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## SquareCirclez Mathematics, learning, computing, travel - and whatever...

• 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 Tutor
by 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...

• Online Algebra Math Tutor
by Hugo Pegley on June 15, 2022 at 4:12 am

Many private and public high schools and colleges require students to take at least one algebra course to complete the fundamental graduation requirements. Still, math classes can be particularly challenging for some learners. Algebra is a broad math subject that students must grasp to learn more complex math. While not as difficult as more advanced The post Online Algebra 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... Picking the Best Online Precalculus Math Tutor Students who want to go on to study math, science,... Reviewing Six Online Math Tutoring Services - What’s the Best? Math is an exciting field of study that can lead...

• Best Online Calculus Math Tutor: How to Choose
by Hugo Pegley on June 15, 2022 at 4:11 am

Calculus and math require tremendous background information, practice, and good problem-solving skills compared to other school subjects. Teachers in traditional classrooms don't always have the time and resources to ensure students fully understand a subject. But an online calculus math tutor can help you improve your test scores with one-on-one problem solving and personalized live The post Best Online Calculus Math Tutor: How to Choose first appeared on SquareCirclez. Related posts: 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... Picking the Best Online Precalculus Math Tutor Students who want to go on to study math, science,... How to Choose a Math Tutor Are you in need of mathematics support, or do you...

## Recent Questions - Mathematics Stack Exchange most recent 30 from math.stackexchange.com

• Please give me a detailed explanation on how angle alpha in second quadrant make points (cos $\alpha$ , sin $\alpha$ ) in second quadrant
by Midhun Raj on August 8, 2022 at 4:01 am

How come point B make (cos $\alpha$ , sin $\alpha$) for a unit circle If it was in the first quadrant i could figure it out.But since it is in the second quadrant how come it happen.You cant directly go for a right angle triangle. Angle $\angle BAD$ is making 180-$\alpha$ degree ..But i cant figure it out the more useful facts on how its making cos $\alpha$, and sin $\alpha$ as coordinates of point B. Please help me...If this is a stupid question ..please have some kindness towards me. n

• Proving $\sum_{j=1}^{n+1} {2n+2 \choose 2j-1} {j-1/2 \choose n}=2(n+1)^2$
by Z Ahmed on August 8, 2022 at 3:58 am

I have given a partial answer to a very interesting recent post Find $f^{(n)}(1)$ on $f(x)=(1+\sqrt{x})^{2n+2}$, where it remains to prove that $$\sum_{j=1}^{n+1} {2n+2 \choose 2j-1} {j-1/2 \choose n}=2(n+1)^2.$$ Wolfarm Mathematica supports this result, I want your help in proving this.

• Proof of boundedness involving gradients
by Jason Miller on August 8, 2022 at 3:54 am

Define: $$f(z) = \frac{1}{m}\left(F_1(z) + \cdots F_m(z)\right),$$ where $F_i$-s are some differentiable functions. Given that: $$\label{single} \frac{1}{m} \sum_{j = 1}^m \left\|\nabla F_{j}(z)-\nabla f(z)\right\|^{2} \leq \sigma^{2}, \; %\forall j \in [m], \forall z.$$ Define: $$f_1(z) = \frac{1}{m_1}\left(F_1(z) + \cdots F_{m_1}(z)\right); \;\; f_2(z) = \frac{1}{m_2}\left( F_{m_1+1} \cdots F_m(z)\right),$$ for some $m_1 <m$ and $m_2$ < m such that $m_1 + m_2 = m$. Prove: \begin{aligned} \frac{1}{m_1} \sum_{j = 1}^{m_1} \left\|\nabla F_{j}(z)-\nabla f_1(z)\right\|^{2} &\leq \sigma_1^{2}, \; %\forall j \in [m_1], \; \forall z, \\ \frac{1}{m_2} \sum_{j = m_1+1}^{m} \left\|\nabla F_{j}(z)-\nabla f_2(z)\right\|^{2} &\leq \sigma_2^{2}, \; %\forall j \in [m]\setminus[m_1], \; \forall z. \end{aligned} for some $\sigma_1$ and $\sigma_2$. I'm wondering if one can prove this, if not, is there any counter examples?

• If the determinant of a matrix goes to infinity, does the quadratic form of its inverse goes to zero?
by zzzhhh on August 8, 2022 at 3:34 am

This question occurs to me while I am self-studying machine learning. Let's assume there is a sequence of non-singular matrices $\{A_n\}$ whose size is the same and whose determinant goes to infinity: $$\lim\limits_{N\to\infty}|A_n|=+\infty.$$ Consider the sequence of quadratic forms of corresponding matrix inverses: $$\{q_n\buildrel \wedge \over =a^TA_n^{-1}a\}$$ where the vector $a$ is a general non-zero constant vector. Do we have that this sequence vanishes in the limit $$\lim\limits_{N\to\infty}q_n=0?$$ I have an inclination to agree with it, but my math background is not strong to prove it. If, in the end, it is not true in general, what additional condition do we need to establish this limit? Thank you.

• set of Convergent complex sequences is not smooth
by Bediipo on August 8, 2022 at 3:34 am

Prove that C (The Set of all Convergent complex Sequences) fails to be smooth.

## Data & Society Data & Society advances public understanding of the social implications of data-centric technologies and automation.

• Data & Society Names Sona Rai as Director of Communications
by chris on June 15, 2022 at 7:44 pm

June 15, 2022—Following an extensive national search, Data & Society is delighted to announce the appointment of Sona Rai as its next director of communications. Rai has more than 15 years of interdisciplinary communications experience in the fields of government, media, civil rights, immigration, and criminal legal system reform, and has worked closely with academics

• Welcoming Data & Society’s 2022–23 Faculty Fellows
by chris on June 8, 2022 at 6:34 pm

June 8, 2022—Data & Society is pleased to welcome Lindsey D. Cameron and Christina N. Harrington to our 2022–23 Faculty Fellowship Program. Starting this September, the program will benefit from their unique perspectives and expertise as they conduct rigorous interrogations of data-intensive systems of government and the ways these systems intersect with race. Their work

• Data & Society Welcomes Cindy Cohn to Its Board of Directors
by chris on June 1, 2022 at 3:00 pm

June 1, 2022—Data & Society is pleased to announce that Cindy Cohn, a prominent civil liberties attorney specializing in internet law, has joined its board of directors. Cohn is the executive director of the Electronic Frontier Foundation (EFF), leading the organization in its advocacy for civil liberties on the internet. A fierce defender of free

• Janet Haven Appointed to the National AI Advisory Committee
by chris on April 14, 2022 at 9:15 am

April 14, 2022—Data & Society is thrilled to announce that our Executive Director, Janet Haven, has been appointed to the National AI Advisory Committee by the US Secretary of Commerce. She joins 26 other committee appointees from across academia, the nonprofit sector, civil society, and private industry who will advise the President and the National

• Data & Society Welcomes Ellen Pao & Raina Kumra to its Board of Directors
by veronica on January 11, 2022 at 3:00 pm

Data & Society is delighted to welcome Ellen Pao and Raina Kumra to our Board of Directors.  Ellen Pao is a tech investor and advocate, the former CEO of reddit, and a cofounder of the award-winning diversity and inclusion nonprofit Project Include. Her writing has appeared in WIRED, The New York Times, The Washington Post,

## MIT News - Data | Big data | Analytics | Statistics | IDSS | Operations research MIT news feed about: Data | Big data | Analytics | Statistics | IDSS | Operations research

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## Mathematics – Wolfram Blog News, Views and Insights from Wolfram

• New in 13: Cryptography, Blockchains & NFTs
by Stephen Wolfram on April 8, 2022 at 6:32 pm

Two years ago we released Version 12.0 of the Wolfram Language. Here are the updates in cryptography, blockchains and NFTs since then, including the latest features in 13.0. The contents of this post are compiled from Stephen Wolfram’s Release Announcements for 12.1, 12.2, 12.3 and 13.0.   Cryptography & Security (December 2020) One of the

• The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics
by Stephen Wolfram on March 8, 2022 at 12:43 am

One of the many surprising (and to me, unexpected) implications of our Physics Project is its suggestion of a very deep correspondence between the foundations of physics and mathematics. We might have imagined that physics would have certain laws, and mathematics would have certain theories, and that while they might be historically related, there wouldn’t be any fundamental formal correspondence between them. But what our Physics Project suggests is that underneath everything we physically experience there is a single very general abstract structure—that we call the ruliad—and that our physical laws arise in an inexorable way from the particular samples we take of this structure. We can think of the ruliad as the entangled limit of all possible computations—or in effect a representation of all possible formal processes. And this then leads us to the idea that perhaps the ruliad might underlie not only physics but also mathematics—and that everything in mathematics, like everything in physics, might just be the result of sampling the ruliad.

• Learning Differential Equations in 10 Hours or Fewer with the Wolfram Language
by Luke Titus on January 19, 2022 at 3:00 pm

Differential equations are a cornerstone of modern mathematics. From quantum mechanics to population dynamics and stock market predictions, they play a crucial role in understanding the world around us. For this reason, courses on differential equations are core for many undergraduate degrees in the natural sciences, engineering and other fields. Today, I am proud to

• The Singular Euler–Maclaurin Expansion A New Twist to a Centuries-Old Problem
by Andreas A. Buchheit on June 30, 2021 at 5:32 pm

Of all mathematical operations, addition is the most basic: It’s what we learn first in school. Historically, it is the most ancient. While the simple task of getting the sum of two numbers is simple, sums of many numbers can easily turn into a challenging numerical problem if the number of summands is very large.

• Is Your Function Continuous? Squaring Away the New Function Properties in the Wolfram Language
by Devendra Kapadia on March 30, 2021 at 8:17 pm

The Wolfram Language has several hundred built-in functions, ranging from sine to Heun. As a user, you can extend this collection in infinitely many ways by applying arithmetic operations and function composition. This could lead you to defining expressions of bewildering complexity, such as the following: &#10005 f = SinhIntegral[ LogisticSigmoid[ ScorerHi[Tanh[AiryAi[HermiteH[-(1/2), x] - x

• 3D-Printed Jewelry Made with the Wolfram Language Showcases the Beauty of Mathematics
by Christopher Hanusa on February 15, 2021 at 8:09 pm

I enjoy turning mathematical concepts into wearable pieces of art. That’s the idea behind my business, Hanusa Design. I make unique products that feature striking designs inspired by the beauty and precision of mathematics. These pieces are created using the range of functionality in the Wolfram Language. Just in time for Valentine’s Day, we recently launched Spikey earrings in

by Becky Song on February 12, 2021 at 8:51 pm

Math is one of the main things that deters students from wanting to learn more about chemistry. Being a chemical engineering student, I understand this, especially for students who just have to get chemistry out of the way as a general education requirement. Essentially, step-by-step solutions are like your own on-demand math tutor: in addition

• How We Navigated a Hybrid Remote Learning Environment Using Wolfram Technology
by Timothy Newlin on January 14, 2021 at 6:00 pm

The past year of learning ushered in a variety of new experiences for instructors and students alike, and the United States Military Academy at West Point was no exception. In addition to masks in the classroom, reduced class sizes to allow for social distancing, rigorous testing and tracing efforts, and precautionary remote video classes, we

• New Wolfram Language Books on Wolfram|Alpha, Calculus, Applied Engineering and System Modeler
by Paige Bremner on October 29, 2020 at 3:24 pm

The pandemic has postponed or canceled a lot of things this year, but luckily learning isn’t one of them. Check out these picks for new Wolfram Language books that will help you explore new software, calculus, engineering and more from the comfort of home. Hands-on Start to Wolfram|Alpha Notebook Edition New from Wolfram Media and