What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics
Irreducibility and the Schoenemann-Eisenstein criterion | Famous Math Probs 20b | N J Wildberger
In the context of defining and computing the cyclotomic polynumbers (or polynomials), we consider irreducibility. Gauss's lemma connects irreducibility over the integers to irreducibility over the rational numbers. Then we describe T. Schoenemann's irreducibility criterion, which uses some
From playlist Famous Math Problems
I define one of the most important constants in mathematics, the Euler-Mascheroni constant. It intuitively measures how far off the harmonic series 1 + 1/2 + ... + 1/n is from ln(n). In this video, I show that the constant must exist. It is an open problem to figure out if the constant is
From playlist Series
Theory of numbers: Congruences: Euler's theorem
This lecture is part of an online undergraduate course on the theory of numbers. We prove Euler's theorem, a generalization of Fermat's theorem to non-prime moduli, by using Lagrange's theorem and group theory. As an application of Fermat's theorem we show there are infinitely many prim
From playlist Theory of numbers
The hyperbolic Ax-Lindemann conjecture - Emmanuel Ullmo
Emmanuel Ullmo Université Paris-Sud February 7, 2014 The hyperbolic Ax Lindemann conjecture is a functional transcendental statement which describes the closure of "algebraic flows" on Shimura varieties. We will describe the proof of this conjecture and its consequences for the André-Oort
From playlist Mathematics
Writing an OS in Rust - Part 11b - Linked List Allocator
This is my version of Philipp Oppermann's "BlogOS". It's a baremetal operating system that can boot off of a USB stick on any BIOS-compatible machine, which is pretty amazing. I'm going to be following the whole blog, one video at a time, and running the OS using QEMU instead of booting a
From playlist Rust OS
A (compelling?) reason for the Riemann Hypothesis to be true #SOME2
A visual walkthrough of the Riemann Zeta function and a claim of a good reason for the truth of the Riemann Hypothesis. This is not a formal proof but I believe the line of argument could lead to a formal proof.
From playlist Summer of Math Exposition 2 videos
Mertens Conjecture Disproof and the Riemann Hypothesis | MegaFavNumbers
#MegaFavNumbers The Mertens conjecture is a conjecture is a conjecture about the distribution of the prime numbers. It can be seen as a stronger version of the Riemann hypothesis. It says that the Mertens function is bounded by sqrt(n). The Riemann hypothesis on the other hand only require
From playlist MegaFavNumbers
This video given Euler's identity, reviews how to derive Euler's formula using known power series, and then verifies Euler's identity with Euler's formula http://mathispower4u.com
From playlist Mathematics General Interest
Writing an OS in Rust - Part 11c - Fixed-Size Block Allocator
This is my version of Philipp Oppermann's "BlogOS". It's a baremetal operating system that can boot off of a USB stick on any BIOS-compatible machine, which is pretty amazing. I'm going to be following the whole blog, one video at a time, and running the OS using QEMU instead of booting a
From playlist Rust OS
GCSE Science Revision Biology "Classification"
Find my revision workbooks here: https://www.freesciencelessons.co.uk/workbooks In this video, we look at how Linnaeus organised his classification system and then look at the three domain system that is used today. We then explore the use of evolutionary trees. Image credits: Elephant B
From playlist Biology Paper 2 Variation and Evolution
Euler's Formula for the Quaternions
In this video, we will derive Euler's formula using a quaternion power, instead of a complex power, which will allow us to calculate quaternion exponentials such as e^(i+j+k). If you like quaternions, this is a pretty neat formula and a simple generalization of Euler's formula for complex
From playlist Math
Writing an OS in Rust - Part 12c - A Simple Executor
This is my version of Philipp Oppermann's "BlogOS". It's a baremetal operating system that can boot off of a USB stick on any BIOS-compatible machine, which is pretty amazing. I'm going to be following the whole blog, one video at a time, and running the OS using QEMU instead of booting a
From playlist Rust OS
Writing an OS in Rust - Part 1 - A Freestanding Rust Binary
This is my version of Philipp Oppermann's "BlogOS". It's a baremetal operating system that can boot off of a USB stick on any BIOS-compatible machine, which is pretty amazing. I'm going to be following the whole blog, one video at a time, and running the OS using QEMU instead of booting a
From playlist Rust OS
Writing an OS in Rust - Part 9 - Paging Implementation
This is my version of Philipp Oppermann's "BlogOS". It's a baremetal operating system that can boot off of a USB stick on any BIOS-compatible machine, which is pretty amazing. I'm going to be following the whole blog, one video at a time, and running the OS using QEMU instead of booting a
From playlist Rust OS
Writing an OS in Rust - Part 12a - Futures
This is my version of Philipp Oppermann's "BlogOS". It's a baremetal operating system that can boot off of a USB stick on any BIOS-compatible machine, which is pretty amazing. I'm going to be following the whole blog, one video at a time, and running the OS using QEMU instead of booting a
From playlist Rust OS
Writing an OS in Rust - Part 11a - Bump Allocator
This is my version of Philipp Oppermann's "BlogOS". It's a baremetal operating system that can boot off of a USB stick on any BIOS-compatible machine, which is pretty amazing. I'm going to be following the whole blog, one video at a time, and running the OS using QEMU instead of booting a
From playlist Rust OS
Writing an OS in Rust - Part 5 - CPU Exceptions
This is my version of Philipp Oppermann's "BlogOS". It's a baremetal operating system that can boot off of a USB stick on any BIOS-compatible machine, which is pretty amazing. I'm going to be following the whole blog, one video at a time, and running the OS using QEMU instead of booting a
From playlist Rust OS
How to derive Euler's formula using differential equations! Free ebook http://bookboon.com/en/introduction-to-complex-numbers-ebook A somewhat new proof for the famous formula of Euler. Here is the famous formula named after the mathematician Euler. It relates the exponential with cosin
From playlist Intro to Complex Numbers
Writing an OS in Rust - Part 12d - Async Keyboard Input
This is my version of Philipp Oppermann's "BlogOS". It's a baremetal operating system that can boot off of a USB stick on any BIOS-compatible machine, which is pretty amazing. I'm going to be following the whole blog, one video at a time, and running the OS using QEMU instead of booting a
From playlist Rust OS