Online Mathematics Courses & Certifications

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 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. 

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. In the course, there will be 36 lectures divided into 12 weeks duration. 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 Engineering Mathematics II online course is a 12-week course and the second part of Engineering Mathematics training. This programme is an undergraduate-level core course, and a  part of the mathematics category, offered by IIT Kharagpur. The course will be instructed in English by Prof Jitendra Kumar.

The Engineering Mathematics II certification syllabus deals with the essential and fundamental aspects of mathematics required for undergraduate science or engineering studies. Some of the topics covered under the course in the first eight weeks are vector calculus, numerical and complex analysis, and Laplace Transform methods applied to several engineering-related problems. 

Towards the end, the last four weeks of the Engineering Mathematics II training deals with module five, including in-depth information about the Fourier Series Representation and Transform.  The course also has many reference materials to help the candidates do their research. Candidates may even register for the exam and receive an e-certificate based on their eligibility.

The Fuzzy Sets, Logic and Systems & Applications by Swayam is designed in a definite structure to meet the knowledge requirements of students, researchers, and practicing engineers. The course deals with the fuzzy systems theory. The multiple values in fuzzy logic that the system deals with, are described in the course. This course also provides case studies of certain fuzzy logic usage from real-life.

This course is available on the Swayam online learning platform. Swayam provides free access to its courses. This course can be accessed on the Swayam website or from the downloaded Swayam app. This course is verified by one of the prestigious technology institutions of India, IIT Kanpur.  It is supported and initiated by NPTEL and MHRD respectively.

The Fuzzy Sets, Logic and Systems & Applications certification is valuable as it is government-initiated and nationally coordinated. The certification will help all those candidates aspiring for better future opportunities. The certification will have the logos of IIT Kanpur and NPTEL. It will also have the photograph of the candidates and the final score of the candidates.

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.