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Quick Facts

Medium Of Instructions	Mode Of Learning	Mode Of Delivery
English	Self Study	Video and Text Based

Course Overview

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 Highlights

Elective Online Course
12 Weeks Duration
Offered by IIT Madras

Programme Offerings

Certificate of completion
Practical Learning
Hands-on Experience

Courses and Certificate Fees

Fees Informations	Certificate Availability	Certificate Providing Authority
INR 1000	yes	IIT Madras

The Introduction to Algebraic Geometry certification fees is free. However, if you want a certificate, you must register and take the proctored exam at designated centers, which is optional and comes with a fee of Rs 1000.

Introduction to Algebraic Geometry Certification Fee Structure

Particulars	Total Fees
Introduction To Algebraic Geometry (exam)	Rs 1000/-

Eligibility Criteria

Academic Qualifications

Prerequisites for the Introduction to Algebraic Geometry certification course include a solid understanding of basic algebra and some familiarity with commutative algebra concepts like prime ideals and tensor products.

Certification Qualifying Details

To receive the Introduction to Algebraic Geometry certification by Swayam, you need a minimum average assignment score of 10/25 and an exam score of 30/75.

What you will learn

After completing the Introduction to Algebraic Geometry certification syllabus, you will delve deeply into Commutative Algebra and Algebraic Geometry, gaining a comprehensive understanding of their fundamental principles and their intricate relationship. You will explore advanced topics such as ring theory, algebraic varieties, schemes, sheaf theory, and cohomology, among others.

Upon completion of the Introduction to Algebraic Geometry training, you will develop a strong grasp of key concepts, enabling you to analyse and solve complex problems in both fields. You will cultivate essential skills in mathematical reasoning, abstraction, and critical thinking.

Who it is for

StatisticianData ScientistActuaryMathematician

The Introduction to Algebraic Geometry online course is suitable for individuals seeking to explore advanced topics in mathematics and expand their knowledge beyond introductory levels. This course is particularly relevant for:

Admission Details

Follow these steps to join the Introduction to Algebraic Geometry classes:

Step 1: Browse the URL below:

https://onlinecourses.nptel.ac.in/noc23_ma63/preview

Step 2: Click on the “Sign-in/ Register” button

Step 3: Fill out the necessary details and submit the form

The Syllabus

Topics in Commutative Algebra: Integral Extensions, Going-up and Going-down theorems.

Topics in Commutative Algebra (Contd.): Valuation Rings, Noether Normalization lemma, Discrete Valuation Rings, Dimension Theory, Affine Algebraic Sets, Weak Nullstellensatz, Strong Nullstellensatz.

Regular Morphisms, Abstract Algebraic Sets, Zariski Topology on Affine Spaces, Irreducible Components, Affine and Quasi-affine Varieties, Projective Spaces.

Zariski Topology on Projective Spaces, Projective and Quasi-projective Varieties, Regular Functions on Quasi-projective Varieties, Presheaves & Sheaves, Morphisms of Presheaves & Sheaves.

Stalks, Sheafification, Push-forward, Inverse Image, Subsheaves, Gluing of Sheaves, Prevarieties, Ring of Regular Functions and Field of Rational Functions on Affine Varieties.

Equivalence of Categories between the Category of Affine k-varieties and the Category of Finitely Generated Integral Domains over k, Closed and Open Immersions, Constructible Sets, Chevalley's Theorem, Product of Prevarieties.

Products and Coproducts in a Category, Product of Quasi-affine Varieties, Diagonal Morphisms, Varieties, Global Regular Functions on Projective Varieties are Constants.

Segre Embeddings, d-uple embedding, Gluing Morphisms, Finite Morphisms.

Immersions, Subvarieties, Criterion for Closed Immersions, Graph of a Morphism, Separatedness.

Proper Morphisms, Complete Varieties, Zariski Tangent Space, Singular & Non-singular Points.

Blow-ups, Smooth Morphisms, Sard's Theorem, Bertini's Theorem.

Abstract Non-singular Curves, Introduction to Affine Schemes.

Evaluation process

The Introduction to Algebraic Geometry certification offers an optional exam. Your final score is determined by averaging the best 8 out of 12 assignments (25%) and your proctored exam score (75%).

IIT Madras Frequently Asked Questions (FAQ's)

1: What background knowledge do I need for the Introduction to Algebraic Geometry online course?

You should have a strong understanding of basic algebra, including groups, rings, fields, and modules. Additionally, a basic knowledge of commutative algebra concepts and general topology is beneficial.

2: How will the Introduction to Algebraic Geometry certification benefit my career prospects?

This course will equip you with advanced mathematical skills and insights applicable to various industries, including algebraic statistics, coding, artificial intelligence, and mathematical modelling.

3: What is the Introduction to Algebraic Geometry online course duration and workload?

The course spans 12 weeks and is structured as an elective, covering advanced topics in both commutative algebra and algebraic geometry.

4: Are there any prerequisites for enrolling in the Introduction to Algebraic Geometry certification course?

Yes, you should have a solid foundation in basic algebra and some familiarity with commutative algebra concepts. While not mandatory, a basic understanding of general topology will also be helpful.

5: How will this course be taught?

The course will involve a combination of lectures, readings, problem sets, and possibly hands-on projects or presentations. You will engage with the material through both theoretical study and practical application.