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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

  • How one can choose some sum to verify the inequality: $S_1≥S_2+a+ b×S_3+ c×S_4$
    by Safwane on March 28, 2024 at 5:13 pm

    Let $0<a<1,b>1,c>1$ be some real numbers. Let $S$ denotes the sum of all the terms $d^{j},j=0,..,m$,where $d≥3$. Define $S_1,S_2,S_3,S_4$ be partial sums of the terms $d^{j},j=0,..,m$ such that the union of all these sums is equal to $S$. Then my question is: How one can choose those four sum to verify the inequality: $$S_1≥S_2+a+ b×S_3+ c×S_4$$

  • Understanding GAGA correspondence from some basic questions
    by Lelong Wang on March 28, 2024 at 5:12 pm

    On page 78 of Hartshorne's "Algebraic Geometry," we encounter the following correspondence: Proposition 2.6: Let $k$ be an algebraically closed field. There exists a natural, fully faithful functor $t: \mathfrak{Var}(k) \rightarrow \mathfrak{Sch}(k)$ from the category of varieties over $k$ to schemes over $k$. For any variety $V$, its topological space is homeomorphic to the set of closed points of $\operatorname{sp}(t(V))$ (where $\operatorname{sp}(t(V))$ denotes the underlying topological space), and its sheaf of regular functions is obtained by restricting the structure sheaf of $t(V)$ via this homeomorphism. In other words, one can associate a scheme to a variety since $t$ is faithful. Now, let $k=\mathbb{C}$. Then one can also associate a scheme to a complex analytic variety, via the well-known GAGA theorem. GAGA also tells us that many things are equivalent between the scheme category and the complex analytic category; in fact, the correspondence between them is a fully faithful functor. We denote this functor by $G$. (I believe $t^{-1}$ aligns with the GAGA correspondence, as suggested by references on page 439 and page 81-2.14-d in Hartshorne book; however, this is not the focus of this post.) However, several important questions arise, which may require additional conditions on the involved schemes: Question: Is $H^i(X, F)\cong H^i(G(X), G(F))$ true, where $F$ is some good sheaf on the scheme $X$? If $X$ is birational to $Y$, then is $G(X)$ birational (or bimeromorphic) to $G(Y)$? Suppose $f: X\to Y$ is a morphism of schemes, and the generic fiber $X_{\eta}$ is rational, i.e., birational to $\mathbb{P}^n_{K}$, where $K$ is the function field of $X$. Then is the general fiber of $G(f): G(X)\to G(Y)$ birational to $\mathbb{CP}^n:=\mathbb{C}^{n+1}/\sim$, where the general fiber means the fiber over an analytic Zariski open subset of $G(Y)$. Any comments and recommended references would be greatly appreciated.

  • Optimal strategy in one-player game
    by Kilkik on March 28, 2024 at 5:09 pm

    You are playing a one-player game with two opaque boxes. At each turn, you can choose to either "place" or "take". "Place" places $1 from a third party into one box randomly. "Take" empties out one box randomly and that money is yours. This game consists of 100 turns where you must either place or take. Assuming optimal play, what is the expected payoff of this game? Note that you do not know how much money you have taken until the end of the game. It is obvious that the more you take, the less you can earn, for example if you place at turn $1$ and then keep taking, the expected payoff is $0.5$. I thought of doing the opposite and keep placing until the $100$th turn where we have already placed $99\$$. Let $X_n$ denote the amount in box $1$ at the $n$th turn. $X_n$ follows a binomial distribution Bin($n,0.5$). For box $2$, its amount $Y_n$ is $n-X_n$ which is also Bin($n,0.5$). Hence, after the $99th$ "place", there is on average $49.5\$$ in each box which you take at the $100$th turn meaning the expected payoff is $49.5\$$. Is this right ? Is there a better strategy I am not thinking of ?

  • Find all incongruent primitive roots of a number
    by Gottfried Leibniz on March 28, 2024 at 5:09 pm

    I am trying to find all incongruent primitive roots of $14$. I know that there are $\phi{(\phi{(14)})}=2$ incongruent primitives roots, where I have found that both $3$ and $5$ are primitive roots mod $14$. My question is: why aren't $11$ and $13$ also primitive roots mod 14? Both $11^6 \equiv 13^6 \equiv 1$ mod $14$, by Euler's Theorem. So why are there only $2$ incongruent solutions mod $14$.

  • Different definition of subsequences in Kelley's General Topology
    by NotNow11 on March 28, 2024 at 5:06 pm

    I have a question that may seem trivial. I am studying Kelley's General Topology. I was reading Chapter 2 when I came across an unusual definition. Tipically, I define a subsequence as follows: a subsequence of the sequence $(a_n)_{n \in \mathbf{N}}$ is any sequence of the form $(a_{n_k})_{k \in \mathbf{N}}$ where $(n_k)_{k > \in \mathbf{N}}$ is a strictly increasing sequence of positive integers. Whereas in the book, it says that: $T$ is a subsequence of a sequence $S$ iff there is a sequence $N$ of non-negative integers such that $T = S \circ N$ (equivalently, $T_i = > S_{N_i}$ for each $i$) and for each integer $m$ there is an integer $n$ such that $N_i \geq m$ whenever $i \geq n$. I can deduce that this two definitions are not the same and it may seem that one definition implies the other. Am I right or wrong? Can someone formally explain me the difference and how these two are related? Thank you 🙂


Surrey Mathematics Research Blog The blog on research in mathematics at the University of Surrey

  • Dorje Brody appointed to a Visiting Professorship at Tokyo University for Spring 2024
    by Tom Bridges on March 27, 2024 at 4:28 pm

    Dorje Brody is in Japan this spring for a research visit to Tokyo University. He has been formally appointed to a Visiting Professorship for the period 16 March to 31 May. The photo below shows Dorje along with the Dean and his host Professor, at the appointment ceremony.

  • Werner Bauer is a session convenor and presenter at EGU 2024 in Vienna funded by the IMA
    by Tom Bridges on March 21, 2024 at 6:12 pm

    Werner Bauer will be attending the European Geophysical Union 2024 General Assembly which will be held in Vienna from 14-19 April. The EGU generally attracts over 15,000 onsite participants from over 100 countries as well has virtual participants. Werner is convenor of the session on “Advances in Numerical Earth System Modeling: Identifying Systematic Errors and

  • Vasileios Moustakis passes PhD confirmation examination
    by Tom Bridges on March 21, 2024 at 3:32 pm

    Congratulations to Vasileios Moustakis for passing his PhD Confirmation viva! It was held today (Thursday 21 March), and his examiners were Werner Bauer and Cesare Tronci. The title of his report “Boundary integrability in massless AdS₃”. His supervisors are Alessandro Torrielli and Andrea Prinsloo. The photo below shows Vasileios giving a presentation on PhD Day

  • 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


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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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