Swayam Mathematics Courses & Certifications

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.

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.

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 ‘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.

The Numerical Methods: Finite Difference Approach course by Swayam is an advanced learning program for postgraduates 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 Engineering Mathematics - I in Assamese certification course serves as a cornerstone for studies in sciences and engineering. Covering differential and integral calculus, linear algebra, and differential equations, it addresses topics like derivatives, integrals, matrix algebra, and differential equation solutions. The course equips students with indispensable mathematical tools vital across diverse scientific disciplines.

Catering to a broad audience in science and engineering fields, the Engineering Mathematics - I in Assamese certification by Swayam emphasises essential mathematical principles. It navigates through Mean Value Theorems, Maxima and Minima, Vector Spaces, Eigenvalues, and more, providing a robust framework for understanding complex problem-solving techniques.

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