‘Groups’ Underpin Modern Math. Here’s How They Work

‘Groups’ Underpin Modern Math. Here’s How They Work

Figuring out what subgroups a group contains is one way to understand its structure. For example, the subgroups of Z6 are {0}, {0, 2, 4} and {0, 3}—the trivial subgroup, the multiples of 2, and the multiples of 3. In the group D6, rotations form a subgroup, but reflections don’t. That’s because two reflections performed … Read more

Jets vs. Vikings 2024 livestream: How to watch NFL for free

Jets vs. Vikings 2024 livestream: How to watch NFL for free

TL;DR: Live stream New York Jets vs. Minnesota Vikings for free on ITVX. Access this free streaming platform from anywhere in the world with ExpressVPN. The NFL is back in London, but anyone from around the world can watch the New York Jets take on the Minnesota Vikings without spending anything. There’s a quick and … Read more

Announcing Startup Battlefield 200 at Disrupt 2024

Announcing Startup Battlefield 200 at Disrupt 2024

TechCrunch Disrupt 2024, which takes place from October 28-30 at Moscone West in San Francisco, is rapidly approaching. Today we’re thrilled to announce the 200 startups selected to participate in this year’s Startup Battlefield 200 (SB 200) cohort. TechCrunch’s editorial staff read, vetted and debated over thousands of applications. Narrowing the group down to 200 … Read more

Bose QuietComfort Ultra headphones review: Noise-canceling powerhouse

Bose QuietComfort Ultra headphones review: Noise-canceling powerhouse

Bose has rightfully earned its reputation for not only delivering great sound, but also innovating to drown out the background. Its headphones don’t come out with the same cadence other brands do, and that’s definitely not a bad thing. Quality should last, after all. The Bose QuietComfort Ultra headphones are a prime example, given they’ve … Read more

Google’s circular, double-sided Gboard keyboard is as crazy as it sounds

Google’s circular, double-sided Gboard keyboard is as crazy as it sounds

TL;DR Google Japan has announced a double-sided circular keyboard. The product is the latest quirky keyboard from the regional division. This keyboard isn’t actually for sale, but Google has open-sourced blueprints so you can make your own. Google Japan is known for its quirky keyboard inventions, such as a keyboard cup and a “stick” keyboard. … Read more

China Trained a 1-Trillion-Parameter LLM Using Only Domestic Chips

China Trained a 1-Trillion-Parameter LLM Using Only Domestic Chips

“China Telecom, one of the largest wireless carriers in mainland China, says that it has developed two large language models (LLMs) relying solely on domestically manufactured AI chips…” reports Tom’s Hardware. “If the information is accurate, this is a crucial milestone in China’s attempt at becoming independent of other countries for its semiconductor needs, especially … Read more

NYT Mini Crossword today: puzzle answers for Sunday, October 6

NYT Mini Crossword today: puzzle answers for Sunday, October 6

The New York Times has introduced the next title coming to its Games catalog following Wordle’s continued success — and it’s all about math. Digits has players adding, subtracting, multiplying, and dividing numbers. You can play its beta for free online right now. In Digits, players are presented with a target number that they need to … Read more

How to Create Your Own Letterhead in Microsoft Word

How to Create Your Own Letterhead in Microsoft Word

A letterhead is a collection of text, images, and colors at the top of a letter that contains various details about who you are as a sender. In Microsoft Word, you can either create these using templates or start from scratch, and—most importantly—save your finalized design for repeated use. Any time you’re working on a … Read more

How airline seats became key tech products

How airline seats became key tech products

Chris Baraniuk It’s estimated that one third of the world’s airline seats are made in Northern Ireland In a warehouse building in a quiet town in Northern Ireland, a robot arm is opening and closing an airplane meal table over and over again. It has been programmed to carry out this mundane task no fewer … Read more