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This tool combines the power of mathematical computation engine that excels at solving mathematical formulas with the power of artificial intelligence large language models to parse and generate natural language answers. This creates a math problem solver that's more accurate than ChatGPT, more flexible than a math calculator, and provides answers faster than a human tutor.

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Problem Solver Subjects

Our math problem solver that lets you input a wide variety of math math problems and it will provide a step by step answer. This math solver excels at math word problems as well as a wide range of math subjects.

• Math Word Problems
• Pre-Algebra
• Geometry Graphing
• Trigonometry
• Precalculus
• Finite Math
• Linear Algebra

Here are example math problems within each subject that can be input into the calculator and solved. This list is constanstly growing as functionality is added to the calculator.

Basic Math Solutions

Below are examples of basic math problems that can be solved.

• Long Arithmetic
• Rational Numbers
• Operations with Fractions
• Ratios, Proportions, Percents
• Measurement, Area, and Volume
• Factors, Fractions, and Exponents
• Unit Conversions
• Data Measurement and Statistics
• Points and Line Segments

Math Word Problem Solutions

Math word problems require interpreting what is being asked and simplifying that into a basic math equation. Once you have the equation you can then enter that into the problem solver as a basic math or algebra question to be correctly solved. Below are math word problem examples and their simplified forms.

Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?

Simplified Equation: 17 - x = 8

Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?

Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)

Simplified Equation: {r = d + 12, d = b + 6, r = 2 �� b}

Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left?

Simplified: 40 - 10 - 5

Pre-Algebra Solutions

Below are examples of Pre-Algebra math problems that can be solved.

• Variables, Expressions, and Integers
• Simplifying and Evaluating Expressions
• Solving Equations
• Multi-Step Equations and Inequalities
• Ratios, Proportions, and Percents
• Linear Equations and Inequalities

Algebra Solutions

Below are examples of Algebra math problems that can be solved.

• Algebra Concepts and Expressions
• Points, Lines, and Line Segments
• Simplifying Polynomials
• Factoring Polynomials
• Linear Equations
• Absolute Value Expressions and Equations
• Radical Expressions and Equations
• Systems of Equations
• Quadratic Equations
• Inequalities
• Complex Numbers and Vector Analysis
• Logarithmic Expressions and Equations
• Exponential Expressions and Equations
• Conic Sections
• Vector Spaces
• 3d Coordinate System
• Eigenvalues and Eigenvectors
• Linear Transformations
• Number Sets
• Analytic Geometry

Trigonometry Solutions

Below are examples of Trigonometry math problems that can be solved.

• Algebra Concepts and Expressions Review
• Right Triangle Trigonometry
• Radian Measure and Circular Functions
• Graphing Trigonometric Functions
• Simplifying Trigonometric Expressions
• Verifying Trigonometric Identities
• Solving Trigonometric Equations
• Complex Numbers
• Analytic Geometry in Polar Coordinates
• Exponential and Logarithmic Functions
• Vector Arithmetic

Precalculus Solutions

Below are examples of Precalculus math problems that can be solved.

• Operations on Functions
• Rational Expressions and Equations
• Polynomial and Rational Functions
• Analytic Trigonometry
• Sequences and Series
• Analytic Geometry in Rectangular Coordinates
• Limits and an Introduction to Calculus

Calculus Solutions

Below are examples of Calculus math problems that can be solved.

• Evaluating Limits
• Derivatives
• Applications of Differentiation
• Applications of Integration
• Techniques of Integration
• Parametric Equations and Polar Coordinates
• Differential Equations

Statistics Solutions

Below are examples of Statistics problems that can be solved.

• Algebra Review
• Average Descriptive Statistics
• Dispersion Statistics
• Probability
• Probability Distributions
• Frequency Distribution
• Normal Distributions
• t-Distributions
• Hypothesis Testing
• Estimation and Sample Size
• Correlation and Regression

Finite Math Solutions

Below are examples of Finite Math problems that can be solved.

• Polynomials and Expressions
• Equations and Inequalities
• Linear Functions and Points
• Systems of Linear Equations
• Mathematics of Finance
• Statistical Distributions

Linear Algebra Solutions

Below are examples of Linear Algebra math problems that can be solved.

• Introduction to Matrices
• Linear Independence and Combinations

Chemistry Solutions

Below are examples of Chemistry problems that can be solved.

• Unit Conversion
• Atomic Structure
• Molecules and Compounds
• Chemical Equations and Reactions
• Behavior of Gases
• Solutions and Concentrations

Physics Solutions

Below are examples of Physics math problems that can be solved.

• Static Equilibrium
• Dynamic Equilibrium
• Kinematics Equations
• Electricity
• Thermodymanics

Geometry Graphing Solutions

Below are examples of Geometry and graphing math problems that can be solved.

• Step By Step Graphing
• Linear Equations and Functions
• Polar Equations

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StudyX Math Solver AI, powered by ChatGPT, GPT-4o and Claude 3.5, utilizes advanced AI technology and code interpreters to achieve a remarkable 92% accuracy in solving diverse math questions. Ask your question and get step-by-step solutions in seconds now!

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How Can Math Solver Assist You with Your Math Homework?

Image and Formula OCR Recognition

Our math solver uses AI-powered technology to accurately recognize and interpret mathematical expressions and formulas from images, enabling seamless problem-solving from various sources.

Step-by-Step AI-powered Solutions

Our AI is powered by ChatGPT and GPT4, with code interpreters, offering higher accuracy and providing systematic, step-by-step solutions to mathematical problems. This ensures comprehensive and accurate problem-solving processes.

Support All Mathematical Problems

We offer comprehensive support for a wide range of mathematical problems, leveraging AI capabilities to enhance accuracy and versatility in addressing diverse mathematical challenges.

What Can Math Solver Help You?

Algebraic equations and inequalities.

Offer step-by-step solutions for solving algebraic equations and inequalities, aiding in a comprehensive understanding of the problem-solving process.

Geometric Figures

Provide methods for calculating the area and perimeter of various geometric shapes, facilitating accurate and efficient problem-solving.

Calculus Problems

Assist with complex calculus problems, including differentiation and integration, through systematic and detailed solutions.

Trigonometry and Triangle Problems

Address trigonometric functions and problems related to triangles, ensuring thorough and accurate problem-solving processes.

Probability and Statistics

Provide assistance with probability and statistics problems, offering detailed explanations and solutions to enhance understanding.

Linear Algebra

Offer comprehensive support for linear algebra problems, including matrix operations and systems of equations, through systematic and detailed solutions.

Frequently Asked Questions

Why choose studyx's math solver.

Based on our experimental results, StudyX's Math Solver has achieved an accuracy rate exceeding 92%, surpassing the accuracy of GPT-4. Following its release on the GPT Store, StudyX's Math Solver successfully secured a position in the Top 5 of the GPT Store's education ranking.

Can Math Solver generate solid geometry figures？

Our Math Solver is primarily designed for solving algebraic, equations, and mathematical problems and does not include the capability to generate solid geometry figures so far.

Can this Math Solver solve complex differential problems?

Yes, it can provide a step-by-step solution to the problems.

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More than Just a Math Solver

Become a member of StudyX and improve your study experience through StudyX's AI and Community guidance, as well as 7/24 AI Tutor assistance.

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The Must-Have Math AI & Calculator for Students

Don't stress over math for another minute. Instantly get step-by-step solutions to all types of math problems. Try our math solver for free.

Instantly Solve Math Problems with Our Math AI Tool

Stop searching for math answers in the back of the textbook. Mathful's math solver shows you how to get there yourself. Type or upload a photo of any math question, and we will provide the full working out, so you can learn as you go.

Cutting-Edge Photo Math Solver that Outshines ChatGPT

Our photo math solver can instantly scan image uploads of math problems to provide step-by-step solutions with unmatched accuracy and precision, making it a far more powerful alternative to conversational AI tools like ChatGPT.

Key Features of Our Powerful Math AI Solver

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Our AI math solver provides step-by-step math answers with an unparalleled level of precision, ensuring accurate solutions for your math problems.

Forget about expensive math tutors our AI math solver helps you or your children solve math problems for free in one click. Save money while getting accurate solutions.

10+ Math Branches Covered

Our AI math problem solver helps you effortlessly handle questions in various mathematical subjects, including algebra, calculus, geometry, and more.

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Get detailed, step-by-step mathematical explanations 24/7 from our AI math problem solver. Master math effortlessly online.

Quick & Precise Math Calculator With Steps

Using advanced AI algorithms, our step-by-step math calculator can process complex math problems to generate accurate and detailed solutions in seconds. They include:

• Basic arithmetic operations
• Trigonometric functions
• Linear and quadratic equations
• Derivatives and integrals
• Matrix operations
• And so much more!

3 Simple Steps to Use Our Math Solver & Calculator

Have trouble with a math problem or just want to check your work? Our math AI is ready to help. Here's how:

Input Your Math Problem

Type the math problem into the input box or upload an image of the math problem. Alternatively, input the problem into our math calculator.

Let Mathful Formulate a Solution

Our math AI or math calculator will work to generate a detailed, accurate solution to your math problem.

Get Math Answer Instantly

Nearly instantly you'll receive the step-by-step answer to your math problem so you can actually learn.

What is Math AI?

Math AI tools like Mathful are designed to assist users in solving mathematical problems, equations, and calculations. We utilize machine learning algorithms and natural language processing to interpret user input, perform complex computations, and provide step-by-step solutions.

Math AI can be beneficial for students, researchers, and professionals who require assistance in understanding and solving mathematical problems efficiently.

Can a math AI help me improve my math grades in school?

Certainly! A math solver like Mathful can significantly boost your math grade by offering round-the-clock access to step-by-step solutions across a wide array of math topics, from algebra to calculus.

Does this math AI tool cover all types of math?

Yes, Mathful is capable of tackling any type of math question, from arithmetic and geometry to algebra and number theory.

How long does it take for the math AI solver to get an answer to my math question?

Once you submit your math problem, Mathful will quickly formulate the correct answer and generate a solution almost instantly.

Can I try the Mathful AI math solver for free?

Yes, the Mathful AI math problem solver is free to try. Cost-friendly subscriptions are available to ask even more math questions.

Is the math solver and math calculator accurate?

Yes, the math solver and step-by-step math calculator provided by Mathful are designed to deliver highly accurate results. Utilizing advanced AI algorithms, these tools process and solve a vast range of math problems with precision.

Is the math AI and math calculator safe to use?

Yes, our math solver and step-by-step math calculator use encrypted transmissions, and your personal information is never stored or shared. It was created with your privacy and safety in mind.

Why should I use a photo math solver?

By using a photo math solver, you can simply take a photo of a math problem. No more need to type out complex equations or search for similar examples online. It's an instant way to begin tackling your math homework or study questions.

What problems can I solve with a math calculator?

With a math calculator from Mathful, you can solve a broad spectrum of mathematical problems across various domains, including basic arithmetic operations, algebraic equations, and geometry calculations to more complex calculus derivatives and integrals.

Solve Math Problems Easily with Our Math Solver & Math Calculator

Get instant, accurate answers to your math problems and boost your math grade. Try our AI math problem solver and math calculator with steps for free today.

7 Best Math Solver Apps and Websites

We have already talked about math learning apps for Android and iOS before. These apps allow you to study and brush up on mathematical concepts regardless of where you are. But what do you do when you get stuck on a problem and there is no one to help you out? The answer is easy. There are tons of apps and websites that you can use to solve math problems in no time. So if you don’t want to depend on anybody, here are some of the best math solver apps and websites you can try. Let’s begin.

How to Tackle Homework with Math Solver Apps

1. mathway: scan photos, solve problems.

Mathway is the most recommended app when it comes to math problem-solving apps. It covers a large area of mathematics such as basic math, algebra, trigonometry, calculus, etc. So whether you want to solve basic square roots or word out complicated limits and derivatives, this one is the only tool you may need.

Mathway also allows you to connect with experts. You can submit your question for a fee of $5/month (one pending question at a time) or $30/month (1st plan + 20 sessions live with experts).

To start solving problems, all you have to do is select a subject area and take a photo of the question. Moreover, if you want to type in the question, you can do that with the keyboard as well. The numbers on the keyboard keep changing according to the subject of your choice. The best part is that it shows you steps to solve each problem. However, it is behind the paywall and would cost you $9.99/month. This also removes ads.

• Cover multiple areas (algebra, trigonometry, calculus, etc.)
• Supports three types of input (keyboard, camera, voice)
• Stp by step problem solving
• No sign-in required
• Ask an expert might be costly for many

Get Mathway for ( iOS | Android | Web )

2. Slader Homework Answer‪s

If you have a lot of math questions, taking a picture or typing each problem can be a big hassle. Since most math problems are extracted out of textbooks, why not simply scroll through the questions/answers from the book itself? This app does exactly that. You can scan the barcode of a book or browse from the category of the books already solved.

In addition to high school math (pre-algebra, geometry, trigonometry) and upper-level math (differential equations, statistics, etc.), it also covers other subjects such as English, management, accounting, etc. Although the app has a large database of books, there are chances that you won’t find the book you’re looking for. Moreover, most of the advanced math books are locked. So you can only view them by upgrading to a premium plan that comes at $3.99/monthly.

• Find math solutions book-wise
• Clearly shows chapter number, page, and exercise number
• Users can rate and comment on solutions
• Very slow to load
• Tons of banner ads
• Limited database of books
• No option to scan questions

Get Slader Homework Answer‪s for ( iOS | Android )

3. Cymath – Math Problem Solver

Cymath is similar to Mathway, however, I like it more because of a few additional features. But before that, let’s first talk about the common features. Both math solver apps allow you to capture math problems and have keyboard input as well. However, Mathway has far more sub-fields of math when compared to Cymath. I tried a few algebra questions where both performed well. However, Cymath often showed errors when I ran trigonometry questions.

In conclusion, if you want to cover a large area of subjects and want extreme accuracy, Mathway is still better.

Cymath shines in a few other aspects, for example, the history section and the ability to bookmark solutions. This comes in handy whenever you are stuck and wish to refer to an old problem. In addition, it also has a learning tab that has common references, practice questions and also discusses one problem each week. The plus version comes at $4.99/month. It removes ads, shows the step-by-step solutions, and even answer why a certain step is used (in addition to how).

• Covers most topics (algebra, calculus, graphing)
• Clean interface (easy to browser)
• Supports image and keyboard input
• History and bookmark option
• Stumbles a bit on accuracy
• Not as comprehensive as Mathway

Get Cymath – Math Problem Solve‪r for ( iOS | Android )

4. Geometry solver ² lite

Most math solver apps don’t deal with geometry, but here is an app that does it well. So the next time you struggle to find the area of a figure or you cannot recall a specific formula, you know where to look. You can easily toggle between 2D or 3D figures from the sidebar. Moreover, all the figures are given in a listicle form along with a line diagram for easy understanding.

The calculation is also extremely easy. All you have to do is add the variables and the app will show you all the results live as you change these variables in real-time. In case you do not want to rely on the auto-calculation feature, it shows all the formulae in the same tab for quick reference as well. While all the formulas are free, the calculator for several figures is locked. On the plus side, you can simply watch a 15 seconds video ad to unlock them. If you do not wish to see ads, you have the option to remove ads and unlock all figures by paying a $3.99/one-time fee.

• 2D ad 3D figure section
• Auto-calculator with variables
• Lists all the formulas (area, perimeter, centroid, etc.)
• Purely a geometry app

Get Geometry solver ² lite for ( iOS | Android )

5. Google Lens (Homework)

Did you know you can use the Google Search app to solve math problems? Very few people know about it and I’m sure even less actually use it. In order to use this feature, you must have the Google Search app installed. Simply tap on the camera icon and select the Homework option from the bottom. Now all you have to do is point the camera towards the question and adjust the frame accordingly.

If the app can scan the question successfully, you’ll get a preview for the same. If it’s not accurate you have the option to edit the question. You can also view the solution step-wise. Google also has another problem-solving app Socratic ( iOS , Android ) that covers all subjects. You can try that as well however it doesn’t allow you to upload questions from your gallery. Hence when your friends send you a problem on WhatsApp, using the Google Search app is a better solution.

• Shows step by step solution
• Allows you to edit the question
• See similar questions/concepts with Google search results
• Not a dedicated math solver app
• Might not work for advance math

Get Google Search App for ( iOS | Android )

6. QuickMath

If you prefer using a PC over the phone to study, you should check QuickMath’s website. The website isn’t fancy but easily solves basic math problems. Similar to the math solver apps we have discussed above, it solves math problems automatically. Whether you are in school or college, it covers a vast array of subjects. You can solve simple equations, algebra, calculus, percentage problems, etc.

The website is easy to browse and all the options are well laid out. You can click on the type of question from the side or top bar. Once you scroll down, you can also view a step-by-step solution for any given problem. In addition to that, it also provides a brief explanation for each step.

• Easy to switch between types of questions
• Solves both basic and advanced math problems
• Features help and tutorial section
• Step by step explanation
• No option to upload questions
• On-screen keyboard is a flimsy way to type (personal choice)

Get QuickMatch for ( iOS | Android | Web )

7. WolframAlpha

Wolfram is often called a search engine for solving problems. Unlike Google which heavily relies on search results, Wolfram uses deep computational power (extremely sourced and curated data) to solve mathematical equations and has a vast variety of areas it deals with. You can solve problems related to elementary math, algebra, calculus geometry, etc. To begin, type the question, upload a picture, even just paste a link containing the question.

Wolfram Alpha will likely solve all your problems. The only hiccup is that a lot of great features are exclusive to the pro version which comes at $5.59/monthly. This not only unlocks step-by-step solutions but also adds useful features like practice problems, guided calculators (finance, nutrition, etc), option to download results, etc. If you are a student, I highly recommend you try this. It’s a great factual resource not only for solving maths but other subjects such as chemistry, engineering, economics, stats, etc. too.

• Solutions based on factual data
• Covers most subject besides mathematics
• Useful features behind the paywall (step-by-step solution, download results, etc.)

Visit WolframAlpha

Closing Remarks: Which Math Solver Apps Should You Choose

In my opinion, Mathway is the perfect app, to begin with. It deals with most of the problems in addition to being accurate. You can type, use voice command and even capture questions to find answers. If you’re on PC, try the QuickMath website which will work in most cases.

Also Read: 19 Best Math Game Apps for Android and iOS

Vaibhav is a broadcast journalist with a keen interest in tech. He doesn't believe in fanboying a specific product. He writes about things he believes are actually helpful in some way to the user.

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Solvely - AI Math Solver

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Using Video Projects to Reinforce Learning in Math

A collaborative project can help students deeply explore math concepts, explain problem-solving strategies, and demonstrate their learning.

Problem-solving, and the creativity that generates and fuels it, lies at the heart of mathematics. Mathematics is essentially about reasoning and much less about memorization or even procedural skills, although both processes are meaningful and useful to simplify and support problem-solving. The National Council of Teachers of Mathematics (NCTM) has consistently advocated to keep problem-solving as the centerpiece of mathematics teaching, and global trends in mathematics education have increasingly emphasized problem-solving and mathematical modeling.

Problem-solving allows students to deepen their conceptual comprehension and appreciate the usefulness and relevance of mathematics. Thus, it generates and fosters interest, engagement, and a deeper understanding of the world around them. Because problem-solving is often used in the mathematics classroom, it’s particularly important to find fresh and interesting ways to attract and maintain students’ engagement.

Video Projects Support Interest in Problem-Solving 

To this end, I assign video projects to my students. In groups of two or three, they solve a set of problems on a topic and then choose one to illustrate, solve, and explain their favorite problem-solving strategy in detail, along with the reasons they chose it. The student-created videos are collected and stored on a Padlet even after I have evaluated them—kept as a reference, keepsake, and support. I have a library of student-created videos that benefit current and future students when they have some difficulties with a topic and associated problems.

Some topics in mathematics are well-suited for applications and problem-solving. These are usually multistep problems that require a combination of strategies and procedural fluency. Typical examples are the motion, work, and mixture problems in algebra, the optimization problems in precalculus or calculus, and related rates problems in calculus.

This collection of student-created videos is about related rates problems (note that some links may not work, as this collection is old). Video activities based on problem-solving can be done at any level of mathematics, as problem-solving is a task in which children are engaged in math class from an early age.

Useful Recording Tools

Some examples of useful recording apps include Screencastify , ScreenPal , iMovie , and QuickTime . Each of them has pros and cons, so I suggest looking at the particular specifications of each tool in terms of the number and length of videos allowed by the free version of those apps. I let my students choose what app they want to use to create their videos—they are generally very familiar with this sort of technology and may be more at ease with one tool over another. All they have to produce is a usable link to their video that will be posted on the common Padlet.

Loom is an intuitive, user-friendly screen recording tool that can record audio, video, browser windows, or entire screens in a Chrome extension, desktop app, or mobile app. You can sign up for a free Loom for Education account; students don’t need an account to watch a teacher’s videos, but they will in order to create their own videos.

Loom’s training module is thorough and includes tutorials, special feature descriptions, and examples. Once you click the Loom icon, there’s a short countdown that precedes the recording. When you stop the recording, a link automatically saves to your clipboard and can be easily shared via email, social media, or an embed code.

The videos will also save to your personal library and can be shared to a team library to make them easily accessible to colleagues. Editing features are quite limited (trimming and changing playback speed), which means you may have to do multiple takes, but teachers can control the settings for comment and download options. 

4 Problem-Solving Strategies

Mathematician George Polya outlined a four-step model in his famous book, How to Solve It . It involves understanding the problem, devising a plan, carrying it out, and finally looking back and reflecting. These are the strategies that my students must demonstrate while creating their videos. 

• Understand the problem: Students reread the problem carefully, summarize and rewrite the information in mathematical notation, use keyword analysis, draw a picture or a diagram, or even act out the scenario.
• Devise a plan: Looking for patterns and solving a simpler problem are my favorite approaches, but other ideas—guess-and-check, working backward, eliminating possibilities, using a formula and solving an equation—can work well too, depending on the circumstances. Most often, for good problems, several of these strategies have to be employed at the same time and help support confidence in the solution.
• Carry out the plan: This is where “show your work” comes in with full force. Communicating their thoughts and ideas is paramount: Students should be systematic, show their thinking in a logical progression, check their work, and be flexible and persistent.
• Look back and reflect: It’s important to consider which part of the problem was the most challenging and why, which process was most effective, and other strategies that could have worked. This makes for more efficient and deeper learning.

Related rates problems can be intimidating at first, and it is useful for students to write out explicitly the steps and strategies they take to solve the first few problems.

My students come up with a model that follows the previously mentioned steps. It includes labeling the rates with their units and sign, an understanding of the rate they must find, finding at least one equation that binds the variables together, differentiating this equation with respect to time, plugging in the given information, and, finally, writing a short sentence that summarizes their conclusion (including sign and units). 

Benefits of the Video Activity

My students and I have experienced several benefits of this task.

Students are encouraged to communicate mathematically. The importance of communication among learners is also heavily emphasized in the NCTM publication Principles and Standards for School Mathematics .

Student collaboration. Viewing learning as a collective endeavor , rather than an individual competition, helps students develop their social and collaborative skills. When students take joint responsibility for their learning—sharing ideas and resources—it fosters a safe environment where they perceive each other as allies rather than competitors, which increases engagement and academic achievement. 

Problem-solving skills are strengthened. As reported in the Executive Summary of the NCTM Principles and Standards for School Mathematics , when solving mathematical problems, students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations that serve them well beyond the classroom. 

Teachers can clearly see students’ understanding. This includes conceptual understanding, procedural precision, logical and analytical thinking, problem-solving strategies, and clarity of communication.

A sense of belonging in math class is cemented. The experience generates positive, affirmative memories—the goal of social and emotional learning—and “ encourages student focus and motivation, improves relationships between students and teachers, and increases student confidence and success .” It should be promoted, particularly in the STEM disciplines.

 In other words, it’s a keeper.

AI Math Helper: Scan Solve App 4+

Homework solver, photo help, oleksandr suprunenko, designed for iphone.

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Unlock the secrets of math with AI Math Helper, the innovative app designed to transform your mobile device into a powerful educational ally! Whether you're a student grappling with complex problems, a lifelong learner refining your knowledge, or a professional in need of a quick calculation, AI Math Helper is your go-to solution. Core Features: > Smart Equation Scanner: Effortlessly scan any mathematical problem or formula with your device's camera. Say goodbye to manual input and hello to instant clarity. > Step-by-Step Solutions: Not just answers! Our app provides comprehensive, detailed explanations for each step, empowering you to understand the 'how' and 'why' behind the solution. > AI-Powered Chat: Stuck on a tricky concept? Our intelligent AI chat is ready to assist. Ask any theoretical question or seek guidance on equations, and receive instant, reliable support. > Personalized Learning Journey: Keep track of your progress with a customizable history and favorites section. Review past problems or revisit favorite solutions anytime, anywhere. AI Math Helper is more than just an app - it's your personal tutor, ready to demystify math at every level. It's math made accessible, intuitive, and infinitely more enjoyable. Ready to revolutionize the way you interact with math? Download AI Math Helper: Scan & Solve now and step into a world where every math problem is an opportunity to learn and excel! Terms of use: https://math-formulaa.com/terms.html

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Welcome to the Future of Education! > Minor Bug Fixes > Improving of the Chat Tutor algorithms

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The developer, Oleksandr Suprunenko , indicated that the app’s privacy practices may include handling of data as described below. For more information, see the developer’s privacy policy .

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The following data may be used to track you across apps and websites owned by other companies:

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UNDER CONSTRUCTION

Team assignments, team membership spreadsheet sessions by names 1pm groups by names 2:30pm groups by names sessions by kerberos, class overview, introduction considerations for taking the subject this term team study & problem solving team protocols & daily participation grades weekly schedule class website grades midterms & final exam participation problem sets online feedback problems weekly reading comment in the nb annotation system --> collaboration latex macros textbooks and reading -->, introduction, this subject offers an introduction to discrete mathematics oriented toward computer science and engineering. see also the introductory video on the website 6.042r/mitx . in spring '18 there will be class sessions mwf: 1－2:30pm in 32-044 & 32-082 2:30－4pm in 32-044 there are no separate recitations. students will be assigned to sessions and teams by the second week of class. students generally work with the same team throughout the term. (contact 6042-webmaster@mit.edu about changing assignments.) there are three main topics: fundamental concepts of mathematics: definitions, proofs, sets, functions. discrete structures: elementary number theory, graphs, counting. discrete probability theory. the prerequisite is 18.01 (first term calculus), in particular, some familiarity is expected with sequences and series, limits, and differentiation/integration of single variable functions. the goals of the class are summarized in a statement of class objectives and educational outcomes ., considerations for taking the subject this term.

The sessions are open book, and laptops, tablets, etc., are encouraged for viewing class related material (viewing extraneous stuff like email or facebook is a no-no).

Each team will have a TA/LA coach who serves as a facilitator and provides feedback on solutions. The coach will initially resist answering questions about the material, always trying first to find a team member who can explain the answer to the rest of the team. Of course the coach will provide hints and explanations when the whole team is stuck. An instructor and a supervising TA circulate among the teams and oversee class activity. See the description of team protocols and grading for more information about team activities.

Team Grading & Protocols

Department requirement.

This subject is required of all Computer Science (6-3) majors and is in a required category for Math majors taking the Computer Science option (18C). It covers many mathematical topics that are essential in Computer Science and are not covered in the standard calculus or algebra curriculum. In addition, the subject teaches students about careful mathematics: precisely stating assertions about well-defined mathematical objects and verifying these assertions using mathematically sound proofs. While some students have had earlier exposure to some of these topics, in most cases they learn a lot more in 6.042J/18.062J.

Some students already have a firm understanding of sound proofs and familiarity with a significant fraction of the covered topics from Math teams, competition, or similar experience. They should discuss with the instructor and their advisor the possibility of substituting another subject for 6.042. It is also possible for qualified students to get credit for the class by serving as a Lab Assistant .

Weekly Schedule

Reading for each class will be assigned from our own class textbook ., videos and online feedback questions, online questions based on video mini-lectures and the text are due before each class., problem sets, psets will be posted at least a week in advance and are due on friday in weeks without a midterm., detailed calendar, the complete schedule includes topic and reading listings for each class, as well as pset due dates and midterm dates. class calendar . -->, class website, grades for this course will be based on your scores in the following categories. max (midterm 1, final - midterm 1 portion): 12% max (midterm 2, final - midterm 2 portion): 12% max (midterm 3, final - midterm 3 portion): 12% max (midterm 4, final - midterm 4 portion): 12% final - section 5 material: 12% class participation: 20% problem sets: 15% mitx: 5% each section will be graded out of 5 points. a weighted average of 4.5 or better will get an a; 3.5 - 4.5 will get a b; 2.5 - 3.5 will get a c; and any score below 2.5 will be discussed. we may lower these cutoffs, but we will not raise them., midterms and final exam, the material will be divided into 5 sections. there will be ninety minute midterms on the first 4 sections during the semester, and a three hour final exam that will cover all 5 sections. midterms take place from 7:30－9pm. dates and locations for exams can be found in the class schedule and the class gcal feb 21 mar 14 apr 4 apr 25 --> your score for the first four sections will be the maximum of your grade on the midterm and the corresponding material on the final. your score for the fifth section will be your score for that portion of the final. this means you are required to attend the final to receive a score for the fifth section (but you are welcome to skip the remaining 4 sections). this also means you can skip the midterms and take just the final, but we do not necessarily recommend this. the sections are weighted 12% each. note that each numerical quiz score will be translated into an integer from 1-5 with the following meanings: 5 - thorough understanding of the topic 4 - adequate understanding of the topic 3 - some understanding of the topic 2 or 1 - poor understanding of the topic these will not be based on class averages but rather decided on an exam-by-exam basis. you may want to read professor winston's article on grades for more information. exam questions will typically be variations of prior problems from class and psets. the best way to prepare is to review the published solutions of these problems. each exam focuses on material not covered by prior exams; midterms will not cover material introduced the day before the exam. a single double-sided crib sheet is allowed for each midterm. two double-sided crib sheets are allowed for the final exam., class participation, your team coach will assign you a grade for each class session. see the description of team protocols and grading for more information on how class session scores are assigned. the lowest three (3) class session scores will not count in grade calculation. no makeup is required for these dropped scores. this effectively gives you three class sessions you can miss without penalty. the three absences are treated as personal days which may be used for sick leave, professional conflicts like job interviews, or sleeping in. however, we strongly recommend saving these absences for valid excused reasons (e.g. medical emergencies, religious holidays, personal emergencies). provided your previous absences are excused, we can definitely help you make up any additional absences beyond the three. please email [email protected] for more information or clarification on these policies. note that missing credit for three or fewer class sessions guarantees you a grade of a 5. any additional absences (that have not been excused) will penalize your grade significantly., there will be eight psets during the semester. psets are 15% of the final grade. devoting up to 3.5 hours each week working on a pset is, for most students, crucial for mastering the covered material. a good portion of each midterm exam and the final will be based on pset problems. there are separate web pages with pset submission instructions . you may make up one pset during the semester and that score will be dropped when calculating the average. we suggest making up your numerically lowest score. the makeup policy page has more details on making up a pset., online feedback problems, online problems to be completed before most class meetings are posted on the 6.042r/mitx website. these consist of straightforward questions that provide useful feedback on comprehension of the covered material. (some students prefer as an advance guide to try the online problems before reading the text or watching videos; that's fine.) watching designated videos on the 6.042r/mitx website is helpful for many students but is optional . it's always a good idea to review the four-per-page slide handouts and have them handy in class. like team problem solving in class, online problems are graded solely on participation : students receive full credit as long as they try the problem, even if their answer is wrong. online feedback problems count for 5% of the final grade., collaboration, you are encouraged to collaborate on problem sets , but you must write up your own solutions alone without your collaborators ., other sources, questions, suggestions, and complaints to the staff, messages for the staff can be posted (publicly or privately) on the class piazza forum or by email to 6042-staff@mit.edu pictures and email addresses for individual staff members are available. email links are also available on stellar., latex macros.

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Why Tipping Is Everywhere

In the united states, many say tipping is expected in more places these days. here’s how tipping culture exploded..

This transcript was created using speech recognition software. While it has been reviewed by human transcribers, it may contain errors. Please review the episode audio before quoting from this transcript and email [email protected] with any questions.

Hello. Excuse me?

My name is Sabrina. This is Claire. We’re journalists. Could we ask you a question?

You just did.

[LAUGHS]: Another one. [UPBEAT MUSIC]

What is your view of tipping?

I think it’s become excessive. Whatever they do, they got that jar and they’re wanting you to put a tip in there.

They have the iPad. And it’s like, all right, how much you want to tip? And it’s like you bought a $5 coffee. It’s like, all right, well, tip $3.

There’s a lot of pressure. You feel like you have to tip. And I feel like people are watching you at that moment.

Yeah, yeah. I feel a lot more pressure to tip more. Wages haven’t kept up, so I feel like I should be tipping more. And it’s annoying because my wages haven’t gone up either, so it’s annoying.

The other day I just bought a loaf of bread, and the tip thing came up, gave me the option of 15 percent or 20 percent. Do I really have to tip somebody to buy a loaf of bread?

I went to the self-service machine. And it was like, add a tip. And it’s like add a tip for what? I’m the one that did the work, you know what I’m saying?

You’re like, I should be tipping myself.

I actually am a tip worker. We’re literally paid less wages in order for the customers to pay us.

What do tips mean for you and your work?

It’s how I feed my family.

Yes. 100 percent.

Unless you work in the service industry, you don’t really understand how crucial tipping is.

Tips mean a lot. They are 60 percent, 50 percent of my paycheck. And my hourly is pretty low to begin with.

Whatever I get at the end of the night goes towards dinner. Or for example, I didn’t have money for sanitary pads one time. And then that tip, grabbed it.

I feel like a lot of people feel like you did nothing for me. You just put a cup on the counter and I took it. Like, why should I pay you extra for that?

What do you say to someone who says that? You didn’t do anything, you just put my food in a bag.

If you knew what my paycheck looked every week, you would think different. Or maybe not, maybe you don’t feel bad for me and you’re like, get a different job. But like, this is a job I’m good at and the job I like. And I’d like to be able to make a living off of it. That extra dollar or two really makes a difference.

From “The New York Times,” I’m Sabrina Tavernise and this is “The Daily.”

Tipping, once contained to certain corners of the economy, has exploded, creating confusion and angst and now even becoming an issue in the presidential campaign. Today, economics reporter, Ben Casselman, cracks open the mystery of this new era of tipping.

It’s Thursday, August 29.

So Sabrina.

Can I ask you a personal question?

What is your philosophy on tipping?

[LAUGHS]: Exactly.

Sabrina, I think I’m a sucker. Look, I’ve always tried to be a good tipper in restaurants. It feels like part of the deal.

I worked as a waitress for many years. That was the only way I actually made money. If there’s no tip, there’s no salary. Restaurants, it’s a rule.

Absolutely. But now tipping is everywhere. You see these tip screens in places you never would have tipped before. I mean, never mind the coffee shop, you see it at the fast food place. You see it at the oil change place. I’ve heard stories of people seeing it at the self-checkout line. Who’s even getting that tip?

And every time a tip screen pops up, I always tip.

Oh, my god, Ben, so do I.

It’s totally irrational. I hate it. But there’s some part of me, and I don’t love this about myself, that is just convinced somebody is going to be sitting there judging me or I’m terrified that they’re going to. And, oh, my god, if I click No Tip, am I a bad person?

And someone behind me in line might see that.

I can’t click that No Tip button.

I am exactly the same. Every single time I’m presented with this iPad screen thingy, the tips come up. I press max, 30 percent. My husband, an economist, thinks this is ridiculous.

He says, you’re tipping 30 percent on a bottle of water someone just handed you. Don’t do that. That is crazy. But I keep doing it because I can, so I should. I don’t know, I have guilt about it.

Your husband is objectively correct. This is crazy. But tipping is not about objective cold economic logic. It’s emotional. It’s cultural.

There are norms around it. And right now, we have no idea what those norms are. And so we’re all stuck in this panicked moment of trying to decide which button you press and whether you should be expected to tip in this circumstance.

OK, so we are both suckers. We’ve established that. What we need to do now is figure out this panicked moment. I want you to explain this to me, Ben. Why has tipping exploded?

I think there are three reasons. The first of these is just technology. Several years ago, we started to see these tablet-based checkout systems everywhere. And it’s very easy to just add a tip screen onto there, that little, do you want to add a tip, 10 percent, 15 percent, 20 percent.

Right. And as I had less cash and then no cash in my wallet, this was always the way I paid for things.

Yeah, so it became very easy technologically to add tipping. But then the real shift came in the pandemic.

If you think back to that moment, many of us were lucky enough to be able to work from home and to be relatively safe. And we felt a lot of gratitude for the people who weren’t able to do that, who were bringing us food and delivering groceries. And so there was an explosion in tipping. And an explosion in tipping, even in places where we didn’t used to tip.

If you go and pick up takeout at a restaurant, you probably always tip your delivery driver. But if you went to the restaurant and you picked it up, you didn’t tip there. But now in the pandemic moment, they add a tip screen saying, would you like to tip? And yeah, of course, I’d like to tip. These people are risking their lives out there to make my chicken tikka masala.

Right. You basically wanted to tip the UPS guy.

Yes. And so we were tipping everybody. And so that allowed tipping to spread into these new areas. It got a beachhead in places where it didn’t used to be.

And maybe if the story ended there, it would have been this moment in time and then it all would have gone back to the way it always used to be. But that didn’t happen because we had this intense worker shortage when things started to reopen.

And how does that fit into this?

Businesses start to reopen. They need workers. They’re having a hard time finding them. Workers are reluctant to come back for all sorts of reasons. And tipping became a way of attracting workers.

Businesses were paying more, but they were also looking for other ways to get workers. And saying, we’ll add a tip screen that’ll boost your pay further. And if there’s one coffee shop where there’s a tip screen and there’s another coffee shop where there isn’t, you can be pretty sure which one you’re going to go work at.

Completely. I mean, we were talking to workers yesterday, and they were very specific about which chain stores allowed tips and which ones didn’t. And they much preferred working for the ones that allowed tips. I mean, it makes sense.

And I asked them, as a proportion of your earnings, how much are tips? Tips are a lot. Does that mean you make less in the place that doesn’t have the screen that allows it? Absolutely.

We saw workers demanding this. In fact, when some Starbucks stores were unionizing, one of the things they demand is, we want to be able to take tips on credit card payments.

Interesting, yeah.

This became a source of negotiation between businesses and their workers. And the thing is, once that happens, it’s really hard to put the genie back in the bottle.

But why? I mean, this all sprung up into our lives in the matter of a couple of years. So why can’t it go back to the way it was just as quickly?

Imagine that coffee shop worker that you were talking to yesterday, who’s now making, in many cases, 20 percent, 30 percent, even 40 percent of their earnings in tips. The business can’t just say, never mind, we’re going to get rid of the tip screen. Maybe, we’ll put out a tip jar and people can leave $1 or $2 when they want to. That’s a huge pay cut for that worker.

OK, they could instead say we’re going to get rid of tipping and we’re going to raise your pay. Instead of paying you $15 an hour and $5 in tips, we’ll give you $20 an hour. But now the business is going have to raise prices as a result.

And you, Sabrina, the coffee-drinking public are going to say, no way, I’m not going there and paying $8 for my latte or whatever the price may be. And so for the business, they can’t just get rid of the tip, because they can’t just cut off the pay and they can’t raise prices enough to raise pay accordingly.

Right. Nonstarter for the business.

Can’t work for them. And the worker is certainly not going to stick around if they try to do that.

So has there been some experimentation with this? I mean, have restaurants actually tried to go tipless?

Yeah, so we’ve seen an example of exactly this. A few years back, Danny Meyer, a big New York restaurateur, and a bunch of other restaurants as well tried getting rid of tipping completely. They said, this system is unfair, it’s unequal. We’re going to raise wages for everybody, for waiters, but also for cooks.

We’re going to raise our prices, accordingly, to pay for that. And customers will understand. They’ll understand that they’re paying the same amount at the end of the day, it just is in the form of a direct cost instead of a cost plus a tip. And it didn’t work.

For a bunch of reasons. But mostly because customers looked at the price on the menu and people didn’t want to pay it. I also think, look, we all complain about tipping. But customers also kind of like the tip. They kind of like looking generous.

You get to show off to your date or to your father-in-law. And, of course, you can, at least in theory, express your dissatisfaction by withholding a tip or by tipping less. Not you and me, we apparently don’t do that. But some people do, I hear.

The restaurant’s like, suckers, OK, great. Yeah, we don’t even have to worry about them.

Customers rebelled against the idea of not tipping. And most of those restaurants eventually went back to the old model.

Interesting. So we do have this love-hate relationship with tipping.

Yes. We hate being asked, but we like the control. And I think that is part of why all these changes feel so difficult for so many people, because it doesn’t necessarily feel like you have the control anymore.

That screen in front of you with the barista watching you, with the person in line behind watching you —

Oh, my gosh, I’m sweating already.

— you don’t feel like can press the No Tip button. Or at least suckers like you and me don’t.

Exactly. The choice is gone.

The choice is gone. Or the choice, at least, is sort of psychologically more taxing.

Right. [LAUGHS]

You feel pressured to do it.

OK, so that’s the customer experience. But with this new uptick in tipping, one question I always have is, is the worker on the other side of the screen getting this tip or will the business owner pocket it?

The worker is getting the tip with some caveats. By law, the business owner or the managers, they can’t take the tips. If you click a Tip button or you leave $1 in the tip jar or you tip in any way, if that ends up in the pockets of the business owner or the general manager or what have you, that is wage theft. It happens. We certainly hear stories about it happening, but it’s certainly not legal and it’s certainly not the norm.

That doesn’t mean that the worker, the person who hands you your latte, is the person getting your dollar. It often gets pooled across all of the workers who are working that shift or even all of the workers who work over an entire week. But it’s going to the workers.

People like us can rest assured that the workers are getting the full benefit of that tip that you’re pushing.

In many ways, what you are doing as the customer is you are subsidizing the wage. If you, you coffee shop worker, want to get $25 an hour, you don’t care whether that’s $20 in pay and $5 in tip or $25 in pay or any breakdown of that.

$25 is $25.

$25 is $25. When I leave a tip of $1, on some level, that’s $1 less that coffee shop has to pay you, the barista. Tips are helping the business pay their workers. They’re shifting. The business is shifting some of the burden for paying its workers off of its revenue onto its customers.

In other words, you and I, Ben, we are kind of helping foot the bill for these wages.

Absolutely. And from the businesses’ perspective, that’s a pretty great deal, because they basically get to charge, say, $4 for the latte and then for the customers who are willing to pay more, they’re basically charging more. Those people throw on the tip.

It’s a way of the business getting the maximum dollars that it can out of the maximum number of customers that it can attract.

But for workers, this system where they’re increasingly reliant on customer tips carries some real risks.

[UPBEAT MUSIC]

We’ll be right back.

Tell me about these risks of our tipping system.

Look, tipping has always had a lot of problems associated with it. If you think in restaurants, they’re often really big pay disparities where the servers at the front of the house, who are getting tipped, often make a lot more money, especially at a nice restaurant, than the cooks and dishwashers and all of the people at the back of the house.

You hear these stories of people going to cooking school and then basically bailing on the cooking career and becoming waitresses and waiters because it’s just more money.

Yeah. And then within tipped occupations, there’s a lot of inequity here. There have been studies that have shown that a pretty young woman gets tipped better than other people, that white people often get tipped better. There are tons of problems around sexual harassment, because if your earnings are dependent on the table that you’re serving liking you, then maybe you put up with things that workers shouldn’t have to put up with.

Those are the problems that have always existed in this system. But then as tipping spreads, the risk is, first, just more workers have to deal with this, but also that more workers become more dependent on tips for their earnings.

In the short term, this has all worked out pretty well for workers. This has been a period where they’ve been in hot demand, and so their wages have been rising. And at the same time, they’ve gotten all these tips on top of that. And that’s been really great.

But it’s not clear that that’s true over the longer term. Over the long run, you could imagine that all of these businesses get to just raise wages more slowly, that tips sort of eat away at wages over time. And then if we ever see customers pull back a little bit, tip less, then all of a sudden, all of these workers could really suffer.

Basically, you’re describing a system in which the earnings are just more vulnerable, more dependent on the kindness of strangers.

Yeah. And more at risk if those strangers become a little less kind.

Yes. And this issue has become so much a part of the national conversation that it’s actually entered the presidential race. Both former President Trump and Vice President Kamala Harris have announced policy plans to help service workers. And essentially, they’re calling for no tax on tips.

Yeah, that’s right. So President Trump announced this several weeks ago as his big new “no taxes on tips” proposal. Kamala Harris followed up and basically endorsed that proposal, again, a little while later. We don’t have a lot of details on how this would work. But essentially, it would mean that if you earn tips, those tips are exempt at least from federal income tax.

What would that mean?

Let me tell you, economists hate this idea. Left-wing economists and right-wing economists, this is one point they can kind of all agree on.

And why do they hate it?

Because they say it’s unfair. It singles out this one group of workers for special treatment. The person who works at McDonald’s who doesn’t get tipped, they don’t benefit from this. The retail worker doesn’t benefit from this. It’s just this one group of workers who get this special treatment where they don’t have to pay taxes.

Right. Right.

But there’s also maybe an even more fundamental issue, which is that if you think you hate tipping now, if these proposals go through, you’re going to see so much more tipping.

Uh-oh, I’m holding on to my hat.

Because it’s basically a subsidy for tips.

As a worker, we said before, you don’t care whether you make, $25 an hour or $20 plus $5 an hour in tips, except that if some of that money isn’t taxed, you want more of that. You want more tips.

Basically, you want your entire salary to be a tip.

Ideally, right? And so that works great for the business perspective. Great, I don’t need to pay my workers.

[LAUGHS]: Wee!

It’s all tips now. Workers happy about that. What that means is you’re going to see more businesses looking for ways to have their workers count as tipped. Maybe you start to see tips in places that we’re not seeing them at all. Maybe you really do start to pay tips at a retail outlet, at a gas station.

Grocery store?

At a grocery store, why not? And the issue there, beyond just it being annoying for you and me, is that it further ingrains this system. All those problems that we were talking about in tipping now involves even more workers across the economy. And they’re even more vulnerable to that possibility that you and I start tipping a little bit less.

Ben, how would you describe where we are in this tipping moment? Is this just the new normal?

I think we’re still in a period of transition here. The fact that we’re having this conversation on some level tells you that we’re not totally in a new normal yet. You don’t leave a restaurant and say to yourself, man, I can’t believe I was asked to tip. But we’re still all the time having this conversation about, you wouldn’t believe I got asked to tip at the self-checkout.

Right. The bakery, for god’s sake.

It’s still a transition. It’s still happening. Over time, norms will develop. We’ll figure out the places where we tip and the places where we don’t, and how much and all of that.

But the dust hasn’t quite settled yet.

It hasn’t settled. But I think what we do know is that we’re not going back. We’re now going back to a world where we only tip in those set of circumstances where we used to. And remember, this whole transition has happened during a period of relative economic strength, when people have had money to go out and spend and to tip. The question is, what happens when that’s no longer true?

Right. When there’s a recession, people are going to be nervous about their pocketbooks and probably won’t be as generous.

Whenever we get to the next recession, it will be the first one in this new era of tipping.

And there’s a whole new group of workers who are going to lose out when that happens, who are dependent on tips and will suffer when customers start pulling those tips back.

Ben, thank you.

Sabrina, thank you so much. And the screen is just going to ask you a couple of questions at the end here.

[LAUGHS]: Ben, 30 percent.

Here’s what else you should know today. On Wednesday, at least 10 Palestinians were killed when hundreds of Israeli troops launched major raids overnight in the occupied West Bank, targeting Palestinian militants, after what Israel said was months of rising attacks. The operation, the largest since 2023, followed months of escalating Israeli raids in the occupied territory, where nearly three million Palestinians live under Israeli military rule.

And the Supreme Court maintained a temporary pause on a new plan by President Biden to wipe out tens of millions of dollars of student debt. The plan was part of the president’s approach to forgiving debt after the Supreme Court rejected a more ambitious proposal last year that would have canceled more than $400 billion in loans. The scaled-down plan was directed at certain types of borrowers, including people on disability and public service workers. The court’s decision leaves millions of borrowers enrolled in the new plan in limbo.

Today’s episode was produced by Mooj Zadie, Asthaa Chaturvedi, Eric Krupke, and Clare Toeniskoetter. It was edited by Lisa Chow and Brendan Klinkenberg, contains original music by Dan Powell, Marion Lozano, and Rowan Niemisto, and was engineered by Chris Wood. Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly.

[THEME MUSIC]

That’s it for “The Daily.” I’m Sabrina Tavernise. See you tomorrow.

• Apple Podcasts
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Hosted by Sabrina Tavernise

Featuring Ben Casselman

Produced by Mooj Zadie Asthaa Chaturvedi Eric Krupke and Clare Toeniskoetter

Edited by Lisa Chow and Brendan Klinkenberg

Original music by Dan Powell Marion Lozano and Rowan Niemisto

Engineered by Chris Wood

Listen and follow ‘The Daily’ Apple Podcasts | Spotify | Amazon Music | YouTube | iHeartRadio

Tipping, once contained to certain corners of the economy, has exploded, creating confusion and angst. Now, it is even becoming an issue in the U.S. presidential campaign.

Ben Casselman, who covers the U.S. economy for The New York Times, cracks open the mystery of this new era of tipping.

On today’s episode

Ben Casselman , a reporter covering the U.S. economy for The New York Times.

Background reading

How to deal with the many requests for tips .

Former President Donald J. Trump called Vice President Kamala Harris a “copycat” over her “no tax on tips” plan.

There are a lot of ways to listen to The Daily. Here’s how.

We aim to make transcripts available the next workday after an episode’s publication. You can find them at the top of the page.

The Daily is made by Rachel Quester, Lynsea Garrison, Clare Toeniskoetter, Paige Cowett, Michael Simon Johnson, Brad Fisher, Chris Wood, Jessica Cheung, Stella Tan, Alexandra Leigh Young, Lisa Chow, Eric Krupke, Marc Georges, Luke Vander Ploeg, M.J. Davis Lin, Dan Powell, Sydney Harper, Michael Benoist, Liz O. Baylen, Asthaa Chaturvedi, Rachelle Bonja, Diana Nguyen, Marion Lozano, Corey Schreppel, Rob Szypko, Elisheba Ittoop, Mooj Zadie, Patricia Willens, Rowan Niemisto, Jody Becker, Rikki Novetsky, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Olivia Natt, Daniel Ramirez and Brendan Klinkenberg.

Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Sam Dolnick, Paula Szuchman, Lisa Tobin, Larissa Anderson, Julia Simon, Sofia Milan, Mahima Chablani, Elizabeth Davis-Moorer, Jeffrey Miranda, Maddy Masiello, Isabella Anderson, Nina Lassam and Nick Pitman.

Ben Casselman writes about economics with a particular focus on stories involving data. He has covered the economy for nearly 20 years, and his recent work has focused on how trends in labor, politics, technology and demographics have shaped the way we live and work. More about Ben Casselman

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The Calculus Calculator is a powerful online tool designed to assist users in solving various calculus problems efficiently. Here's how to make the most of its capabilities:

• Begin by entering your mathematical expression into the above input field, or scanning it with your camera.
• Choose the specific calculus operation you want to perform, such as differentiation, integration, or finding limits.
• Once you've entered the function and selected the operation, click the 'Go' button to generate the result.
• The calculator will instantly provide the solution to your calculus problem, saving you time and effort.
• \lim_{x\to 3}(\frac{5x^2-8x-13}{x^2-5})
• \lim _{x\to \:0}(\frac{\sin (x)}{x})
• \int e^x\cos (x)dx
• \int \cos^3(x)\sin (x)dx
• \int_{0}^{\pi}\sin(x)dx
• \frac{d}{dx}(\frac{3x+9}{2-x})
• \frac{d^2}{dx^2}(\frac{3x+9}{2-x})
• implicit\:derivative\:\frac{dy}{dx},\:(x-y)^2=x+y-1
• \sum_{n=0}^{\infty}\frac{3}{2^n}
• tangent\:of\:f(x)=\frac{1}{x^2},\:(-1,\:1)

calculus-calculator

• The Art of Convergence Tests Infinite series can be very useful for computation and problem solving but it is often one of the most difficult...

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