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
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Video class: Algebraic Topology 0: Cell Complexes
1h08m
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Video class: Algebraic Topology 1: Homotopy Equivalence
1h08m
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Video class: Algebraic Topology 2: Introduction to Fundamental Group
1h05m
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Video class: Algebraic Topology 3: Fundamental Group is a Group!
1h01m
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Video class: Algebraic Topology 4: Brouwer Fixed Point Theorem
1h06m
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Video class: Algebraic Topology 5: Homeomorphic Spaces have Isomorphic Fundamental Groups
1h07m
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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
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Video class: Algebraic Topology 9 : Deck Transformations of Covering Spaces
1h12m
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Video class: Algebraic Topology 10: Simplicial Homology
1h26m
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Video class: Algebraic Topology 11: What is homology measuring?
1h00m
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Video class: Algebraic Topology 12: Intro to Singular Homology
0h55m
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Video class: Algebraic Topology 13: Homotopy Equivalence Preserves Homology
1h06m
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Video class: Algebraic Topology 14: Exact Sequences
0h54m
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Video class: Algebraic Topology 15: Exact Sequence of Homology and Excision
0h57m
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Video class: Algebraic Topology 16: Singular Homology = Simplicial Homology
0h42m
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Video class: Algebraic Topology 17: Degree and Cellular Homology
1h06m
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Video class: Algebraic Topology 18: Mayer-Vietoris
0h58m
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Video class: Algebraic Topology 19: Category Theory
1h00m
Topology
Unlock Your Mathematical Potential: Free Topology Courses Online
If you're intrigued by the fascinating branch of mathematics known as Topology, you're in luck! We have compiled an exclusive collection of free online courses on Topology, a compelling subcategory of Algebra. Dive deep into the study of spaces, continuity, and the fascinating properties that remain unchanged under continuous transformations. Enhance your mathematical intuition and analytical skills with these exceptional, freely accessible online resources.
Whether you're a beginner setting out to grasp the fundamentals or an advanced learner aiming to refine your knowledge in Algebraic Topology and Geometry, these courses will guide you every step of the way, absolutely free of cost!
Featured Free Courses in Algebraic Topology and Algebraic Geometry:
- Algebraic Topology by Andrews University: Delve into fundamental topics such as homotopy and simplicial complexes. This comprehensive course offered by Andrews University will solidify your foundational understanding and prepare you for further exploration in Topology.
- Algebraic Topology Course by Roman Sauer: Level up your knowledge with this detailed Algebraic Topology online course by Roman Sauer. Explore advanced topics like fundamental groups, covering spaces, and homology theory, all completely free!
- Algebraic Geometry by VisualMath: Embark on a visual learning experience with this engaging Algebraic Geometry course. Perfect for learners who appreciate graphical representations and examples to simplify complex topological concepts.
Why enroll in these free Topology courses online?
- No Cost, High-Quality Education: Get access to high-quality lecture materials and knowledgeable instructors without any financial investment.
- Flexible Learning: Learn at your own pace and convenience, ideal for students, educators, researchers, or math enthusiasts.
- SEO Optimized: We've highlighted these free algebraic topology courses to make it easy for you to locate and begin learning quickly!
Don't miss the opportunity to enhance your expertise in this fundamental mathematical sub-discipline. Discover the universe of Topology now by enrolling in these excellent online classes. Start today, completely for free!
This free course includes:
24 hours and 3 minutes of online video course
Exercises to train your knowledge
Certificate of course completion
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