Home Collections 10 Best NPTEL Online Math Courses

# 10 Best NPTEL Online Math Courses

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0 Interested in developing good Mathematics skills but not sure where to look? A group of 5+ members at takethiscourse.net has compiled down a list containing 10 best NPTEL online courses for Mathematics. These Math courses have been specifically handpicked by the team and we assure you enrolling in one of these Math courses would be a convenient option for you.

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## List of 10 Best NPTEL Online Math Courses for Mathematics:

###  Calculus of One Real Variable

• Prof. Joy deep Dutta via NPTEL
• Co-ordinated by: IIT Kanpur
• 8 Weeks duration
• Discipline: Mathematics

A very thorough Mathematics course from the list of Best Math Courses that is going to help you understand the calculus behind one real number. The Math course starts with an introduction to numbers where the instructor is going to give you a briefing on different variables and numbers. After that, he is going to talk about what countability and uncountability are. Then, you will be learning all about what irrational numbers are and the instructor is also going to explain different examples of irrational numbers to help you understand them even better. Going further in this Math Courses, you will get to know what functions are in detail.
Similarly, after functions, your next topic will be about the limit of functions. Then the limit of functions 2 will also be discussed in detail. Your next topic will be about continuous functions and then understanding the intermediate value theorem. Furthermore, you will also learn about what supremum and infimum are. The Math course has a variety of quizzes and assignments instructed by the instructor for you to solve so don’t skip this section. Other topics like rules of differentiation, Rolle’s theorem, monotonic functions, and inverse functions, and many more will be discussed as well. You might also be interested in Ivy League Math courses.

###  Numerical Methods

• Prof. Ameeya Kumar Nayak & Prof. Sanjeev Kumar via NPTEL
• Co-ordinated by: IIT Roorkee
• 8 Weeks duration
• Discipline: Mathematics

From the list of Top Math Courses, This is a very theoretical course that has a detailed explanation of what numerical methods are. The course starts with detailed instruction on what error analysis and linear systems are. After that, you will get to understand what Gaussian elimination with partial pivoting is. Not just that, the instructor also aims to talk about what LU decomposition is in a step-by-step guide. Similarly, the next topic will be about Jacobi and Gauss-Seidel methods. The instructor has a detailed lecture video on both these methods.
Going further in this Math Courses, you’ll get to understand the different iterative methods, and then comes the next unit where you will first get an introduction to non-linear equations and the bisection method. Then the instructor has explained really well what the Newton-Raphson method is. After that, the fixed point iteration method will also be taught. Thus these and many other topics are lined up for you once you start the course.

### Linear Algebra

• Prof. Pranav Haridas via NPTEL
• 12 Weeks duration
• Discipline: Mathematics

If you wish to learn all about linear algebra and all its fundamentals then this course from our Math Courses list is what you need to enroll in. The course first starts with an introduction to vector spaces and all the examples of vector spaces will be discussed in detail. After that, vector subspaces will be discussed as well. Next, you’ll get to understand what linear combinations and span are. Furthermore, the instructor will also talk about what linear independence is. Then other topics like basis, dimension, and replacement theorem consequences will also be a part of this Math course.
Now moving on to the next week, your first topic will be understanding rank nullity. After that, you will get to know all about linear transformation, linear transformation basis, and matrices in detail. Similarly, the next topic that the instructor has explained in detail is the invertible linear transformations and matrices. Going further in this Math Courses, the instructor will talk about the change of basis, the product of vector spaces, quotient spaces, and dual spaces. Similarly, moving on to some advanced topics like row operations, the rank of a matrix, inverting matrices, determinants, and more. So, enroll now in these Math Courses and learn all about linear algebra from the comfort of your home. You can learn geogebra online courses and classes at your ease and pace.

###  Higher Engineering Mathematics

• Prof. P.N. Agrawal via NPTELCo-ordinated by: IIT Roorkee
• 12 Weeks duration
• Discipline: Mathematics

Are you interested in knowing the types of topics that are a part of higher engineering mathematics? The instructor of this Math course aims to help you understand all about higher engineering mathematics by discussing all the relevant topics in detail. The first topic is the symbolic representation of statements. After that, the instructor will talk about tautologies and contradictions in detail. Next, you will get to learn what predicates and quantifiers are and their purpose in higher engineering mathematics. Similarly, you will also get to know what the validity of arguments is. After that, the next topic is language and grammar.
Going further in this Math Courses, you’ll get to understand what finite-state machines are. Right after this, the instructor will talk about what partially ordered sets are in a step-by-step guide. Then, you’ll understand what lattices is. Similarly, the instructor will talk about Boolean algebra where this topic will be explained in quite detail by the instructor. After that, you will learn what logic gates are. The next topic will be the Karnaugh maps where the instructor will be explaining all about it in detail. Other topics like paths and connectivity, subgraphs and traversable multigraphs, directed and undirected graphs, and many more will be discussed.

### Integral Transforms And Their Applications

• Prof. Sarthok Sircar via NPTEL
• 12 Weeks duration
• Discipline: Mathematics

In this course of Best Math Courses you will get to know everything there is about integral transforms and it includes an understanding of all its applications as well. The instructor will first talk about what Fourier Transforms is. After that, the instructor will talk about the properties of Fourier Transformation, then understanding what Shanon’s sampling theorem is. Next, you will know all about what Gibb’s phenomena are. When the instructor is done explaining all about these topics, you’ll move on to some advanced topics like what Laplace transforms is. Then you will get to know about the inverse Laplace transform and its initial and final value theorems in detail.
Going further in this Math Courses, you will get a chance to understand all about the applications of Fourier-Laplace Transforms. Next, the instructor will give you an introduction to Hankel transforms, then Mellin Transforms. Similarly, you will also get a detailed explanation of Hilbert Transforms. Other topics like Legendre Transform, Inverse Z-transform, applications of Z-transform, Radon Transform, and many more will be discussed in detail.

### Essential Mathematics for Machine Learning

• Prof. S.K. Gupta and Prof. Sanjeev Kumar via NPTEL
• Co-ordinated by: IIT Roorkee
• 8 Weeks duration
• Discipline: Mathematics

This is a very interesting, engaging yet challenging course that demands complete determination from the learner to be able to make the most out of this course. The Mathematic course encloses in it everything you need to understand about Mathematics for Machine Learning. After enrolling in the course, you will first get an introduction to what the course has to offer and then a brief explanation on vectors will be given. After that, you’ll understand what vector spaces are through definitions and different examples. Next, you will understand what vector subspaces are in detail through examples. You will also get to know about their properties, basis, and dimensions.
Moving on, your next topic will be about linear transformations and norms and spaces. Then, you will learn about orthogonal complements and projector operators in detail. Similarly, the instructor will also be explaining all about Eigen pairs and their properties. Furthermore, you will also learn what special matrices are and all their properties in detail. Going further, you will get a chance to understand what the least square approximation and a minimum norm solution is. This is how you will get to understand all the beginner and advanced level topics of Mathematics for Machine Learning through this Math course. You can also checkout UCSD Math courses.

### Scientific Computing using Matlab

• Prof. V.K. Agarwal via NPTEL
• Co-ordinated by: IIT Delhi
• 11 Weeks duration
• Discipline: Mathematics

Do you know what MATLAB in scientific computing is and what it does? In this course that is one of Top-level course from Math Courses List, the instructor is going to help you understand all about scientific computing using MATLAB. The course starts with an introduction to what MATLAB is and after that, you will learn to plot functions in MATLAB in a step-by-step guide. You will learn about symbolic computation in MATLAB after understanding the plotting of functions in MATLAB. Next, the instructor is going to explain all about the floating-point representation of a number.
Going further in this Math Courses, you will be taught the iterative method for solving nonlinear equations. After that, you will learn about the bisection method for solving nonlinear equations in detail. You will understand what the order of convergence of an iterative method is in detail as well. Then the next topic will be about the Raphson method for solving nonlinear equations. Similarly, you will get complete know-how of what a linear system of equations is. After that, there will be a detailed discussion on the iterative method for solving a linear system of equations. These and many other topics will be discussed as you proceed forward so enroll now and start learning today.

### Matrix Analysis with Applications

• Prof. S.K. Gupta and Prof. Sanjeev Kumar via NPTEL
• Co-ordinated by: IIT Roorkee
• 8 Weeks duration
• Discipline: Mathematics

This is an advanced level course from the list of Math Courses that has an explanation of all the topics that are relevant to the matrix analysis in detail. The Math course starts with an introduction to the elementary row operations and after that, the instructor will talk about what the Echelon form of a matrix is. Similarly, you will also get a detailed explanation of what the rank of a matrix is. Next, you will understand the system of linear equations in detail. The instructor has divided the whole Math course into different weeks and in each week you will be learning something new and advanced compared to the previous weeks. Next, you will get an introduction to vector spaces. And after that, you will learn about subspaces, basis and dimension, nullity, and more.
Going further, you will get to understand what the inverse of a linear transformation is. After that, there will be many other topics discussed in detail. These Math Courses include understanding Eigenvalues and Eigenvectors, Cayley-Hamilton Theorem, and Minimal Polynomial. Similarly, diagonalization, gram Schmidt process, vector and matrix norms, inner product spaces, normal matrices, evaluation of matrix functions, and many other topics will be discussed in detail.

### Mathematical Finance

• Prof. Siddhartha P.Chakrabarty via NPTEL
• Co-ordinated by: IIT Guwahati
• 12 Weeks duration
• Discipline: Mathematics

A very informational course from the list of Best Math Courses to help you understand all about Mathematical finance from the comfort of your home. The course is divided into different modules and in the first module, you will get an introduction to financial markets and bonds. Next, you will get an introduction to stocks, futures, and forwards, and swaps in detail. Similarly, the instructor will also explain to you all about the time value of money and then what risk-free assets are. Furthermore, you will get to know all about the interest rates, present value, future values, annuities, amortization, etc. The instructor will also explain to you what bond yield is and the price yield curve.
Going further, you will learn about the Markowitz theory, return and risk, and two asset portfolio. After that, you will be learning about the fundamentals of derivatives. Similarly, you will gain complete know-how of what bounds on options are. Next, you will learn about derivative pricing by replication in the binomial model. Thus, these Math Courses and many other topics will help you understand all the financial terms at your ease and pace.

### Introduction to Methods of Applied Mathematics

• Prof. V.K. Agarwal via NPTEL
• Co-ordinated by: IIT Delhi
• 12 Weeks duration
• Discipline: Mathematics

This course from the list of best math courses as the name suggests is a complete introduction to all the methods of applied mathematics. The course has all such topics in it that can help you develop a strong base of applied mathematics methods from the scratch. You will get an introduction to first-order differential equations. After that, the instructor will talk about the second-order linear differential equations. Then, you will understand the factorization of the second order differential operator in detail.
Going further, you will get a chance to understand the power series solution of the general differential equation. After that, you’ll learn all about the Green’s function and its purpose in detail. Next, there will be a detailed discussion on the adjoint linear differential operator. Similarly, you will also get to understand the Sturm-Liouville problem. Other different topics like Laplace transformation, Fourier series, Gibbs phenomenon, Fourier integral and Fourier transformation, and many more will be discussed.

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### Conclusion:

These are the names and details of the 10 best NPTEL online courses for Mathematics and is one of the best and convenient plus feasible way for any learner to enroll and start learning from the comfort of their homes. So, enroll in any of these 10 Math courses now and don’t forget to stay home, stay safe, and never stop learning.