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Mathematics for Computer Science

This course covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.

How Big Could a Space Habitat Get?

How big could space habitats really get? From O’Neill cylinders to Ringworlds and Topopolises, we explore the true limits of megastructure scale.

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Watch my exclusive video Chronoengineering: https://nebula.tv/videos/isaacarthur–… Join this channel to get access to perks: / @isaacarthursfia 🛒 SFIA Merchandise: https://isaac-arthur-shop.fourthwall… 🌐 Visit our Website: http://www.isaacarthur.net ❤️ Support us on Patreon: / isaacarthur ⭐ Support us on Subscribestar: https://www.subscribestar.com/isaac-a… 👥 Facebook Group: / 1,583,992,725,237,264 📣 Reddit Community: / isaacarthur 🐦 Follow on Twitter / X: / isaac_a_arthur 💬 SFIA Discord Server: / discord Credits: How Big Could a Space Habitat Get? Written, Produced & Narrated by: Isaac Arthur Editor: Tim Liusko Graphics from Fishy Tree, Jarred Eagley, Jeremy Jozwik, J. Dixon, Ken York, Udo Schroeter Music Courtesy of Chris Zabriskie & Stellardrone Select imagery/video supplied by Getty Images Music by Epidemic Sound: http://nebula.tv/epidemic & Stellardrone Chapters 0:00 Intro 2:03 Basics of Habitat Scaling 9:30 Cylinder & Ring Habitats — Linear and Radial Extremes 11:00 Banks Orbitals 12:42 Ringworlds 16:24 Chrono-Engineering 17:24 The Topopolis 21:03 Planet-Wrapping Habitats 22:55 Matrioshka Shellworlds 26:17Alternative & Exotic Designs.

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Quantum Teleportation Was Performed Over The Internet For The First Time

Scientists achieved the ‘impossible’ in 2024, teleporting a quantum state through more than 30 kilometers amid a torrent of internet traffic.


In 2024, a quantum state of light was successfully teleported through more than 30 kilometers (around 18 miles) of fiber optic cable amid a torrent of internet traffic – a feat of engineering once considered impossible.

The impressive demonstration by researchers in the US may not help you beam to work to beat the morning traffic, or download your favorite cat videos faster.

However, the ability to teleport quantum states through existing infrastructure represents a monumental step towards achieving a quantum-connected computing network, enhanced encryption, or powerful new methods of sensing.

Researchers successfully 3D print one of industry’s hardest engineering materials

Tungsten carbide–cobalt (WC–Co) is prized for its hardness, but that same property makes it unusually difficult to shape. The current process is wasteful and expensive for the yield produced, and an economically sensible method for creating these materials is long overdue.

WC-Co cemented carbides are important in fields that require high wear resistance and hardness, such as cutting and construction tools. Currently, these carbides are made using powder metallurgy, utilizing high pressure and sintering machines to combine the WC and Co powders to yield a manufactured cemented carbide.

Though this method does produce highly durable and hard final products, a lot of expensive material is used, and the yield is suboptimal.

Encapsulated PbS quantum dots boost solar water splitting without sacrificial agents

A research team affiliated with UNIST has developed stable and efficient chalcogenide-based photoelectrodes, addressing a longstanding challenge of corrosion. This advancement paves the way for the commercial viability of solar-driven water splitting technology—producing hydrogen directly from sunlight without electrical input.

Jointly led by Professors Ji-Wook Jang and Sung-Yeon Jang from the School of Energy and Chemical Engineering, the team reported a highly durable, corrosion-resistant metal-encapsulated PbS quantum dot (PbS-QD) solar cell-based photoelectrode that delivers both high photocurrent and long-term operational stability for photoelectrochemical (PEC) water splitting without the need for sacrificial agents. The research is published in the journal Nature Communications.

PEC water splitting is a promising route for sustainable hydrogen production, where sunlight is used to drive the decomposition of water into hydrogen and oxygen within an electrolyte solution. The efficiency of this process depends heavily on the stability of the semiconductor material in the photoelectrode, which absorbs sunlight and facilitates the electrochemical reactions. Although chalcogenide-based sulfides, like PbS are highly valued for their excellent light absorption and charge transport properties, they are prone to oxidation and degradation when submerged in water, limiting their operational stability.

Quantum defects in carbon nanotubes as single-photon sources

This Review surveys progress in the development of carbon nanotubes as single-photon sources for emerging quantum technologies, with a focus on chemical synthesis and quantum defect engineering, computational studies of structure-property relationships, and experimental investigations of quantum optical properties.

Stabilized iron catalyst could replace platinum in hydrogen fuel cells

Japan and California have embraced hydrogen fuel-cell technologies, a form of renewable energy that can be used in vehicles and for supplying clean energy to manufacturing sectors. But the technology remains expensive due to its reliance on precious metals such as platinum. Engineers at Washington University in St. Louis are working on this challenge, finding ways to stabilize ubiquitous iron components for use in fuel cells to replace the expensive platinum metals, which would make hydrogen fuel-cell vehicles more affordable.

Cost challenges for fuel-cell vehicles

“The hydrogen fuel cell has been successfully commercialized in Japan and California in the U.S.,” said Gang Wu, a professor of energy, environmental and chemical engineering at the McKelvey School of Engineering. “But these vehicles struggle to compete with the battery vehicle and combustion engine vehicle, with cost being the main issue.”

Study reveals microscopic origins of surface noise limiting diamond quantum sensors

A new theoretical study led by researchers at the University of Chicago and Argonne National Laboratory has identified the microscopic mechanisms by which diamond surfaces affect the quantum coherence of nitrogen-vacancy (NV) centers—defects in diamond that underpin some of today’s most sensitive quantum sensors. The study has appeared in Physical Review Materials and was selected to be an Editors’ Suggestion paper.

“One long-standing challenge has been understanding why shallow NV centers lose coherence so quickly,” said Giulia Galli, professor at the University of Chicago Pritzker School of Molecular Engineering (UChicago PME) and senior scientist at Argonne National Laboratory. “By combining first-principles surface models with quantum dynamics simulations, we understood that the culprit of decoherence is not just which spins live on the diamond surface, but how they move: surface noise is dynamical.”

The findings of the study provide clear, physics-based guidelines for engineering diamond surfaces that help preserve quantum coherence, a key requirement for quantum sensing and emerging quantum information technologies.

Tuning topological superconductors into existence by adjusting the ratio of two elements

Today’s most powerful computers hit a wall when tackling certain problems, from designing new drugs to cracking encryption codes. Error-free quantum computers promise to overcome those challenges, but building them requires materials with exotic properties of topological superconductors that are incredibly difficult to produce. Now, researchers at the University of Chicago Pritzker School of Molecular Engineering (UChicago PME) and West Virginia University have found a way to tune these materials into existence by simply tweaking a chemical recipe, resulting in a change in many-electron interactions.

The team adjusted the ratio of two elements— tellurium and selenium —that are grown in ultra-thin films. By doing so, they found they could switch the material between different quantum phases, including a highly desirable state called a topological superconductor.

The findings, published in Nature Communications, reveal that as the ratio of tellurium and selenium changes, so too do the correlations between different electrons in the material—how strongly each electron is influenced by those around it. This can serve as a sensitive control knob for engineering exotic quantum phases.

Dream engineering can help solve ‘puzzling’ questions: Study offers insights to optimizing sleep

We’ve all heard the best approach to solve a problem is to “sleep on it.” It turns out there may be more truth to this adage than previously thought. While stories abound of eureka moments surfacing from dreams, scientific evidence has remained elusive, due to the challenge of systematically manipulating dreams.

A new study by neuroscientists at Northwestern University validates the possibility of influencing dreams and offers a crucial step to support the theory that dreams in REM sleep—the rapid eye movement phase of sleep in which lucid dreaming can occur—may be especially conducive to helping individuals come up with creative solutions to a problem.

The study has been published in the journal Neuroscience of Consciousness.

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