MSc Maths Syllabus, Subjects, 1st Year, Year Wise, Semester Wise, Projects, Books

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 AlsoHow 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

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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)
  • Mathematical Logic
  • Number theory
  • Distribution Theory
  • Calculus of Variation & Integral Equation
  • Automata Theory
  • Mechanics
  • Algebraic Geometry
  • Galois Theory
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

Master of Science [M.Sc] (Mathematics) : 18 answered questions

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Ques. Should I go for M.Math program at ISI Kolkata?

● Top Answer By Ritwik Patnayak on 16 Sept 21

Ans. M.Math is quite thorough in different ways, it is best not to end up opting for it without vital information. As a brief interpretation, you really do not require programming skills to further opt for the M.Math course.  A very intensive knowledge of linear algebra, real analysis, and basic abstract algebra is required prior to joining the M.Math course. Despite that, the course is very challenging.  The academic background does not necessarily affect the course you are about to take up. There are students who arrive from an engineering background.  It is best to go through the coursework of Mathematics and decide whether or not you are inclined towards it or not.  M.Math students usually secure placements at a variety of companies, but achieving that howsoever is extremely difficult. Thus, choose only if you are confident. Read more
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Ques. What's the reputation of the South Asian University in Delhi for an MSc in applied mathematics?

● Top Answer By Suhani Kashyap on 23 Jun 21

Ans. South Asian University is a central funded government university. According to my friend studying there, It is not only an exceptional university in India but only one among the records of international universities in the world. This international university was established by a member of the SAARC. It was a dream project of Dr. Man Mohan Singh which he had proposed in the 13th SAARC summit held in Dhaka. It was later in the 14th summit that the establishment of this university was decided to be held in India. It provides courses of Applied Math, Biotechnology, Computer Science, Development Economics, International relations, Sociology, and Legal Studies. Its permanent campus is under construction in Maidan Garhi, Delhi while being operated from Akbar Bhawan, Chanakyapuri. SAARC consists of 8 countries which are India, Afghanistan, Bangladesh, Bhutan, Maldives, Nepal, Pakistan, and Sri Lanka. Therefore, the degree given by the university is recognized by the UGC of all 8 countries. The tag of SAARC attached would benefit your career in foreign countries as well. SAU has its own limitations as it is a new university. SAU is yet to be known among the scholarly and creating its name. Due to its less popularity, the entrance competition is not very tough. However, students prefer IITs, DU, and JNU for their post-graduate studies ignoring the high-level facilities provided at SAU.Read more
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Ques. Should I opt for an M. Sc. Math course in BITS Pilani?

● Top Answer By Trina Saha on 22 Jul 21

Ans. You are perhaps going for one of the most difficult streams of M.Sc, which is, of course, Maths. Few of my friends are studying there and as they have mentioned, by the time you reach your third year, one of the subjects in Maths would have a good number of theorems. The next thing you would have is coordinate geometry as a part of your Maths 1. This would come in handy while solving double/triple integrations. However, this is still the base of things. It gets complicated ahead- although, not sure if that would be in the third year essentially. Perhaps for better clarity, you should try and reach out to someone who is actually doing his/her M.Sc from BITS Pilani Now, when it comes to application and coding Mathematics, the wisest combination to opt for is M.Sc Maths along with CS. By the time you become a pro at coding, these math concepts wherein you studied geometry might come in handy for the applications that you would use. Try and sustain a CGPA of 8+, if you are genuinely serious about carrying along with CS as a second subject option. My friends mentioned that students who are carrying along two degrees at the same time have CS as their ultimate aim. There were a few friends of mine who with a double degree, either ended up slogging into semesters, achieved CS with hardly any effort, and eventually, some of them had to choose chemical/civil out of sheer compulsion.Read more
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Ques. How is the integrated MSc at BIT Mesra?

● Top Answer By Arun Biswas on 12 Apr 23

Ans. If you are interested in pursuing a career in research, the integrated MSc program offered by BIT Mesra is a great option to consider. Here are some key points to keep in mind: The program offers a comprehensive curriculum that covers a wide range of topics in mathematics, computing, physics, chemistry, and food technology. This provides students with a strong foundation in the fundamentals of science and prepares them for advanced study and research. One of the unique features of the program is that it offers an exit option after the third year , allowing students to leave with a BSc degree if they choose to do so. This is not available at many other colleges and can be helpful for those who may want to pursue other options after completing their undergraduate studies. If you choose to continue with the program and complete the full five-year integrated MSc, you will have the opportunity to specialize in mathematics and computing , which is equivalent to a computer science degree. This specialization can be particularly useful if you are interested in pursuing a career in software development or data science. While placements should not be the primary focus of a science degree, the mathematics and computing specialization at BIT Mesra has a good placement record . Students who work hard and excel in their studies can expect to have job opportunities available to them after graduation. The Integrated MSc program at BIT Mesra is a rigorous and demanding course of study. It requires a strong commitment to hard work and dedication to succeed. However, for those who are passionate about science and research, it can be a highly rewarding and fulfilling experience.Read more
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Ques. Will SBI Bank give a education loan to a student of MSc Maths at Bits Goa?

● Top Answer By Vatsal Mishra on 09 Aug 21

Ans. Yes, SBI will give you an education loan irrespective of your choice of course. Most importantly, it is not important whether you are a student or not at BITS Goa. SBI offers loans to all students studying in famous and recognized colleges.  Usually, education loans are provided mostly for Professional courses at post-graduation level. You must check whether BITS Goa is listed or not. You can do so by visiting the nearest SBI Branch. Getting an education loan in BITS Goa isn't that tough. The loan will be sanctioned without any obstacles.Read more
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