Online Mathematics Courses & Certifications

The Swayam programme is initiated by the Indian government which targets to provide education to all among the youth of India. They have courses divided into nine categories, keeping in mind all students across India. Their courses are free of cost and each category has a number of courses that are beneficial for a better professional life. 

Numerical analysis is also known as computational mathematics is a course offered by swayam, which is basically needed to solve the problem and design functions on a computer. Some problems and functions are very complex and long and thus cannot be done by simple algebra and hence many mathematicians, physicians, and experts from other fields resort to the use of numerical analysis. It is used as a substitution for the complex methods of solving problems like definite integration, differential equations, interpolation, and many more. It is a time-saving formula. 

It is a very important and common topic. Some universities offer it as a core course. Any student from the field of engineering, computer science, mathematics, statistics, electronics, chemistry, or physics and opt for this. It is an interdisciplinary course used by many teachers, researchers, students, etc.

BCOC-134 Business Mathematics and Statistics Certification helps students to learn how to make decisions when presented with incomplete information through comprehensive coverage of statistical methods, management mathematics and probability and extensive examples and questions for students on business and accounting courses. Commercial organizations and companies use mathematics and statistics in many applications such as accounting, inventory management, marketing, sales forecasting, and financial analysis.

BCOC-134 Business Mathematics and Statistics Classes help candidates undertaking this course to develop the abilities to deal with numerical and quantitative issues in business and thus enable the use of statistical, graphical and algebraic techniques and methods wherever relevant to solve the issues. 

The Introduction to Geometry program, which is provided by edX in association with the SchoolYourself institute, explains geometry to the candidates from the very beginning. It introduces the candidates to the basics of geometry which includes triangles, quadrilaterals, polygons and line segments. It also talks about the history of geometry which began 200 years ago way before rockets were launched and explain the proof of 3D and 2D shapes.

This course does not fail to answer questions like, “What are parallel lines?” or “How big is an angle?” and then gradually proceed to more complex problems and theorems like the Pythagorean and Cavalieri’s principle. The course deals with finding the area of triangles using more than one formula, volume and surface area of different objects and it also discovers many shortcuts to counting numbers.

It explains candidates about the estimates of the size of Earth and teaches about other high school geometry concepts perpendicular lines and segments. Introduction to Geometry course is funded partly by Wertheimer Fund.

AP® Calculus: Challenging Concepts from Calculus AB & Calculus BC is well formulated to provide students with examination-style questions, video lectures, and assignments for learning in a more dynamic way The syllabus includes all the necessary topics that will help students master both calculus on BC and calculus on AB. All the sections and subsections will be covering all the important and demanding topics in this domain.

For a better understanding of the students, the entire course is divided and subdivided into topics and each of the concepts is vividly described using- interactive and descriptive graphs, practice sets, and video lectures by the professors of DavidsonNext. Throughout the session, all the students will be guided and trained. Periodic assessments will take place to track the student's performance and help them learn. The course will be guiding students to build a strong foundation in calculus so that they can pursue career options in academic research.

The Mastery of Math for Middle School - Decimals Online Course is a specialized course aimed at teaching professionals and aspiring teachers who wish to learn about innovative approaches to solve mathematical operations. The course offered by subject experts explores different strategies to solve mathematical problems involving decimals.

Through the Mastery of Math for Middle School - Decimals Training, learners will be introduced to new methods and strategies of solving maths questions through e-learning content and videos. After completing all course assessments steps, learners will receive a Mastery of Math for Middle School - Decimals Certification by TCS iON.

The Mastery of Middle School Mathematics - Number Operations Training Course is a self-paced certificate course that both experienced school teachers and freshers who wish to gain in-depth knowledge of number operations. The course is offered in an online format and the e-learning content provides learners with specialized strategies of teaching and learning numbers and number operations.

After completing the course steps including all module assignments and assessments, learners will be receiving a Mastery of Middle School Mathematics - Number Operations Certification by TCS iON. The course is provided completely free of cost in English medium. It can be completed within a duration of 13 weeks.

The Mastery of Math for Middle School - Multiples and Factors Online Course is a micro-course that is aimed at middle school teachers, aspiring teachers and maths specialists who wish to gain a detailed understanding of multiples and factors. The free certificate course is offered in a self-paced manner through videos and e-learning content.

Through the Mastery of Math for Middle School - Multiples and Factors Certification by TCS iON, learners will be introduced to different innovative teaching and learning strategies. The course will be evaluated through module assignments and course assessments at the end of which learners will be provided with a certificate of participation.

The Mastery of Middle School Mathematics - Fractions Training Course is a self-paced online course that educates learners about fractional numbers, mathematical operations on fractions and decimals. The course offered by experts through the TCS iON platform is aimed at middle school teachers and maths specialists who wish to gain skills in mathematical operations.

The course is open to both aspiring teachers and professionals who are interested in learning about innovative strategies. After all the assessments and module assignments are completed, learners will be rewarded with a Mastery of Middle School Mathematics - Fractions Certification. The course requires learners to contribute about 2 to 3 hours for the course.

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

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

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

Discrete Mathematics is known as the language of computer science. Learning discrete mathematics is going to be useful in many fields like data science, software engineering and machine learning. 

In this course, students will be solving math puzzles with proofs and their explanations to understand the concept of Discrete Mathematics thoroughly. The concepts of discrete mathematics today are used in various ways to understand different scenarios and the problems in all branches of computer science, such as programming languages, automated theorem proving, software development, computer algorithms and cryptography.

Swayam Discrete Mathematics Course is designed in a way to make sure students learn the concept of discrete mathematics in a fun way so they can understand its applications easily. 

Students don't need to have any prerequisites for this course, just a basic understanding of high school level algebra and arithmetic is required.

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 Applied Linear Algebra online course introduces the fundamentals of eigenspaces, inner products, vector spaces, and linear transformations to electrical engineering aspirants. This program encompasses all the core learnings to help candidates master these concepts and progress to the further applied for linear Algebra courses. The training falls under these categories - ‘Instrumentation and Control’, ‘Signal Processing and Communication’ and ‘Communications Engineering, Electrical, and Electronics’. 

Spread across 12 weeks, the Applied Linear Algebra certification syllabus comprises vector spaces, eigenvalues’ applications, and positive operators. Candidates learn about solving linear equations, inner product spaces, normal operators, quotient space, and other critical learning areas. Set in the postgraduate/undergraduate level, this curriculum is a core program, currently ongoing on Swayam. 

The Applied Linear Algebra training also offers course certificates to eligible candidates, who register and clear Swayam’s program-end proctored test. Upon doing so, students will earn a digitally-verified certification with their credentials and institution logos, bearing testimony of their acquired knowledge in the concepts taught. The course also houses industry support from Artificial Intelligence, Communications, and Analytics. 

The intention behind learning the Advanced Partial Differential Equations program is to understand the physical phenomenon occurring in nature. In this course, candidates will explore the basic ideas, inner workings, and characteristics of first-order equations. They will then progress to three fundamental second-order equations. 

As mentioned before, the Advanced Partial Differential Equations certification syllabus will begin with the study of first-order equations such as the Burgers equation, entropy solutions, Reinmann problem, etc. After that, the course will explore the Laplace equation, Wave equation, and Heat equation in detail. 

This course is an AICTE approved faculty development program. Individuals participating in the Advanced Partial Differential Equations Certification will go through a twelve-week process where they will learn through online lectures and weekly assignments under the guidance of Professor Kaushik Bal from IIT Kanpur. Participants of the course will be eligible to achieve a certificate by scoring well in assignments as well as a final offline exam.

The Applied Linear Algebra for Signal Processing, Data Analytics and Machine Learning certification is offered by Swayam. The course will provide you with fundamental knowledge about the core concepts of Linear algebra. Linear algebra plays a significant role in a wide range of fields and has multiple applications, including data analysis, wireless communication, machine learning, finance and control, and signal processing. 

The Applied Linear Algebra online programme is approved by AICTE and has been designed as an attempt to teach the cutting edge and diverse applications of linear algebra. If you are from the IT and engineering field, you will be interested in learning about the advanced concepts as they are extremely significant in multiple industries today. Thus, you can increase your knowledge and hiring prospects by enrolling on the course offered by Swayam in association with IIT Kanpur. 

Besides, the Applied Linear Algebra certification will run for 12 weeks for free, and you can earn an e-certificate by taking a proctored exam. The training is a part of IIT Kanpur’s Faculty Development Programme (FDP). Apart from UG and PG students, practising scientists, engineers, and managers from various fields can purse the FDP.

Advanced Probability Theory program is a core course in mathematics designed for undergraduate and postgraduate students who want to learn probability concepts from Kolmogorov’s Axioms. This financial industry-supported course will cover a variety of topics in 12 weeks.

Advanced Probability Theory certification will be conducted through a series of online lectures and regular assignments. Participants of the course can also appear for the final exam in person and gain a certificate upon passing all the criteria.  The educator for this course is Professor Niladri Chatterjee from IIT Delhi. 

Advanced Probability Theory will go through topics such as cumulative function distribution, probability density function and provide an introduction to the concept of a random variable. Participants will also learn about probability distributions, the function of one or two random variables, and the overview of order statistics. This is an AICTE approved program that also provides a list of books and references for the benefit of the participants.

This Basic Calculus – 1 online course is offered by the Swayam online learning platform. It is coordinated by NPTEL. This course aims to guide basic calculus to all types of candidates irrespective of their social standing. The duration of this course is 12 weeks. The course will follow the referenced book chapters 1 to 5. The candidates will revise certain notions they learned in school and also will get introduced to new notions.

This course is primarily intended for those candidates who are at the undergraduate level pursuing Bsc. The calculus taught in this course will be an updated version of the calculus taught in schools. This course is accredited by NPTEL. The lectures of this course will be around 40-45 minutes. The instructor will solve about 100 problem exercises and show usage of graphs.

The Basic Calculus – 1 certification will have the logos of NPTEL and the Indian Institute of Technology Madras. The certification will benefit the candidates academically and professionally. The certification will be provided in the e-format. This makes it easily shareable on all platforms such as LinkedIn.

The Algebra-II program is a 12-week course in algebraic equations and concepts. It is a continuation study with advanced concepts. Set at a postgraduate level of study, one learning module is assigned per week. Students can previously complete the first course and proceed to cover advanced topics of the second course.

Based on mathematics, the Algebra-II certification syllabus covers core topics in algebra such as multilinear equations, tensor products, extensions, and fields. Candidates will also learn about Galois, Krull-Schmidt, and Jordan-Holder’s theorem in algebra. Learners can choose to attend a proctored exam by paying a nominal fee.

The Algebra-II online course is instructed by the faculty of the Institute of Mathematical Sciences, Chennai. Prof. Amritanshu Prasad and Prof. S Viswanath from the institute are the mentors. Students need to secure minimum scores in the assignments and the proctored exam scheduled for the certificate. Additionally, the faculties specify references and books learners can follow while studying.

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.

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 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.  

This course is offered under NPTEL, funded by MoHRD, by IIT Kharagpur. It is aimed at teaching the basic mathematics that is essential in every stream of undergraduate studies in the categories of engineering and sciences. The course comprises topics in integral and differential calculus, linear algebra, and differential equations which students will be able to apply in a number of engineering problems. 

This course will contain topics like Taylor's and Maclaurin's Theorems, Indeterminate Forms, Mean Value Theorems, etc. Partial derivatives, Taylor's development of functions of several variables, minima and maxima, and differentiability are also part of the course. 

The course also teaches Leibnitz rule (differentiation under the integral sign), improper integrals, applications of multiple integrals and multiple integrals, their properties. Other topics incorporated in a series of 60 lectures over the course of 12 weeks, include Linear Equations’ Systems, Dimension and Basis of a Vector Space, Properties of a Matrix and its Rank, Vector Spaces.

The Numerical Methods for Engineers course by Swayam is designed to give an overview of various numerical methods that are of great interest to scientists and engineers. This course focuses on the numerical techniques, its analysis and its properties. The theory behind numerical methods and applications of them are also discussed. Numerical methods are mainly used by computers to solve iterative and step-wise problems which are tedious to solve by hands.

This course covers concepts like curve fitting, interpolation, regression, linear systems and mathematical concepts like algebra, integration and differentiation. Various computational tools like FLUENT, Aspen, FORTRAN and MATLAB are used for teaching. Algebraic equations are solved using open and bracketing methods like Regula-Falsi, Bisection, Secant, Multivariate Newton’s method, Newton Raphson and Fixed point iteration.

The 12-week programme comprises weekly assignments and 2.5 hours of video tutorial every week. A discussion forum for clearing the doubts of the participants is also available. This course would greatly benefit the candidate to improve their problem solving ability.

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

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

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

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

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

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

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

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

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

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

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