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Course Description This course covers elementary discrete mathematics for science and engineering, with a focus on mathematical tools and proof techniques useful in computer science. Topics include logical notation, sets, relations, elementary graph theory, state machines and invariants, induction and proofs by contradiction, … Show more
Less than a week after it became Europe’s latest unicorn, Swedish vibe coding startup Lovable is now also a centaur — a company with more than $100 million in annual recurring revenue (ARR). Lovable took only eight months since its launch to get here, thanks to the skyrocketing popularity of its AI-powered website and app builder. The startup claims it now has more than 2.3 million active users, and last reported 180,000 paying subscribers. With only 45 full-time employees, and 14 open positio
The year is 2025 ...and we're still working on it! Matter replicators, organic transporters, and warp drives are a little hazy on the timeline, but it seems like the holodeck and emergency medical hologram are just about here. This guide is intended to be a comprehensive look at the tech that Star Trek suggested to drive humanity forward ad astra per aspera. The emphasis is on innovations that don't violate physics according to present consensus understanding. Go ahead and explore boldly, and
When you open your Netflix app, it's easy to be overwhelmed by the number of shows to choose from. All that choice can make it hard to figure out what to stream -- we've all done the infinite scroll, spending an hour looking for something before just giving up and watching old episodes of Seinfeld. Not to mention the fact that some shows have a shorter shelf life than others and it's hard to tell when something will leave the platform forever. That's why we've handpicked some of the most enterta
Would you like to work nearly double the standard 40-hour week? It’s a question that many startups in the US are asking prospective employees—and to get the job, the answer needs to be an unequivocal yes. These companies are embracing an intense schedule, first popularized in mainland China, known as “996,” or 9 am to 9 pm, six days a week. In other words, it’s a 72-hour work week. The 996 phenomenon in China gave rise to major protests and accusations of “modern slavery,” with critics blaming
is a deputy editor and Verge co-founder with a passion for human-centric cities, e-bikes, and life as a digital nomad. He’s been a tech journalist for 20 years. The Starlink Mini satellite dish is now even better thanks to the $119 LinkPower 1 power bank from PeakDo. The battery locks securely to the back of SpaceX’s smallest terminal and provides over 4.5 hours of uninterrupted Internet connectivity. The LinkPower’s battery can also charge simultaneously over USB-C from your car, solar generat
Gupshup, a business messaging startup that began its journey in India over two decades ago and became a unicorn four years ago, has raised a new over $60 million round — but is keeping its new valuation under wraps. In 2021, Gupshup raised two funding rounds within four months, securing $340 million from prominent investors including Tiger Global, Fidelity Management, Think Investments, and Malabar Investments. These rounds — the startup’s first in roughly a decade — valued Gupshup at $1.4 bill
SpaceX is nine full-scale test launches into developing its enormous, nearly 400-feet-tall Starship, the most powerful rocket ever built. Over the last two and a half years, we've seen over half a dozen spectacular explosions. Two launches earlier this year sent massive streaks of debris hurtling over the Turks and Caicos Islands, prompting airspace closures. Its most recent test in May ended in an uncontrolled splashdown in the Gulf of Mexico after helplessly spinning on its axis and suffering
We're roughly six months into Donald Trump's trade war, and tech firms remain in a fog, unsure what tariffs or retaliations could be coming next. To shed light on this struggle, we invite you to join us for an Ars Live talk at 1 pm ET on Thursday, July 24, with Consumer Technology Association (CTA) Vice President of International Trade Edward Brzytwa. We'll be discussing how tech firms are responding to tariffs so far and how looming chip tariffs could pose the biggest hurdle yet in sourcing al
Stargate, the ambitious joint venture announced at the White House back in January between OpenAI, Oracle, the Japanese holding company Softbank, and others, appears to be struggling to deliver on its bold promises just six months later. The Wall Street Journal reported today, citing unnamed sources, that the Stargate Project has yet to finalize any deals for new data centers. The report also says the group is scaling back its near-term goals. When it was announced on Jan. 21, Stargate was pit
We may know how the new Resident Evil movie fits in with the games. Matt Shakman talks about working with the Russo Brothers to prep the Fantastic Four for Avengers: Doomsday. Plus, Ross Duffer debunks those wild Stranger Things season 5 runtime rumors. Spoilers, away! Wonder Woman The Wrap reports that Supergirl screenwriter Ana Nogueira has been tapped to pen DC Studio’s fast-tracked Wonder Woman movie. Resident Evil A synopsis for the new Resident Evil movie (via DanielRPK and Comic Book)
Programmable optics startup Lumotive has added a few more strategic backers to its recent Series B round. Redmond, Washington-based Lumotive reopened its recent Series B funding round to bring in Amazon, through its Amazon Industrial Innovation Fund, and ITHCA Group, the technology investment arm of Oman’s sovereign wealth fund, as investors. These fresh funds bring the company’s Series B round to $59 million, up from the $45 million Lumotive initially closed in February. The startup has raise
In 2024, astronomers surmised that Betelgeuse might have a stellar “buddy.” If this hypothetical companion existed, it would help answer some questions about the red supergiant’s strange glowing patterns. As it turns out, these suspicions were correct. After numerous false signals and empty search results, astronomers with NASA’s Ames Research Center have confirmed that Betelgeuse does, in fact, have a tiny buddy star. The young star, with a mass about 1.5 times that of the Sun, likely exerts s
Cantor Fitzgerald, a financial services company led by the sons of US Commerce Secretary Howard Lutnick, is creating a way for investors to bet that President Donald Trump’s signature tariffs will be struck down in court. Traders at the firm’s investment banking subsidiary, Cantor Fitzgerald & Co., say they have the capacity to buy the rights to hundreds of millions of dollars in potential refunds from companies who have paid Trump’s tariffs, according to documents viewed by WIRED. Lutnick ran
Elon Musk’s obsession with colonizing Mars is polluting Earth. As SpaceX seeks to ramp up its launches of Starship, it’s also expanding its splashdown area where pieces of the rocket are allowed to litter the Pacific Ocean. A recent expansion threatens marine wildlife surrounding a sacred island in native Hawaiian tradition. The Federal Aviation Administration (FAA) approved SpaceX’s request to rain down debris in the waters surrounding Mokumanamana, an uninhabited island in Northwestern Hawaii
As Donald Trump has given the automotive industry whiplash with his tariffs, which have, at different periods, applied to cars and car parts or haven’t applied at all. While it was hard to tell how the import tax would hit auto manufacturers, the impact is starting to look more concrete, and it ain’t pretty. As CNBC notes, Stellantis, the maker of Jeep, Dodge, Fiat, Chrysler, and Peugeot, warned on Monday that it’s expecting to lose about $2.6 billion this quarter due to Trump’s tariffs, accordi
Cantor Fitzgerald, a financial services company led by the sons of US Commerce Secretary Howard Lutnick, is creating a way for investors to bet that President Donald Trump’s signature tariffs will be struck down in court. Traders at the firm’s investment banking subsidiary, Cantor Fitzgerald & Co., say they have the capacity to buy the rights to hundreds of millions of dollars in potential refunds from companies who have paid Trump’s tariffs, according to documents viewed by WIRED. Lutnick ran
Intuitive Surgical, an American biotechnology company, introduced DaVinci surgical robots in the late 1990s, and they became groundbreaking teleoperation equipment. Expert surgeons could operate on patients remotely, manipulating the robotic arms and their surgical tools based on a video feed from DaVinci’s built-in cameras and endoscopes. Now, John Hopkins University researchers put a ChatGPT-like AI in charge of a DaVinci robot and taught it to perform a gallbladder-removal surgery. Kuka sur
Welcome back to TechCrunch Mobility — your central hub for news and insights on the future of transportation. Sign up here for free — just click TechCrunch Mobility! A little bird Image Credits:Bryce Durbin If it wasn’t obvious before, it is now. Uber wants a big piece of the autonomous vehicle technology pie. The ride-hailing company has spent the past two years locking in partnerships with just about every AV company you can think of, and across every sector, including delivery, robotaxis,
Starlink is nearly twice as fast as it was two years ago, according to a new report from the speed test site Ookla. (Disclosure: Ookla is owned by the same parent company as CNET, Ziff Davis.) Median download speeds from the satellite internet provider have steadily ticked up over the past few years, going from 53.95 megabits per second in 2022 to 104.71Mbps today. That’s an impressive feat considering Starlink added about 5 million customers over the same period and recently passed the 6 milli
TechCrunch Disrupt 2025 is just around the corner, and with more than 10,000 startup and VC leaders heading to Moscone West in San Francisco this October 27 to 29, the Expo Hall is where connections get made and business gets done. If you’ve been thinking about showcasing your company, consider this your nudge — exhibitor spots are filling fast, and once they’re gone, they’re gone. Exhibiting at Disrupt isn’t just about having a table, it’s about putting your startup in front of the people who
Days after AI coding startup Windsurf announced that it’s being acquired by Cognition, Windsurf exec Jeff Wang took to X to offer more details about the drama and uncertainty around the deal. Windsurf was previously reported to be in acquisition talks with OpenAI, but that deal fell apart, with Google DeepMind instead hiring the startup’s CEO Varun Mohan, co-founder Douglas Chen, and some of its top researchers. Google would reportedly license Windsurf’s technology as part of the $2.4 billion d
Autonomous robotics startup Cartken, known for its four-wheeled robots that deliver food on college campuses and through Tokyo’s bustling streets, has found a new area of focus: industrials. Cartken co-founder and CEO Christian Bersch told TechCrunch that applying its delivery robots to industrial settings was always in the back of his mind as they built the startup. When companies started reaching out about using their robots in factories and labs, Cartken took a closer look. “What we found i
Andy Byron, the startup executive at the center of an extraordinary social media furor, has resigned as CEO of data operations startup Astronomer. Byron, who is married, was captured on a Coldplay concert “kiss cam” with his arms around the company’s chief people officer Kristin Cabot. After Byron and Cabot quickly tried to hide from the camera, Coldplay singer Chris Martin joked, “Either they’re having an affair or they’re just very shy.” Video of the awkward incident soon went spectacularly
Astronomers have spotted a planetary system being conceived from the swirl of gas and dust surrounding a star — giving us an unprecedented, real-time look at how our solar system would've formed some 4.6 billion years ago. The findings, published as a study in the journal Nature, are the first time we're seeing such an early stage of planets being formed anywhere in the cosmos. "We've captured a direct glimpse of the hot region where rocky planets like Earth are born around young protostars,"
SpaceX employees are more likely to be injured while working at Starbase than any of its other manufacturing facilities, according to company worker safety records reviewed by TechCrunch. Starbase, a sprawling launch-and-manufacturing site that recently incorporated as its own Texas city, logged injury rates almost six times higher than the average for comparable space vehicle manufacturing outfits and nearly three times higher than aerospace manufacturing as a whole in 2024, according to Occup
SpaceX employees are more likely to be injured while working at Starbase than any of its other manufacturing facilities, according to company worker safety records reviewed by TechCrunch. Starbase, a sprawling launch-and-manufacturing site that recently incorporated as its own Texas city, logged injury rates almost six times higher than the average for comparable space vehicle manufacturing outfits and nearly three times higher than aerospace manufacturing as a whole in 2024, according to Occup
Even after pouring $2 billion into its much-maligned Starliner spacecraft, NASA and Boeing remain committed to getting back off the ground. As Ars Technica reports, the head of NASA's commercial crew program, Steve Stich, revealed last week that Boeing and its propulsion supplier, Aerojet Rocketdyne, are making considerable changes to the astronaut shuttle following a disastrous first crewed mission to the International Space Station last year. The spacecraft experienced several "in-flight ano
SpaceX employees are more likely to be injured while working at Starbase than any of its other manufacturing facilities, according to company worker safety records reviewed by TechCrunch. Starbase, a sprawling launch-and-manufacturing site that recently incorporated as its own Texas city, logged injury rates almost six times higher than the average for comparable space vehicle manufacturing outfits and nearly three times higher than aerospace manufacturing as a whole in 2024, according to Occup
This has been an epic year for movies, and 2025 is only halfway over. A collection of tentpole titles and must-see blockbusters has already hit the big screen. The trend of studios mining established IP continues, and popular franchises' remakes, sequels and spin-offs will compete for audiences' attention. James Gunn's Superman was way up on our list of must-see blockbusters in 2025, which was compiled at the beginning of the year. If you read my review, you'll know that it delivered. Anthony