Swayam Mathematics Courses & Certifications

The Differential Equations For Engineers certification course introduces essential differential equations and their solution methods to students in physical, and mechanical sciences, and engineering. Covering both ordinary and partial differential equations, it equips students with vital skills for analysing and solving equations prevalent in scientific and engineering contexts.

With the Differential Equations For Engineers certification by Swayam, students delve into topics such as the classification of differential equations, analytical and numerical solution methods, and practical applications in engineering. Students gain a solid understanding of differential equations, enabling them to tackle mathematical challenges in their respective fields confidently.

The Calculus of One Real Variable programme is an undergraduate level training. Swayam offers 40 lectures divided into a course plan of eight weeks. The curriculum aims to familiarise students with the elementary and advanced aspects of the calculus of a single variable. Candidates will find several applications of this knowledge in engineering, economics, and science domain.

The Calculus of One Real Variable online programme provides all-encompassing learning content about functions like continuous functions, inverse functions, transcendental functions, and limits and derivatives of a function. Students will also master the intermediate value theorem, Rolle’s Theorem, Lagrange’s mean value theorem, and maximum value theorem. Swayam also allows students to avail of the course free of cost.

Furthermore, Joydeep Dutta, who is presently a professor of Economics at IIT Kanpur’s Department of Humanities and Social Sciences, will teach you the course. Students from engineering, mathematics, economics, and science streams will benefit from the Calculus of One Real Variable certification training. 

Pursuing Calculus of Several Real Variables programmes will help students who want to learn advanced Physics, Mathematics, Economics, Engineering, Business Management, Operations Research, and even Biology. The curriculum is divided into an 8-week plan. Jaydeep Dutta, a professor with the Department of Humanities and Social Sciences at Indian Institute of Technology (IIT) Kanpur, will be your programme instructor.

When it comes to multivariable calculus, the first issue is that of limits. And when you have a function in two variables, you are working with a plane instead of a line. There are infinite approaches to reach a given point on a plane, and the limits that you take must give you the same value through all of these countless approaches. That is what the Calculus of Several Real Variables course covers extensively.

The Calculus of Several Real Variables training also covers the basics of vectors, continuity, partial derivatives, multiple integrals, the Stokes theorem, Gauss divergence theorem, Green’s theorem, and Taylor’s theorem. The undergraduate-level course is entirely online. Students will receive accreditation from IIT Kanpur and National Programme on Technology Enhanced Learning (NPTEL) if they fulfil the certification eligibility criteria.

The Numerical methods course by Swayam is one of the tremendous courses that has its application in engineering and science fields. This course contains basic mathematical concepts like differentiation, differential equations and integration. In the digital world, numerical computation plays an important role in solving logical operations. In most of these operations, it is difficult to obtain results in an analytical manner. The main objective of this course is to provide algorithms and numerical methods for solving problems.

Real life problems from Engineering and sciences are solved using linear and nonlinear equations. Apart from this, the course also covers matrix problems that are solved using eigenvalues and eigenvectors. It also covers concepts like Jacobi theorem, Interpolation, difference tables, difference operators, forward difference, backward difference, Newton’s divided difference interpolation and Lagrange interpolation. 

The system for solving first and second order ordinary differential equations are taught through methods like Euler method, Modified Euler method, Milne PC method and Runge-Kutta method. 

This programme helps the engineers to tackle various industrial and engineering related problems. Implementation of numerical methods to solve the problems will make the candidate a great problem solver with high accuracy in problem solving.

The Basic Calculus 1 and 2 online course offers a better understanding of the Calculus taught in classes 11 and 12. The course will explain in detail the methodologies of calculus. The topics such as differentiability, continuity of a function, and its applications will be discussed. The course will teach how to interpret a real number. The course will provide an understanding of the results. The series representation will be shown in the course curriculum.

The course is an online-based learning program. The course offers free access. The candidates who belong to disadvantaged groups of society will be benefitted. The course is offered on the NPTEL platform. The course will be accredited by the Indian Institute of Technology Kanpur. The course will be graded on the 6 best assignments out of 8 assignments and the final exam.

The Basic Calculus 1 and 2 certification is offered by NPTEL and can be e-verified. The certification is shareable on all platforms such as Linkedin, Facebook, Instagram, and many more. The certification will help gain new professional networks. This course is initiated by the government of India so the course certification is authentic and verifiable.

The online certification program on Basic Linear Algebra by Swayam is formulated as a basic session for interested students who wish to pursue higher academic knowledge in the field of engineering studies. The candidates who want to pursue a higher education qualification in the field of mathematics can also register for the Basic Linear Algebra training.  

The students in the Basic Linear Algebra certification syllabus will cover all the primary and basic tools that are used in the domain of “basic linear algebra”. The online session for a period of twelve weeks will be covering the topics namely- gram-Schmidt process, inner product spaces, rank-nullity, linear transformations, determinants, invertibility,  rank, diagonalization,  similarity, and applications. After completing the course, the Basic Linear Algebra certification benefits the students by clearing their doubts in the- Rn, rank of a matrix, linear independence, and subspaces. Students after completing the course the students will get to practice real-world cases.

The Computational Science in Engineering certification course enables students to understand the needs of the rapidly evolving field of computer science. Students can approach a wide array of challenges in the areas of social sciences and engineering through the power of computation. Spread over eight weeks, the course falls under the domain of Aerospace engineering. 

The Computational Science in Engineering certification syllabus ensures that students understand the different engineering and science phenomena via simulations. They are taught the much-required mathematical modeling skills, efficient algorithms, numerical analysis, software design, computer architecture, and much more. 

The goal of the Computational Science in Engineering training is to let students explore the basics of scientific computing. This includes the framework observed in applied mathematics such as ODEs, Linear algebra, and PDEs. Students who sign up for this undergraduate course are taught by Professor Ashok De, Associate Professor, Department of Aerospace Engineering at IIT Kanpur currently 

Introduction to Rings and Fields certification course has been designed with the objective of covering the basics of the abstract rings and the subsequent fields. The course will also offer knowledge on the algebra sequence. Candidates will also be taught how to prove certain theorems in a simpler manner.

The course focuses on the prime, maximal ideas and the various other rings of the domain. The students will be exposed to the theory of field as well so that they grow more. Examples have been used more so that the candidates are able to relate the learning and remember it for a longer period of time.

Introduction to Rings and Fields online course comes with the certification. The candidates will be receiving it after they complete the course. The candidates must ensure that they perform well in all the learning materials offered to them. The course will also prepare the candidates for some of the industries.

Graph Theory certification course puts forward the various basic knowledge for the candidates. The minute details of the topics have been covered in these topics. The main objective of the course is to offer a comprehensive introduction to the graph theory. Sessions have been designed with emphasis on a single topic in every module.

The candidates will be acquiring skills on putting large sums of data into visual form. The candidates will be studying graphs through a framework so that it becomes easy for the candidates to have proper learning on this. The different types of graphs have been illustrated so the participants are able to have a clear concept in each of them.

Once the candidate completes the Graph Theory online course, a certification has also been included. The candidates will be exposed to the learning methodology where they will be coming across simpler ways of acquiring the knowledge.

The Introductory Mathematical Methods for Biologists certification course focuses on a comprehensive framework of the particular major with an analytical approach. For biology students, it is an introductory mathematics course with the purpose of teaching them to do quantitative analysis of biological processes. Students will be instructed on how to explain biological processes using the vocabulary of mathematics, how to write basic mathematical equations for different phenomena that exist in biology. The Introductory Mathematical Methods for Biologists training will undertake the beginner’s concepts in a mathematical approach that will help the biology student to get better learning of each and every module of this particular curriculum. The course’s lectures are structured into different weekly sessions focusing on the main and core aspects of the field. The candidate can avail different benefits by doing this course in the end by getting Introductory Mathematical Methods for Biologists certification. Candidates can get intellectual learning that will be supported by the industrial side that will help them to take this course more fluently. This is a core structure to be completed in eight weeks as prescribed by the UGC. The course is categorized into biological science and bioengineering.

The Partial Differential Equations – I course by Swayam is the first course in a two-part course series. There will be around 20 hours of online learning spread over eight weeks. You will build a robust foundation on Partial Differential Equations or PDE over the course duration.

Through the Partial Differential Equations – I certification course, you will learn the geometry and analysis behind the core PDE concepts. And move beyond the problem-solving techniques to understand PDE theories in-depth. However, it will primarily focus on classical geometry and calculus variables.

The Partial Differential Equations – I course will first introduce you to the scope of the PDE study, followed by methods of characteristics, multi-variables, and classification in First Order equations. There will also be weekly assignments to help you test your progress.

The intended audience for the Partial Differential Equations – I programme are students and teachers belonging to the Mathematics, Science, and Engineering disciplines. However, this online course is still open to all interested candidates, irrespective of their background.

The Introduction To Galois Theory online course is provided to all the applicants by the Indian Institute of Technology, Madras. The course covers the subject line of mathematics. Participants who enrol for this programme will be able to learn about the aspects related to Galois theory. The course is entirely an online session for 8 weeks. The programme does not require students to undergo any long procedure of admission or entrance. The Introduction To Galois Theory certification course is free to be joined by the students who are interested in the discipline. The course provides unlimited access to the students to gain information from the programme.

The Introduction To Galois Theory programme includes video lectures, assignments, problem-solving assessments, and other activities for the proper understanding of the concepts to the students. Candidates can also gain certification for the course upon the successful completion of the programme. The course allows the candidates to be informed through the topics without any restrictions in regards to the attendance or timings of the sessions. An offline exam is conducted by the provider of the Introduction To Galois Theory training at the end of the programme so that the students gain the certificate. 

The Mathematical Methods in Physics 1 course by Swayam aims to help aspiring physicists develop a solid background in mathematics. The concepts covered in this course will make the mathematical aspects of the subject more accessible to the candidate. 

Professor Auditya Sharma, a top faculty from IISER Bhopal, teaches the Mathematical Methods in Physics 1 certification program provided by Swayam. It is accredited by IISER Bhopal and is an FDP course that has been approved by AICTE. It is a core program spanning weeks of extensive learning and falls under the category of mathematics. Moreover, this online course is purposefully designed for UG-level students. 

The Mathematical Methods in Physics 1 course will be taught online via video tutorials. There will be graded tests and internal assessments, and free study material for the candidate to access. Candidates will also be eligible for the course e-certificate if they sit for the end-term offline exam.

The Multivariable Calculus certification course is an undergraduate-level introductory program spread over eight weeks. It is offered to students with a background in engineering and sciences. Various topics related to calculus functions of two or more variables like differentiation and integration are discussed along with other applications. 

The Multivariable Calculus training also throws light on vector functions calculus and its wide array of applications.  This core course falls under the ‘‘Mathematics’’ domain and is offered by Professors S.K Gupta and Sanjeev Kumar from IIT Roorkee. Both the trainers are associate professors from the Institute’s Department of Mathematics and have several published research papers under their name.

The Multivariable Calculus certification syllabus covers the multivariable calculus topics extensively. Concepts ranging from limits, continuity, and partial derivatives to Taylor’s theorem, polar curves, and multiple integrals comprise this curriculum. Moreover, the certification issued contains the student’s name, his/her photography, the logos of NPTEL and IIT Roorkee, and their acquired final exam scores.

There has been a lot of advances in computer hardware and software libraries. Due to this, we can undertake scientific computing that requires high precision and with relative ease. Tools in Scientific Computing program is an elective course that explores various methods of computing. It emphasizes hands-on implementation while covering all the theory-based topics. The course will talk about major problems you might encounter while implementing these scientific computing tools. 

The syllabus of Tools in Scientific Computing certification has been developed by faculty at IIT Guwahati. This AICTE approved FDP course is available on Swayam, an online learning platform with support from the Government of India. Professor Aditya Bandopadhyay will be teaching this course. This is an undergraduate/postgraduate course in mechanical engineering, computational mechanics, and computational engineering.  

Tools in Scientific Computing is a digital course that uses assignments and practical usage of Python, GNU Octave, and C-based PETSC as learning tools. You can also opt for an e-certificate by sitting for an offline exam at the end of the term. 

The ‘Calculus for Economics, Commerce and Management’ certification is a study of the mathematical tools and techniques to evaluate problems and solve problems to arrive at logical conclusions. This online course offers a better understanding of the scope of calculus in economics, commerce, and management domains. This free online certification is provided by Swayam in collaboration with the National Programme on Technology Enhanced Learning (NPTEL). 

Prof. I. K. Rana, an emeritus fellow from the department of mathematics at the Indian Institute of Technology Bombay will be the course instructor for this program to guide the students in developing their foundational skills of the concepts of calculus and its applications. The course classes are scheduled for eight weeks and the students are expected to form discussion groups to optimize the learning experience aided by the online resources and references. 

The ‘Calculus for Economics, Commerce and Management’ online certification program helps students receive an E-certificate at the end of the course after completing the course and assessments with the two credit points.

The ‘First Course on Partial Differential Equations - II’ online course is designed for the students to enable them to learn about the mathematical concepts and theories of partial differential equations and their applications. This certification program is provided by Swayam, a free online education portal in association with National Programme on Technology Enhanced Learning (NPTEL). The course classes are organized for a time period of eight weeks.

The instructors for this training program are professor A.K. Nandakumaran, faculty at the department of mathematics in the Indian Institute of Science Bangalore, and professor P.S.Datti a former faculty member of the Tata Institute of Fundamental Research-Centre for Applicable Mathematics, Bangalore. The curriculum is delivered through videos, lectures, books, other online resources, and the students are assessed by the weekly assignments and the final certification exam.

The ‘First Course on Partial Differential Equations - II’ online training offers the students with certification and credit points at the end of the course for the eligible candidates. 

The ‘Introduction to Abstract Group Theory’ online certification course is offered for the students to understand the concepts of abstract groups. The course enables students to study the definitions, fundamental properties, and structuring theorems in group theory. This free online certification program is provided by the Swayam online portal with the National Programme on Technology Enhanced Learning (NPTEL).

The instructor for this online program is professor Krishna Hanumanthu from the Chennai Mathematical Institute (CMI). The classes of this online training program are conducted for eight weeks in an online virtual environment aided by videos, lectures, course modules, examples, books, references, and other online resources. The students of this core course in their undergraduate or postgraduate level will gain both theoretical and hands-on insights with this course.

The ‘Introduction to Abstract Group Theory’ online course helps students receive certification according to the eligibility standards at the end of the course with credit points worth the certification.

The ‘Introduction to Abstract and Linear Algebra’ online certification course is developed for the students to get introduced to the theories and principles involved in the domain of abstract and linear algebra. This free online training is provided by the Swayam online education portal in collaboration with the National Program for Technology Enhanced Learning (NPTEL). The classes of this program are held in the virtual platform with the videos and lectures aided by books, references, and other resources for a period of eight weeks.

This core course is drafted for the undergraduate and postgraduate students of the engineering and science fields to gain from the theoretical and practical insights on the applications of these mathematical concepts. The course instructor is the associate professor Sourav Mukhopadhyay, faculty in the department of mathematics at the Indian Institute of Technology Kharagpur.

The ‘Introduction to Abstract and Linear Algebra’ online certification course enables the candidates to receive a certificate with two credit points by the end of this All India Council for Technical Education approved course.

The Probability for Computer Science Certification Course is a massive open online course that discusses the important topics in probability. The course available in online format on the Swayam learning platform is not a typical mathematics course. The course will familiarise learners with the concepts of probability along with its applications in algorithms and computer science. The Probability for Computer Science Training will be provided by Prof. Nitin Saxena of IIT Kanpur. The course will be taught via video lectures and is aimed at the undergraduate or post-graduate level. The model of assessments constitutes assignments and exams upon completion of which, learners will receive the  Probability for Computer Science Certification by NPTEL and IIT Kanpur.

Instrumentation and Process Control in the Food Industry is an 8-week online programme. The course is meant for undergraduate-level students who intend to step into the food industry. The Instrumentation and Process Control in Food Industry Certification Course is an online free programme offered by Swayam in collaboration with  IIT Kharagpur. Though it is free to join and pursue, the learners are required to sit for the exam and secure a certification qualifying score to get a hold of the certificate. 

Instrumentation and Process Control in Food Industry Certification is a course that is approved by AICTE (All India Council for Technical Education). The courses will guide you through process control and instrumentation in the food industry. Plus, the learners will explore stability analysis, food process control, control tuning and the like. The course is led by Prof. Ashis Kumar Datta who is a faculty at the Department of Agricultural and Food Engineering at IIT Kharagpur. 

Probability and Stochastics for Finance Certification will start with basics of probability as a tool to understand randomness and introduces the candidates to the main concepts, notions and results of stochastic financial mathematics.

Probability and Stochastics for Finance Classes provides necessary information for those individuals and professionals dealing with stochastic calculus and pricing in the models of financial markets such as SENSEX, NIFTY and operating under uncertainty.

All students enrolled will get a Probability and Stochastics for Finance Certification by Indian Institute of Technology Kanpur (IIT Kanpur) under the Swayam Initiative by Government of India. 

The Modern Algebra certification course explores algebra's role in abstracting geometric concepts and numbers, offering insights into their fundamental properties and enabling manipulations beyond direct means. It caters to undergraduate science and engineering students over an 8-week duration, highlighting algebra's pivotal applications in real-world scenarios, especially within Computer Science and Engineering's foundational realm.

With the Modern Algebra certification by Swayam, students delve into algebra's abstract nature, grasping its profound implications on geometry and numeric principles. By manipulating these abstractions, the course showcases how algebra fuels real-life mathematical applications, serving as a vital toolset for problem-solving and computation in science, engineering, and computing disciplines.

The objective of the Groups: Motion, Symmetry and Puzzles online course by SWAYAM is to encourage learners to explore and enjoy different aspects of groups. The programme is not specifically about group theory. Instead, it is about the importance of groups and why one should study them. The course curriculum also offers a glimpse into abstraction and why it is an indispensable mathematical tool. Candidates will learn all this and more, only in four short weeks.

The Groups: Motion, Symmetry and Puzzles programme welcomes anyone and everyone interested in understanding the significance of group theory and abstractions. Be it school seniors, science and engineering undergraduates, or even Masters and Doctorate scholars; everyone is welcome.

There are several assignments that candidates can undertake to evaluate their learning. Additionally, they can take the term-end exam to earn a course certification. They can do so by paying an examination fee and visiting any one of the designated test centres to appear for the assessment. 

The Numerical Methods: Finite Difference Approach course by Swayam is an advanced learning program for postgraduates and undergraduates from Science and Engineering backgrounds. This short, four-week training teaches students about partial differential equations, their different classes, and their solution methods. Falling under the ‘‘Mathematics’ ’ purview, it is a core curriculum set at the PG-level. 

The Numerical Methods: Finite Difference Approach certification syllabus also deals with the solution methods’ stability analysis and convergence. Since the curriculum covers this subject’s vital topics, it will allow candidates to solve numerous science and engineering problems once they finish every module. This training also has various applications in engineering sciences diverse fields. Thus, it is widely recognized by General Electric, TCS, ABB, Nuclear Industries, and similar companies. 

What’s more, students seeking job opportunities in organizations such as those mentioned above can opt for the Numerical Methods: Finite Difference Approach certification for a significant boost. Paying the required fees and clearing its eligibility, they can obtain this e-verifiable certificate to show recruiters. 

Modelling is imperative for understanding a large-scale process’s dynamics. Undertaking the process’s model equations-based virtual experiments, one can optimise operating conditions or/and design the systems efficiently. In most of these practical procedures, model equations deal with numerous parameters, ultimately resulting in partial differential equations (PDEs). The Partial Differential Equations (PDE) For Engineers programme helps candidates obtain holistic knowledge about this.

This four-week course in Partial Differential Equations (PDE) For Engineers: Solution by Separation of Variables by Swayam is an elective programme. Here, students will learn about the various solutions undertaken by process engineers to solve PDEs, including the separation of variables, which is this training’s primary focus. Falling under the ‘Mathematics’ category, this is a PG/UG-tier curriculum.

This training aims to establish solution technique skills among students, helping them become fluent in solving PDEs for various engineering applications. The curriculum also includes an optional Partial Differential Equations (PDE) For Engineers: Solution by Separation of Variables certificate. Interested applicants can obtain this by submitting all their assignments and clearing the course-end test. 

The ‘Decision-Making Under Uncertainty’ online course is a study about the various kinds of techniques and strategies used in decision-making for different situations. This operations research and management science course is provided by the online education portal Swayam by the government of India with the National Programme on Technology Enhanced Learning (NPTEL). The online classes of this elective program are conducted for a duration of four weeks. 

This course belonging to the domain of commerce and operations management is instructed by Prof. Natarajan Gautam teaching Industrial and Systems Engineering from Texas A&M University. The students of this AITCE approved course are engaged with online learning methods aided by the online resources and lectures with the books and reference materials to gain both theoretical and experimental knowledge.

The ‘teaching Industrial and Systems Engineering’ online training enables students to get an online course certificate and academic course credits after completing the program.

The ‘Laplace Transform’ online course is a study about the mathematical tool that is used to solve the various kinds of differential equations, difference equations, and integral equations that are found in the fields of engineering and other primary sciences such as physics, chemistry, biology, economics, and other technological domains. This mathematics certification program is provided by the free online education platform Swayam along with the National Programme on Technology Enhanced Learning (NPTEL). The online course classes are held through video lectures for a period of four weeks. The course mentor for this AICTE approved elective course is assistant professor Indrava Roy from The Institute of Mathematical Sciences, Chennai. The books and reference materials are given in the program to aid the experiential learning process for the candidates. The ‘Laplace Transform’ online certification course enables eligible students to gain course certificates and academic credits after successful completion of the course.

The ‘Our Mathematical Senses Part 1: Geometry of Vision’ online course is offered for the students to gain perspectives of the geometrical space around us and also know about the various mathematical concepts and theories associated with geometric and topological space. This online certification course is provided by the Swayam education portal, an initiative of the government of India, and the National Programme on Technology Enhanced Learning (NPTEL). 

The duration of this program is scheduled for four weeks and this is an elective course for the students of undergraduate level. This mathematics course is led by the course instructor Prof. Vijay Ravikumar(mathematician and artist) at the Chennai Mathematical Institute. The students of this program are enabled to acquire both theoretical and practical knowledge of the concepts through the virtual and experiential learning mode. 

The ‘Our Mathematical Senses Part 1: Geometry of Vision’ training course equips students with the course certificate and academic course credits after successful completion of the course.