Algebraic Geometry (book)

Algebraic topology: Introduction

This lecture is part of an online course on algebraic topology. This is an introductory lecture, where we give a quick overview of some of the invariants of algebraic topology (homotopy groups, homology groups, K theory, and cobordism). The book "algebraic topology" by Allen Hatcher men

From playlist Algebraic topology

algebraic geometry 14 Dimension

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the dimension of a topological space, algebraic set, or ring.

From playlist Algebraic geometry I: Varieties

Algebraic geometry 44: Survey of curves

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives an informal survey of complex curves of small genus.

From playlist Algebraic geometry I: Varieties

What is... an elliptic curve?

In this talk, we will define elliptic curves and, more importantly, we will try to motivate why they are central to modern number theory. Elliptic curves are ubiquitous not only in number theory, but also in algebraic geometry, complex analysis, cryptography, physics, and beyond. They were

From playlist An Introduction to the Arithmetic of Elliptic Curves

Algebraic geometry 1 Introduction

This lecture is part of an online algebraic geometry course (Berkeley math 256A fall 2020), based on chapter I of "Algebraic geometry" by Hartshorne. The full set of lectures is in the playlist "Algebraic geometry I: varieties". (The course continues in the playlist "Algebraic geometry I

From playlist Algebraic geometry I: Varieties

The differential calculus for curves, via Lagrange! | Differential Geometry 4 | NJ Wildberger

We rejuvenate the powerful algebraic approach to calculus that goes back to the work of Newton, Euler and particularly Lagrange, in his 1797 book: The Theory of Analytic Functions (english translation). The idea is to study a polynomial function p(x) by using translation and truncation to

From playlist Differential Geometry

An introduction to algebraic curves | Arithmetic and Geometry Math Foundations 76 | N J Wildberger

This is a gentle introduction to curves and more specifically algebraic curves. We look at historical aspects of curves, going back to the ancient Greeks, then on the 17th century work of Descartes. We point out some of the difficulties with Jordan's notion of curve, and move to the polynu

From playlist Math Foundations

AlgTopReview: An informal introduction to abstract algebra

This is a review lecture on some aspects of abstract algebra useful for algebraic topology. It provides some background on fields, rings and vector spaces for those of you who have not studied these objects before, and perhaps gives an overview for those of you who have. Our treatment is

From playlist Algebraic Topology

Complex numbers and curves | Math History | NJ Wildberger

In the 19th century, the study of algebraic curves entered a new era with the introduction of homogeneous coordinates and ideas from projective geometry, the use of complex numbers both on the curve and at infinity, and the discovery by the great German mathematician B. Riemann that topolo

From playlist MathHistory: A course in the History of Mathematics

Math Major Guide | Warning: Nonstandard advice.

A guide for how to navigate the math major and how to learn the main subjects. Recommendations for courses and books. Comment below to tell me what you think. And check out my channel for conversation videos with guests on math and other topics: https://www.youtube.com/channel/UCYLOc-m8Wu

From playlist Math

The Best Geometry Book for Beginners

This is probably the easiest geometry book! This means it's a perfect book for people who are just starting out and want to learn the very basics. If you want to learn geometry on your own via self-study it is hard to think of a better option. This is also excellent if you are studying geo

From playlist Book Reviews

Commutative algebra 1 (Introduction)

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. https://link.springer.com/book/10.1007/978-1-4612-5350-1 This is a short introductory lecture, and gives a few examples of the

From playlist Commutative algebra

Math Books From Floor To Ceiling

In this video I go over some of my math books! Please subscribe, like, and share. Thank you:) Here are the books. Abstract Algebra by Pinter https://amzn.to/3QviWF4 Functional Analysis by Bachman and Narici https://amzn.to/3Pr2kg4 Statistics by Weatherburn https://amzn.to/3C8OkVw Probabil

From playlist Book Reviews

My (Portable) Math Book Collection [Math Books]

Here's a look at my personal math book collection that I keep with me wherever I stay for a decent period of time. Enjoy! Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additi

From playlist Math Book Reviews

Learn Math Beyond Calculus || 5 Different Subjects

In this video I go over 5 math books that cover 5 different subjects that are typically studied beyond calculus. These topics all have certain pre-reqs but nothing says you can't just jump in and learn what you can! The topics are Linear Algebra, Real and Complex Analysis, Differential Geo

From playlist Book Reviews

Math Most People Never See

This video will show you math subjects that most people never see. Many of these subjects are graduate level but some are also undergraduate level. What other areas of math do you think most people never see? Leave a comment below:) All the Math You Missed: https://amzn.to/3ZCaebJ Applied

From playlist Book Reviews

Math Book with Tons of Topics

This math book covers geometry, trigonometry, algebra, calculus, etc. It was published in 1965 and it is called Foundations of Advanced Mathematics and it was written by Kline, Oesterle, and Willson. Here is one version https://amzn.to/3EQuwqd Useful Math Supplies https://amzn.to/3Y5TGcv

From playlist Book Reviews

Tropical Geometry - Lecture 2 - Curve Counting | Bernd Sturmfels

Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)

From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels

algebraic geometry 16 Desargues's theorem

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers Desargues's theorem and duality of projective space.

From playlist Algebraic geometry I: Varieties

Elliptic Curves: Good books to get started

A few books for getting started in the subject of Elliptic Curves, each with a different perspective. I give detailed overviews and my personal take on each book. 0:00 Intro 0:41 McKean and Moll, Elliptic Curves: Function Theory, Geometry, Arithmetic 10:14 Silverman, The Arithmetic of El

From playlist Math