How many Danes are actually infected? This calculation tries to give the answer | Coronavirus - TV 2

An engineer's math has gone viral. If you make a few reservations, it can actually give a bearing on the number, experts say.
 

Photo: JumpStory

På bare få uger har 40 millioner mennesker på verdensplan læst en ingeniørs analyse af covid-19-epidemien, according to Silvie Ulrikke Østebø, Journalist hos TV 2 Nyhederne.

Analysen "Corona: Why you must act now", som er udgivet på blogsiden Medium, har fået så stor opmærksomhed, fordi den forsøger at give et klart svar på spørgsmålet, som myndighederne ikke har kunnet svare på:

Hvor mange er reelt er smittet med coronavirus?

Kun 2046 er lige nu testet positiv for virussen i Danmark, men fra eksperter lyder det, at der er et enormt mørketal. Det er dette tal, som Tomás Pueyo, VP Growth at Course Hero har fundet en udregningsmetode for.

I denne artikel vil logikken bag udregningerne blive forklaret.

Derudover retter to danske eksperter et kritisk blik på dem. For selvom Tomas Pueyo er ingeniør, så arbejder han til dagligt indenfor reklamebranchen og er altså ikke sundhedsfaglig ekspert...

Udregningen
Fordi dem, der har mistet livet, i gennemsnit har været syge i 17,3 dage forud for døden, kan man regne bagud. De 52, som i Danmark er døde frem til den 27. marts, har altså i gennemsnit haft coronavirussen i kroppen siden 10. marts.

De 52 personer udgjorde 0,87 procent af alle smittede på daværende tidpunkt. Altså antager vi i udregningen, at 99,13 procent af smittetilfældene samme dag IKKE førte til døden.

På de 17,3 dage, det har taget en gruppe at gå fra at blive syge til at miste livet, er antallet af sygdomstilfælde samtidig blevet fordoblet med en faktor 2,8. Fordi 6,2 går 2,8 gange op i 17,3.

Og så er det bare at udregne. 

Der er altså 41.626 personer, som er smittede med coronavirus i Danmark, ifølge denne udregning...

Usikker metode - men peger på det rigtige 
Men kan man overhovedet regne med de tal, som Tomas Pueyo fremstiller? Kan man regne med en ingeniør, som ikke er ekspert i coronavirus, der opsætter modeller med en lang række antagelser?

Både og, lyder det fra Lasse Engbo Christiansen, som er matematiker fra DTU og netop arbejder med computermodeller for sygdomsspredning i et samfund. Han har læst analysen i Medium, men ikke nærstuderet matematikken bag.

- Ingeniørens udgangspunkt er jo at råbe folk op ved at vise, hvor mange der er smittede. Og det gør han jo effektivt, siger han.

- Jeg må citere statistikeren George Box: All models are wrong but some are useful (alle modeller er forkerte, men nogle er brugbare, red.).
Read more... 

Source: TV 2

Robots Are Very Good At Social Distancing | Robotics - Benzinga

Originally posted here...

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Consumer concerns about autonomous robots may give way to more favorable impressions as demand for human-free delivery grows during the coronavirus outbreak by FreightWaves.

Robots Are Very Good At Social Distancing

Not so long ago, a "techlash" threatened to derail progress on autonomous transportation, and critics talked about corrective actions such as socializing autonomous delivery robots to make the technology more palatable.

Coronavirus has since shifted the conversation, away from socialization and toward social distancing. That's good news for autonomous delivery companies...

There will also be "a radical change" in the cultural attitudes of consumers in Western countries, Russi believes. Until now, a majority of people viewed automation as a ‘scary' or ‘creepy' substitute to ‘warm' human contact," he said.

"From now on, they will likely be more welcoming."
Read more...

Source: Benzinga

Robots here to help | Tech - Innovators Magazine

Humankind could do with a bit of help right now and robots might just be able to provide some much needed support, observes Susan Robertson, co-founder of Innovators Magazine. 

Photo: Heriot-Watt University

Thanks to a world first pioneered at the UK’s National Robotarium at Heriot-Watt University in Edinburgh, a new multi-user conversational robot is being developed that will safely enhance elderly healthcare. Pioneered through an international collaboration of European and Asian institutions, the project, called SPRING (Socially Pertinent Robots in Gerontological Healthcare) is funded by Horizon2020, and is the first to come from the Robotarium. These Socially Assistive Robots (SARs) will be able to talk and interact with elderly citizens in healthcare facilities – with social distancing already built in.

“This type of technology is touch-free and hands-free so will be in great demand in the future as it will reduce the risk and spread of infection,” said Professor Oliver Lemon from Heriot-Watt University...

COVID-19
The touch-free and hands-free nature of the SPRING developed robots are hugely important factors in light of infectious diseases like COVID-19. Stopping any spread through touch is a key element of this innovation. And a group of international experts in robotics have penned an editorial this week stating that robots are already combating the COVID-19 pandemic.

“Already, we have seen robots being deployed for disinfection, delivering medications and food, measuring vital signs, and assisting border controls,” the researchers wrote in Science Robotics.
Read more... 

Source: Innovators Magazine

Google and the Oxford Internet Institute explain artificial intelligence basics with the ‘A-Z of AI’ | AI - VentureBeat

Paul Sawers, Staff Writer at VentureBeat inform, Artificial intelligence (AI) is informing just about every facet of society, from detecting fraud and surveillance to helping countries battle the current COVID-19 pandemic. 

Google and the Oxford Internet Institute launch the A to Z of AI

But AI is a thorny subject, fraught with complex terminology, contradictory information, and general confusion about what it is at its most fundamental level. This is why the Oxford Internet Institute (OII), the social and computer science department of the U.K.’s University of Oxford, has partnered with Google to launch a portal with a series of explainers outlining what AI actually is — including the fundamentals, ethics, its impact on society, and how it’s created.

At launch, the “A-Z of AI” covers 26 topics, including bias and how AI is used in climate science, ethics, machine learning, human-in-the-loop, and Generative adversarial networks (GANs)...

Google’s People and AI Research team (PAIR) worked with Gina Neff, a senior research fellow and associate professor at OII, and her team to select the subjects they felt were pivotal to understanding AI and its role today...

You can peruse the guide in its full A-Z form or filter content by one of four categories: AI fundamentals, Making AI, Society and AI, and Using AI.
Read more...

Source: VentureBeat

Coronavirus lockdown: 10 free online computer science courses from Harvard, Princeton & other top universities to study | Videos - Gadgets Now

Check out these free online computer science courses, as Gadgets Now reports.

https://www.gadgetsnow.com/videos/10-free-online-computer-science-courses-from-harvard-princeton-more-to-do-during-coronavirus-lockdown/videoshow/74835973.cms

Here are 10 free online computer science courses from Harvard, Princeton & other top universities that you may want to consider to upskill yourself and make the most of the lockdown period.
(Note that only basic or introductory courses are listed and there are thousands of free online courses available which you can try.)
Read more...

Source: Gadgets Now

Pioneering deep learning in the cyber security space: the new standard? | Cybersecurity - Information Age

Applying deep learning in the cyber security space has many benefits, such as the prediction of unknown threats and zero time classification, explains Nick Ismail, editor for Information Age. 

Will cyber security solutions move from machine learning to deep learning?

The use of deep learning in the cyber security space is an emerging trend. But, it has the potential to transform a security model that is currently broken, by predicting new attacks before they’ve breached an organisation’s network or device.

“Cyber security has a coronavirus situation every day,” said Jonathan Kaftzan, VP Marketing at Deep Instinct, during his presentation as part of the latest IT Press Tour.

Deep learning neural models can predict new variations of existing cyber attacks that occur daily, while the majority of current solutions in the market can only detect infected systems or anomalies, contain and remediate them — this is costly and unsustainable...

Deep learning vs machine learning
Deep learning is a sub category in a family of algorithims under machine learning, while machine learning is a broad set of algorithms under artificial intelligence.

Everyone is talking about AI, but it has been around for many years. You can define the technology as a system that mimics human intelligence by making decisions. There are many forms of human intelligence, such as if you do a. then b. will happen — many systems are already using this type of rule-based decision-making. 
Read more...

Source: Information Age

The Beginner's Guide To Data Visualization for Mobile Games | Member Blogs - Gamasutra

The following blog post, unless otherwise noted, was written by a member of Gamasutra’s community.

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Alex Moukas, Founder & CEO of Wappier (www.wappier.com) reports, For all our strengths, humans aren’t very good at bulk data processing. 

For all our strengths, humans aren’t very good at bulk data processing.

Instead, thanks to the power of our optic nerves, we’re much better equipped for symmetry detection and spatial awareness. Data needs to be transformed into something we find visually meaningful before we can draw any actionable inferences. For mobile game developers in particular, this presents a unique challenge. 

With an addressable audience of more than 2.4 billion people, mobile games deal with unparalleled volumes of player data. Thankfully, specialized frameworks have been developed to collect and store this information, but the sheer amount of data makes it uniquely challenging to derive actionable insights. 

This is where data visualization comes in...

Visualizing Engagement

High-level averages can be represented easily enough through simple numerical displays broken down by game version or user segment. Detailed game-specific data sets however, often require more sophisticated visualizations. Anything relating to location data, such as the distribution of defenses in a build & battle mobile strategy title, are often best visualized using heat maps. These are typically two-dimensional charts with localized areas that have been color-coded along a warm-to-cool spectrum in relation to player activity. Designers can utilize heat maps to better optimize user interfaces.
Read more...

Source: Gamasutra

Maplesoft launches new version of Maple mathematics software | Simulation - Automotive Testing Technology International

A new version of Maplesoft’s Maple mathematical software is now available by Rachel Evans, Deputy Editor at UKi Media & Events.

Photo: Automotive Testing Technology International

The 2020 updates are said to provide a more powerful math engine, improved tooling for interactive problem solving, and application development.

Highlights include new algorithms and solving techniques in differential equations, calculus, abstract algebra, integral transforms, graph theory, physics and other areas of math, including science and engineering.

Other new features include enhanced programming tools to help program users find and fix problems in their own code, and improved signal processing abilities for the exploration of signals of all types, which include data, image and audio processing...

Karishma Punwani, director of product management at Maplesoft, commented, “Maple is used by all sorts of different people, from students taking their first steps in algebra and calculus, to teachers delivering engaging, effective lectures, researchers developing their own algorithms or solving cutting edge problems, engineers designing new technologies, and scientists learning more about how our world works.
Read more...

Source: Automotive Testing Technology International

New mathematical model can more effectively track epidemics | Computers & Math - Science Daily

Summary:
As COVID-19 spreads worldwide, leaders are relying on mathematical models to make public health and economic decisions. A new model improves tracking of epidemics by accounting for mutations in diseases. Now, the researchers are working to apply their model to allow leaders to evaluate the effects of countermeasures to epidemics before they deploy them.

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John Sullivan, Senior Editor at Princeton University, Engineering School writes, As COVID-19 spreads worldwide, leaders are relying on mathematical models to make public health and economic decisions.

A new model developed by Princeton and Carnegie Mellon researchers improves tracking of epidemics by accounting for mutations in diseases. Now, the researchers are working to apply their model to allow leaders to evaluate the effects of countermeasures to epidemics before they deploy them.

A new model developed by Princeton and Carnegie Mellon researchers improves tracking of epidemics by accounting for mutations in diseases. Now, the researchers are working to apply their model to allow leaders to evaluate the effects of countermeasures to epidemics before they deploy them.

"We want to be able to consider interventions like quarantines, isolating people, etc., and then see how they affect an epidemic's spread when the pathogen is mutating as it spreads," said H. Vincent Poor, one of the researchers on this study and Princeton's interim dean of engineering.

The models currently used to track epidemics use data from doctors and health workers to make predictions about a disease's progression. Poor, the Michael Henry Strater University Professor of Electrical Engineering, said the model most widely used today is not designed to account for changes in the disease being tracked...

"The spread of a rumor or of information through a network is very similar to the spread of a virus through a population," Poor said. "Different pieces of information have different transmission rates. Our model allows us to consider changes to information as it spreads through the network and how those changes affect the spread."
Read more...

Additional resources
Journal Reference:

1. Rashad Eletreby, Yong Zhuang, Kathleen M. Carley, Osman Yağan, H. Vincent Poor. The effects of evolutionary adaptations on spreading processes in complex networks. Proceedings of the National Academy of Sciences, 2020; 117 (11): 5664 DOI: 10.1073/pnas.1918529117

Source: Science Daily

Five tips for moving teaching online as COVID-19 takes hold | Career - Nature.com

Universities are closing worldwide, forcing instructors to turn to remote teaching. Here’s some expert advice on how to embrace the digital classroom, says Virginia Gewin, freelance writer in Portland, Oregon.

Academics face empty classrooms during the current coronavirus pandemic.
Photo: Matteo Corner/EPA-EFE/Shutterstock

In early February, Leonardo Rolla had about two weeks to work out how to start teaching online. A mathematician at the National Scientific and Technical Research Council in Buenos Aires, Rolla also teaches maths for two terms each year at New York University (NYU) Shanghai in China. He had been visiting family when the outbreak of the COVID-19 coronavirus forced universities in China to shut down, and he could not return to Shanghai.

For Rolla, who had never taught an online class, the transition required many hours of work and a great deal of patience. He had to learn the technology and identify the best teaching tactics for his advanced linear-algebra class of 33 students. Part of the problem was that his students are in a time zone 11 hours ahead of him.

With technological help from colleagues at NYU Shanghai, he developed a strategy for teaching remotely from the other side of the world. Each day, using a program called Voice-Thread, he records several short videos of himself explaining maths concepts, adding up to 15–30 minutes collectively...

Working together 
Rolla has one crucial tip: seek constant feedback from students. “I am the director of this movie,” he says, “but we are all in this together.” He asks his students precise questions to demonstrate what they have just learnt and how each concept builds on their existing base of knowledge. He also asks for feedback to improve the course. When students asked for more concrete examples of complex, abstract theorems to make sure they understood the concepts, he obliged. “The biggest risk is that you become a talking head explaining things that students are not following,” he says, “and they give up and just pretend.” His video-based approach has earned high praise from students and colleagues.
Read more...

Additional resources 
doi: 10.1038/d41586-020-00896-7

Source: Nature.com 

University mathematician calculates Minnesota COVID-19 cases | Video - KEYC

Take a closer look at this video.

Amid the spread of coronavirus throughout the world, you've likely heard the terminology for the need to "flatten the curve". Minnesota State University, Mankato math teacher Kurt Grunzke, has been studying the growth of the outbreak in Minnesota through algebraic formulas.

There’s a mathematician at MSU Mankato whose been calculating predictions on the growing number COVID-19 cases in Minnesota by Gage Cureton, Multi-Media Journalist.

There’s a mathematician at Minnesota State University, Mankato whose been calculating predictions on the growing number COVID-19 cases in Minnesota.

Minnesota Covid-19 Exponential Growth Part 7
 

Minnesota State University, Mankato math teacher Kurt Grunzke’s predictions for the amount of those infected in Minnesota on Monday were off just by three cases, but he is happy to say that his predictions are slightly off, and Tuesday’s reported cases of 262 were lower than his initial estimate of 324.

He says he doesn't expect to get too close that often this early, and he's using math equations to help educate the public about what they may expect in the future as reported cases continue to grow... 

“The rate is very closely connected to the testing, and when we have testing up like we did yesterday at about 1,000, we found 66 cases. So from looking at two days’ data points, we doubled the number of testing and we about doubled the amount of infections. So as testing goes up we can expect to see more numbers. Another reason we can expect to see more numbers is this basic model of exponential growth that I’m following - that I’m reasonably within a certain degree of error - the numbers are going to get bigger," says Grunzke.

Read more...

Source: KEYC and Kurt Grunzke Channel (YouTube)

Suggested Books Today | Books - Helge Scherlund's eLearning News

Check out these books below by Cambridge University Press.

Photo: JumpStory

Dynamics of Multibody Systems

Dynamics of Multibody Systems

This fully revised fifth edition provides comprehensive coverage of flexible multibody system dynamics. Including an entirely new chapter on the integration of geometry, durability analysis, and design, it offers clear explanations of spatial kinematics, rigid body dynamics, and flexible body dynamics, and uniquely covers the basic formulations used by the industry for analysis, design, and performance evaluation...

Illustrated with a wealth of examples and practical applications throughout, it is the ideal text for single-semester graduate courses on multibody dynamics taken in departments of aerospace and mechanical engineering, and for researchers and practicing engineers working on a wide variety of flexible multibody systems.

• Includes a new chapter on the integration of geometry, durability analysis, and design
• Existing chapters have been fully updated and revised
• Provides clear and complete coverage of spatial kinematics, rigid body dynamics and flexible body dynamics

Date Published: March 2020
Read more...

Mining of Massive Datasets

Mining of Massive Datasets

Written by leading authorities in database and Web technologies, this book is essential reading for students and practitioners alike. The popularity of the Web and Internet commerce provides many extremely large datasets from which information can be gleaned by data mining...

The authors explain the tricks of locality-sensitive hashing and stream-processing algorithms for mining data that arrives too fast for exhaustive processing. Other chapters cover the PageRank idea and related tricks for organizing the Web, the problems of finding frequent itemsets, and clustering. This third edition includes new and extended coverage on decision trees, deep learning, and mining social-network graphs.

• Contains brand new material on deep learning, decision trees, and mining social-network graphs
• Includes a range of more than 250 exercises to challenge even the most able student
• Slides, homework assignments, project requirements, and exams are available from www.mmds.org

Date Published: January 2020
Read more...

Scaling up Machine Learning - Parallel and Distributed Approaches 

Scaling up Machine Learning
Parallel and Distributed Approaches

This book presents an integrated collection of representative approaches for scaling up machine learning and data mining methods on parallel and distributed computing platforms. Demand for parallelizing learning algorithms is highly task-specific: in some settings it is driven by the enormous dataset sizes, in others by model complexity or by real-time performance requirements...

Extensive coverage of parallelization of boosted trees, SVMs, spectral clustering, belief propagation and other popular learning algorithms, and deep dives into several applications, make the book equally useful for researchers, students and practitioners.

• A comprehensive view of modern machine learning, covering most of the contemporary research on large-scale problems
• Presents methods for scaling up a wide array of learning tasks, including classification, clustering, regression and feature selection
• Shows how to run state-of-the-art machine learning algorithms, such as boosted decision trees and SVMs, on multiple parallel-computing platforms

Date Published: March 2018
Read more...

Solutions Manual for Actuarial Mathematics for Life Contingent Risks
 

Solutions Manual for Actuarial Mathematics for Life Contingent Risks

This must-have manual provides detailed solutions to all of the 300 exercises in Dickson, Hardy and Waters' Actuarial Mathematics for Life Contingent Risks, 3 edition. This groundbreaking text on the modern mathematics of life insurance is required reading for the Society of Actuaries' (SOA) LTAM Exam...

Beyond professional examinations, the textbook and solutions manual offer readers the opportunity to develop insight and understanding through guided hands-on work, and also offer practical advice for solving problems using straightforward, intuitive numerical methods. Companion Excel spreadsheets illustrating these techniques are available for free download.

• Complete solutions to all exercises in the required text for the Society of Actuaries' (SOA) LTAM Exam
• Solutions designed by authors to facilitate exam preparation and to deepen learning
• Companion spreadsheets available online show implementation of computational methods

Publication planned for: April 2020
Read more...

During Coronavirus - Social Distancing:
Stay home and switching to eLearning and read 📚books.

Source: Cambridge University Press.

Social Distancing: How Many People Is Too Many? | Science - WIRED

Schools and sports leagues are shutting down. But experts say it's still safe for most people to shop for groceries and meet in small groups, says Aarian Marshall, Staff Writer - WIRED.

Silhouette of a crowd in the stands at a soccer game
Photo: Laurence Griffiths/Getty Images

My cousin had to cancel his bar mitzvah, which was planned for Saturday in Washington, DC. Some 100 people were scheduled to be there, but like many houses of worship this week, the synagogue suspended its services to help prevent the spread of the coronavirus. For my cousin, it means postponing the payoff from years of study and a celebration with friends and family.

Many other Americans are in similar situations during the outbreak of Covid-19, which has sickened more than 4,100 Americans and killed more than 40, according to an online tally being kept by Johns Hopkins University. Schools, religious institutions, and sports and concert venues have closed. Those who can work from home have been urged to do so. The White House reportedly overruled a proposal from the Centers for Disease Control that would have urged anyone over 60 to avoid airplane travel...

From a mathematical perspective, determining how big a crowd is safe depends on a couple of key questions: How many people in a given area are infected with the disease? And how big is the event? If you know those things, you can estimate the probability of someone getting infected at the event. An elegant “Covid-19 Event Risk Assessment Planner” by Georgia Tech quantitative biologist Joshua Weitz makes the following calculation: If, say, 20,000 cases of infection are actively circulating in the US (far more than are known so far), and you host a dinner party for 10 folks, there’s a 0.061 percent chance that an attendee will be infected. But if you attend a 10,000-person hockey match, there’s a 45 percent chance. Hence the suspension of the NHL season, along with the NBA, March Madness, and Major League Baseball. 
Read more...

Source: WIRED

Stanford 3D computer graphics pioneer Pat Hanrahan wins $1M Turing Award | Computing - Stanford Report

Hanrahan splits the prize with one-time mentor and Pixar colleague Ed Catmull. The pair’s work continues to transform film, video games, virtual reality and more by Andrew Myers, associate director of communications at the Stanford University School of Engineering. 

Ed Catmull, left, and Pat Hanrahan were instrumental in the development of computer-generated imagery, known as C.G.I.
Photo: Pixar/Deborah Coleman (Catmull) - Andrew Brodhead/Stanford University

In recognition of his “revolutionary impact” on computer-generated animation, Stanford computer scientist and engineer Patrick M. “Pat” Hanrahan will share the 2019 Turing Award from the Association of Computing Machinery (ACM) – often described as the “Nobel Prize” of computing.

“The announcement came totally out of the blue and I am very proud to accept the Turing Award,” said Hanrahan, who is the Canon Professor in the School of Engineering and a professor of computer science and of electrical engineering at Stanford University. “It is a great honor, but I must give credit to a generation of computer graphics researchers and practitioners whose work and ideas influenced me over the years.”
Hanrahan splits the award and its $1 million prize with one-time mentor and colleague Edward “Ed” Catmull, former president of Pixar and Disney Animation Studios. The pair’s recognition marks only the second time that the award has been given for computer graphics...

While at Stanford, Hanrahan pioneered many new techniques in computer graphics, including “physically based rendering,” a way of modeling light sources and materials and then simulating the process of light interacting with them in a virtual scene. Hanrahan has taught the course CS348b: Computer Image Synthesis, since his arrival at Stanford; this led to a book on the topic, titled Physically Based Rendering: From Theory to Implementation, written by his former graduate students Matt Pharr and Greg Humphreys. The book explains how to implement a ray tracer using “literate programming,” a technique invented by Donald Knuth, another Turing laureate from Stanford.
Read more...

Recommended Reading

Physically Based Rendering:
From Theory to Implementation

Source: Stanford Report 

Mathematics pioneers who found order in chaos win Abel prize | Nature.com

Hillel Furstenberg and Gregory Margulis applied theories of probability, randomness and dynamic systems to other areas of maths, inform Davide Castelvecchi, Senior Reporter at Nature.

Hillel Furstenberg (left) and Gregory Margulis were jointly awarded the 2020 Abel Prize.
Photo: Yosef Adest, Dan Renzetti

Two mathematicians who used randomness to cast new light on the certainties of mathematics will share the 2020 Abel Prize — one of the field’s most prestigious awards.

Israeli Hillel Furstenberg and Russian-American Gregory Margulis won “for pioneering the use of methods from probability and dynamics in group theory, number theory and combinatorics”, the Norwegian Academy of Science and Letters announced on 18 March. Each of them bridged gaps between diverse areas of maths, solving problems that had seemed beyond reach...

Chaotic systems
A common thread in the work of both mathematicians has been the use of techniques from ergodic theory, a field of maths that originated in the study of physics problems such as the motion of billiard balls or planetary systems. Ergodic theory studies systems that evolve in time, eventually exploring virtually all their possible configurations. These systems are typically chaotic, meaning that their future behaviour can only be guessed using probability.

But that randomness can be a strength when applied to other mathematical problems...

The Abel Prize is named after Norwegian mathematician Niels Henrik Abel (1802–29) and was established in 2003. The two winners will share 7.5 million Norwegian kroner, or about US$ 834,000.

Because of the ongoing coronavirus pandemic, the academy decided to postpone the award ceremony, which normally would have taken place in Oslo in June. Instead, the 2021 ceremony will celebrate winners for both the 2020 and 2021 prizes. “It’s extraordinary times, so we have to do things a little bit differently this year,” Munthe-Kaas says.
Read more... 

Additional resources
Mathematics pioneers who found order in chaos win Abel prize  
doi: 10.1038/d41586-020-00799-7 

Source: Nature.com

‘Rainbows’ Are a Mathematician’s Best Friend | Mathematics - Quanta Magazine

Kevin Hartnett, senior writer at Quanta Magazine argues, “Rainbow colorings” recently led to a new proof. It’s not the first time they’ve come in handy.

Photo: Color-coding a Latin square and its graph can reveal a lot about them.

Recently, Quanta reported on the new solution to a problem called Ringel’s conjecture. Part of the proof involved using rainbow colorings, special color-coded ways of visualizing information. But the colorful technique has actually been helping mathematicians solve puzzles for a long time, and it figures in an even harder related problem that mathematicians are eyeing next.

Ringel’s conjecture is a problem in combinatorics where you connect dots (vertices) with lines (edges) to form graphs. It predicts that there’s a special relationship between a type of large graph with 2n + 1 vertices and a proportionally smaller type of graph with n + 1 vertices...

Eventually, mathematicians discovered that one way to investigate this is to turn the square into a graph. To do this, place three vertices on the left side of the page, representing the three columns. Then place three vertices on the right side of the page, representing the rows. Draw edges connecting each vertex on the right with each vertex on the left. Each edge, being the combination of a specific row and column, represents one of the nine boxes. For example, the edge between the top vertex on the right and the top vertex on the left corresponds to the box in the first row and the first column (the top left box in the Latin square)...

However, the methods that came to fruition in the Ringel proof seem likely to be applicable to graceful labeling — and mathematicians are eager to see just how far they can push them.
Read more...

Source: Quanta Magazine

Five Ways to Promote Student Autonomy in Online Discussions | Online Education - Faculty Focus

“Write an initial post and then reply to two of your classmates.” by Cassandra Sardo, instructional designer in the Office of Digital Learning at the New Jersey Institute of Technology and Justin York, PhD, instructional design coordinator in the Center for Innovation in Teaching & Learning at the University of Illinois at Urbana-Champaign.

Five Ways to Promote Student Autonomy in Online Discussions
Photo: Faculty Focus

These are the standard requirements for students participating in online course discussions. Discussions in an online course play a vital role in creating substantive interactions, aiming to capture the spirit of discourse in face-to-face settings. This, however, can look and feel like busy work, making the purpose of online discussions unclear to students. 

The standard blueprint is safe but has been exhausted. “Initial posts” can be counterintuitive—in essence, they require students to complete small writing assignments individually before giving other students feedback on their work (Liberman, 2019). How can we think outside of the box of posting and replying when it comes to these discussions? One way is to use online discussions as an opportunity to promote student autonomy and ask students to be active participants not only in how they respond to class discussions, but how they initiate them. Here are five considerations for promoting student autonomy while also breaking the online discussion mold: 
Read more...

Source: Faculty Focus