Free Mathematics Courses & Certifications

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 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.

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.

The ‘Complex Analysis’ online certification course enables students to learn about the foundational level mathematics focussing on complex numbers and the complex analysis functions. This online course attempts to discuss the implications of complex numbers that offer the spectral theorem for matrices. This free National Program for Technology Enhanced Learning (NPTEL) course is provided by the Swayam education portal. It is a core course for undergraduate and postgraduate level students and is scheduled for twelve weeks. The classes are held online through videos, lectures, weekly assignments, and other online resources.

The instructor for this online training is Dr. Pranav Haridas, assistant professor at the Kerala school of mathematics. The students of this course are given an opportunity to explore the theoretical and practical implications of complex numbers in the mathematics domain.

The ‘Complex Analysis’ certification course ensures a course certificate and credit points after successfully completing this AICTE recognized course and the certification exam.

The ‘Computational Commutative Algebra’ certification course is an elective course for the students to develop their understanding of the computation of the rings, ideals, and modules with the help of a computer. This course enables students to get an overview of commutative algebra with a focus on the computations and the techniques behind them. This free online training course is provided by the Swayam education portal along with the National Program for Technology Enhanced Learning (NPTEL). The classes for this course are conducted online for a period of twelve weeks.

The students of this program are led by the instructor, Prof. Manoj Kummini from the Chennai Mathematical Institute (CMI). In this course, candidates will get a theoretical and hands-on experience with the computational tool Macaulay2. This program can be downloaded and installed locally or can also be worked with the online version for smaller computations.

The ‘Computational Commutative Algebra’ online training program ensures an E-Certificate and credit points after completing the course and the assessments successfully.

An invitation to Topology certification by IMSC via Swayam is a 12-week online course. Through this online certification course, students will be exposed to the investigation and formalization of the abstract notion of a “space” under a minimum set-theoretic structure, known as a topology. An invitation to Topology certification syllabus provides foundational theory in topology which plays a crucial role in modern mathematics, and by extension, other mathematical sciences. This is a free course and anyone interested in learning topology can enrol in this online course offered by the Institute of Mathematical Sciences, Chennai (IMSC) via Swayam. 

Spread across 12 weeks, An invitation to Topology online course equips learners with the concepts of Topological spaces, Subspace Topology, Box and Product topology, and Metric topology. The course also provides a certificate on the completion of the exam which is conducted at the designated exam centres.

An introduction to Point-Set-Topology Part-I certification by IIT Bombay via Swayam explores the definition of metric spaces and topological spaces. This is a 12-week online course that deals with topological aspects of metric spaces. An introduction to Point-Set-Topology Part-I certification course will expose students to three crucial theorems on complete metric spaces while providing them with the structure of completion of metric spaces. Through An introduction to Point-Set-Topology Part-I online course, students will get familiar with topological spaces, building new topologies from the old, Bases and subbases, I and II countability, connected and path connectedness, separability, and others.

An introduction to Point-Set-Topology Part-I certification syllabus discusses the meaningful study of analysis and further topology. In the end, the course gives outstanding results such as Urysohn’s lemma and Titze’s extension theorem and some applications. An introduction to Point-Set-Topology Part-I classes are backed up by a strong team of tutors solving all the queries. The classes also include several online interactive sessions.

The Algebraic Combinatorics certification by the Institute of Mathematical Sciences (IMSc), Chennai is designed to introduce students to some influential paradigms in modern combinatorics. They are combinatorial classes and combinatorial species, Möbius inversion on partially ordered sets, and the Lindström-Gessel-Viennot lemma. The Algebraic Combinatorics training course is a 12-week online course delivered via Swayam. The Algebraic Combinatorics certification syllabus also provides learners with the theory of symmetric functions.

Students from science and engineering backgrounds having studied mathematics and computer science are best suited for the Algebraic Combinatorics certification course. The course will be taught by two instructors covering powerful paradigms in modern combinatorics. There are three credit points in the Algebraic Combinatorics online course that will be awarded to students after completion of the course. Students will also receive a certificate upon successful completion of the final exam. 

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 duration of the Introduction to Probability Theory and Statistics certification course is 12 weeks. The prerequisite for this course is the students must have a basic course on Linear Algebra and Calculus. The course curriculum covers a wide range of topics related to concepts of probability theory and statistics.

 This certification course is a core type and is designed for Undergraduate and Postgraduate students. The Introduction to Probability Theory and Statistics certification by NPTEL equips the candidates with essential skills and knowledge to apply the learned concepts for handling various real-world problems. Students will gain hands-on experience with the support of industry experts.

Also Read: Online Mathematics Courses & Certifications

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 program on AP Calculus BC by edX is a collaborative effort between the course-offering institution Davidson College, edX, and the College Board. The course has been designed to help you prepare for the Advanced Placement Calculus BC exam and conquer this subject’s most challenging aspects.

During the AP Calculus BC certification course, you will learn from the best AP instructors from across the country. Each session begins with an instructor’s video lecture, followed by hands-on exercises like data analysis, tutorials, and interactive graphs. Moreover, the highly experienced instructors divide the modules into bite-sized learning cycles, thus adding structure to difficult study sections.

Falling under the ‘Math’ field of study, the AP Calculus BC certification syllabus consists of short video lectures, simulations, AP style questions to analyze your understanding, practice problems, and interactive exercises to prepare you for exams. Candidates can enroll in this programme for free, and choose to pay for the verified certification, offered by Davidson College and edX. There is a time limit until which the course remains accessible in the audit track chosen by the candidates. But in the case of selection of the verified track, the candidates will have unlimited access to the course materials.

The Introduction to Probability Management certification course offered by edX is a guide for beginners who wish to learn the basics of probability, uncertain numbers, the arithmetic of uncertainty, developing risk models, and the relation between risk and uncertainty.

The Introduction to Probability Management training allows them to create interactive simulations, which can be shared among their team members working on Excel. The candidate will comprehend the flaw of averages, and understand the main reason behind the delay in projects. The Introduction to Probability Management certification benefits aim to focus on performing calculations of uncertain values from which productive results can be obtained. Also, the candidate will learn about Post Traumatic Statistics Disorder (PTSD) using limbic analysis and develop a plan to rectify the uncertainties.

An official certificate duly signed by the instructor will be issued after completion of the Introduction to Probability Management by edX. This certificate provided to the applicants will add a skill to their CV or resume and can be shared in the job application procedure and other platforms like LinkedIn or Upwork. Edx gives two options to enrol in the programme, namely, verified and audit modes. The verified mode provides a certificate of completion and unlimited access whereas the audit mode gives access only for a limited period. 

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.