Free Mathematics Courses & Certifications

Linear Algebra Refresher Course Certification is a short-term certificate to brush up on the basics of matrix theory and linear algebra. Emphasis will be given to topics that will be useful in other disciplines as well, including systems of equations, vector spaces, determinants, eigenvalues, similarity, positive definite matrices, etc.

Candidates enrolling in this course will learn about the concepts in linear algebra and simultaneously by applying them in computer programs. At the end of Linear Algebra Refresher Course Classes, students can code their own personal library of linear algebra functions that they would have learned in this course and hence can be used to solve real-world problems.

All candidates undertaking the course shall receive Linear Algebra Refresher Course Certification by Udacity.

The course Advanced Linear Algebra: Foundations to Frontiers by edX offers a comprehensive course format that enables candidates to understand the fundamental concepts of linear algebra. The course equips the candidates with the opportunity to increase and build their knowledge of the primary key concepts for data and computational scientists.

Through the course, candidates will develop and enhance their knowledge, skills, and understanding of practical algorithms, matrix, and linear algebra for computational uses. The candidates will learn about the various tasks performed by the computer based on the fundamentals of algebra like analysing the effects of floating-point arithmetic.

The candidates with the help of this course will be able to master the learning of advanced linear algebra in a span of just 16 weeks. The course gives the ease to the candidates to learn at their own pace while learning from the reputed instructors from The University Of Texas at Austin. There are two modes of enrolment for this course; paid with the certificate and free without the certificate. Students who choose the free enrolment mode will get access to the course only for a limited duration. 

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 16 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 Certification Course by Swayam in Partial Differential Equation is very vital for the students from physics, mathematics and engineering backgrounds. The course mainly focuses on the first and second order of linear PDE. The course is very helpful in building a strong base in Partial Differential Equation. Upon completion of Course in Partial Differential Equation by Swayam one will be eligible for the certification.

The Certification Course by Swayam in Partial Differential Equation will have a tenure of 15-weeks and will have the level of postgraduate. The course in Partial Differential Equation by Swayam will enhance one’s skill in the different aspects of Partial Differential Equation.

The Certification Course by Swayam in Partial Differential Equation will be held online and the students don’t have to come to the center. The entire course in Partial Differential Equation by Swayam can be perused from one’s own home. While pursuing this course candidate will have the opportunity of doubt clearing.

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

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

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

One of the most productive subjects in college studies is Algebra and it also happens to be one of the most confusing ones. The course College Algebra and Problem Solving offer to teach the applicants this subject while making the concepts easy and using an adaptive method of educational impairment which ensures that the candidates have mastered the previous topics before moving on to the next ones.

Applicants will learn complex contents like general polynomial functions, quadratic functions, as well as exponential functions through self-paced, online sessions from experts in this academic field. It will also give them skills that provide them with the techniques for a problem-solving approach.

Candidates will be able to vent out any doubt that they have regarding the College Algebra and Problem Solving certification course via discussions which will also increase their understanding of the concepts and they can also get their queries solved with coaching granted to each individual one by one. The candidates can enrol on the course either in paid certificate mode or free audit mode. In the former mode, the learners will have unlimited access and a certificate of completion whereas, in the latter mode, they will be given only limited access to the programme. 

Calculus is one of the demanding courses that are often the core requirement for many global universities. The intermediate course on Precalculus is aimed at aspirants who wish to upgrade their calculus skills for a brighter future opening more academic opportunities. The course is offered by the online education provider: edX, in association with Arizona State University under the guidance of experienced faculty of the same university. The flexible learning system of ALEKS along with a chance of getting credit-eligibility, the Precalculus online certification program bags academic as well as professional gains. This three-credit course also satisfies the Mathematical Studies (MA) general studies requirement at Arizona State University. 

The course focuses mainly on preparing in calculus with the understanding of its functions like exponential, linear, polynomial, trigonometric, logarithmic, and rational; and with quantitative reasoning. From building a strong base on algebraic skills to developing advanced skills like the usage of functions in real-world setup, this intermediate course on calculus ensures an in-depth study on the central topic of learning. This programme has two options to enrol; paid and free modes. The paid mode provides a certificate of completion and unlimited access to the course while the free audit mode gives access only for a limited duration.

The Linear Algebra - Foundations to Frontiers course offered by the University of Texas at Austin available on the edx platform is a package of expertly crafted course material and follows a different approach of teaching to benefit their learners with deep knowledge. 

The course provides the participants with subjective knowledge of partitioned matrices, linear transformations, matrices, vector spaces and systems of linear equations, characteristics of special matrices, subspaces, and algorithms for matrix computations, eigenvalues, eigenvectors, linear least-squares, and characterizations of linear independence. 

The course follows a visual, applicable, and illustrative method of teaching linear algebra that makes this course a golden opportunity for candidates residing worldwide. This self-paced course offers flexible learning and makes it suitable for working professionals. The course is recommended for engineers, scientists, mathematicians, and people dealing with large datasets. 

The course also comes in handy to graduates and undergraduates studying in this field. At the end of the course, a verified certificate is awarded to the candidates which acts as a bonus and serves the candidate's purpose of taking this course. There is a time frame for the candidates to finish the course in case they have selected the audit track progressing at their speed. Whereas if they have selected the verified track, they will have unlimited time access to finish the course.

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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.