functionals with the help of examples and exercises. |
| Linear Algebra and its Applications |
David Lay, R Steven, Judi McDonald |
The book comprehensively deals with the concepts of spanning, vector space, eigenvalues and least squares. |
| Introduction to Real Analysis |
Robert G Bartle, Donald R Sherbet |
It delves into the concept of real analysis and its application to engineering, computer science and other physical sciences. |
| Differential Equations |
Shepley Ross |
Differential Equations deals is a treatise on the methods of solving differential equations and analyses of various differential models. |
| An Introduction to the Theory of Groups |
Joseph Rotman |
A celebrated work on linear and abstract algebra and other structures such as vector spaces and rings. |
| Basic Multivariate Calculus |
Marsden, Weinstein |
It delves into the equations having various variables, double and triple integrals with the help of comprehensive examples. |
| Elementary Number Theory |
David Burton |
It is a popular book prescribed for Mathematics and Computer Science students providing information on the classical number theory. |
Entrance Exams for Mathematics
- CUET PG- Central University Entrance Test is an all-India entrance exam conducted by National Testing Agency for admissions to postgraduate courses. This is a computer-based exam for admissions to top central and state universities in India for M.Sc Mathematics course.
- CUET UG- Central University Entrance Test is an all-India entrance exam conducted by National Testing Agency for admissions to undergraduate courses. This is a computer-based exam for admissions to top central and state universities in India for B.Sc Mathematics course. Most of the colleges have started to consider this score for admissions.
- IIT JAM- Joint Admission Test is conducted by Indian Institute of Technology for admissions to M.Sc courses across top IITs. This exam is highly competitive and tough which thousands of test-takers across India. It also provides admissions to integrated M.Sc- P.hD courses in IITs and IISc.
- IISER Entrance Exam- Indian Institute of Science Education and Research conducts this prestigious exam for admissions to the BS-MS dual degree programme in Basic Sciences.
- TIFR GS- Tata Institute of Fundamental Research conducts TIFR GS entrance exam for admissions to integrated 5-year MSc courses and Ph.D. courses. After clearing the entrance, candidates proceed for interview round and final selection is made on the basis of scores of interviews.
Distance Programme for Mathematics
Distance programmes are very popular for students who are not able to pursue full-time courses, can pursue distance education. Due to flexibility, candidates can finish the course within three years or maximum within six years.
For pursuing undergraduate course, candidate must have completed 10+2 or equivalent qualification and must have studied Mathematics as a compulsory subject. For postgraduate course, candidate must be a graduate in Mathematics or studied Mathematics in graduation level from a recognised board. The course fee ranges between INR 6000- INR 15,000 per annum. Some of the top institutes providing distance education programmes in Mathematics are as follows:
- IGNOU
- OSOU
- Savitribai Phule Pune University School of Open Learning
- Directorate of Distance Education, Osmania University
- LPU Online
- Directorate of Distance Education, Kurukshetra University
Top Colleges for Mathematics
The top colleges offering various courses in Mathematics are as follows:
| College | Syllabus |
|---|---|
| Christ University | Syllabus |
| Mount Carmel College | Syllabus |
| ICFAI University | Syllabus |
| Indus University | Syllabus |
| Kalinga University | Syllabus |
| Central University of Rajasthan | Syllabus |
| Deshbandhu College, Delhi University | Syllabus |
| Kalindi College, Delhi University | Syllabus |
| Dyal Singh College, Delhi University | Syllabus |
| St. Stephen's College, Delhi University | Syllabus |
Also Read: Top Colleges for Mathematics
Frequently Asked Questions (FAQs) on Mathematics Syllabus
Q. Why is Mathematics popular course?
Q. What is the course curriculum for Mathematics?
Q. What are the common entrance exams for Mathematics?
- CUET UG
- CUET PG
- IIT JAM
- IISER entrance exam
- TIFR GS
- APEAMCET
Q. What are the popular colleges offering Mathematics?
- Delhi University
- Christ University
- Banaras Hindu University
- Tata Institute of Fundamental Research
- Chennai Mathematical Institute
Q. Is distance programme in Mathematics course valid?
- IGNOU
- DDE, Osmania University
- DDE, Kurukshetra University
Q. What are the specialisations offered in Mathematics?
- Real Analysis
- Laplace Systems
- Group Theory
- Applied Mathematics
- Operations Research
- Set Theory
Q. What is the fee structure for Mathematics?
Q. What are the various core subjects offered under Mathematics?
- Differential Equations
- Group Theory
- Metric Spaces
- Multivariate Calculus
- Linear Algebra
- Differential Geometry
- Set Theory
Q. What are the various elective subjects offered under Mathematics?
- Differential Geometry of Manifolds
- Lattice Theory
- Number Theory
- Biomathematics
- Probability Theory and Statistics
- Harmonic Analysis
- Measure and Integration
Q. What is the application of Mathematics course?
Q. What is the eligibility for pursuing Mathematics?
- Undergraduate course- Must have passed Class 12th from recognised board with Mathematics as a compulsory subject.
- Postgraduate course- Candidate should have completed Bachelor's in Mathematics from a recognised university.
- Doctoral course- Candidate should have pursued Master's course from a recognised university before applying for the doctoral programme.
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Popular Maths Course Colleges in India
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Most Popular Courses
Popular Courses
- B.Sc. (Hons.) in MathematicsBanaras Hindu University
- M.Sc. in MathematicsBanaras Hindu University
- B.Sc. (Hons.) in Applied MathematicsJamia Millia Islamia
- B.Sc. (Hons.) in MathematicsJamia Millia Islamia
- M.Sc. in Mathematics with Computer ScienceJamia Millia Islamia
- M.Sc. in MathematicsHansraj College, University of Delhi
- B.Sc. (Hons.) in MathematicsHansraj College, University of Delhi
- B.Sc. (Hons.) in MathematicsHindu College, University of Delhi
- M.Sc. in Operational ResearchHindu College, University of Delhi
- B.Sc. (Hons.) in MathematicsMiranda House, University of Delhi
Popular Maths Course UG Courses
UG Courses
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3771 Colleges
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189 Colleges
- B.Sc(Hons.)
34 Colleges
- B.Ed
25 Colleges
- UG Diploma
10 Colleges
Popular Maths Course PG Courses
PG Courses
- M.Sc.
2302 Colleges
- M.A.
79 Colleges
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7 Colleges
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4 Colleges
- Master of Surgery
2 Colleges
News & Updates
Student Forum
Anything you would want to ask experts?Answered 3 weeks ago
BIT Mesra has a seat intake of 77 for the BSc in Mathematics and Computing programme. The seat allotment in this course is done based on JEE scores. In addition, 50% of the seats are reserved for candidates belonging to the state of Jharkhand and 50% for other state candidates. The mentioned seat in
A
Beginner-Level 5
Answered a month ago
The key highlights of IIT Mandi placements for its MSc in Applied Mathematics Class of 2022, 2023 and 2024 are tabulated below:
Year | Number of students sitting for campus placement | Number of students placed | Median Salary (in INR LPA) |
|---|---|---|---|
2020-22 | 20 | 16 | 12 |
2021-23 | 36 | 29 | 8 |
2022-24 | 47 | 14 | 7.2 |
Contributor-Level 10
Answered a month ago
- Global perspectiveStudying mathematics in a different country can help you understand how it's used and taught around the world.
- Language skillsMany universities require students to demonstrate proficiency in the local language
A
Contributor-Level 10
Answered a month ago
Students pursuing an BSc in Mathematics have access to a variety of career options. You can choose to pursue further education after finishing the course. You can also look for jobs in various sectors. The following are some of the most common industries in which BSc Mathematics graduates can find e
A
Contributor-Level 10
Answered a month ago
The elective subjects highlight the important career skills that candidates require to excel in the course and career and can be chosen based on the candidate's area of interest, the scope for higher education, etc. Below is a list of electives offered in BSc Mathematics:
- Analytical Geometry
- Vector Ca
A
Contributor-Level 10
Answered a month ago
In DU, admissions are done on the basis of Best Four Subjects' Marks or BFS Marks. BFS is calculated by choosing best three marks of your subjects of 10+2 and including English/Hindi.
Now, admission in Maths (H) in DU depends upon your category and the college you wish to go for. The following are mi
A
Contributor-Level 10
Answered a month ago
The counseling process for a BSc in Mathematics can include the following steps:
- Exam: Candidates apply for counseling after receiving their entrance exam results. Exam bodies publish the final answer key, which is used to calculate the results.
- University cut-off lists: Participating universities pub
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Contributor-Level 10
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How many seats does BIT Mesra have for integrated BSc in Mathematics and Computing?