Get updates on Eligibility, Admission, Placements Fees Structure
Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Course Overview
Learners pursuing the Topology Certification will encounter crucial ideas like continuity, convergence, compactness, separability, and connectedness that are crucial in numerous applications of mathematics.
Students will learn definitions in Topology Classes and build examples and counterexamples based on definitions. Topology Certification Syllabus includes a variety of definitions, theorems, continuity, convergence, and their justifications. All students get a Topology Certification by University of Mumbai under the Swayam Initiative by the Government of India.
The Highlights
- Provided by University of Mumbai
- Online course
- 12 Weeks course
- Learn at your own pace
- Shareable Certificate
- Expert Lectures
Programme Offerings
- video lectures
- Study Materials
Courses and Certificate Fees
| Fees Informations | Certificate Availability | Certificate Providing Authority |
|---|---|---|
| INR 1000 | yes | Mumbai University |
If you want a certificate, you have to register and write the final exam which will be notified well in advance, however it is optional for a fee of Rs 1000.
The Topology Certification Fees is nil. It's open for all interested candidates.
Topology Certification Fees
Description | Amount |
Course Fees | Free |
Course Fees (with certification) | INR 1000/- |
Eligibility Criteria
Certificate Qualifying Details
E-certificates will be issued to all such participants who get 30% weightage internal assessment and 70% weightage main examination.
Work experience
No prior work experience is necessary to register in this certificate programme.
What you will learn
The types and topological properties of these subsets will be covered in the Topology Certification Course along with the question of whether intervals are formed by their union, intersection, or complement. Students will benefit from Topology Training that explains the concepts of a neighbourhood of a point on a line, limit points of a set, and the Bolzano Weierstrass Theorem.
The following learning outcomes are achieved upon successful conclusion of this Topology Certification:
- Understand standard concepts of Set theory
- Analyse structure of Sets and other abstract algebraic structures
- Describe when a set is open and establish the relationship between open and closed sets
Who it is for
If the appropriate students apply for the online course Topology, there will be excellent employment prospects.
Admission Details
Students are urged to enrol in Topology Certification by taking the following measures as soon as the course's admission period opens.
Step 1: Visit the official website
Step 2: Fill up the application form
Step 3: Upload all necessary documents
Step 4: Pay the required fee online (if you need certification)
The Syllabus
- Set Theory, Relations and Functions
- Metric spaces
- Interior/Boundary/limit points, closure
- Sequences, Convergence and properties
- Completion, Compactness and Connectedness of Metric Spaces.
- Compactness & Equivalent Conditions for Compact Metric Spaces
- Topological Spaces, Basis, suspaces, product topology
- Separation axioms, First and Second Countability, Baire space
- Compactness in general topological spaces, Continuity and compactness,Subspace, Lebesgue covering lemma.
- Tube lemma and it's application, Metrizable spaces and heriditary properties of topological spaces.
- Product of Regular spaces, Connectedness.
- Quotient topology, quotient spaces and Tychonoff theorem.
Evaluation process
Yes, there will be assessments and one Final Exam.
Instructors
Mumbai University Frequently Asked Questions (FAQ's)
Topology, also known as rubber-sheet geometry, is the study of the characteristics of spaces that are invariant under any continuous deformation.
The classes are administered through pre-recorded videos and lectures.
Pure mathematics subfields of geometry and topology make up a very active area of central significance in the current mathematical landscape.
The instructor for this course is Mandar Bhanushe - Mathematics Faculty at the Institute of Distance and Open Learning, University of Mumbai.
Riemann surfaces in complex analysis, Differential equations, dynamical systems, and knot theory are a few of the varied applications. It is also employed in string theory, a branch of physics, to explain the universe's space-time organisation.