Free online courseAlgebraic geometry
Duration of the online course: 10 hours and 43 minutes
New course
Dive into the essentials of Algebraic Geometry with VisualMath's engaging online course, from varieties and sheaves to tropical geometry concepts.
Course Description
Explore the fascinating world of Algebraic Geometry with VisualMath's comprehensive online course designed for beginners and enthusiasts. This in-depth course delves into fundamental concepts such as algebraic varieties, conic sections, ideals of sets, and the foundational principle of Hilbert’s Nullstellensatz. Gain insight into the coordinate ring and understand the significance of the Zariski topology in algebra. Learn about the dimension of a variety and how regular functions play a role with the identity theorem and examples provided for clarity.
Advance your understanding with thematic explorations of sheaves across multiple takes, alongside ringed spaces and their relevance. Discover the essence of prevarieties, abstract varieties, and projective space, including projective varieties and the projective Nullstellensatz. Traverse the concepts of projective closures, Segre and Veronese embeddings, and delve into the intriguing realms of Grassmanians, with a focus on Plücker coordinates and Schubert calculus.
Develop your skills by examining birational maps, the process of a blow-up, and understanding tangent cones and smooth varieties. Study the Jacobi criterion, dual curves, and the mystery of the 27 lines. Schemes are explored in much detail across multiple sessions, covering regular functions, morphism of schemes, sheaves of modules, tautological sheaves, skyscraper sheaves, and the process of sheafification.
Gain a robust insight into quasi-coherent sheaves, Kähler differentials, and the complexities of sheaf cohomology. Finally, venture into the emerging field of tropical geometry with this meticulously crafted course that aims to lay a strong foundational understanding while intriguing the mind with abstract and applied aspects of algebraic geometry.
Course content
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Video class: What is...algebraic geometry?
0h17m
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Exercise: What is the main focus of algebraic geometry?
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Video class: What are...algebraic varieties?
0h14m
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Exercise: What is a fundamental concept in algebraic geometry?
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Video class: What are...conic sections?
0h09m
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Exercise: What Determines the Type of a Conic Section?
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Video class: What are...ideals of sets?
0h12m
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Exercise: What is a key concept in algebraic geometry?
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Video class: What is...Hilbert’s Nullstellensatz?
0h10m
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Exercise: What is Hilbert's Nullstellensatz primarily concerned with?
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Video class: What is...the coordinate ring?
0h12m
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Exercise: What is a coordinate ring in algebraic geometry?
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Video class: What is...the Zariski topology?
0h10m
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Exercise: What is the Zariski topology primarily composed of in algebraic geometry?
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Video class: What is...the Zariski topology in algebra?
0h10m
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Exercise: What is a key goal of algebraic geometry?
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Video class: What is...the dimension of a variety?
0h10m
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Exercise: What is the correct notion of dimension in algebraic geometry?
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Video class: What are...regular functions?
0h10m
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Exercise: What is a regular function in algebraic geometry?
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Video class: What is...the identity theorem?
0h11m
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Exercise: What is the Identity Theorem in complex analysis about?
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Video class: What are...examples of regular functions?
0h09m
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Exercise: What is the concept behind localization in algebraic geometry?
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Video class: What are...sheaves, take 1?
0h13m
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Exercise: What is a major distinction between real and complex manifolds?
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Video class: What are...sheaves, take 2?
0h10m
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Exercise: What is a sheaf in the context of algebraic geometry?
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Video class: What are...sheaves, take 3?
0h09m
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Exercise: What is a locality condition in the concept of sheaves?
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Video class: What are...examples of sheaves?
0h13m
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Exercise: What is a fundamental concept illustrated by the graph example?
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Video class: What are...ringed spaces?
0h11m
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Exercise: What is a key concept in understanding varieties through ringed spaces?
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Video class: What is...the Why of ringed spaces?
0h12m
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Exercise: What is the key role of ringed spaces in algebraic geometry?
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Video class: What are...prevarieties?
0h11m
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Exercise: What is an affine variety in algebraic geometry?
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Video class: What are...(abstract) varieties?
0h09m
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Exercise: What is a key condition that distinguishes manifolds from problematic spaces in topology?
Topology
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Algebraic Geometry
Explore Free Algebraic Geometry Courses Online
Discover the fascinating intersection of algebra and geometry with our curated selection of free courses in Algebraic Geometry. As a specialized sub-discipline of algebra, Algebraic Geometry unravels the study of geometric structures defined by polynomial equations.
We have specifically curated top-quality online resources to help students and enthusiasts alike dive deep into Algebraic Geometry at no cost. Whether you're a mathematics student, educator, or researcher, these free courses provide an excellent way to enhance your mathematical understanding and skills.
- Algebraic geometry by VisualMath – Immerse yourself in this engaging and visually intuitive course designed to simplify complex algebraic geometrical concepts. Ideal for visual learners, this course covers essential topics using engaging explanations and clear visuals.
Our collection allows you to access valuable educational content anytime, anywhere, completely free. With clear, step-by-step tutorials, these courses cater to both beginners looking to grasp foundational concepts and advanced learners aiming to strengthen their expertise in Algebraic Geometry.
Join a growing community of mathematical minds eager to master Algebraic Geometry. Take advantage of this exceptional opportunity to learn, strengthen your algebra foundations, and broaden your mathematical horizons – all for free!
This free course includes:
10 hours and 43 minutes of online video course
Exercises to train your knowledge
Certificate of course completion
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