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  • Math Homework Help: A Guide to the Best AI Math Solver of 2023
    by 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 Solvers
    by 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 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...


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

  • Inconsistent Function Monotonicity from hand and Mathematica image
    by 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 functions
    by 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 Mathematics
    by 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 fluids
    by 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 London
    by 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 University
    by 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 project
    by 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


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Mathematics – Wolfram Blog News, Views and Insights from Wolfram

  • Hypergeometric Functions: From Euler to Appell and Beyond
    by 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 Language
    by 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 Language
    by 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 Language
    by 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 Language
    by 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 Language
    by 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 Edition
    by 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 Levels
    by 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 13.1
    by 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


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