Swayam Mathematics Courses & Certifications

The Introductory Course In Real Analysis certification is a foundational program crucial for pure and applied Mathematics and Statistics, serving as a cornerstone in science and engineering. Tailored for undergraduate and postgraduate students, the 12-week curriculum strikes a balance between basic concepts and advanced theory, incorporating real-world examples.

The Introductory Course In Real Analysis certification by Swayam offers application-oriented problems to enhance practical understanding. With widespread support from universities, engineering colleges, IITs, and IISER, the course offers a comprehensive overview, ensuring students develop a robust understanding of Real Analysis for diverse applications in their academic and professional pursuits.

The Rock Mechanics and Tunneling certification course provides a deep dive into load transfer mechanisms and stability analysis of geotechnical structures on rocks, essential for civil and mining engineers. It also explores the efficiency and applications of tunnelling for underground transport systems. Students will gain practical skills applicable to infrastructure and mining sectors.

The Rock Mechanics And Tunneling certification by Swayam delves into topics such as rock behaviour under various loads, principles of rock mechanics, and tunnel design and construction. This elective equips students with valuable insights and hands-on experience, preparing them for careers in Civil Engineering with a focus on rock mechanics and tunnelling applications.

The Statistical Learning For Reliability Analysis certification course is a comprehensive exploration of techniques aimed at deriving meaningful insights from data. Covering topics such as machine learning, hypothesis testing, and variance analysis, it caters to students from diverse backgrounds like Computer Science, Engineering, and more.

The Statistical Learning For Reliability Analysis certification by Swayam provides a solid foundation in statistical learning methodologies. Students gain valuable skills applicable across academia and industry, meeting the demands of IT companies. Upon completion, learners are well-equipped to tackle real-world data analysis challenges and contribute effectively to data-driven decision-making processes in various sectors.

The Rings And Modules certification course offers a comprehensive introduction to the two core components of abstract algebra. The course covers fundamental concepts like ring definitions, homomorphisms, and submodule structures. Designed for undergraduates and postgraduates interested in mathematics, it provides a solid foundation for further study or research in algebra.

Split into two six-week segments, the Rings And Modules certification by Swayam delves into Ring Theory and Module Theory. Topics include ideals, quotient rings, module homomorphisms, direct sums, and tensor products. Students will gain essential skills in understanding and analyzing algebraic structures, preparing them for more advanced studies in abstract algebra.

The Introduction to Algebraic Geometry certification course explores the intricate relationship between Commutative Algebra and Algebraic Geometry, motivating students to delve deeper into both subjects. Through topics such as ring theory, algebraic varieties, and cohomology, students gain insights applicable to fields like algebraic statistics and artificial intelligence.

With the Introduction to Algebraic Geometry certification by Swayam, students develop a holistic understanding of mathematics, preparing them for advanced studies or careers in coding, mathematical modelling, and artificial intelligence. The course encourages students to see the elegance and applicability of these subjects in various industries, making it a valuable asset for students.

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 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 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.

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 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 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 

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.

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 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 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 ‘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.

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 ‘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.