Free Courses & Certifications

The Introduction To Algebraic Geometry And Commutative Algebra certification is an online program that does not require any fees to be paid by the students to be a part of the program. Candidates who pursue this course will get an understanding of topics related to algebraic geometry such as rings and ideals, theorems, topology, etc. The Introduction To Algebraic Geometry And Commutative Algebra training can be joined by graduates as well as postgraduate students since this is not only a beginner level of the program but includes topics from advanced level too. The course is being offered to the students by the Indian Institute of Science through the platform of Swayam that provides a thorough online and self-paced program to all the participants.

The certificate for the course can also be obtained by a participant when the candidate has completely covered the whole Introduction To Algebraic Geometry And Commutative Algebra certification syllabus along with assignments or assessment included in the course. The certification for the program comes at a cost along with an offline exam which needs to be given according to the terms and conditions of the provider of the course. The course needs only a time period of up to 3 months to cover it entirely but in case the candidate wants to go for a longer period of time, he can do so without having to pay any extra amount due to the course being a self-paced Introduction To Algebraic Geometry And Commutative Algebra program.

The Introduction To Algebraic Topology (Part-I) Certification course is a master's level program and requires fundamental knowledge in the field of point-set topology and group theory. The course also touches upon the modern aspects of mathematics. The course will be offered to the candidates by IIT, Bombay and the syllabus of the Introduction To Algebraic Topology (Part-I) program is similar to the program of the National Centre for Mathematics. The course deals with different topics throughout the syllabus like path homotopy, convex geometry, covering spaces, and many more topics which gives a variety of knowledge to the students. 

The Introduction To Algebraic Topology (Part-I) certification syllabus of the course can be completed according to the pace of the candidate although the set timing for the completion of the training is 3 months. Candidates need not buy any external study material or notes as the course includes the full package of study material, assignments, tests, fonts clearing discussion platform, etc. The other benefits of the Introduction To Algebraic Topology (Part-I) by Swayam include a certification which will be provided to the students only if they acquire the passing grades in the exam and register for the same by paying the exam fees. 

The online course on Integral and Vector Calculus by Swayam will be offering a detailed introduction to the topic of - integral and vector calculus.  The program will deal in a descriptive way with the concepts of- Riemann sum, partition, and Riemann Integrable functions and their applications as well as their properties. The online course will also discuss the fundamentals of- anti-derivatives. 

The online certification course will teach the students over the course of twelve weeks about the classical theorems of integral calculus that also includes the - fundamental theorem of integral calculus. The Integral and Vector Calculus online course curriculum includes the concepts of-  differentiability, gradient, divergence, directional derivative, and their geometrical interpretation and curl of vector functions in real-world functions. 

The important and fundamental topics of - theorems of vector calculus: Gauss’s, Green’s, and Stoke’s theorem will also be discussed in the course. To help the applicants understand in a more comprehensive manner the course has been structured as - core.

The Introduction to Commutative Algebra program by Swayam is a twelve-week online course, designed for individuals who want to research areas such as algebraic geometry, commutative algebra, algebraic number theory, etc. It is an AICTE approved FDP curriculum, intended for postgraduate-level students.

Curated by IIT Madras, the Introduction to Commutative Algebra certification syllabus covers crucial topics such as ring homomorphism, prime and maximal ideals, Jacobson radical, module homomorphisms, submodules, and tensor product of modules. The exact properties of the tensor product and Noetherian rings are also a part of this comprehensive course. The Institute’s Professor A. V. Jayanthan will teach this course.

Moreover, the Introduction to Commutative Algebra training requires learners to have the necessary knowledge of linear algebra, basic ring theory, and group theory. Students will receive assignments and study through Swayam’s video lectures during the course. In the end, learners need to pass the final exam and meet all the certifying criteria to obtain their course certificates.

The Online certification course on the Measure Theory by Swayam will be covering the key concepts and principles that are involved in integration and measure. The course will begin the training by introducing the candidates to the applications of- integration theory and the abstract measures along with their applications. In the next half of the online course, the trainers will be dealing with the theories that pertain to- the Lebesgue measure and its real-world applications.

The course will also provide the students with a detailed study of Borel measures on locally compact Hausdorff spaces. The Measure Theory certification syllabus will also comprehensively elaborate on the principles of- Lp spaces and product measures along with Fubini’s theorem. In the period of twelve weeks, the applicants will also be provided with the assignments on several classical results such as- the Ries representation theorem, the  Radon-Nikodym theorem, and the Lebesgue differentiation theorem.

Linear algebra is a continuous form of maths as it allows us to model natural phenomena and understand the theory behind machine learning and deep learning. It is an integral subject in mathematics applied in engineering, science, and other mathematical areas like geometry and functional analysis. Linear Algebra by Swayam is an online program that emphasizes the crucial concepts of linear algebra and gives a thorough introduction to this foundational subject.

The Linear Algebra online course has been designed by the Kerala School of Mathematics expert faculty. The training falls under the domains of foundations of mathematics and algebra. It is spread over 12 weeks and is free to enroll for all learners. 

Furthermore, Linear Algebra training by Swayam will offer a certificate to students who finish the whole course, including assignments, and qualify for the exam. Students will learn through various examples and use their problem-solving skills to deal with many mathematical problems. No charges are applicable for enrollment.

The Ordinary and Partial Differential Equations and Applications certification course is designed with complete overview of the differential equations and its relative significance. This course is a standard curriculum that is offered to UG/PG engineering or science students. It requires the presence and uniqueness of an ODE solution, homogeneous and non-homogeneous linear differential equation systems, second-order homogeneous differential equation power series solution. 

The Ordinary and Partial Differential Equations and Applications training will undertake both aspects of the curriculum in an analytical and practical manner that will help the candidate to be more productive and effective in their respective major. This course has considerable applications in numerous engineering and science areas, such as control theory, numerical analysis, dynamic systems, etc. The main motive will be focused towards the core elements of the major that have a significant role in the functioning of the problem-solving areas. 

This course will provide a quick overview of the whole curriculum in the beginning and then later it will be directed to the new modules, framework, theorems, challenges and limitations that are associated with this particular programme along with that, the candidate will be provided Ordinary and Partial Differential Equations and Applications certification that will help them to pursue further courses in same field. 

The Numerical Linear Algebra online course has been structured as a basic and fundamental course for the students who are pursuing their postgraduate or undergraduate level degree course from the stream of science or engineering. 

The Numerical Linear Algebra certification benefits the registered students by providing them the core concepts regarding- stability of numerical algorithms, matrix algebra, stability of nonlinear systems, conditioning and condition number,  vector and matrix norms, convergent matrices, computer arithmetic, sensitivity analysis, singular value decomposition (SVD), least square solutions, algebraic and geometric properties of SVD, Power method and applications, Householder matrices and applications, QR method, Jacobi method for finding the eigenvalues of a given matrix. 

The Numerical Linear Algebra certification course will be dealing with all the real world applications of the numerical linear algebra concept in the diverse fields of - sciences and engineering. The twelve weeks course will be emphasised on topics like- control theory, numerical analysis, image processing and dynamical systems.

Probabilistic Methods in PDE by Swayam is designed by IISER Pune and verified by NPTEL. Professor Anindya Goswami instructs this ongoing elective program that spans 12 weeks. The course falls under the purview of Mathematics and is based on two books, namely: Semigroup Theory and Stochastic Calculus. Candidates seeking certificates can also acquire them by paying and registering for the proctored evaluation. 

The Probabilistic Methods in PDE certification syllabus introduces you to a potent research tool related to the differential equations theory. The curriculum aims to offer expertise on probability theory and PDE, considering the absence of extensive learning material on this topic. Young researchers who have to undergo time-consuming research with scattered references have easy access to the course’s compiled information, offering in-depth insights.

The Probabilistic Methods in PDE program is an advanced curriculum but is also ideal for mathematical finance, probability theory, PDE, or mathematical physics aspirants. The instructor will explain several complex theorems from the books mentioned above during the course lectures to facilitate a comprehensive approach towards the subject.

The Optimization from Fundamentals certification course is a structural framework set for improving the learning of the field in a more effective way. From its fundamentals, this course will cover the subject of Optimization. A summary of actual analysis and convexity will begin with it. Linear programming, convex optimization and nonlinear programming, complementarity concerns and algorithms for the same will cover this basis. 

With dynamic optimization, the Optimization from Fundamentals training will stop. The course will give a complete framework of what's the level of optimization in different sectors and now where it stands and what are the problems and challenges, it suffers.  

The Optimization From Fundamentals certification will give an assurance that the candidate is more effective in the respective field, which will help him to undertake the same major in their respective upcoming future. The course is more tilted towards the understanding of the core elements that play the main role in the functioning of optimization principle. The students who will get enrolled in the programme will study various elements that are so vital for the functioning of the fundamentals and Optimization from Fundamentals certification syllabus will mainly consulate with that only. 

The online Variational Calculus and its applications in Control Theory and Nanomechanics training course has been designed as an introductory session to the main theory and applications that are related to variational calculus to problems with respect to- physics, geometry, and differential equations along with mechanics. This course on Variational Calculus and its applications in Control Theory and Nanomechanics by Swayam provides the students with adequate knowledge on the topics of- ordinary differential equations, vector calculus, and basic mechanics. In the course tenure, the applicants will be learning about the new applications that are being applied in- physics, biology, mathematics, chemistry, and engineering. 

The Variational Calculus and its applications in Control Theory and Nanomechanics certification benefit the students as this will serve as a reference for advanced study and research in the same domain. After completing the course the students will have their skills increased in the field of functionals that contains several dependent variables.

SageMath is a python based, free and open-source computer algebra system (CAS). The software is being used widely to explore applied linear algebra, calculus, and numerical methods. The Computational Mathematics with SageMath course by Swayam aims to deep dive give practical learning to the applications of SageMath in the concepts mentioned earlier.

The Computational Mathematics with SageMath certification syllabus covers a range of topics like python, classes in python, use of NumPy, SciPy, and SymPy, exploring SageMath, local maximum and minimum, and the like. The AICTE verified course is perfectly suited to students wishing to pursue their careers in the data science or numerical computations industry.

Besides, the Computational Mathematics with SageMath online course is taught by an experienced professor from chemical technology, Mumbai, called Prof. Ajit Kumar. The 12-week course will contain weekly assignments for evaluation through which the students will be able to track their progress.

The Transform Calculus and its applications in Differential Equations online course will help candidates learn about the basic techniques involved in the integral. The simpler ways of dealing out with the equations and coming up with the solution in a quick span of time will be taught to the candidates.

The candidates will be exposed to high-level concepts as well so that there is no difficulty in the process of learning. The course will train the students with the basic Integral Transform techniques. The candidates will be learning everything this topic covers within this time. The high-level concepts will also be touched by the experts.

The Transform Calculus and its applications in Differential Equations training come with certification, so the learning is a fun process. The candidates will have all the learning materials with them prior to the starting of the course and can carry on with their learning anytime they wish to.

The Fourier Analysis and Its Applications online course has been selected as the basic theoretical applications and aspects of the topics that are directly or indirectly related to the topic of Fourier. 

The Fourier Analysis and Its Applications certification syllabus will be conducted for a total of 12 weeks and will be covering the topics namely- The space S of rapidly decreasing functions, Application to PDEs, Fourier transform as an operator from S to S, and the Plancherel's theorem, Cesaro summability - Fejer's theorem and its applications, Basic convergence theorem of Fourier series and its applications and Sturm-Liouville problems and its applications. 

With the help of lecture videos, assignments, tests, and case study guides, the students will be taught the basics of the concept of  Fourier. The diverse applications of the subject of mathematics will also be covered in a descriptive way in the online course on Fourier Analysis and Its Applications by Swayam.

The Linear Algebra online program is a Swayam course provided by the Ministry of Education(Government of India) and is designed by the National Programme on Technology Enhanced Learning(NPTEL) and the Indian Institute of Science in Bangalore. This course is part of the mathematics domain and will take twelve weeks for the students to complete the training.

The course instruction is done by Prof. Dilip. P. Patil, a faculty member of the department of mathematics in IISC. The course materials that include books, references, and assignments will be a source of extensive learning of the subject. 

The Linear Algebra training provides expertise that enables students to equip themselves with valuable mathematical insights that improve their job skills. The students of this course will develop their knowledge of the geometric concepts involved in mathematical applications and other algebraic principles. This core course will fetch the candidates three credit points and a certificate from Swayam that is recognized by NPTEL and IISC Bangalore.

The ‘Advanced Engineering Mathematics’ online course is a study about the analytical functions and applications of the various concepts and ideas that form the core of engineering mathematics. The National Program for Technology Enhanced Learning program (NPTEL) free online course is offered on the Swayam education platform for the undergraduate and postgraduate students of engineering and science.

The course curriculum is designed and provided by the Indian Institute of Technology Roorkee for twelve weeks. This certification course is a core course for undergraduate-level students. The course educator for this program is Dr. P. N. Agarwal from the department of mathematics at IIT Roorkee. The students of the ‘Advanced Engineering Mathematics online training program can earn three credit points. The candidates will also receive a course certificate that is e-verifiable with the authenticated logos of NPTEL and IIT Roorkee. The twelve weeks of training on the theoretical principles of the mathematical aspects of engineering and sciences enables the students to develop expertise in this domain.

The ‘Algebra - I’ online certification program is a core course for the students of mathematics that is focused on delivering the students insights on the foundational concepts of algebra. This free online course is provided by Swayam educational platform in collaboration with the National Programme on Technology Enhanced Learning (NPTEL). The course classes are held online in a virtual environment through videos, lectures, online resources, and assessments. The students of this course will take about twelve weeks to complete the course.

The instructors for this online training program are mathematics faculties from The Institute of Mathematical Sciences in Chennai, Prof. S Viswanath, and Prof. Amritanshu Prasad. The candidates of this mathematics course will gain a comprehensive understanding of the theoretical and practical aspects of algebra in this course.

By the end of this postgraduate level course, the students of the ‘Algebra - I’ training program will be given E-Certificate with the credit points. 

The ‘Combinatorics’ online certification course is created for the students to engage and discuss the various aspects of counting and the study of patterns in this course. The students of this course will engage in enhancing their knowledge of mathematics and algebra. The free online learning course is provided by Swayam in collaboration with the National Program for Technology Enhanced Learning (NPTEL). The classes for this program are conducted online aided by lectures, videos, books, and reference materials for about twelve weeks.

The instructor for this program is Prof. Narayanan N from the department of physics at the Indian Institute of Technology Madras. The students of this undergraduate level mathematics and algebra course will gain insights into the concepts of combinatorics.

The ‘Combinatorics’ online training program equips students with the E-Certificate and credits points after successfully completing this core course approved by the All India Council for Technical Education. The students are evaluated based on their weekly assignments and final examination for the certification.

The ‘Complex Analysis’ online certification course enables students to learn about the foundational level mathematics focussing on complex numbers and the complex analysis functions. This online course attempts to discuss the implications of complex numbers that offer the spectral theorem for matrices. This free National Program for Technology Enhanced Learning (NPTEL) course is provided by the Swayam education portal. It is a core course for undergraduate and postgraduate level students and is scheduled for twelve weeks. The classes are held online through videos, lectures, weekly assignments, and other online resources.

The instructor for this online training is Dr. Pranav Haridas, assistant professor at the Kerala school of mathematics. The students of this course are given an opportunity to explore the theoretical and practical implications of complex numbers in the mathematics domain.

The ‘Complex Analysis’ certification course ensures a course certificate and credit points after successfully completing this AICTE recognized course and the certification exam.

The ‘Computational Commutative Algebra’ certification course is an elective course for the students to develop their understanding of the computation of the rings, ideals, and modules with the help of a computer. This course enables students to get an overview of commutative algebra with a focus on the computations and the techniques behind them. This free online training course is provided by the Swayam education portal along with the National Program for Technology Enhanced Learning (NPTEL). The classes for this course are conducted online for a period of twelve weeks.

The students of this program are led by the instructor, Prof. Manoj Kummini from the Chennai Mathematical Institute (CMI). In this course, candidates will get a theoretical and hands-on experience with the computational tool Macaulay2. This program can be downloaded and installed locally or can also be worked with the online version for smaller computations.

The ‘Computational Commutative Algebra’ online training program ensures an E-Certificate and credit points after completing the course and the assessments successfully.

An invitation to Topology certification by IMSC via Swayam is a 12-week online course. Through this online certification course, students will be exposed to the investigation and formalization of the abstract notion of a “space” under a minimum set-theoretic structure, known as a topology. An invitation to Topology certification syllabus provides foundational theory in topology which plays a crucial role in modern mathematics, and by extension, other mathematical sciences. This is a free course and anyone interested in learning topology can enrol in this online course offered by the Institute of Mathematical Sciences, Chennai (IMSC) via Swayam. 

Spread across 12 weeks, An invitation to Topology online course equips learners with the concepts of Topological spaces, Subspace Topology, Box and Product topology, and Metric topology. The course also provides a certificate on the completion of the exam which is conducted at the designated exam centres.

An introduction to Point-Set-Topology Part-I certification by IIT Bombay via Swayam explores the definition of metric spaces and topological spaces. This is a 12-week online course that deals with topological aspects of metric spaces. An introduction to Point-Set-Topology Part-I certification course will expose students to three crucial theorems on complete metric spaces while providing them with the structure of completion of metric spaces. Through An introduction to Point-Set-Topology Part-I online course, students will get familiar with topological spaces, building new topologies from the old, Bases and subbases, I and II countability, connected and path connectedness, separability, and others.

An introduction to Point-Set-Topology Part-I certification syllabus discusses the meaningful study of analysis and further topology. In the end, the course gives outstanding results such as Urysohn’s lemma and Titze’s extension theorem and some applications. An introduction to Point-Set-Topology Part-I classes are backed up by a strong team of tutors solving all the queries. The classes also include several online interactive sessions.

The Algebraic Combinatorics certification by the Institute of Mathematical Sciences (IMSc), Chennai is designed to introduce students to some influential paradigms in modern combinatorics. They are combinatorial classes and combinatorial species, Möbius inversion on partially ordered sets, and the Lindström-Gessel-Viennot lemma. The Algebraic Combinatorics training course is a 12-week online course delivered via Swayam. The Algebraic Combinatorics certification syllabus also provides learners with the theory of symmetric functions.

Students from science and engineering backgrounds having studied mathematics and computer science are best suited for the Algebraic Combinatorics certification course. The course will be taught by two instructors covering powerful paradigms in modern combinatorics. There are three credit points in the Algebraic Combinatorics online course that will be awarded to students after completion of the course. Students will also receive a certificate upon successful completion of the final exam. 

The Functional Analysis certification course is a postgraduate level programme in the field of mathematics. The online course mainly focuses on learning partial differential equations with a modern perspective in addition to other topics. The course covers all the fundamental and important theorems, normed linear spaces, and weak topology, etc. The course would be perfect for those candidates who are pre equipped with the information of basic linear algebra and topology.  The course deals with 12 different topics that are covered every week.

Candidates who would want to pursue this Functional Analysis online course will get to collect information on linear transformations, different theorems, reflexivity, some practical examples, etc. Candidates would be offered a certificate at the end of the course if they choose to pay for the exam fees and qualify for the exam with passing grades. Candidates can take up this course at any time and there is no rush to complete the Functional Analysis certification syllabus since it is a self-paced online course. The course is provided by IIT, Madras and mentored by the faculty member of the Institute of Mathematical Sciences, Chennai.

The Fundamentals of Conduction and Radiation course can be accessed from the Swayam website. Swayam was created by the government of India to increase access to education among even the most disadvantaged sections of society. This course will be beneficial for students to analyse, solve, and model a broad range of engineering applications that involve conduction and radiation.

The Swayam courses are free. The courses are designed by experts in their respective areas. But candidates who want to get certified from Swayam have to submit the course assessments and sit for an end-term, in-person exam. There is an exam fee that has to be paid for the end-term exam. Course instructors Professor Amaresh Dalal and Professor Dipankar N. Basu, are faculty members of the Mechanical Engineering Department of IIT Guwahati.

The Fundamentals of Conduction and Radiation course by Swayam enables candidates to analyse, model, and solve a wide variety of engineering applications that are based on the theories of conduction and radiation. The course is focused on teaching candidates problem-solving skills.

This programme is a pan-India initiative by SWAYAM, an offering provided by the Indian Government focusing on the realisation of the three basic principles of education policy-quality, fairness, and access through various online education programs for poor students across the country. In order to bring each student the best teaching resources, this course makes up for the digital scarcity faced by students so far and trains them to use online education models for education.

For chemical engineering students, the Certification Programme on Heat Transfer is a basic course on heat transfer which is also important for disciplines such as nanotechnology and mechanical engineering. This course starts with basic concepts and control equations, involves basics and applications, and gradually develops into the design of related industrial units. It will enable students to understand core scientific problems and encourage them to solve problems on their own.

The basic concepts will enhance students' lateral thinking ability and integrate the concerned concepts seamlessly for them to utilise in many processes and problems related to heat transfer. The learning can be deployed in related industries including all chemical processing industries, solar and nuclear energy, thermal energy, as well as industries having such plant designs.

Swayam's Solid Mechanics is a 12-week online programme. The training covers the fundamental concepts of strain and stress in 3-D deformable bodies, along with the extension, bending, and torsion of beams. The course belongs to the advanced mechanic's domain and offers a curriculum segmented in 12 sections.

The online Solid Mechanics programme includes extensive learning content about the one-dimensional theory of beams, Mohr's circle, Euler Bernoulli and Timoshenko beam theories, Castigliano's theorem, and more.

Students study the different theories of failure and its applications, critical to the design of machine elements in the industry. For those who are interested in receiving certification from IIT Madras and the National Programme on Technology Enhanced Learning (NPTEL), must finish the assignments and qualify the test.

Applicants can register for the certificate programme in Solid Mechanics through a quick online process. Moreover, Ajeet Kumar, an associate professor from the Department of Applied Mechanics in IIT Delhi, will be your instructor, while you will get access to the all-encompassing curriculum free of cost.

This course, offered under the NPTEL program which is run by Swayam and is funded by MoHRD. It is aimed at teaching the basics of mechanics, essential in most streams of sciences and engineering studies at the undergraduate level. The course consists of topics in computational mechanics, mechanical engineering, computational engineering, advanced dynamics and vibration, advanced mechanics. 

Engineering Mechanics is the subject that forms a foundational knowledge base for those interested in mechanical engineering. All the concepts taught in this course are required to study subjects like Strength of Materials, Theory of Machines, Machine Design, FEA, Mechanical Vibration, etc., which is basically every subject in Mechanical Engineering.

Concepts of engineering mechanics ranging from production technology to design sciences to thermal sciences are used everywhere in this field. It is very important that you take the subject seriously if you wish to pursue Mechanical Engineering. This course will give you the basic knowledge required to apply the principles taught during this course to solve engineering mechanics problems.