Free online courseAlgebraic Topology
Duration of the online course: 24 hours and 3 minutes
New course
Explore Algebraic Topology at Andrews University, covering cell complexes, homotopy, homology, and cohomology in a comprehensive online course.
Course Description
Explore the fascinating world of Algebraic Topology with this comprehensive course offered by Andrews University. Delve into key concepts and discover the foundation of Algebraic Topology, covering a range of intriguing subjects. Begin with the study of Cell Complexes and understand how they form the building blocks of topological spaces.
Progress to investigating Homotopy Equivalence and grasp how different shapes and structures can be transformed into each other without tearing or gluing. This leads into an understanding of the Fundamental Group, a crucial concept that examines loops within a space and their role in classifying topological spaces.
The course introduces the Brouwer Fixed Point Theorem, a compelling result that asserts the existence of fixed points under certain conditions. You will also explore the concept that homeomorphic spaces have isomorphic fundamental groups, enhancing your understanding of space classification.
Gain insights into the Seifert-Van Kampen Theorem and its application in calculating fundamental groups, followed by an examination of Covering Spaces and their distinct properties. Learn about Deck Transformations and how they relate to fundamental groups.
Expand your knowledge through Simplicial and Singular Homology, identifying how these sophisticated tools measure and classify spaces. The course delves into Exact Sequences in homological algebra, illustrating their significance in topological applications.
A special focus is placed on the relationship between Singular Homology and Simplicial Homology, as well as the application of Complex Homology in understanding geometric and algebraic structures. Explore the Mayer-Vietoris sequence to see how it assists in computing homology groups for complex shapes.
Conclude with an introduction to Category Theory, providing a broader context for understanding mathematical structures and relationships. The course wraps up with an in-depth look into Cohomology and the intriguing concept of the Cup Product, concluding with real-world applications on constructs like the Torus.
This Algebraic Topology course offers a profound exploration of topology, providing invaluable insights for students pursuing studies in algebra or related fields.
Course content
-
Video class: Algebraic Topology 0: Cell Complexes
1h08m
-
Video class: Algebraic Topology 1: Homotopy Equivalence
1h08m
-
Video class: Algebraic Topology 2: Introduction to Fundamental Group
1h05m
-
Video class: Algebraic Topology 3: Fundamental Group is a Group!
1h01m
-
Video class: Algebraic Topology 4: Brouwer Fixed Point Theorem
1h06m
-
Video class: Algebraic Topology 5: Homeomorphic Spaces have Isomorphic Fundamental Groups
1h07m
-
Video class: Algebraic Topology 6: Seifert-Van Kampen Theorem
1h16m
-
Video class: Algebraic Topology 7: Covering Spaces
1h00m
-
Video class: Algebraic Topology 8: Properties of Covering Spaces
1h08m
-
Video class: Algebraic Topology 9 : Deck Transformations of Covering Spaces
1h12m
-
Video class: Algebraic Topology 10: Simplicial Homology
1h26m
-
Video class: Algebraic Topology 11: What is homology measuring?
1h00m
-
Video class: Algebraic Topology 12: Intro to Singular Homology
0h55m
-
Video class: Algebraic Topology 13: Homotopy Equivalence Preserves Homology
1h06m
-
Video class: Algebraic Topology 14: Exact Sequences
0h54m
-
Video class: Algebraic Topology 15: Exact Sequence of Homology and Excision
0h57m
-
Video class: Algebraic Topology 16: Singular Homology = Simplicial Homology
0h42m
-
Video class: Algebraic Topology 17: Degree and Cellular Homology
1h06m
-
Video class: Algebraic Topology 18: Mayer-Vietoris
0h58m
-
Video class: Algebraic Topology 19: Category Theory
1h00m
This free course includes:
24 hours and 3 minutes of online video course
Exercises to train your knowledge
Certificate of course completion
100% free, from content to certificate
This online course can only be accessed through the Cursa App. Download it using the QR code or the links below:
This online course can only be accessed through the Cursa app. Install it using the links below:
-
Study for free!
Here you never pay! Not even for the certificate, because everything in the app is 100% free!
-
Improve your resume!
There are more than 4,000 free courses for you to study anything that interests you!
-
Free Digital Certificate!
Complete the course and issue your internationally recognized Digital Certificate free of charge.
More free courses at Algebra
Free CourseBasics of Algebra
5
(3)
0h37m
5 exercises
Free CourseAlgebra Introduction
5
(2)
1h18m
6 exercises
Free CourseLinear Algebra Course
5
(1)
10h49m
46 exercises
Free CourseLinear algebra
4.91
(119)
27h55m
35 exercises
Free CourseAlgebra
4.89
(55)
3h18m
25 exercises
Free CourseIntermediate Algebra
4.82
(22)
54h38m
43 exercises
Free CoursePrealgebra
3.58
(52)
38h54m
44 exercises
Free CourseCollege Algebra Full Course
New course
6h43m
6 exercises
Free CourseMath Fundamentals Algebra
New course
2h09m
14 exercises
Free CourseAdvanced Algebra Lessons
New course
4h42m
12 exercises
Free CourseBasics of Algebra
5
(3)
0h37m
5 exercises
Free CourseAlgebra Introduction
5
(2)
1h18m
6 exercises
Free CourseLinear Algebra Course
5
(1)
10h49m
46 exercises
Free CourseLinear algebra
4.91
(119)
27h55m
35 exercises
Free CourseAlgebra
4.89
(55)
3h18m
25 exercises
Free CourseIntermediate Algebra
4.82
(22)
54h38m
43 exercises
Free CoursePrealgebra
3.58
(52)
38h54m
44 exercises
Free CourseCollege Algebra Full Course
New course
6h43m
6 exercises
Free CourseMath Fundamentals Algebra
New course
2h09m
14 exercises
Free CourseAdvanced Algebra Lessons
New course
4h42m
12 exercises
Free text courses
Download the App now to have access to + 3300 free courses, exercises, certificates and lots of content without paying anything!
-
100% free online courses from start to finish
Thousands of online video courses, audio or text courses.
-
More than 48 thousand free exercises
To test your knowledge during online courses
-
Valid free Digital Certificate with QR Code
Generated directly from your cell phone's photo gallery and sent to your email
Download our app via QR Code or the links below::.
