List of Online Courses and Certifications

Intended for an electrical engineering audience, the Probability Foundations for Electrical Engineers certification by Swayam touches upon the fundamental aspects of the probability theory. Probability theory and its models play a significant part in various aspects of design and implementation, communications, networking applications, and signal processing. 

Besides, the Probability Foundations for Electrical Engineers certification syllabus covers vital concepts of probability like conditional probability, continuous random variables, discrete random variables, variance, correlation, and the like. This AICTE approved course will require candidates to have basic calculus knowledge to better grasp the course. 

The Probability Foundations for Electrical Engineers online course is taught by two eminent professors from IIT Madras known as Prof. Andrew Thangaraj and Prof. Aravind R, who hails from the electrical engineering department. Although the course isn’t directly relevant to industries, it is a foundational path towards various other courses like Wireless/Digital communication, adaptive signal processing, and the like.

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 Basic Real Analysis certification course has been designed with the aim to cover several basic concepts such as real line, differentiation as well as integration. The course prepares candidates for future courses. The theorems have been well explained so that the basics are clear for the aspirants. Theories and logics have been covered in every module of the basic real analysis course. 

The course will also be enhancing the skills of the individuals registering for the course. Discussion forums boosts up the confidence level, by offering rigorous learning during the learning phase of course. Assignments, reading sessions, video lectures and quizzes have been designed which ensures that the participants are having smooth learning.

Aspirants registering for the Basic Real Analysis online course will be able to solve the problems easily after the learning they acquire. Different terminologies such as limit superior and limit inferior have been included in the course.

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 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. 

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 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 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.

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.

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.

An introduction to Smooth Manifolds course by SWAYAM is spread over 12-weeks and falls under Mathematics. This elective course introduces learners to the fundamental concepts of the smooth manifold theory. It is a Faculty Development Programme (FDP) approved by the AICTE.

In addition to online video lectures, this course also includes books and references. Moreover, An Introduction to Smooth Manifold's certification syllabus is curated by the Indian Institute of Science, Bangalore. The curriculum comprehensively touches upon Stokes theory, orientation, submanifolds, topology, Frobenius theory, and much more. It splits into 12 learning modules, scheduled for every week.

Professor. Harish Seshadri from IISc Bangalore instructs the An Introduction to Smooth Manifold's online course. Students can choose to verify the skills acquired in this course with a certificate. For that, they need to pay the necessary certification fee. Ph.D. and Masters's students in Information theory, Robotics, Mathematics, Physics, Control theory, or Climate Sciences can enrol in this certification course. 

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 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 Biostatistics and Mathematical Biology course is designed to help candidates learn the fundamentals of mathematics that are required for biologists. It will help them learn the principles that govern the behaviour and systems in living beings. Further, the curriculum covers modern topics of biostatistics such as box-plots, Bayesian probability, statistical power, maximum likelihood, and the like.

Furthermore, the Swayam Biostatistics and Mathematical Biology programme cover essential topics of mathematical biology, which get covered rarely by universities. It includes permutation and combination, odds ratio, and relative risk, among others. Also, the award-winning tutor and science writer, Dr Felix Bast, teach this course.

Moreover, the Biostatistics and Mathematical Biology online course by Swayam is application-oriented. The programme is made interactive by the games and fun facts that are included in it. During the course, the emphasis is given to analysing data and strategic decision making about the right test to use during the right situation, which has become essential in solving the problems.  

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.

The Real Analysis I programme by Swayam is a 12-week programme, available at the undergraduate level. The course instructor is Prof. Jaikrishnan J, who is an assistant professor at IIT Palakkad with expertise in Complex analysis. 

The online Real Analysis I course aims to the students who want a deeper understanding of the subject calculus or for students who wish to pursue more complex subjects like Statistics, Computational Complexity, Theoretical Physics, among others. 

Moreover, various top companies such as DeepMind, Microsoft Research, and Google, support the Real Analysis I certification programme. With a comprehensive curriculum, candidates will become familiar with the set theory and logic behind the real analysis, along with necessary computational functions. 

While the online course is available to candidates free of cost, they must have studied mathematics up to class XII to enrol in Real Analysis I course. Moreover, if candidates want a certificate upon course completion, they need to pay for a certification exam and clear it. 

The completion of a Discrete Mathematics Certification will lay the groundwork for enrolling in higher-level maths courses like real analysis, abstract algebra, maths modelling, geometry, and topology. 

Discrete Mathematics Classes shall discuss the symbolic logic techniques which are required for the algebraic understanding of circuits and computer logic and layer introduce you to Boolean algebras with the help of certain examples based on objects.

Discrete Mathematics Certification Syllabus will discuss how to express the overall functioning of a circuit mathematically in terms of certain suitably defined functions called Boolean functions and also consider a simple circuit design problem to illustrate the applications of the relationship between Boolean functions and circuits. 

All students get a Discrete Mathematics Certification by MPSTME, NMIMS Deemed University, Vile Parle West, Mumbai under the Swayam Initiative by the Government of India. 

Mathematics is a subject that plays a significant role in human life and existence and can solve many complex real-life problems. Mathematical concepts have the power to explain the mysteries and complexities of the universe. The Mathematical Analysis online course is an attempt to provide a thorough understanding of some complex mathematical concepts to science stream students.

The Mathematical Analysis programme consists of 40 modules, tests and assignments and is a 10-week- long core course. This is a comprehensive course provided by Swayam in association with MES College of Engineering Kuttippuram of Kerala. Over the course of 10 weeks, you will learn some basic and some complex mathematical concepts which will prove most useful for students pursuing B.Sc in Maths degree from any university.

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. 

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.

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. 

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 ‘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 Heat Transfer certification is meant for students who want to get admitted to an undergraduate course. The course covers the broad subject line of heat transfer that takes place in different processes of different kinds of chemical industries. Candidates who are willing to learn from this college will be able to learn the basics of different modes of heat transport. 

The estimated time taken to complete the Heat Transfer certification syllabus is 12 weeks. Since the course is a self-paced program, students will be able to complete the curriculum according to their willingness. The course is provided by the Indian Institute of Technology, Bombay, and will contain 60 lectures in totality.

The Heat Transfer online course also provides the provision of certificates to the students. Participants can achieve a certificate for this online program by qualifying for the examination conducted by the creator offline. For a better learning experience of the course for the students, students will be provided with all the study notes, tests, quizzes, assessments, and other activities without any cost. 

The Basic Statistical Mechanics Certification Course is a 12 week-long massive open online course that educates learners on the fundamentals of statistics and mechanics. The course is provided on the Swayam online learning platform and led by thy Prof. Biman Bagchi of IIT Bombay. The course is suitable for students aspiring to work in the field of pharmaceutical and fuel cell companies.

The Basic Statistical Mechanics Training is provided through video lectures and course materials by experts. The course can be completed within a duration of 12 weeks and is easily accessible online. Once all steps of course lessons and evaluations are completed, learners will receive the Basic Statistical Mechanics Certification by NPTEL and IIT Bombay.

The Introduction to LASER certification course provides a great deal of exposure to the scientists, teachers, working engineers, or anybody interested in knowing how LASERS work. Spread over 12 weeks, this elective course is offered by Prof. M. R Shenoy, a faculty of IIT Delhi.  He joined IIT Delhi in 1988 and is known for his collaborative research on Integrated Optical Devices. 

The Introduction to LASER certification syllabus gives students deep insights into the principle functioning behind the lasers. It also deals with the issues concerned with the design and output characteristics of the Lasers along with resonator physics. 

The Introduction to LASER training is an ‘applied’ course in nature. It could be opted by students studying B.E/B.Tech (3rd/4th year)/M.Sc (2nd year)/M.Tech (1st year). Moreover, the course is approved by the AICTE as an FDP course. It mandates a sincere and regular effort on the part of the student to obtain expertise in the subject. 

The Statistical Mechanics online course offers a fundamental understanding of statistical mechanics and thermodynamics. It begins with the basic concepts of thermodynamics and takes on statistical mechanics principles towards the end. The program does mandate any prior exposure to the topics.

The Statistical Mechanics course syllabus covers topics like laws of thermodynamics, entropy, types of canonical ensemble, the theory of probability, and quantum mechanics. The program is a core course in the Physics discipline. Over the 12 weeks, you will be provided with high-quality video lectures delivered by Prof. Dipanjan Chakraborty.

IISER Mohali provides the Statistical Mechanics certification course in conjunction with Swayam. If you wish, you can also opt for the digital course certificate issued by Swayam. This certificate can be easily attached to your CV and LinkedIn profile. However, you will have to register for an exam by paying the requisite fee and pass the test to receive the e-certificate.

Designed by IIT Roorkee, the Introduction to Atmospheric and Space Sciences online course features their professor, MV Sunil Krishna, as the program instructor. The curriculum will span over 12 weeks and is divided into 60 presentations, each around 30 minutes long. This elective training will deal with the Earth’s atmosphere and space physics.

The Introduction to Atmospheric and Space Sciences certification is appropriate for students at the graduate and postgraduate level, covering aspects about the Earth’s atmospheric evolution and the chemical and physical reasons behind weather and climate changes. Candidates will study the Earth’s ionosphere, neutral atmosphere, and several plasma processes during this course. The principles of the interrelations between space and atmospheric physics as well as basic scientific tools and techniques will be discussed as well.

The Introduction to Atmospheric and Space Sciences training will conduct weekly practice assignments to promote better knowledge acquisition. Towards the end, candidates can also opt for the external proctored exam. The digital certificate will be provided based on the assignment and the exam scores.

The Advanced Atmospheric Physics certification by IIT Roorkee is a 12-week online course. This online certification course focuses on providing students with knowledge of advanced aspects of atmospheric and space physics. The Advanced Atmospheric Physics online course provides learners with the basics of inertial and non-inertial forces and the various dynamical phenomena. It also equips them with the understanding of various crucial aspects such as atmospheric waves and instabilities. The Advanced Atmospheric Physics certification syllabus will teach students about Atmospheric dynamics, Apparent forces, effective gravity, Thermal wind, Sound waves, gravity waves, Magnetosphere, and more.

The Advanced Atmospheric Physics training course can be an extension to the earlier NPTEL course: Introduction to atmospheric and space sciences. Offered via Swayam, students of B.Tech/ MSc/ MTech/ and Pre-PhD can enrol in this Advanced Atmospheric Physics certification by IIT Roorkee. After completing this online course, students can apply for jobs in R&D-based organizations like DRDO, ISRO, NCMRWF, and IMD.