MSc Maths Syllabus trains students with highly advanced core mathematical subjects like calculus, geometry, algebra, statistics etc. The students are trained in analytical skills with problem solving interests. MSc Maths Syllabus contains independent research and lecture-based modules.
MSc Maths helps students to become skilled in areas such as data analysis, corporate and academic fields, banking and financial analysis etc. MSc Maths Syllabus contains subjects like Algebra, Topology, Real Analysis, Complex Analysis, Ordinary Differential Equations, Functional Analysis etc
See Also: How to become a Mathematician?
The students will have to apply for 83 credits in total over the 2 years. The core subjects have 47 credits assigned, program electives have 21 credits, 3 credits for open electives and 12 credits for Dissertations. Some of the elective subjects of the MSc Maths Syllabus are Number Theory, Algebra, Real Analysis, Linear Programming, Fluid Mechanism etc
See Also:
Table of Contents
3.1 First Semester
3.2 Second Semester
3.3 Third Semester
3.4 Fourth Semester
- MSc Math Entrance Exam Syllabus
- MSc Maths honors Syllabus
- MSc Applied Maths Syllabus
- MSc Maths Books
7.1 First Year
7.2 Second Year
- DU MSc Maths Entrance Syllabus
- MSc Maths Syllabus in BITS Pilani
- MSc Maths Syllabus in Calcutta University
- MSc Maths Syllabus MG University
- IGNOU MSc Maths Syllabus
- MSc MathsTeaching Methodology and Techniques
13.1 MSc Math Projects
MSc Maths Course Details
| Course Name | Master of Science in Maths |
| Course Level | Postgraduate Course |
| MSc Maths Duration | 2 years |
| MSc Maths Admission Process | Entrance exam/merit basis. |
| MSc Maths Top Entrance Exam | IIT JAM, CUCET, NEST, CUCET, etc. |
| MSc Maths Eligibility | Minimum of 50% score in aggregate in graduation with English and Math as compulsory subjects. |
| MSc Maths Top Colleges | Miranda House, Hindu College, Madras Christian College, Loyola College, Hans Raj College, Stella Maris College, and Sri Venkateswara College. |
| MSc Maths Fees | INR 30,000 - INR 4,00,000 |
MSc Maths Syllabus
| Semester I | Semester II |
|---|---|
| Algebra - I | Algebra - II |
| Topology - I | Topology - II |
| Real Analysis | Complex Analysis |
| Ordinary Differential Equations | Functional Analysis |
| Mathematicians and the History of Maths | Partial Differential Equations |
| Discrete Maths | Mathematical Modelling and Numerical Analysis - I |
| Semester III | Semester IV |
| Differential Geometry | Measure And Integration |
| Mathematical Methods | Elective IV |
| Numerical Analysis - II | Elective V |
| Fluid Mechanics | Elective VI |
| Elective I | - |
| Elective II | |
| Elective III |
MSc Maths Semester Wise Syllabus
The semester wise syllabus helps students understand the subjects that they will be studying.
MSc Maths First Semester Subjects
- Algebra: Algebra deals with symbols and the rules for manipulating those symbols, which represent quantities without fixed values, called variables
- Topology: The arrangement of nodes and connections within a network is called topology. It explains how a network is connected, and how the information in the network flows.
- Real Analysis: Real Analysis formalizes the study of numbers and functions and investigates important concepts such as limits and continuity.
See Also: Maths Courses
MSc Maths Second Semester Subjects
- Complex Analysis: Complex analysis is the study of complex numbers together with their derivatives, manipulation, and other properties. Complex analysis is an extremely powerful tool with an unexpectedly large number of practical applications to the solution of physical problems.
- Functional Analysis: Functional analysis is a model of a psychological formulation designed to understand the functions of human behavior. It has its origins in behavioral psychology. At its core, the functional analysis assumes that all behavior is learned and that all behaviors serve some purpose.
- Partial Differential Equations: A partial differential equation is one of the types of differential equations, it contains unknown multi-variables with their partial derivatives.
See Also: Quantitative Modelling Courses
MSc Maths Third Semester Subjects
- Differential Geometry: Differential geometry studies the geometry of smooth shapes and smooth spaces or smooth manifolds.
- Mathematical Methods: Mathematical methods include the Finite Difference Method, Numerical Model, Electromagnetism, Boundary Condition, Continuum, Hydrodynamics, Water Distribution System and Genetic Algorithm.
- Numerical Analysis: Numerical analysis solves continuous problems using numeric approximation. It involves designing methods, useful in cases where the exact solution is impossible to calculate.
See Also: Numerology Courses
MSc Maths Fourth Semester Subjects
- Measure And Integration: Measure and Integration studies that smaller functions have smaller integrals, and that two integrable functions having the same integral over every set are almost equal.
MSc Math Entrance Exam Syllabus
| PART A | English |
| General Awareness | |
| Mathematical Aptitude and Analytical Skills | |
| PART B | Algebra |
| Real Analysis | |
| Complex Analysis | |
| Integral Calculus | |
| Differential Equations | |
| Vector Calculus | |
| Linear Programming |
MSc Maths Honors Syllabus
MSc Maths can be studied with honours. Here students take up Maths as the honours subjects and have various pass subjects associated with it.
| Semester I | Semester II |
|---|---|
| Algebra and Calculus | Discrete Maths-II |
| Discrete Maths and Descriptive Statistics | Number Theory and Trigonometry |
| Computer Fundamentals and MS Office | Ordinary Differential Equations |
| Solid Geometry | Programming in Visual Basic |
| English | Regression Analysis and Probability |
| Vector Calculus | |
| English-II | |
| Semester III | Semester IV |
| Data Structures using C | Groups and Rings |
| Programming in C and Numerical Methods | Integral Equations |
| Elementary Inference | Real Analysis and Numerical Analysis |
| Hydrostatics | Methods of Applied Maths |
| Sequences and Series | Practical / Computational work to be performed on computers using EXCEL / SPSS) |
| Special Functions and Integral Transforms | - |
MSc Applied Maths Syllabus
MSc Applied Maths is a branch of Maths postgraduate course. The subjects included focuses mainly on applied Maths.
| Semester I | Semester II |
|---|---|
| Applied Maths | Topology |
| Linear Algebra | Functional Analysis |
| Discrete Maths Structure | Rings and Modules 1 |
| Elements of Prob. and Statistics. | Measures and Integration |
| Complex Analysis | Ordinary Differential Equations |
| Real Analysis 1 | |
| C programming | |
| Linera Programming | |
| Real Analysis 2 | |
| Semester III | Semester IV |
| Functional Analysis | Dynamical Systems |
| Numerical Analysis | Fluid Mechanics |
| Mathematical Methods | Advance courses on differential equations |
| Non- Linear Programming | Classical Mechanics |
MSc Maths Books
Students need to check the books for each year because a good book with help them understand all the concepts of MSc Maths.
MSc Maths First Year Books
| Name of the Book | Author |
|---|---|
| Topics in Algebra, | I.N. Herstein |
| Linear Algebra A Geometrical Approach, | S. Kumaresan |
| Introduction to Real Analysis | Robert G. Bartle Donald R. Sherbert |
| Introduction to Graph Theory | Douglas B West |
| Abstract Algebra | David S Dummit, Richard M Foote |
| Introduction to Topology and Modern Analysis | George F. Simmons |
| The Quick Python Book, | Vernon L. Ceder |
| The elements of Complex Analysis, | Chaudhary. B |
| Measure Theory and Integration | G. de Barra |
MSc Maths Second Year Books
| Name of the Book | Author |
|---|---|
| Partial Differential Equations | Phoolan Prasad and Renuka Ravindran |
| Multivariate Analysis | Limaye Balmohan Vishnu |
| Functional Analysis | Somasundaram. D |
| Operations Research: Theory and Applications | J.K. Sharma |
| Elementary number Theory, | David M. Burton |
| Differential Manifolds | Serge Lang |
| Combinatorics theory and applications | V Krishnamoorthy |
| Fundamentals of Mathematical Statistics | S.C Gupta and V.K Kapoor |
| Applied Abstract Algebra | R-Lidi, G. Pliz |
| Differential Equations | Shepley L. Ross |
DU MSc Maths Entrance Syllabus
| Topics |
|---|
| Elementary set theory, Finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property, supremum, infimum. |
| Sequence and series, Covergence limsup, liminf. |
| Bolzano Weierstrass theorem, Heine Borel theorem. |
| Continuity, Uniform continuity, Intermediate value theorem, Differentiability, Mean value theorem, Maclaurin’s theorem and series, Taylor’s series. |
| Sequences and series of functions, Uniform convergence. |
| Riemann sums and Riemann integral, Improper integrals. Monotonic functions, Types of discontinuity. |
| Metric spaces, Completeness, Total boundedness, Separability, Compactness, Connectedness. |
| Functions of several variables,Directional derivative, Partial derivative. |
| Eigenvalues and eigenvectors of matrices, Cayley-Hamilton theorem. |
| Divisibility in Z, congruences, Chinese remainder theorem, Euler’s ?- function |
| Groups, Subgroups, Normal subgroups, Quotient groups, Homomorphisms, Cyclic groups, Cayley’s theorem, Class equations, Sylow theorems. |
| Vector spaces, Subspaces, Linear dependence, Basis, Dimension, Algebra of linear transformations, Matrix representation of linear transformations, Change of basis, Inner product spaces, Orthonormal basis |
| Rings,fields, Ideals, Prime and Maximal ideals, Quotient rings, Unique factorization domain, Principal ideal domain, Euclidean domain, Polynomial rings and irreducibility criteria. |
| Existence and Uniqueness of solutions of initial value problems for first order ordinary differential equations, singular solutions of first order ordinary differential equations, System of first order ordinary differential equations, General theory of homogeneous and non-homogeneous linear ordinary differential equations, Variation of parameters, Sturm Liouville boundary value problem, Green’s function. |
| Lagrange and Charpit methods for solving first order PDEs, Cauchy problem for first order PDEs, Classification of second order PDEs, General solution of higher order PDEs with constant coefficients, Method of separation of variables for laplace. Heat and Wave equation. |
| Numerical solutions of algebraic equations, Method of iteration and Newton-Raphson method, Rate of convergence, Solution of systems of linear algebraic equations using Guass elimination and Guass-Seidel method, Finite differences, Lagrange, Hermite and Spline interpolation, Numerical integration, Numerical solutions of ODEs using Picard, Euler, modified Euler and second order Runge- Kutta methods. |
BITS Pilani M.Sc. Maths Syllabus
BITS Pilani is one the leading colleges for technical subjects. The syllabus of MSc Maths in BITS Pilani is mentioned below:
| Semester I | Semester II |
|---|---|
| General Biology | Probability and Statistics |
| Chemistry I | Chemistry II |
| thermodynamics | Maths II |
| Maths I | Physics II |
| Physics I | workshop practice |
| Engineering Graphics | Computer Programming |
| semester III | Semester IV |
| Electrical Sciences I | Structure and Properties of Material |
| Maths III | Electrical Sciences II |
| Computer Programming II | Measurement Techniques II |
| Measurement Techniques I | Technical Report Writing |
| Principles of Management | Two Electives |
| One Elective | - |
Practice School I
| Algebra I | Algebra II |
| Elementary Real Analysis | Measure and Integration |
| Introduction to Topology | Intro to Functional Analysis |
| Graphs and Networks | Differential Geometry |
| Optimization | Numerical ANalysis |
| Data Processing | Operations Research |
| Six electives Courses | Practice School II Or Dissertation |
Electives
| Discrete Structures for Computer Sciences | Algebraic & Differential Topology |
| Fuzzy Logic and Applications | Distribution Theory |
| Complex Analysis | Discrete Mathematical Structures |
| Concepts of Geometry | Ordinary Differential Equations |
| Topological Groups | Partial Differential Equations |
| Combinatorial Maths | Integral Equations |
| Non-Linear Optimisation | Commutative Algebra |
Calcutta University M.Sc. Maths Syllabus
Calcutta University is one of the oldest Universities in India. The MSc Maths Syllabus at Calcutta University is mentioned below:
| Semester I | Semester II |
|---|---|
| Group Theory | Linear Algebra |
| Ring Theory | Real Analysis- II |
| Real Analysis- I | Complex Analysis- II |
| Complex Analysis -I | General Topology -II |
| Ordinary Differential Equation | Functional Analysis |
| General Topology-I | Discrete Maths -II |
| Differential Geometry of Curves & Surfaces | Theory of Manifold |
| Discrete Maths- I | - |
| Multivariate Calculus | - |
| Semester III | Semester IV |
| Field Extension | Algebraic Topology -II |
| Algebraic Topology -I | Partial Differential Equation |
| Elective I | Computational Maths (Theory) (Choose any one of the Below)
|
| Elective II | Elective I |
| - | Elective II |
| - | Computational Maths (Practical) |
| - | Dissertation, Internal Assessment, Seminar & Grand Viva |
MSc Maths Syllabus at MG University
MG University is ranked in the top 50 Universities in India with more than 100 affiliated colleges in Kerala. The MSc Maths Syllabus in MG University is mentioned below:
| Semester I | Semester II |
|---|---|
| Abstract Algebra | Advanced Abstract Algebra |
| Linear Algebra | Advanced Topology |
| Basic Topology | Numerical Analysis with Python |
| Real Analysis | Complex Analysis |
| Graph Theory | Measure and Integration |
| Semester III | Semester IV |
| Advanced Complex Analysis | Spectral Theory |
| Partial Differential Equations | Analytic Number Theory |
| Multivariate Calculus and Integral Transforms | Elective 1 |
| Functional Analysis | Elective 2 |
| Optimization Technique | Elective 3 |
IGNOU MSc Maths Syllabus
IGNOU is the leading provider of Distance Education in India. The MSc Maths Syllabus in IGNOU is mentioned below:
| Semester I | Semester II |
|---|---|
| Programming & Data Structures | Algebra |
| Linear Algebra | Functional Analysis |
| Real Analysis | Probability and Statistics |
| Complex Analysis | - |
| Differential Equations and Numerical Solutions | |
| Semester III | Semester IV |
| Mathematical Modelling | Coding Theory |
| Graph Theory | Cryptography |
| Design & Analysis of Algorithms | Soft Computing & its Applications |
| Pattern Recognition & Image Processing | Project |
| Computer Graphics | - |
MSc Maths Teaching Methodology and Techniques
MSc Maths focuses on different aspects of Maths and commerce. Lecture, inductive, deductive, heuristic or discovery, analytic, synthetic, problem-solving, laboratory and project methods are some of the teaching methods of Maths. The problem-solving method is considered suitable for teaching Maths. It is a strategy, where the teacher demonstrates concepts and students learn by observing.
- Assignments/Viva voce
- Following course module books
- Research work
- Internships
MSc Math Projects
Maths Project propose is to help students in visualizing the concepts, theorems, principles and the underlying process involved in solving them. It also helps in improving problem-solving capability which leads to learning concepts in a fulfilling way for a lifetime. A project in maths refers to learning some topic that is not part of the curriculum.
Some of the popular project topics are:
- A Study Of Mfuzzy Subgroups And Their Level Subgroups
- A Study Of Common Fixed Point Approximations For Finite Families Of Total Asymptotically Non-Expansive Semigroup In Hyperbolic Spaces
- Images Of Maths Stakeholders In Teaching And Learning Maths At Secondary Schools In Sokoto State
MSc Maths Syllabus: FAQs
Ques. What is MSc Maths?
Ans. MSc Maths is a two-year postgraduate degree course designed to provide the knowledge of advanced Maths and incorporates reasoning, thinking, and research skills.
Ques. What are the core subjects in MSc Maths?
Ans. Some of the corse subjects of MSc Maths are:
- Algebra
- Real Analysis
- Topology
- Ordinary Differential Equations
- Discrete Maths
- Eminent Mathematicians and the History of Maths
- Complex Analysis
- Functional Analysis
- Partial Differential Equations
Ques. What are the elective subjects in MSc Maths?
Ans. Electives in MSc Maths includes:
- Electromagnetism in Special Relativity
- Rings and Modules
- The Four-Vector Formulation of Special Relativity
- Applications of Special Relativity
- Canonical Transformations
- Fluid Mechanics
Ques. What is the salary of an MSc Maths graduate?
Ans. MSc Maths Graduate can get minimum salary of INR 6 to 9 LPA for freshers.
Ques. What are the top colleges for MSc Maths?
Ans. Top colleges for MSc Maths are Miranda House, Hindu College, Madras Christian College, Loyola College, Hans Raj College, Stella Maris College, and Sri Venkateswara College.
Ques. What course can be done after MSc Maths?
Ans. Courses that can be done after MSc Maths are:
- Master of Philosophy in Applied Maths.
- Master of Philosophy in Mathematical Science.
- Master of Philosophy in Maths.
- Master of Philosophy in Maths and Statistics.
- Doctor of Philosophy in Applied Maths.
Ques. What are the Job Options after MSc Maths?
Ans. Job options after MSc Maths:
- Junior Associate Professor.
- Online Tutor.
- Junior Research Scientist.
- Mathematician.
- Market Researcher.
- Economist.
Ques. What is the eligibility criteria for admission to MSc Maths?
Ans. Candidates should have a minimum of 50% score in aggregate in graduation from any recognized university with english and math as compulsory subjects.
Ques. What are the skills required to pursue MSc Maths?
Ans. Skills required to pursue MSc Maths:
- critical thinking.
- problem solving.
- analytical thinking.
- quantitative reasoning.
- ability to manipulate precise and intricate ideas.
- construct logical arguments and expose illogical arguments.
Ques. Is it worth doing MSc in Maths?
Ans. Yes, because MSc in Maths gives students solid core education. It is a professional course, thus it makes aspirants capable of having a good job scope and skills
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