Online Mathematics Courses & Certifications

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.

The Numerical methods course by Swayam is one of the tremendous courses that has its application in engineering and science fields. This course contains basic mathematical concepts like differentiation, differential equations and integration. In the digital world, numerical computation plays an important role in solving logical operations. In most of these operations, it is difficult to obtain results in an analytical manner. The main objective of this course is to provide algorithms and numerical methods for solving problems.

Real life problems from Engineering and sciences are solved using linear and nonlinear equations. Apart from this, the course also covers matrix problems that are solved using eigenvalues and eigenvectors. It also covers concepts like Jacobi theorem, Interpolation, difference tables, difference operators, forward difference, backward difference, Newton’s divided difference interpolation and Lagrange interpolation. 

The system for solving first and second order ordinary differential equations are taught through methods like Euler method, Modified Euler method, Milne PC method and Runge-Kutta method. 

This programme helps the engineers to tackle various industrial and engineering related problems. Implementation of numerical methods to solve the problems will make the candidate a great problem solver with high accuracy in problem solving.

Mathematics is the language of Technology, Engineering, and Science.  Calculus is a rudimentary mathematical topic in any engineering or science-based program. That’s why, to prepare you for the introductory calculus courses, edX has designed the Pre-University Calculus training. The program provides a refresher in five essential topics: differentiation, functions, integration, equations, and analytic geometry.

The self-paced Pre-University Calculus program features seven modules and one final exam. The modules themselves have short three-five minute videos in engineering, science, and technology. Moreover, you also get to test your knowledge by tackling interactive exercises and weekly homework. When you’re done with the curriculum, you’ll feel a lot more confident in negotiating with your first university-level calculus course.

After you’ve completed the Pre-University Calculus Certification syllabus, you will be relatively familiar with basic mathematical concepts and necessary definitions. You get to access the course material such as the videos and exercises for free. However, if you wish to have access to the final exam and certificate, you will need to purchase the certificate experience, priced at a nominal fee.

Becoming a skilled mathematical professional requires immaculate focus and training, but you must also create a strong foundation to handle numerous industry exercises. One of the core areas is Algebra, learning in which you’ll be able to interpret an array of equations and functions, hassle-free. The College Algebra certification course by edX provides a holistic package to this aid, where you’ll become fluent in Algebraic fundamentals.

A Doane University offers the College Algebra certification syllabus that covers critical areas such as inverse functions, graphs, polynomial functions, linear inequalities, exponential functions, equations and their linear systems, and many more. Successful course-takers will become adept in demonstrating increased skills in logical thinking and problem-solving. They will seamlessly pursue further education or employment in this field.

edX believes in furnishing a convenient studying experience and hence, offers the College Algebra online course at entirely no cost. Students will complete the curriculum comfortably in just eight short weeks, dedicating eight to twelve hours per week. Since it is at the intermediate level, learners don’t need to fulfill any eligibility criteria to enroll. The candidates are given the option of two tracks which may be chosen so that the course can be completed. Both the course tracks are self-paced but there is a time limit until which the course remains accessible in the audit mode. But in the case of the verified track, the candidates will be able to access the course materials for an unlimited period of time.

The Basic Calculus 1 and 2 online course offers a better understanding of the Calculus taught in classes 11 and 12. The course will explain in detail the methodologies of calculus. The topics such as differentiability, continuity of a function, and its applications will be discussed. The course will teach how to interpret a real number. The course will provide an understanding of the results. The series representation will be shown in the course curriculum.

The course is an online-based learning program. The course offers free access. The candidates who belong to disadvantaged groups of society will be benefitted. The course is offered on the NPTEL platform. The course will be accredited by the Indian Institute of Technology Kanpur. The course will be graded on the 6 best assignments out of 8 assignments and the final exam.

The Basic Calculus 1 and 2 certification is offered by NPTEL and can be e-verified. The certification is shareable on all platforms such as Linkedin, Facebook, Instagram, and many more. The certification will help gain new professional networks. This course is initiated by the government of India so the course certification is authentic and verifiable.

The online certification program on Basic Linear Algebra by Swayam is formulated as a basic session for interested students who wish to pursue higher academic knowledge in the field of engineering studies. The candidates who want to pursue a higher education qualification in the field of mathematics can also register for the Basic Linear Algebra training.  

The students in the Basic Linear Algebra certification syllabus will cover all the primary and basic tools that are used in the domain of “basic linear algebra”. The online session for a period of twelve weeks will be covering the topics namely- gram-Schmidt process, inner product spaces, rank-nullity, linear transformations, determinants, invertibility,  rank, diagonalization,  similarity, and applications. After completing the course, the Basic Linear Algebra certification benefits the students by clearing their doubts in the- Rn, rank of a matrix, linear independence, and subspaces. Students after completing the course the students will get to practice real-world cases.

The Computational Science in Engineering certification course enables students to understand the needs of the rapidly evolving field of computer science. Students can approach a wide array of challenges in the areas of social sciences and engineering through the power of computation. Spread over eight weeks, the course falls under the domain of Aerospace engineering. 

The Computational Science in Engineering certification syllabus ensures that students understand the different engineering and science phenomena via simulations. They are taught the much-required mathematical modeling skills, efficient algorithms, numerical analysis, software design, computer architecture, and much more. 

The goal of the Computational Science in Engineering training is to let students explore the basics of scientific computing. This includes the framework observed in applied mathematics such as ODEs, Linear algebra, and PDEs. Students who sign up for this undergraduate course are taught by Professor Ashok De, Associate Professor, Department of Aerospace Engineering at IIT Kanpur currently 

Introduction to Rings and Fields certification course has been designed with the objective of covering the basics of the abstract rings and the subsequent fields. The course will also offer knowledge on the algebra sequence. Candidates will also be taught how to prove certain theorems in a simpler manner.

The course focuses on the prime, maximal ideas and the various other rings of the domain. The students will be exposed to the theory of field as well so that they grow more. Examples have been used more so that the candidates are able to relate the learning and remember it for a longer period of time.

Introduction to Rings and Fields online course comes with the certification. The candidates will be receiving it after they complete the course. The candidates must ensure that they perform well in all the learning materials offered to them. The course will also prepare the candidates for some of the industries.

Graph Theory certification course puts forward the various basic knowledge for the candidates. The minute details of the topics have been covered in these topics. The main objective of the course is to offer a comprehensive introduction to the graph theory. Sessions have been designed with emphasis on a single topic in every module.

The candidates will be acquiring skills on putting large sums of data into visual form. The candidates will be studying graphs through a framework so that it becomes easy for the candidates to have proper learning on this. The different types of graphs have been illustrated so the participants are able to have a clear concept in each of them.

Once the candidate completes the Graph Theory online course, a certification has also been included. The candidates will be exposed to the learning methodology where they will be coming across simpler ways of acquiring the knowledge.

The Introductory Mathematical Methods for Biologists certification course focuses on a comprehensive framework of the particular major with an analytical approach. For biology students, it is an introductory mathematics course with the purpose of teaching them to do quantitative analysis of biological processes. Students will be instructed on how to explain biological processes using the vocabulary of mathematics, how to write basic mathematical equations for different phenomena that exist in biology. The Introductory Mathematical Methods for Biologists training will undertake the beginner’s concepts in a mathematical approach that will help the biology student to get better learning of each and every module of this particular curriculum. The course’s lectures are structured into different weekly sessions focusing on the main and core aspects of the field. The candidate can avail different benefits by doing this course in the end by getting Introductory Mathematical Methods for Biologists certification. Candidates can get intellectual learning that will be supported by the industrial side that will help them to take this course more fluently. This is a core structure to be completed in eight weeks as prescribed by the UGC. The course is categorized into biological science and bioengineering.

The Partial Differential Equations – I course by Swayam is the first course in a two-part course series. There will be around 20 hours of online learning spread over eight weeks. You will build a robust foundation on Partial Differential Equations or PDE over the course duration.

Through the Partial Differential Equations – I certification course, you will learn the geometry and analysis behind the core PDE concepts. And move beyond the problem-solving techniques to understand PDE theories in-depth. However, it will primarily focus on classical geometry and calculus variables.

The Partial Differential Equations – I course will first introduce you to the scope of the PDE study, followed by methods of characteristics, multi-variables, and classification in First Order equations. There will also be weekly assignments to help you test your progress.

The intended audience for the Partial Differential Equations – I programme are students and teachers belonging to the Mathematics, Science, and Engineering disciplines. However, this online course is still open to all interested candidates, irrespective of their background.

The Introduction To Galois Theory online course is provided to all the applicants by the Indian Institute of Technology, Madras. The course covers the subject line of mathematics. Participants who enrol for this programme will be able to learn about the aspects related to Galois theory. The course is entirely an online session for 8 weeks. The programme does not require students to undergo any long procedure of admission or entrance. The Introduction To Galois Theory certification course is free to be joined by the students who are interested in the discipline. The course provides unlimited access to the students to gain information from the programme.

The Introduction To Galois Theory programme includes video lectures, assignments, problem-solving assessments, and other activities for the proper understanding of the concepts to the students. Candidates can also gain certification for the course upon the successful completion of the programme. The course allows the candidates to be informed through the topics without any restrictions in regards to the attendance or timings of the sessions. An offline exam is conducted by the provider of the Introduction To Galois Theory training at the end of the programme so that the students gain the certificate. 

The Mathematical Methods in Physics 1 course by Swayam aims to help aspiring physicists develop a solid background in mathematics. The concepts covered in this course will make the mathematical aspects of the subject more accessible to the candidate. 

Professor Auditya Sharma, a top faculty from IISER Bhopal, teaches the Mathematical Methods in Physics 1 certification program provided by Swayam. It is accredited by IISER Bhopal and is an FDP course that has been approved by AICTE. It is a core program spanning weeks of extensive learning and falls under the category of mathematics. Moreover, this online course is purposefully designed for UG-level students. 

The Mathematical Methods in Physics 1 course will be taught online via video tutorials. There will be graded tests and internal assessments, and free study material for the candidate to access. Candidates will also be eligible for the course e-certificate if they sit for the end-term offline exam.

The Multivariable Calculus certification course is an undergraduate-level introductory program spread over eight weeks. It is offered to students with a background in engineering and sciences. Various topics related to calculus functions of two or more variables like differentiation and integration are discussed along with other applications. 

The Multivariable Calculus training also throws light on vector functions calculus and its wide array of applications.  This core course falls under the ‘‘Mathematics’’ domain and is offered by Professors S.K Gupta and Sanjeev Kumar from IIT Roorkee. Both the trainers are associate professors from the Institute’s Department of Mathematics and have several published research papers under their name.

The Multivariable Calculus certification syllabus covers the multivariable calculus topics extensively. Concepts ranging from limits, continuity, and partial derivatives to Taylor’s theorem, polar curves, and multiple integrals comprise this curriculum. Moreover, the certification issued contains the student’s name, his/her photography, the logos of NPTEL and IIT Roorkee, and their acquired final exam scores.

There has been a lot of advances in computer hardware and software libraries. Due to this, we can undertake scientific computing that requires high precision and with relative ease. Tools in Scientific Computing program is an elective course that explores various methods of computing. It emphasizes hands-on implementation while covering all the theory-based topics. The course will talk about major problems you might encounter while implementing these scientific computing tools. 

The syllabus of Tools in Scientific Computing certification has been developed by faculty at IIT Guwahati. This AICTE approved FDP course is available on Swayam, an online learning platform with support from the Government of India. Professor Aditya Bandopadhyay will be teaching this course. This is an undergraduate/postgraduate course in mechanical engineering, computational mechanics, and computational engineering.  

Tools in Scientific Computing is a digital course that uses assignments and practical usage of Python, GNU Octave, and C-based PETSC as learning tools. You can also opt for an e-certificate by sitting for an offline exam at the end of the term. 

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. 

The ‘Introduction to Abstract Group Theory’ online certification course is offered for the students to understand the concepts of abstract groups. The course enables students to study the definitions, fundamental properties, and structuring theorems in group theory. This free online certification program is provided by the Swayam online portal with the National Programme on Technology Enhanced Learning (NPTEL).

The instructor for this online program is professor Krishna Hanumanthu from the Chennai Mathematical Institute (CMI). The classes of this online training program are conducted for eight weeks in an online virtual environment aided by videos, lectures, course modules, examples, books, references, and other online resources. The students of this core course in their undergraduate or postgraduate level will gain both theoretical and hands-on insights with this course.

The ‘Introduction to Abstract Group Theory’ online course helps students receive certification according to the eligibility standards at the end of the course with credit points worth the certification.

The ‘Introduction to Abstract and Linear Algebra’ online certification course is developed for the students to get introduced to the theories and principles involved in the domain of abstract and linear algebra. This free online training is provided by the Swayam online education portal in collaboration with the National Program for Technology Enhanced Learning (NPTEL). The classes of this program are held in the virtual platform with the videos and lectures aided by books, references, and other resources for a period of eight weeks.

This core course is drafted for the undergraduate and postgraduate students of the engineering and science fields to gain from the theoretical and practical insights on the applications of these mathematical concepts. The course instructor is the associate professor Sourav Mukhopadhyay, faculty in the department of mathematics at the Indian Institute of Technology Kharagpur.

The ‘Introduction to Abstract and Linear Algebra’ online certification course enables the candidates to receive a certificate with two credit points by the end of this All India Council for Technical Education approved course.

The Probability for Computer Science Certification Course is a massive open online course that discusses the important topics in probability. The course available in online format on the Swayam learning platform is not a typical mathematics course. The course will familiarise learners with the concepts of probability along with its applications in algorithms and computer science. The Probability for Computer Science Training will be provided by Prof. Nitin Saxena of IIT Kanpur. The course will be taught via video lectures and is aimed at the undergraduate or post-graduate level. The model of assessments constitutes assignments and exams upon completion of which, learners will receive the  Probability for Computer Science Certification by NPTEL and IIT Kanpur.

Instrumentation and Process Control in the Food Industry is an 8-week online programme. The course is meant for undergraduate-level students who intend to step into the food industry. The Instrumentation and Process Control in Food Industry Certification Course is an online free programme offered by Swayam in collaboration with  IIT Kharagpur. Though it is free to join and pursue, the learners are required to sit for the exam and secure a certification qualifying score to get a hold of the certificate. 

Instrumentation and Process Control in Food Industry Certification is a course that is approved by AICTE (All India Council for Technical Education). The courses will guide you through process control and instrumentation in the food industry. Plus, the learners will explore stability analysis, food process control, control tuning and the like. The course is led by Prof. Ashis Kumar Datta who is a faculty at the Department of Agricultural and Food Engineering at IIT Kharagpur. 

Probability and Stochastics for Finance Certification will start with basics of probability as a tool to understand randomness and introduces the candidates to the main concepts, notions and results of stochastic financial mathematics.

Probability and Stochastics for Finance Classes provides necessary information for those individuals and professionals dealing with stochastic calculus and pricing in the models of financial markets such as SENSEX, NIFTY and operating under uncertainty.

All students enrolled will get a Probability and Stochastics for Finance Certification by Indian Institute of Technology Kanpur (IIT Kanpur) under the Swayam Initiative by Government of India. 

The coursework of the Introduction to numerical analysis course by Coursera has been structured to give the learners an insight into the various concepts of Numerical analysis and to help them develop their career in that direction. This course aims at enabling the candidates to have a detailed understanding of the process of numerical computing which requires assembling building blocks into computational pipelines and a basic understanding of its numerical methods, their strengths, limitations, failure modes and weaknesses. 

Through this coursework, the participants will be trained to analyze and develop the primary characteristics of numerical algorithms. They will be able to represent them with diverse classic problems in numerical mathematics. The process of implementing constructions into working prototypes of numerical code will also be taught. This course is being instructed by Evgeni Burovski who is an assistant professor at the School of Applied Mathematics at HSE.  The instructor ensures to deliver the programme in an interactive manner by including discussion forums, projects, e-learning videos and practice exercises as a part of conducting classes. This course is being offered by the National Research University Higher School of Economics on Coursera.

Harvard University is offering the Fat Chance: Probability from the Ground Up course in partnership with edX. It is a seven-week programme that will cover probability and statistics up to the college level. Thorough video lectures support the programme curriculum. It will enable you to have a deep understanding of what lies at the core of quantitative reasoning.

By taking the Fat Chance online training programme, you will rise over learning through rote formulae and term memorisation. You will hone your basic counting skills, along with their application to probability problems. The curriculum of the programme will also take you through the concepts of expected value, normal distribution, and variance. 

The probability from the Ground Up course by edX will train you to solve even the most complex problems based on stats and probability. Being a self-directed trainer, you can take your time to practice and learn the concepts as per your schedule. Also, as Harvard University is offering the course, the instructors will belong to the premier institution. The programme has two enrolment options; paid certificate mode and free audit mode. In the free audit mode, the students can get access to the programme only for a limited duration. 

The Automata Theory online course is an advanced computer science course developed by Stanford University. It covers finite automata, regular languages, regular expressions, non-deterministic and deterministic automata. Your instructors will also discuss closure properties, decision properties, and pumping lemma for regular and context-free languages.

The Automata Theory certification syllabus covers the Tuning machine. It is a kind of automaton that defines recursively enumerable languages (languages defined reasonably by a computing device of any sort). The curriculum then moves on to the theory of intractability. You will gain expertise in NP-complete problems, a class of intractable problems, as well.

The video lectures are delivered in English, and to help learners follow along, English transcripts are also available. Though it is a self-paced learning programme, you should ideally be dedicating five-to-ten hours to the Automata Theory training. After completing the seven-week training, you can purchase a shareable completion certificate from edX. It will help you highlight all your achievements and increase your employability. Edx has 2 tracks namely the verified track and the audit track which allows the students to finish off the course. During the verified track, the candidates will get unlimited but paid access to the course materials. In the audit track, the candidates will be getting limited but free access to the course materials. 

Learn about the fundamental mathematical concepts of kinematics, calculus, projectile motion, trigonometric functions, vector calculations, and much more, in the A-level Mathematics for Year 13 Course 2 certification course. The Imperial College of London has designed this course to help you succeed in an A-level maths exam with an A* grade. 

The A-level Mathematics for Year 13 Course 2 syllabus delves deeply into topics like general motion, projectile motion, integration and differentiation methods, graphs, diagrams, mathematical symbols, equilibrium, and more, to polish your skills and make you fully prepared to pursue STEM degrees. This is a comprehensive training program that lasts for seven weeks. 

During the A-level Mathematics for Year 13 Course 2 online course, candidates will acquire 360-degree theoretical knowledge and develop skills like problem-solving, fluency, and confidence. Created by the Imperial College, this course is available on edX for free. Candidates can also opt for certification at the end of the programme. The course is self-paced but there is a time limit until which the course remains accessible in the audit mode. But in the case of the verified track, the candidates will have unlimited access but they need to pay some amount.

Imperial College London’s A-level Mathematics for Year 12 – Course 2 certification focuses on helping candidates ace their A-level mathematics tests. Through an in-depth curriculum, the program intends to help students consider how everything they know about mathematics, fits into its vast world. Within a short span of seven weeks, the course content imparts all the vital learnings to shape the candidates as experts in this subject.

Spanning seven modules, the A-level Mathematics for Year 12 – Course 2 certification syllabus covers integral topics, ranging from Newton’s laws and calculus to statistical hypotheses. Through these, you’ll be able to test your initial skillset, correctly understanding how background expertise underpins this A-level programme.

Additionally, the A-level Mathematics for Year 12 – Course 2 training will help you gain the necessary skills such as fluency in applying appropriate answering methods. Candidates ace the confidence of assessing mathematical procedures, problem-solving, deep reasoning through proofs and formulae, and constructing mathematical arguments using critical tools.  Aspirants can also choose the paid accreditation to become verified candidates.

The candidates are given the option of two tracks to choose from so that the course can be completed. Both the course tracks are self-paced but there is a time limit until which the course remains accessible in the audit mode. Again, in the case of the verified track, candidates will be able to access the course materials for an unlimited period of time.

The A-level Mathematics for Year 13- Course 1 by edX is an intermediate-level training, built to help course-takers develop the required skills to ace undergraduate STEM degrees and gain an A*. The curriculum houses seven modules, covering vital topics such as Functions, Algebra, Sequences, Trigonometry, Numerical Methods, etc., thus helping learners gain full competency in A-level Maths.

Offered by Imperial College London, the A-level Mathematics for Year 13- Course 1 certification helps students understand how their knowledge fits into the extensive mathematical world. The curriculum helps them become fluent in various appropriate methods, covering all the core areas. Upon completion, students have ample confidence, deep reasoning skills, problem-solving abilities, and the required knowledge to efficiently put forth mathematical arguments. 

The online A-level Mathematics for Year 13- Course 1 training is for seven weeks, which students can learn in a self-paced manner, using pre-recorded video lessons. After finishing the program, they’ll house the best techniques and skills to apply in their A-level study. If candidates wish to, they can buy the shareable edX certificate, though the course is entirely free. The candidates are given the option of two tracks which may be chosen so that the course can be completed. 

Both the course tracks are self-paced but there is a time limit until which the course remains accessible in the audit mode. But in the case of the verified track, the candidates will be able to access the course materials for an unlimited period of time.

The A-Level Mathematics for Year 12 online course is designed and provided by edX in partnership with Imperial College London.  The program aims to provide you with enough skills to help you ace your A-level maths examinations. Aside from the examination perspective, the course will also encourage you to apply your mathematical learnings to the wider mathematical world.

The A-Level Mathematics for Year 12 certification syllabus is divided into seven modules. These modules cover coordinate geometry, inequalities, polynomial theorems, statistics, graphs, curves, and much more. They are designed to imbue you with mathematical fluency and confidence, along with the ability to construct a well-reasoned mathematical argument and problem-solving prowess.

After completing the A-Level Mathematics for Year 12 by edX, you will have a deeper understanding of the techniques and skills you can apply during your A-level study. What’s more, you also have a chance to earn a course completion certificate at the end of the course. All you have to do is pay a minimal fee, and you’ll get a shareable, verified document that you can showcase to the world and improve your job prospects. Students may enroll in any of the tracks namely verified and audit tracks which may help the candidates learn the prgramme. During the audit track, learning is free for a limited time period whereas during the paid verified track learning can be done for an unlimited period of time.