Online Mathematics Courses & Certifications

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

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

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

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

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

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

The completion of a Discrete Mathematics Certification will lay the groundwork for enrolling in higher-level maths courses like real analysis, abstract algebra, maths modelling, geometry, and topology. 

Discrete Mathematics Classes shall discuss the symbolic logic techniques which are required for the algebraic understanding of circuits and computer logic and layer introduce you to Boolean algebras with the help of certain examples based on objects.

Discrete Mathematics Certification Syllabus will discuss how to express the overall functioning of a circuit mathematically in terms of certain suitably defined functions called Boolean functions and also consider a simple circuit design problem to illustrate the applications of the relationship between Boolean functions and circuits. 

All students get a Discrete Mathematics Certification by MPSTME, NMIMS Deemed University, Vile Parle West, Mumbai under the Swayam Initiative by the Government of India. 

The Introductory Course In Real Analysis certification is a foundational program crucial for pure and applied Mathematics and Statistics, serving as a cornerstone in science and engineering. Tailored for undergraduate and postgraduate students, the 12-week curriculum strikes a balance between basic concepts and advanced theory, incorporating real-world examples.

The Introductory Course In Real Analysis certification by Swayam offers application-oriented problems to enhance practical understanding. With widespread support from universities, engineering colleges, IITs, and IISER, the course offers a comprehensive overview, ensuring students develop a robust understanding of Real Analysis for diverse applications in their academic and professional pursuits.

The Rock Mechanics and Tunneling certification course provides a deep dive into load transfer mechanisms and stability analysis of geotechnical structures on rocks, essential for civil and mining engineers. It also explores the efficiency and applications of tunnelling for underground transport systems. Students will gain practical skills applicable to infrastructure and mining sectors.

The Rock Mechanics And Tunneling certification by Swayam delves into topics such as rock behaviour under various loads, principles of rock mechanics, and tunnel design and construction. This elective equips students with valuable insights and hands-on experience, preparing them for careers in Civil Engineering with a focus on rock mechanics and tunnelling applications.

The Rings And Modules certification course offers a comprehensive introduction to the two core components of abstract algebra. The course covers fundamental concepts like ring definitions, homomorphisms, and submodule structures. Designed for undergraduates and postgraduates interested in mathematics, it provides a solid foundation for further study or research in algebra.

Split into two six-week segments, the Rings And Modules certification by Swayam delves into Ring Theory and Module Theory. Topics include ideals, quotient rings, module homomorphisms, direct sums, and tensor products. Students will gain essential skills in understanding and analyzing algebraic structures, preparing them for more advanced studies in abstract algebra.

The Introduction to Algebraic Geometry certification course explores the intricate relationship between Commutative Algebra and Algebraic Geometry, motivating students to delve deeper into both subjects. Through topics such as ring theory, algebraic varieties, and cohomology, students gain insights applicable to fields like algebraic statistics and artificial intelligence.

With the Introduction to Algebraic Geometry certification by Swayam, students develop a holistic understanding of mathematics, preparing them for advanced studies or careers in coding, mathematical modelling, and artificial intelligence. The course encourages students to see the elegance and applicability of these subjects in various industries, making it a valuable asset for students.

The measure Theory Certification course is a 12-week online programme that offers a comprehensive exploration into the fundamental concepts and applications of measure theory. Students will gain a deep understanding of the theoretical foundations of measure theory and its practical significance in mathematical physics with the Measure Theory Certification by NPTEL.

The measure Theory training will develop the analytical skills necessary to tackle advanced mathematical problems and applications. Students are equipped with a solid foundation in measure theory, empowering them to engage with complex mathematical concepts. They are at the same time provided with a versatile toolkit for solving real-world problems.

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The Commutative Algebra Certification course is a 12-week online programme that provides students with a comprehensive exploration of the foundational principles and advanced topics within the field of abstract algebra. Students delve into the fundamental theorems of algebra through the Commutative Algebra Certification by NPTEL.

The online course develops proficiency among students in manipulating algebraic structures, proving theorems, and solving problems related to commutative rings and modules. The Commutative Algebra certification training strengthens the analytical skills necessary to tackle complex problems in algebraic structures and their applications.

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The Introduction to Algebraic Topology (Part-II) Certification course is a 12-week online programme that delves deeper into the fundamental concepts and techniques of algebraic topology. Students are offered a comprehensive exploration of algebraic structures and topological spaces, focusing on their interplay and applications through the Introduction to Algebraic Topology (Part-II) Certification by NPTEL.

The Introduction to Algebraic Topology (Part-II) training provides a combination of lectures and problem-solving sessions. They will gain a comprehensive understanding of these abstract mathematical structures and their applications in various branches of mathematics. Thus, they will be able to apply them to solve complex problems and contribute to ongoing research in the field. 

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The Partial Differential Equations Certification course is a 12-week online programme that offers a comprehensive exploration of differential equations. Students are provided with a deep understanding of their mathematical foundations and practical significance across various fields through the Partial Differential Equations Certification by NPTEL.

The online course equips students with the analytical and computational tools necessary to tackle real-world problems, providing invaluable skills applicable to research. The Partial Differential Equations certification training empowers them to confidently navigate the complex landscape of partial differential equations and unlock new opportunities for innovation and discovery.

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The Numerical Analysis Certification course is a 12-week online programme that offers a comprehensive exploration of fundamental numerical methods and techniques essential for solving complex mathematical problems. Students are provided with the theoretical foundations and practical applications of numerical algorithms through the Numerical Analysis Certification by NPTEL.

The Numerical Analysis training equips students with the skills necessary to effectively analyse and solve real-world problems using numerical methods. The course masters the art of numerical computation and analysis. They will gain proficiency in implementing numerical algorithms using programming languages such as Python, MATLAB, or R.

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The Matrix Computation and its Applications certification course is a 12-week duration programme. To join this certification course the students must have a basic knowledge of matrix theory. The course provides a comprehensive curriculum to the candidates such as an introduction to binary operations, vector spaces, subspaces, and linearly independent and dependent vectors.

 The Matrix Computation and its Applications certification by NPTEL is designed for undergraduate and postgraduate students. The certification course focuses on applications of matrices in various areas of engineering and science. Students gain hands-on experience and will be able to apply the learned concepts in real-world scenarios with the support of leading industry experts from IIT Delhi.

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

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

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