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- Math Homework Help: A Guide to the Best AI Math Solver of 2025by Casey Allen on December 1, 2024 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 2025 first appeared on SquareCirclez. Related posts: 5 Best Free Math Problem Solvers Math problems allow students to learn new concepts and strengthen... My dilemma - ethical math help Is there a difference between paying someone to do... Buyer’s Guide: TI-84 Graphing Calculator Math classes can be daunting. From a young age, I... Curriculum Webs - more homework needed "Weaving the Web into Teaching and Learning" Cunningham, C and...
- 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
- How to correctly model a grant distribution problem: permutations, combinations, or combinations with repetition?by fexsen on May 12, 2025 at 11:23 am
I'm trying to clarify the correct combinatorial model for the following problem. There is a disagreement between me and another person regarding whether to use permutations, combinations, or combinations with repetition. Problem: "Ten companies are participating in the grant competition in three nominations. Calculate the number of grant distribution options if the same grant values are set for each nomination." There are two interpretations: My interpretation: The categories are distinct, even though the grant amount is the same. Each company can receive only one grant (i.e., at most one award per company). Therefore, we are selecting 3 distinct companies and assigning them to distinct categories, meaning the order matters. Thus, the number of possible distributions is a permutation (or arrangement) of 3 companies from 10: $A_{10}^3 = 10 \cdot 9 \cdot 8 = 720$ The other interpretation: A company can receive multiple grants (up to all three). Since the grant amounts are equal, the categories are treated as indistinguishable. Therefore, the model used is combinations with repetition: $C_{10 + 3 - 1}^3 = \binom{12}{3} = 220$ Question: Which interpretation is more appropriate under standard assumptions, when the problem does not explicitly state whether: A company can receive more than one grant; The categories are distinguishable despite identical grant amounts.
- Can Witnessing theorems in bounded arithmetic be practical?by eerio on May 12, 2025 at 11:17 am
In bounded arithmetic (or bounded reverse mathematics) we study formal systems so weak that the structures of their proofs correspond to some known complexity classes such as PTIME, LOGSPACE or AC0. Here I will refer to the astonishing work of Steven Cook and Phuong Nguyen, "Logical Foundations of Proof Complexity" - specifically, to the draft available here: cook-nguyen.pdf, as the original is non open-access. For motivation: Conceptually the theory VC associated with a complexity class C can prove a given mathematical theorem if the induction hypotheses needed in the proof can be formulated using concepts from C. We are interested in trying to find the weakest class C needed to prove various theorems of interest in computer science. The authors show that weak pigeonhole principle is not provable in theory $VAC^0$ corresponding to $AC^0$ complexity class, but it is provable in $VTC^0$, along with a formula denoting that for every sequence, a sorted sequence exists. Fermat's Little Theorem is not provable in $VPTIME$, condition prime factorization is not in $PTIME$. In the area of bounded arithmetic, Witnessing theorems are studied, which roughly say that if a formula $\forall x \exists y \varphi(x, y)$ is provable in theory $VC$ (for a complexity class $C$), then there exists a function $f$ of complexity $C$ such that $\forall x \varphi(x, f(x))$ is provable in $VC$. So, that we can theoretically extract a real algorithm from a proof of a functional formula! The problem with these theorems are that their proofs typically involve cut elimination theorem or Herbrand's theorem, which say that something is possible to do, but in practice it's not really computationally feasible. As I don't have enough expertise to judge myself, it leads me to thinking that we won't really be able to implement a real code extraction tool from the proofs in these weak logics. My question is: can we actually implement algorithm extraction from a proof of the Witnessing theorem? Maybe I'm wrong in thinking that the current proofs are not convertible to feasible computation? Maybe alternative proofs exist (there are at least 2 for $V^0$ (i.e. $VAC^0$) in the book above), which are computationally feasible? Maybe no feasible proof is known, but theoretically there might exist one? I don't want to list all the technical definitions here, as it would require introducing the two-sorted logic and the bounded arithmetical hierarchy the authors use, which is not strictly essential to this question. But, as an example of a witnessing theorem for AC0: At page 105 (116 of the pdf): Theorem 5.60 (Witnessing Theorem for V0). Suppose that $\varphi (\overrightarrow x, \overrightarrow y, \overrightarrow X, \overrightarrow Y )$ is a $\Sigma^B_0$ formula such that $V^0 \vdash \forall \overrightarrow x \forall \overrightarrow X\exists \overrightarrow y \exists \overrightarrow Y \varphi( \overrightarrow x, \overrightarrow y, \overrightarrow X, \overrightarrow Y )$ Then there are $FAC^0$ functions $f_1, \dots , f_k, F_1, \dots , F_m$ so that $V^0(f_1, \dots , f_k, F_1, \dots , F_m) \vdash \forall \overrightarrow x \forall \overrightarrow X \varphi( \overrightarrow x , \overrightarrow f(\overrightarrow x, \overrightarrow X), \overrightarrow X, \overrightarrow F ( \overrightarrow x, \overrightarrow X)) $
- Question about triangulations of orientable surfaces.by Espace' etale on May 12, 2025 at 11:06 am
Say $S$ is a connected oriented surface with boundary, and $T$ is a triangulation such that the boundary is a union of simplices. Is it always possible to select simple cycles in $T$ (I mean simple closed paths in the 1-skeleton of $T$) that will be a symplectic basis of $H_{1}(S,\partial S)$? If not, is there an upper bound on how complicated such a basis would be (I mean, say, an upper bound on the sum of coefficients and the lengths of the involved cycles, in terms of the size of the triangulation $T$). Any references would be greatly appreciated. I didn't find a reference for this question of selecting a basis homology that is made out of simple cycles in $T$. I will make do even if there is no boundary involved. Thank you!
- A GAP code for certain conditions in finite groupsby M.H.Hooshmand on May 12, 2025 at 10:57 am
Let $ G $ be a finite group and let $ n = |G| $. For each divisor $ d $ of $ n $ such that $ 1 < d \leq \sqrt{n} $, proceed as follows: For every subset $ A \subseteq G $ of size $ d $ that contains the identity element $ 1 $, do the following: For every subset $ B \subseteq G $ of size $ n/d $ such that $ 1 \in B \subseteq \left(G \setminus \left(A^{-1}A\right)\right) \cup \{1\}, $ ($A^{-1}A=\{a_1^{-1}a_2:a_1,a_2\in A\}$) proceed to the next step: Check whether the Minkowski product satisfies $ G = AB $. If such subsets $ A $ and $ B $ can always be found for all valid values of $ d $, then print: ``G is a CFS group.''. Otherwise, print: ``G is not a CFS group.'' and also display the group $ G $, and the first subset $ A $ (along with its size $ d $) for which the condition $ G = AB $ is not satisfied. The following GAP code is written for it (namely, the CFS property): IsCFSGroup := function(G) local n, divs, d, Asets, A, Bsize, Bsets, B, AinverseA, complement, product, success; n := Size(G); divs := Filtered(DivisorsInt(n), d -> d > 1 and d <= Sqrt(n)); for d in divs do Asets := Filtered(Combinations(Elements(G), d), A -> Identity(G) in A); for A in Asets do AinverseA := Set(List(Cartesian(A, A), x -> x[1]^(-1)*x[2])); complement := Difference(Elements(G), AinverseA); AddSet(complement, Identity(G)); # Ensure 1 ∈ B Bsize := n / d; Bsets := Filtered(Combinations(complement, Bsize), B -> Identity(G) in B); success := false; for B in Bsets do product := Set(List(Cartesian(A, B), x -> x[1]*x[2])); if Set(product) = Set(Elements(G)) then success := true; break; fi; od; if not success then Print("G is not a CFS group.\n"); Print("Violating subset A: ", A, "\n"); Print("Size of A (d): ", d, "\n"); return false; fi; od; od; Print("G is a CFS group.\n"); return true; end; But it does not work correctly, e.g., for $S_3$: " G is not a CFS group. Violating subset A: [ (), (1,2,3) ] Size of A (d): 2 false " That is not true. (a) What is wrong with this code (any improvement for it)? (b) Where should it be written in the code if we want to apply one of the following additional conditions? (b1) $A$ or $B$ is a normal subgroup of $G$ (b2) $AB=BA$ Thanks in advance
- Tangent space definition for Euclidean spaceby Sh.A on May 12, 2025 at 10:37 am
I'm following "Lecture notes on Differential Geometry" by Chow and Chow. Their treatment of tangent spaces starts with defining a tangent space of a parametrised submanifold $M^n \subset \mathbb{R}^{n+1}$ of Euclidean space. Here is the (slightly rephrased) relevant excerpt: Let $F: U \subset \mathbb{R}^n \rightarrow M^n$ parametrize a relatively open subset $F(U)$ of a submanifold $M^n \subset \mathbb{R}^{n+1}$. Let $\mathbf{u_0} \in U$. Then, by hypothesis, the derivative $dF_{\mathbf{u_0}}: \mathbb{R}^n \rightarrow \mathbb{R}^{n+1}$ is an injective linear map, and may be defined by $$T_{F(\mathbf{u_0})}M^n := d{F_{\mathbf{u_0}}}(\mathbb{R}^n).$$ While this definition makes sense to me in general, I tried applying it to the Euclidean space of dimension $n$ as a submanifold of $\mathbb{R}^{n+1}$. Here is what I have. For $M^n := \mathbb{R}^n$, let $F: \mathbb{R}^n \rightarrow M^n \subset \mathbb{R}^{n+1}$ be defined by $$F(\mathbf{x_0}) = F(x^1, x^2, \ldots, x^n) = (x^1, \ldots, x^n, 0) \in \mathbb{R}^{n+1}$$. Then, the tangent space $$T_{F({\mathbf{x_0})}}M^n = dF_{x_0}(R^n).$$ Then, the RHS is a linear map, given by the $(n+1) \times n$ matrix $$(dF(\mathbb{R}^n))_{ij} = \partial F^i(\mathbb{R^n})/\partial x^j.$$ For any $x \in \mathbb{R}^n$, the RHS of the last expression becomes a diagonal matrix with an extra row of $0$'s in the $(n+1)$th row. Is this correct?
Surrey Mathematics Research Blog The blog on research in mathematics at the University of Surrey
- Camilla Nobili speaks at conference on Machine Learning and PDEs in Erlangenby Tom Bridges on May 9, 2025 at 5:34 pm
Camilla Nobili was in Germany last week (28-30 April) to give an invited talk at a conference on “Machine Learning and PDEs“. The host for the conference was Friedrich-Alexander University. A link to the conference website is available (link here). Camilla spoke on “Quantification of enhanced dissipation and mixing for time-dependent shear flows“. A video
- Werner Bauer and Robert Piel attend and speak at the European Geophysical Union Conference in Viennaby Tom Bridges on May 8, 2025 at 4:30 pm
The annual EGU General Assembly meeting this year was held in Vienna from 27 April to 2 May. It welcomed 20,984 registered attendees, of which 18,646 made their way to Vienna from 120 countries and 2,338 joined online from 104 countries. Werner Bauer and Robert Piel attended and gave talks. In addition, Werner was the
- Cesare Tronci on research visits to University of California and Los Alamos in New Mexicoby Tom Bridges on May 7, 2025 at 4:36 pm
Cesare Tronci is currently on a research visit to America. On 5-6 May he was visiting University of California at Santa Barbara. His host was Carlos García-Cervera. He gave a talk on “Koopmon trajectories in nonadiabatic quantum-classical dynamics” at UCSB on 6 May (link here). Cesare engaged in research discussion with Carlos and Emmanuel Lorin who
- Paper of Roberto D’Onofrio and Ian Roulstone published in Proceedings A of the Royal Societyby Tom Bridges on May 7, 2025 at 11:00 am
The paper “Monge–Ampère geometry and the Eady problem“, co-authored by Roberto D’Onofrio (former PhD student at Surrey), Giovanni Ortenzi (University of Torino), and Ian Roulstone, has been published today (7 May) in Proceedings A of the Royal Society of London. The paper formalizes the idea of a Chynoweth–Sewell front and illuminates its geometrical meaning from
- Paper of David Lloyd and Naratip Santitissadeekorn on time-series analysis to appear in PhysicaDby Tom Bridges on May 6, 2025 at 11:52 am
The paper “Influence network reconstruction from discrete time-series of count data modelled by multidimensional Hawkes processes“, co-authored by Naratip Santitissadeekorn, Martin Short (Georgia Tech), and David Lloyd, has been accepted for publication in PhysicaD. The paper develops network inference methods for both batched and sequential count data, and they introduce an ensemble-based algorithm, rooted in
FlowingData Strength in Numbers
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- Lawsuits against executive ordersby Nathan Yau on May 8, 2025 at 4:44 pm
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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.
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Mathematics – Wolfram Blog News, Views and Insights from Wolfram
- What’s Up with Daylight Saving Time? A Brief History and Analysis with Wolfram Languageby Nick Lariviere on March 5, 2025 at 5:12 pm
In the next few days, most people in the United States, Canada, Cuba, Haiti and some parts of Mexico will be transitioning from “standard” (or winter) time to “daylight” (or summer) time. This semiannual tradition has been the source of desynchronized alarm clocks, missed appointments and headaches for parents trying to get kids to bed at the right time since 1908, but why exactly do we fiddle with the clocks two times a year?
- A Whole New Ball Game: Game Theory in Wolfram Language 14.2by Marc Vicuna on February 25, 2025 at 6:17 pm
Do you want to make optimal decisions against competition? Do you want to analyze competitive contexts and predict outcomes of competitive events? Do you need to elaborate strategies and plans against adversity and test the effectiveness of those strategies? Or are you simply an undergraduate student struggling to cope with a required course on game
- Master the Basics of Laplace Transforms in Just 15 Lessons with Wolfram Languageby Juan Ortiz on February 5, 2025 at 8:30 pm
The Laplace transform provides effective and easy means for solving many problems that arise in the fields of science and engineering. It is one of the main tools available for solving differential equations. For most of us, the first time we see it is in an introductory differential equations course. Wolfram Language provides an ideal
- Learn Complex Analysis Today with Wolfram Languageby Marco Saragnese on October 15, 2024 at 3:44 pm
Complex analysis is a versatile tool that is used extensively in science, engineering and other fields. It is also a beautiful topic in and of itself. Hence, a course in complex analysis is a standard part of the curriculum for physics and engineering students and a stepping stone for more advanced topics in mathematics. 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