Free Mathematics Courses & Certifications

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. 

Discrete mathematics is a branch of mathematics and a language of Computer Science used in fields such as data science, software engineering and machine learning. This branch involves the usage of algebra and arithmetic and involves discrete elements. The Discrete Mathematics online course by Swayam intends to explore and explain the topic of discrete mathematics over the course of 12 weeks.

The Discrete Mathematics program will introduce you to various mathematical concepts and theories to help you solve problems and apply proof techniques. The programme endeavours to help you grasp some of the essential ideas in discrete mathematics. The IITB certification also features concepts such as Graph theory, Cardinality theory, Combinatorics, basic number theory, etc. in detail.

The Discrete Mathematics certification course is an undergraduate and postgraduate level course. It falls in the ‘Computer Science and Engineering’ and ‘Foundations of Computing’ categories. Designed by IIT Bangalore, the course has been approved by AICTE and offered by Swayam as a free online learning source.

Mathematical concepts are often complicated, and you might get bored learning them through the traditional chalk and board method. Hence, IIT Ropar has developed an innovative and creative course to teach discrete mathematics through the Discrete Mathematics certification course. The 12-week-long online programme lays emphasis on problem-solving skills and logical thinking.

Discrete mathematics is a significant branch of mathematics used in machine learning, data science, and software engineering. The Discrete Mathematics- IIT Ropar online course has been designed to make learning mathematics fun for students. You can learn through a series of video lectures that include several illustrations, animations and anecdotes to ensure full understanding and retention.

Furthermore, Discrete Mathematics training by Swayam assumes no prerequisites and is open for anyone interested in learning the programme. You can attain an official certificate awarded by Swayam and NPTEL at the end of the programme by qualifying for the final certification examination and all the assignments.

The Introduction To Algebraic Geometry And Commutative Algebra certification is an online program that does not require any fees to be paid by the students to be a part of the program. Candidates who pursue this course will get an understanding of topics related to algebraic geometry such as rings and ideals, theorems, topology, etc. The Introduction To Algebraic Geometry And Commutative Algebra training can be joined by graduates as well as postgraduate students since this is not only a beginner level of the program but includes topics from advanced level too. The course is being offered to the students by the Indian Institute of Science through the platform of Swayam that provides a thorough online and self-paced program to all the participants.

The certificate for the course can also be obtained by a participant when the candidate has completely covered the whole Introduction To Algebraic Geometry And Commutative Algebra certification syllabus along with assignments or assessment included in the course. The certification for the program comes at a cost along with an offline exam which needs to be given according to the terms and conditions of the provider of the course. The course needs only a time period of up to 3 months to cover it entirely but in case the candidate wants to go for a longer period of time, he can do so without having to pay any extra amount due to the course being a self-paced Introduction To Algebraic Geometry And Commutative Algebra program.

The Introduction To Algebraic Topology (Part-I) Certification course is a master's level program and requires fundamental knowledge in the field of point-set topology and group theory. The course also touches upon the modern aspects of mathematics. The course will be offered to the candidates by IIT, Bombay and the syllabus of the Introduction To Algebraic Topology (Part-I) program is similar to the program of the National Centre for Mathematics. The course deals with different topics throughout the syllabus like path homotopy, convex geometry, covering spaces, and many more topics which gives a variety of knowledge to the students. 

The Introduction To Algebraic Topology (Part-I) certification syllabus of the course can be completed according to the pace of the candidate although the set timing for the completion of the training is 3 months. Candidates need not buy any external study material or notes as the course includes the full package of study material, assignments, tests, fonts clearing discussion platform, etc. The other benefits of the Introduction To Algebraic Topology (Part-I) by Swayam include a certification which will be provided to the students only if they acquire the passing grades in the exam and register for the same by paying the exam fees. 

The online course on Integral and Vector Calculus by Swayam will be offering a detailed introduction to the topic of - integral and vector calculus.  The program will deal in a descriptive way with the concepts of- Riemann sum, partition, and Riemann Integrable functions and their applications as well as their properties. The online course will also discuss the fundamentals of- anti-derivatives. 

The online certification course will teach the students over the course of twelve weeks about the classical theorems of integral calculus that also includes the - fundamental theorem of integral calculus. The Integral and Vector Calculus online course curriculum includes the concepts of-  differentiability, gradient, divergence, directional derivative, and their geometrical interpretation and curl of vector functions in real-world functions. 

The important and fundamental topics of - theorems of vector calculus: Gauss’s, Green’s, and Stoke’s theorem will also be discussed in the course. To help the applicants understand in a more comprehensive manner the course has been structured as - core.

The Introduction to Commutative Algebra program by Swayam is a twelve-week online course, designed for individuals who want to research areas such as algebraic geometry, commutative algebra, algebraic number theory, etc. It is an AICTE approved FDP curriculum, intended for postgraduate-level students.

Curated by IIT Madras, the Introduction to Commutative Algebra certification syllabus covers crucial topics such as ring homomorphism, prime and maximal ideals, Jacobson radical, module homomorphisms, submodules, and tensor product of modules. The exact properties of the tensor product and Noetherian rings are also a part of this comprehensive course. The Institute’s Professor A. V. Jayanthan will teach this course.

Moreover, the Introduction to Commutative Algebra training requires learners to have the necessary knowledge of linear algebra, basic ring theory, and group theory. Students will receive assignments and study through Swayam’s video lectures during the course. In the end, learners need to pass the final exam and meet all the certifying criteria to obtain their course certificates.

The Online certification course on the Measure Theory by Swayam will be covering the key concepts and principles that are involved in integration and measure. The course will begin the training by introducing the candidates to the applications of- integration theory and the abstract measures along with their applications. In the next half of the online course, the trainers will be dealing with the theories that pertain to- the Lebesgue measure and its real-world applications.

The course will also provide the students with a detailed study of Borel measures on locally compact Hausdorff spaces. The Measure Theory certification syllabus will also comprehensively elaborate on the principles of- Lp spaces and product measures along with Fubini’s theorem. In the period of twelve weeks, the applicants will also be provided with the assignments on several classical results such as- the Ries representation theorem, the  Radon-Nikodym theorem, and the Lebesgue differentiation theorem.

Linear algebra is a continuous form of maths as it allows us to model natural phenomena and understand the theory behind machine learning and deep learning. It is an integral subject in mathematics applied in engineering, science, and other mathematical areas like geometry and functional analysis. Linear Algebra by Swayam is an online program that emphasizes the crucial concepts of linear algebra and gives a thorough introduction to this foundational subject.

The Linear Algebra online course has been designed by the Kerala School of Mathematics expert faculty. The training falls under the domains of foundations of mathematics and algebra. It is spread over 12 weeks and is free to enroll for all learners. 

Furthermore, Linear Algebra training by Swayam will offer a certificate to students who finish the whole course, including assignments, and qualify for the exam. Students will learn through various examples and use their problem-solving skills to deal with many mathematical problems. No charges are applicable for enrollment.

The Ordinary and Partial Differential Equations and Applications certification course is designed with complete overview of the differential equations and its relative significance. This course is a standard curriculum that is offered to UG/PG engineering or science students. It requires the presence and uniqueness of an ODE solution, homogeneous and non-homogeneous linear differential equation systems, second-order homogeneous differential equation power series solution. 

The Ordinary and Partial Differential Equations and Applications training will undertake both aspects of the curriculum in an analytical and practical manner that will help the candidate to be more productive and effective in their respective major. This course has considerable applications in numerous engineering and science areas, such as control theory, numerical analysis, dynamic systems, etc. The main motive will be focused towards the core elements of the major that have a significant role in the functioning of the problem-solving areas. 

This course will provide a quick overview of the whole curriculum in the beginning and then later it will be directed to the new modules, framework, theorems, challenges and limitations that are associated with this particular programme along with that, the candidate will be provided Ordinary and Partial Differential Equations and Applications certification that will help them to pursue further courses in same field. 

The Numerical Linear Algebra online course has been structured as a basic and fundamental course for the students who are pursuing their postgraduate or undergraduate level degree course from the stream of science or engineering. 

The Numerical Linear Algebra certification benefits the registered students by providing them the core concepts regarding- stability of numerical algorithms, matrix algebra, stability of nonlinear systems, conditioning and condition number,  vector and matrix norms, convergent matrices, computer arithmetic, sensitivity analysis, singular value decomposition (SVD), least square solutions, algebraic and geometric properties of SVD, Power method and applications, Householder matrices and applications, QR method, Jacobi method for finding the eigenvalues of a given matrix. 

The Numerical Linear Algebra certification course will be dealing with all the real world applications of the numerical linear algebra concept in the diverse fields of - sciences and engineering. The twelve weeks course will be emphasised on topics like- control theory, numerical analysis, image processing and dynamical systems.

Probabilistic Methods in PDE by Swayam is designed by IISER Pune and verified by NPTEL. Professor Anindya Goswami instructs this ongoing elective program that spans 12 weeks. The course falls under the purview of Mathematics and is based on two books, namely: Semigroup Theory and Stochastic Calculus. Candidates seeking certificates can also acquire them by paying and registering for the proctored evaluation. 

The Probabilistic Methods in PDE certification syllabus introduces you to a potent research tool related to the differential equations theory. The curriculum aims to offer expertise on probability theory and PDE, considering the absence of extensive learning material on this topic. Young researchers who have to undergo time-consuming research with scattered references have easy access to the course’s compiled information, offering in-depth insights.

The Probabilistic Methods in PDE program is an advanced curriculum but is also ideal for mathematical finance, probability theory, PDE, or mathematical physics aspirants. The instructor will explain several complex theorems from the books mentioned above during the course lectures to facilitate a comprehensive approach towards the subject.

The Optimization from Fundamentals certification course is a structural framework set for improving the learning of the field in a more effective way. From its fundamentals, this course will cover the subject of Optimization. A summary of actual analysis and convexity will begin with it. Linear programming, convex optimization and nonlinear programming, complementarity concerns and algorithms for the same will cover this basis. 

With dynamic optimization, the Optimization from Fundamentals training will stop. The course will give a complete framework of what's the level of optimization in different sectors and now where it stands and what are the problems and challenges, it suffers.  

The Optimization From Fundamentals certification will give an assurance that the candidate is more effective in the respective field, which will help him to undertake the same major in their respective upcoming future. The course is more tilted towards the understanding of the core elements that play the main role in the functioning of optimization principle. The students who will get enrolled in the programme will study various elements that are so vital for the functioning of the fundamentals and Optimization from Fundamentals certification syllabus will mainly consulate with that only. 

The online Variational Calculus and its applications in Control Theory and Nanomechanics training course has been designed as an introductory session to the main theory and applications that are related to variational calculus to problems with respect to- physics, geometry, and differential equations along with mechanics. This course on Variational Calculus and its applications in Control Theory and Nanomechanics by Swayam provides the students with adequate knowledge on the topics of- ordinary differential equations, vector calculus, and basic mechanics. In the course tenure, the applicants will be learning about the new applications that are being applied in- physics, biology, mathematics, chemistry, and engineering. 

The Variational Calculus and its applications in Control Theory and Nanomechanics certification benefit the students as this will serve as a reference for advanced study and research in the same domain. After completing the course the students will have their skills increased in the field of functionals that contains several dependent variables.

SageMath is a python based, free and open-source computer algebra system (CAS). The software is being used widely to explore applied linear algebra, calculus, and numerical methods. The Computational Mathematics with SageMath course by Swayam aims to deep dive give practical learning to the applications of SageMath in the concepts mentioned earlier.

The Computational Mathematics with SageMath certification syllabus covers a range of topics like python, classes in python, use of NumPy, SciPy, and SymPy, exploring SageMath, local maximum and minimum, and the like. The AICTE verified course is perfectly suited to students wishing to pursue their careers in the data science or numerical computations industry.

Besides, the Computational Mathematics with SageMath online course is taught by an experienced professor from chemical technology, Mumbai, called Prof. Ajit Kumar. The 12-week course will contain weekly assignments for evaluation through which the students will be able to track their progress.

The Transform Calculus and its applications in Differential Equations online course will help candidates learn about the basic techniques involved in the integral. The simpler ways of dealing out with the equations and coming up with the solution in a quick span of time will be taught to the candidates.

The candidates will be exposed to high-level concepts as well so that there is no difficulty in the process of learning. The course will train the students with the basic Integral Transform techniques. The candidates will be learning everything this topic covers within this time. The high-level concepts will also be touched by the experts.

The Transform Calculus and its applications in Differential Equations training come with certification, so the learning is a fun process. The candidates will have all the learning materials with them prior to the starting of the course and can carry on with their learning anytime they wish to.

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.

Coursera’s Discrete Mathematics online training programme uncovers the fundamentals of discrete mathematics, and how it also forms the mathematical foundation of information and computer science. You will be familiarized with a wide range of mathematical aspects such as functions, graphs, relations, sets, etc. which are ubiquitous and thoroughly involved in computer science.

The online programme, Discrete Mathematics, is an intermediate-level course and attempts to teach through rigorous methods while also trying to avoid being extra formal. For this, the course not only introduces the concepts and gives the full proof, but also makes the process interesting by showing at least one non-trivial result. Examples and figures will be used whenever possible to avoid extremely formal representation.

The Shanghai Jiao Tong University offers the Discrete Mathematics online course and is known to be one of China’s fastest developing universities. The course curriculum features online video lectures, course readings, quizzes, assignments, and interactive feedback. Moreover, it also provides flexible deadlines for a self-paced learning experience. Upon completion, you will also earn the e-certificate, which can be shared across your LinkedIn profile, CV, or printed resume.

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.