Is there art in number?
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- Math Homework Help: A Guide to the Best AI Math Solver of 2023by Casey Allen on October 24, 2023 at 4:20 am
About a quarter of the average college student's courseload is general education requirements. While these are graduation requirements, they also are usually time-wasters. They're challenging and stressful... but luckily, help is available. If you're looking for quick math homework help, an online AI math solver can bring your grades up quickly and effectively. Read on to The post Math Homework Help: A Guide to the Best AI Math Solver of 2023 first appeared on SquareCirclez. Related posts: 5 Best Free Math Problem Solvers Math problems allow students to learn new concepts and strengthen... Curriculum Webs - more homework needed "Weaving the Web into Teaching and Learning" Cunningham, C and... Buyer’s Guide: TI-84 Graphing Calculator Math classes can be daunting. From a young age, I... My dilemma - ethical math help Is there a difference between paying someone to do...
- 5 Best Free Math Problem Solversby Casey Allen on June 6, 2023 at 3:43 am
Math problems allow students to learn new concepts and strengthen problem-solving skills. But many learners feel confused or frustrated if they can’t find the correct solution. A math problem solver is a handy tool that helps students doublecheck their work and identify errors. However, not all math problem solvers are created equal. Here are the The post 5 Best Free Math Problem Solvers first appeared on SquareCirclez. Related posts: Microsoft Math 3.0 Review MS Math 3.0 is a well-designed computer-based math tool.... Free math software downloads Wanting to use some math software but find it’s too... GraphSketch.com - free online math grapher GraphSketch is a free offering that allows the user to... Context Free math-based art Context Free is software you can use to produce some...
- Reviewing Six Online Math Tutoring Services - What’s the Best?by Hugo Pegley on June 22, 2022 at 4:00 am
Math is an exciting field of study that can lead to a variety of exciting careers or research projects. But if you're a student having difficulty with the topic, you might be thinking about enrolling in an online math tutoring program. This is a great way for you to get assistance in a format and The post Reviewing Six Online Math Tutoring Services - What’s the Best? first appeared on SquareCirclez. Related posts: How to Pick A Live Math Chat Tutoring Service If you’re looking for a live math tutor, you are... How Much Does an Online Math Tutor Cost? Across the world, math is the key to understanding many... Online Algebra Math Tutor Many private and public high schools and colleges require students... Best Online Calculus Math Tutor: How to Choose Calculus and math require tremendous background information, practice, and good...
- Picking the Best Online Precalculus Math Tutorby Hugo Pegley on June 22, 2022 at 3:55 am
Students who want to go on to study math, science, engineering, and other disciplines in college, usually find that their chosen college values some prior knowledge of calculus. An online precalculus math tutor could be the answer. High schools commonly offer precalculus courses in the 11th grade before introducing calculus in the 12th. Precalculus is The post Picking the Best Online Precalculus Math Tutor first appeared on SquareCirclez. Related posts: How Much Does an Online Math Tutor Cost? Across the world, math is the key to understanding many... Best Online Calculus Math Tutor: How to Choose Calculus and math require tremendous background information, practice, and good... Online Algebra Math Tutor Many private and public high schools and colleges require students... Reviewing Six Online Math Tutoring Services - What’s the Best? Math is an exciting field of study that can lead...
- How Much Does an Online Math Tutor Cost?by Hugo Pegley on June 15, 2022 at 4:17 am
Across the world, math is the key to understanding many complex subject matters. It is also imperative that a student does not fall behind, as math typically builds on previous concepts. So, it is no secret that many typical high school and college students struggle in math classes. Due to this fact, skilled math tutors The post How Much Does an Online Math Tutor Cost? first appeared on SquareCirclez. Related posts: Online Algebra Math Tutor Many private and public high schools and colleges require students... Best Online Calculus Math Tutor: How to Choose Calculus and math require tremendous background information, practice, and good... How to Choose a Math Tutor Are you in need of mathematics support, or do you... How to Pick A Live Math Chat Tutoring Service If you’re looking for a live math tutor, you are...
Recent Questions - Mathematics Stack Exchange most recent 30 from math.stackexchange.com
- Inconsistent Function Monotonicity from hand and Mathematica imageby Kozack51 on March 19, 2024 at 3:40 am
$g(x)=\frac{\phi(x)}{1-\Phi(x)}$, where $\phi(x)$ and $\Phi(x)$ are p.d.f and c.d.f of standard normal distribution respectively. $g'(x)=\frac{\phi'(x)(1-\Phi(x))+\phi^2(x)}{(1-\Phi(x))^2}=\frac{\phi(x)}{(1-\Phi(x))^2} \left( \phi(x)-x(1-\Phi(x)) \right)$ since $\phi'(x)=-x\phi(x)$. Let $h(x)=\phi(x)-x(1-\Phi(x))$, $h'(x)$ is thus $\phi'(x)-(1-\Phi(x))+x\phi(x)=\Phi(x)-1 \leq 0$ $h(x)$ is non-increasing, and $\lim_{x\to \infty} h(x)=0 $, thus $h(x)\geq0$ and since $\frac{\phi(x)}{(1-\Phi(x))^2}\geq 0$ then $g'(x)\geq0$. $g(x)$ must be non-decreasing. But in Mathematica, I have this like a wavy line. Mathematica Image What's the problem please!
- Does Hennessy-Milner Theorem hold when I weaken its condition (image-finite) a little?by Cleanlee on March 19, 2024 at 3:40 am
Hennessy-Milner Theorem says that For two image-finite models M,N, we have that the pointed models M,w and N,v are equivalent in semantics (all holds on M,w holds on N,v and vice versa) iff M,w and N,v are bisimilar. Then I wonder whether the conclusion holds if we only restrict one side is image-finite. My intuition is that it cannot hold, and especially, we can find an image-finite model and a non-image-finite model, where the two are equivalent in semantics but not in structure. But the problem I met is that it's hard to find such an example. I've tried a lot but always failed eventually. Thanks for your help.
- Show that $ka \equiv kb \pmod{n}$ implies $a \equiv b \pmod{n}$ if and only if $\gcd(k,n) = 1$.by Aryan Das on March 19, 2024 at 3:34 am
"We know that if and only if means 2 directions- We need to show that Given $ka \equiv kb \pmod{n}$ and $\gcd(k,n) = 1$, we need to show that $a \equiv b \pmod{n}$. This can be shown easily, by writing, $ka = nc + kb \Rightarrow k(a-b) = nc \Rightarrow n \mid k(a-b)$, but $n$ doesn't divide $k$, so $n \mid (a-b) \Rightarrow a \equiv b \pmod{n}$. Given $ka \equiv kb \pmod{n}$ and $a \equiv b \pmod{n}$, show that $\gcd(k,n) = 1$. I am facing a problem in showing this direction... I tried approaches like $ka = nc + kb$, $a = nm + b$, and tried other things like properties as shown in this post, but failed. Please help... I also tried the contradiction method by assuming $\gcd(k,n) = d \neq 1$, but still nothing. Please help, thank you"
- What is the name of this functor's property?by 8k14 on March 19, 2024 at 3:33 am
Assume there is a functor $L$ from a category $C$ to a category $D$ which satisfies the following property: for any objects $X,Y,Z$ from $C$ and morphisms $f\colon X\to Y, g\colon X\to Z$ such that $L(g)=\varphi\circ L(f)$ for some morphism $\varphi\colon L(Y)\to L(Z)$ there is a morphism $h\colon Y\to Z$ such that $\varphi=L(h)$ and $g=h\circ f$. What is the name of this property?
- Residue theorem integral - calculating with trigonometric functionsby Manuel Ballester on March 19, 2024 at 3:27 am
I am trying to solve the following integral: $$I = \int_0^{2\pi} \frac{d\phi}{a + 2 b \cos(\phi) + 2 c \sin(\phi)}$$ We can assume that the denominator is always strictly positive ($a \gg b, c$). Using as example the values $(a, b, c) = (20, 1, 2)$, I could nicely see the smooth integrand function in Desmos Graphing Calculator and also use find the numerical solution using numerical integration in Python. However, now I want to solve it theoretically for general $(a, b, c)$ parameters, and I believe the Residue Theorem is the right approach. I found a countradiction in my reasoning below, and I would greatly appreciate it if you help me find where I made the mistake. Defining $z = e^{i \phi}$, we get $d\phi = \frac{dz}{iz}$. Of course, we can also use $\cos(\phi) = \frac{z + z^{-1}}{2}$, and $\sin(\phi) = \frac{z - z^{-1}}{2i}=-i\frac{z - z^{-1}}{2}$. After the substitution, one gets $$ I = \int_{|z|=1} \frac{dz}{iz \big[ a + b (z + z^{-1}) - i c (z - z^{-1}) \big]} = \int_{|z|=1} \frac{dz}{z^2 (c + i b) + z (i a) + (-c + i b) } = \int_{|z|=1} \frac{dz}{f(z)}$$ We can now find the roots of $f(z)$ using the well-known quadratic equation, yielding $$z_{1,2} = \frac{-a i \pm \sqrt{-a^2 + 4 b^2 + 4 c^2}}{2 (c + ib)}$$ Please note that discriminant must be negative, as it is always the case that $a^2 > 4 b^2 + 4 c^2$, and we can then equivalently write $\sqrt{-a^2 + 4 b^2 + 4 c^2}$ as $i \sqrt{a^2 - 4 b^2 - 4 c^2}$ to work with the root of a positive real number instead. At this point, we now have the integral $$I = \int_{|z|=1} \frac{dz}{(z - z_1)(z-z_2)}$$ And we can directly apply the Residue theorem. Although I was not able to prove it theoretically, I checked numerically (with different parameters) that $z_1$ is within the unit circle, while $z_2$ is outside. Therefore, the theorem tell us that $$I = 2 \pi i \cdot R\bigg(\frac{1}{f(z)}, z_1 \bigg) = 2 \pi i \cdot \lim_{z \rightarrow z_1} (z - z_1) \frac{1}{(z - z_1)(z-z_2)} = \frac{2 \pi i}{z_1 - z_2}$$ Here comes now the contradiction... $$z_1 - z_2 = \frac{\sqrt{-a^2 + 4 b^2 + 4 c^2}}{(c + ib)} = \frac{i \sqrt{a^2 - 4 b^2 - 4 c^2} \cdot (c - ib)}{(c^2 + b^2)}$$ Because $z_1 - z_2$ is not a pure imaginary number and has both real and imaginary part, we get that $I = \frac{2 \pi i}{z_1 - z_2}$ must be a complex number too, also with real and imaginary part, which does not make sense to me, since our original integral $I$ only contained a real function. Thank you very much for any help! PD: I know there are very similar threads (e.g. Residue theorem integration). However, I was not able to solve this particular problem from the other responses.
Surrey Mathematics Research Blog The blog on research in mathematics at the University of Surrey
- Paper of Naratip Santitissadeekorn published in the European Journal of Applied Mathematicsby Tom Bridges on March 18, 2024 at 6:02 pm
The paper “Parametric approach to promote a divergence-free flow in the image-based motion estimation with application to bioirrigation“, co-authored by Naratip Santitissadeekorn, Christof Meile (University of Georgia), Erik Bollt (Clarkson University), and George Waldbusser (Oregon State University), has been published in the European Journal of Applied Mathematics (open access, link here). In the paper, flow
- New postdoc Delyan Zhelyazov joins project of Cesare Tronci on complex fluidsby Tom Bridges on March 18, 2024 at 12:25 pm
Delyan Zhelyazov joined mathematics this month, taking up a three-year position of Postdoctoral Research Assistant on the project of Cesare Tronci, funded by the Leverhulme Trust, on “Solute motion in complex fluids: mathematics and solvation dynamics” (link here). Delyan obtained a PhD in analysis of nonlinear PDEs at the University of L’Aquila in Italy. He
- Elliott Sullinge-Farrall speaks in the Junior Analysis Seminar at Imperial College Londonby Tom Bridges on March 13, 2024 at 6:02 pm
Elliott Sullinge-Farrall visited the Mathematics Department at Imperial College London today, to give a talk in the Junior Analysis Seminar. The title of the talk was “Mean Hadamard Inequalities and Elasticity“. A link to the seminar page with abstract is here. The picture below shows Elliott in front of one of the famous statues at
- Anne Skeldon speaks the ERATO Joint UK-Japan Symposium at Oxford Universityby Tom Bridges on March 13, 2024 at 2:25 pm
Anne Skeldon is an invited speaker at the ERATO UK-Japan Symposium on Circadian Rhythms and Sleep (link here). The meeting is virtual with live presentations broadcast from Oxford University, and takes place from 11-13 March. Anne‘s talk is on “Mathematical modelling of sleep and circadian rhythms and our interactions with society and the environment“. The
- Frédéric Dias visits from École Normale Supérieure Paris-Saclay for breaking water wave projectby Tom Bridges on March 12, 2024 at 5:37 pm
Frédéric Dias, a Professor at École Normale Supérieure Paris-Saclay, visited mathematics yesterday (11 March). He interacted with Tom Bridges and Matt Turner as part of the water wave project which is developing a theory for breaking waves. The team met up online with PhD student Ayoub Mansor, and they discussed the latest results and plans
FlowingData Strength in Numbers
- Visual guide to airfoilsby Nathan Yau on March 18, 2024 at 4:08 pm
Bartosz Ciechanowski is at it again with an in-depth explainer that makes heavy…Tags: airfoil, Bartosz Ciechanowski, flight
- Mile-by-mile map along the path of totalityby Nathan Yau on March 15, 2024 at 11:50 am
On April 8, 2024, the moon is going to completely block the sun…Tags: eclipse, satellite imagery, Washington Post
- Language-based AI to chat with her dead husbandby Nathan Yau on March 15, 2024 at 7:32 am
For the past few years, Laurie Anderson has been using an AI chatbot…Tags: AI, chatbot, Guardian, Large Language Model
- ✚ One Chart to Multiple Chartsby Nathan Yau on March 14, 2024 at 6:30 pm
Every chart type has its trade-offs. So instead of trying to show everything at once, use multiple views to show things separate.Tags: multiples, simplicity
- Maps in the wildby Nathan Yau on March 14, 2024 at 5:00 pm
For the New York Times, Eve Kahn describes the use of maps outside…Tags: decor, New York Times
AnnMaria's Blog Words from the Prez
- Why won’t SAS see this character variable is equal?by annmaria on July 16, 2023 at 6:13 pm
When I selected observations where the character variable was equal to a certain value, SAS returned 0 observations - but I knew there should be a match!
- Macros, SQL and Reading CSV with SAS – Part 1by annmaria on December 27, 2022 at 6:31 am
How can you combine data sets with different variable lengths, different unique identifiers, in a different format than last year? It's easy.
- Converting to fiscal years, using SASby annmaria on January 30, 2022 at 5:50 am
Creating a new variable for fiscal year with SAS is actually super simple.
- Giving Students Their Money’s Worth Onlineby annmaria on August 23, 2020 at 6:26 am
As someone who has taught for over 30 years, and online for most of the last 7, I can tell you that online courses can actually be better.
- Tomorrow, I will be serious. Today, it’s quarantine clothesby annmaria on April 10, 2020 at 2:57 am
In my first ever post on fashion, I discuss rules for attire in web meetings. Number one: Wear clothes.
Data & Society Data & Society advances public understanding of the social implications of data-centric technologies and automation.
- Ensuring “AI Safety” Begins with Addressing Algorithmic Harms Nowby Alessandra Erawan on March 18, 2024 at 1:53 pm
- Response to RFI Related to NIST’s Assignments Under the AI Executive Orderby Alessandra Erawan on February 14, 2024 at 5:38 pm
- Meet Our Advisorsby Alessandra Erawan on February 14, 2024 at 5:02 pm
- Response to OMB’s Artificial Intelligence Draft Memorandumby Alessandra Erawan on December 13, 2023 at 8:18 pm
December 13, 2023 — Data & Society’s comment on the Office of Management and Budget’s (OMB) draft guidance applauds the important steps it takes toward AI accountability, and encourages OMB to keep those measures in its final guidance. As we note, the draft guidance rightly identifies many AI systems that have caused harm to the
- Eleven New Affiliates Join Data & Societyby Alessandra Erawan on December 13, 2023 at 8:18 pm
MIT News - Data | Big data | Analytics | Statistics | IDSS | Operations research MIT news feed about: Data | Big data | Analytics | Statistics | IDSS | Operations research
- Exploring the cellular neighborhoodby Alison Biester | Department of Biology on March 11, 2024 at 8:50 pm
Software allows scientists to model shapeshifting proteins in native cellular environments.
- Using generative AI to improve software testingby Zach Winn | MIT News on March 5, 2024 at 5:00 am
MIT spinout DataCebo helps companies bolster their datasets by creating synthetic data that mimic the real thing.
- Dealing with the limitations of our noisy worldby Adam Zewe | MIT News on March 1, 2024 at 5:00 am
Tamara Broderick uses statistical approaches to understand and quantify the uncertainty that can affect study results.
- Startup accelerates progress toward light-speed computingby Zach Winn | MIT News on March 1, 2024 at 5:00 am
Lightmatter, founded by three MIT alumni, is using photonic technologies to reinvent how chips communicate and calculate.
- Power when the sun doesn’t shineby Deborah Halber | MIT Energy Initiative on February 29, 2024 at 9:45 pm
With batteries based on iron and air, Form Energy leverages MIT research to incorporate renewables into the grid.
- New AI model could streamline operations in a robotic warehouseby Adam Zewe | MIT News on February 27, 2024 at 5:00 am
By breaking an intractable problem into smaller chunks, a deep-learning technique identifies the optimal areas for thinning out traffic in a warehouse.
- “We offer another place for knowledge”by Katherine Ouellette | MIT Open Learning on February 26, 2024 at 7:35 pm
After acquiring data science and AI skills from MIT, Jospin Hassan shared them with his community in the Dzaleka Refugee Camp in Malawi and built pathways for talented learners.
- Putting AI into the hands of people with problems to solveby Zach Winn | MIT News on February 26, 2024 at 5:00 am
Alumni-founded Pienso has developed a user-friendly AI builder so domain experts can build solutions without writing any code.
- Automated method helps researchers quantify uncertainty in their predictionsby Adam Zewe | MIT News on February 21, 2024 at 5:00 am
An easy-to-use technique could assist everyone from economists to sports analysts.
- MIT researchers remotely map crops, field by fieldby Jennifer Chu | MIT News on February 15, 2024 at 5:00 am
The team used machine learning to analyze satellite and roadside images of areas where small farms predominate and agricultural data are sparse.
Mathematics – Wolfram Blog News, Views and Insights from Wolfram
- Hypergeometric Functions: From Euler to Appell and Beyondby Tigran Ishkhanyan on January 25, 2024 at 5:35 pm
Hypergeometric series appeared in the mid-seventeenth century; since then, they have played an important role in the development of mathematical and physical theories. Most of the elementary and special functions are members of the large hypergeometric class. Hypergeometric functions have been a part of Wolfram Language since Version 1.0. The following plot shows the implementation
- Get Down to Business with Finite Mathematics in Wolfram Languageby John McNally on December 22, 2023 at 3:41 pm
“There is every reason to expect that the various social sciences will serve as incentives for the development of great new branches of mathematics and that some day the theoretical social scientist will have to know more mathematics than the physicist needs to know today.” —John G. Kemeny, first author of the original textbook on
- Don’t Be Discreet and Learn Discrete Mathematics with Wolfram Languageby Marc Vicuna on November 29, 2023 at 6:00 pm
“The spread of computers and the internet will put jobs in two categories. People who tell computers what to do, and people who are told by computers what to do.” — Marc Andreessen, inventor of the Netscape browser How is data organized in databases? Why are some computer programs faster than others? How can algorithms
- Learn Multivariable Calculus through Incredible Visualizations with Wolfram Languageby Tim McDevitt on November 6, 2023 at 3:57 pm
Multivariable calculus extends calculus concepts to functions of several variables and is an essential tool for modeling and regression analysis in economics, engineering, data science and other fields. Learning multivariable calculus is also the first step toward advanced calculus and follows single-variable calculus courses. Wolfram Language provides world-class functionality for the computation and visualization of
- Expand Your Understanding of Statistics with Wolfram Languageby Jamie Peterson on June 6, 2023 at 4:27 pm
Statistics is the mathematical discipline dealing with all stages of data analysis, from question design and data collection to analyzing and presenting results. It is an important field for analyzing and understanding data from scientific research and industry. Data-driven decisions are a critical part of modern business, allowing companies to use data and computational analyses
- Stack the Odds in Your Favor and Master Probability with Wolfram Languageby Marc Vicuna on March 24, 2023 at 3:46 pm
“I believe that we do not know anything for certain, but everything probably.” —Christiaan Huygens Have you ever wondered how health insurance premiums are calculated or why healthcare is so expensive? Or what led to the financial crisis of 2008? Or whether nuclear power is safe? The answers to these questions require an understanding of
- Active Learning with Wolfram|Alpha Notebook Editionby Jordan Hasler on January 20, 2023 at 8:16 pm
As you may know from your own experience (or perhaps from the literature on education), passively receiving information does not lead to new knowledge in the same way that active participation in inquiry leads to new knowledge. Active learning describes instructional methods that engage students in the learning process. Student participation in the classroom typically
- Wolfram|Alpha Pro Teaches Step-by-Step Arithmetic for All Grade Levelsby AnneMarie Torresen on August 26, 2022 at 3:12 pm
In grade school, long arithmetic is considered a foundational math skill. In the past several decades in the United States, long arithmetic has traditionally been introduced between first and fifth grade, and remains crucial for students of all ages. The Common Core State Standards for mathematics indicate that first-grade students should learn how to add
- Fractional Calculus in Wolfram Language 13.1by Tigran Ishkhanyan on August 12, 2022 at 9:10 pm
What is the half-derivative of x? Fractional calculus studies the extension of derivatives and integrals to such fractional orders, along with methods of solving differential equations involving these fractional-order derivatives and integrals. This branch is becoming more and more popular in fluid dynamics, control theory, signal processing and other areas. Realizing the importance and potential