Top 250 Websites on EQUATION

Download The Top 250 Websites in Excel

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Math.com - World of Math Online

Free math lessons and math homework help from basic math to algebra, geometry and beyond. Students, teachers, parents, and everyone can find solutions to their math problems instantly.

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eMathHelp - Online Resource for all

Site is created to help people learn math. Includes algebra, calculus, differential equation calculators and notes with many examples. Provides free homework help.

notes, math, algebra, free, homework, calculus, worksheets, education, mathematics

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Equations solver - GetEasySolution.com

One of the best website ever with equation solutions and equations solver for your needs. Solutions for almost all most important equations involving one unknown. Check us and get the easy solution.Just in few seconds you will get the correct solution for your equation.

equation, unknown, solutions, solver, involving

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Web 2.0 scientific calculator

Free Online Scientific Notation Calculator. Solve advanced problems in Physics, Mathematics and Engineering. Math Expression Renderer, Plots, Unit Converter, Equation Solver, Complex Numbers, Calculation History.

calculator, tool, scientific, math, calc, online, web2

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WIRIS | Educational mathematics

wiris, editor, math, online, questionnaires, questions, whiteboard, maths, whiteboards, interactive, exercises, laboratories, mathematical, representation, equation, formula, tools, mathematics, education, formulas, graphical, calculations, calcme, quizzes

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Learn Matched Betting Online Easily | Profit Accumulator

Mаtched bеtting (also known as back bet matching, lay bet matching or double bеtting) is a bеtting technique used by individuals to profit from the free bets and incentives offered by bookmakers. It is generally considered risk-free as it is based on the application of a mathematical equation rather than chance.

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Goins, Writer: On Writing, Ideas, and Making a Difference

A blog by Jeff Goins about writing, creativity, and making a difference in the world.

writing, jeff, goins, write, copy, blogger, process, writers, lesosns, blog, business, creativity, tips, writer, marketing, making, copywriting, difference, blogging

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JETIR- Journal of Emerging Technologies and Innovative Research

Journal of Emerging Technologies and Innovative Research is not limited to a specific field of engineering but is instead devoted to a wide range of subfields in the engineering sciences.

impact, factor, journal, research, international, paper, publication, journals, sciences, science, engineering, 2012, high, food, studies, chemistry, education, 2015, review, applied, technology, year, management, finance, 2014, medical, ieee, university, computer, list, educational, environmental, nursing, stora, enso, 2013, scientific, issn, acta, economics

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Step-by-Step Math Problem Solver

QuickMath allows students to get instant solutions to all kinds of math problems, from algebra and equation solving right through to calculus and matrices.

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A Maths Dictionary for Kids by Jenny Eather| Definitions | Free Math Posters and Charts | Maths Examples | Math Words | Math Glossary | Math Terms |

Interactive, animated maths dictionary with over 630 common math terms and math words explained in simple language with examples. Device friendly version with 950+ entries. Math glossary with math definitions, examples, math practice interactives, mathematics activities, math calculators, math charts and posters. © Jenny Eather 2001-2016.

number, numbers, graph, angle, common, triangle, line, factor, time, math, plot, data, symmetry, decimal, fraction, golden, frequency, square, maths, lines, counting, prism, prime, shapes, unit, notation, denominator, diagram, system, base, order, plane, tables, operations, integer, area, rotation, words, table, clock

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Electronic, Microcontroller and Software Engineering Projects for Students

The one stop educational site for all Electronic and Computer students. If you want to learn something new then we are here to help. We work on Microcontroller

microcontroller, projects, 8051, programming, programmer, embedded, port, electronic, applications, microchip, sort, project, atmel, motor, systems, remote, controls, code, control, circuit, serial, examples, 8052, micro, free, basic, controller, codes, diagonal, series, home, infrared, microcontrollers, books, interfacing, software, robotics, stepper, 8951, automation

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KTU Online

We Provides APJ AbdulKalam Technological University(KTU) oriented Question Papers, Notes, Textbooks, Slides, Results, Syllabus, Timetables, etc

notes, engineering, question, syllabus, kerala, paper, university, students, papers, tech, kalam, exam, login, abdul, college, design, answers, colleges, result, computer, previous, questions, year, results, solved, btech, bank, graphics, mechanics, system, model, student, gate, time, civil, mechanical, electrical, list, cgpa, percentage

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Ask Math Online:Algebra-Geometry-Trigonometry

Ask math provides details on Algebra-Geometry-Trigonometry, Identities, Factorization, Linear equation in one variable, Linear equation in two Variables, Polynomials and precalculus.

activities, trigonometry, online, precalculs, geometry, formula, math

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Wessa.net - Free Statistics and Forecasting Software (Calculators) v.1.2.1

Wessa.net offers free educational forecasting software (time series analysis) and statistics software.

software, free, gini, lorenz, equation, mathematics, plotter, distribution, jenkins, forecasting, correlation, code, statistical, econometrics, calculator, statistics, educational, business, online, time, series, percentiles, quartiles, kurtosis, skewness

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Any Calculator Free Online Calculators For Everything

A hugh collection of free calculators. Any Calculator, Any Use, Any Time. Online calculators for everything.

calculator, calculators, truck, online, time, cost, stop, weight, trucker, fuel, free, speed, travel, news, life, pizza, mortgage, ifta, tire, weather, storage, locations, driving, fluid, loss, insurance, solar, deer, tanning, restoration, calculate, food, hiking, diesel, maps, size, truckers, scales, loan, center

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MacKichan Software - The Home of Scientific WorkPlace, Scientific Word, and Scientific Notebook

MacKichan Software now offers version 5.5 of Scientific WorkPlace, Scientific Word, and Scientific Notebook. You write text and mathematics in your document without having to know a programming language or exit to an equation editor. Evaluate, simplify, solve, and plot functions without the need to master a complex syntax. And typeset documents with LaTeX with just the click of a button.

word, formulas, symbols, mathematical, publishing, mathematics, teaching, processing, calculus, symbolic, maths, algebra, latex, mathml, notebook, workplace, typesetting, equation, scientific, computer, editor, math

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Math Exercises & Math Problems - Questions and Answers

Collection of math exercises and math problems. Primary school, high school and college math problems and math exercises with correct answers.

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stemjock.com - Solutions to STEM Textbooks

This is a website where solutions to textbooks in mathematics, science, and engineering are posted. It is dedicated to the future generations of students.

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Why U

Animated math tutorials

numbers, property, sets, interval, octal, associative, notation, commutative, domain, equation, variable, graph, coordinates, range, cartesian, binary, algebra, animated, tutorial, math, education, topology, infinite, rational, mathematics, integers, series, natural, hexadecimal

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Maxwell''s Equations

Maxwell''s Equations are presented in this tutorial. Gauss''s Law, Faraday''s Law, the non-existance of magnetic charge, and Ampere''s Law are described in an intuitive method, with a focus on understanding above mathematics.

equation, maxwells, equations

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Buy Designer Women Kurtas, Trendy Salwar Kameez, Leggings, Indian Ethnic Jewellery & Fashion Handbags India - Fashion Equation

Fashion Equation is one stop fashion shop for women which offers designer kurtas, ready made salwar suits, printed patiala bottoms, indian jewellery.

template, shopify

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Download forex free trading system and indicators

ForexPops World's Top listed Forex education Site. We spread quality friendly user information for help all forex trader new or old providing information

forex, trading, indicator, strategy, online, broker, strategies, signals, macd, scalping, free, download, indicators, brokers, minute, beginners, youtube, review, africa, south, system, bonus, hour, 2018, chart, news, 2017, candlestick, account, patterns, deposit, daily, spread, leverage, trend, 2019, signal, academy, india, live

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Wise Owl Research | UK Assignment & Dissertation Writing Company

Wise Owl Research is a leading professional academic writing & mathematical equation solving company. We supply custom model assignment answers to support you through your studies. Specialities include UK assignment writing - dissertation statistics & equation solving. Updated 2019 by Wise Owl Research Ltd

assignment

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Robb Nunn, PGA Professional

Robb Nunn, Golf Equation, PGA, Professional, Lessons, Instruction, Golf Lessons, Golf Instruction, Golf Swing Analysis, Golf Swing, Orange, CA.Orange County, CA, Golf Lessons Orange County, Golf Lessons Orange County, CA., Golf Lessons Orange, CA. Best Golf Lessons in Orange County, Best Golf Instruction, Number One Golf Instructor,

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Desire Fashion Shop

Most Desire Fashion For Men, Women & Kids

fashion, fashions, 2018, nova, dresses, style, 2019, king, accessories, jobs, suits, sets, quotes, house, women, valley, week, pants, online, jackets, clothing, moscow, design, movie, socks, tops, ranking, crossword, jeans, show, vests, words, kids, school, university, blazers, tokyo, clothes, coats, logo

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Sergeev''s Home Page

Developing quantum-mechanical perturbation theory for atomic and molecular problems. Many related documents, articles and pictures are available.

series, summation, stark, resonances, divergent, theory, mechanics, schrodinger, equation, perturbation, quantum

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Math Dictionary

Visual Mathematics Dictionary www.education2000.com

property, addition, number, common, angle, factor, inverse, formula, series, area, graph, circle, sequence, base, absolute, complex, closed, identity, angles, degree, function, multiplication, theorem, center, decimal, variable, plane, geometry, numbers, arithmetic, system, binomial, equation, data, geometric, integral, fraction, equality, triangle, event

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Astani Enterprises

"Our primary goal is to add value to real estate projects/ventures by bringing into the equation our abilities and experience. Our effectiveness results from recognizing the necessity to take action, seize the initiative and do whatever required, consistent with our principles and values, to accomplish the task."

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Web 2.0 calculatrice en ligne

Calculatrice de notation scientifique en ligne gratuit. Résoudre les problèmes de pointe en physique, mathématiques et génie. Math Expression de rendu, Parcelles, Unit Converter, Equation Solver, nombres complexes, Histoire de calcul.

calculatrice, calc, outil, scientifique, ligne, calculateur, web2

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Universal Technical Systems

TK Solver, Roarks Formulas for Excel, Advanced Spring Design Software and Integrated Gear Software are used for engineering, plastic gear design analysis, stress, mechanical, thermal, dynamics, statistics, machine design, math modeling, chemical, standards, and consulting.

spring, design, gear, stress, solver, formulas, software, math, calculation, engineering, equation, modeling, systems, technical, universal, analysis, calc, tksolver, strain, load, plastic, compression, metal

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Commission for University Education - Home

Commission for University Education present an overview of higher education in Kenya and to inform the public of the quality assurance mechanisms which have been put in place in the sector. Through this its hoped that there will be greater public awareness on the institutions recognized by the Commission for Higher Education and the World.

education, higher, commission, kenya, qualifications, recognition, equation, universities, charters, award, programmes, status, information, university, institutions, learning, list, services, accreditation, approved

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brandmaier.de - Dr. Brandmaier''s scientific portfolio''

Dr. Andreas M. Brandmaier''s scientific portfolio. Computer and Data Science in Lifespan Psychology.

structural, mining, equation, modeling, music, data, exploratory, psychology, science, clustering, time, classification, series, computer

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Programmer Home - Avrocks

google, windows, server, data, android, microsoft, file, user, plugin, samsung, management, design, code, system, galaxy, access, image, ubuntu, search, arcgis, content, custom, network, service, amazon, field, screen, manager, list, cloud, text, software, database, studio, control, facebook, apache, testing, security, email

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Alloy Carbide Company

Experience with precision tolerances and finishes in both grinding, machining, polishing, brazing, lapping, and evaluation techniques makes Alloy Carbide Co your first choice in repairs and service work. Take advantage of our 300 years of combined experience in our work force to propel your component into the highest quality product possible.

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Family.blog – Get your subdomain of family.blog

family from The American Heritage® Dictionary of the English Language, 4th Edition n. A fundamental social group in society typically consisting of one or two parents and their children. n. Two or more people who share goals and values, have long-term commitments to one another, and reside usually in the same dwelling place. n. All…

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Take Control of your Weight Loss and Diet using Fatburn.com

Take control of your weight loss and live your life your way using fatburn.com to eat a balanced diet of food you actually like, keeping a daily journal and following the simple equation of burning more calories than you consume.

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Web & Mobile App Design & Development India.

Best Web & Mobile App Developer Company in Pune, India. Android App developer | iPhone App developer | iPad App developer | Cross Platform App development

development, developer, design, apps, enterprise, iphone, ipad, equation, master, responsive, application, android, mobile, windows, commerce, developers

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Poweringsoft

Poweringsoft is powerful engineering software blog that will provide you information about some software that used for engineering like for chemical engineering, civil engineering, electrical engineering, numerical methods engineering, manufactur engineering, and other general engineering and also give news information like autos news, gadget news, science development, computers and other

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believable things that hits

light, star, iphone, wars, beer, table, game, giant, lamp, ring, case, dark, glow, bottle, coffee, zombie, wall, inflatable, glass, book, lego, mini, water, shirt, pillow, super, soap, costume, zelda, mario, ball, mask, necklace, control, holder, pool, skull, portable, cube, doctor

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believable things that hits

light, star, iphone, wars, beer, table, game, giant, lamp, ring, case, dark, glow, bottle, coffee, zombie, wall, inflatable, glass, book, lego, mini, water, shirt, pillow, super, soap, costume, zelda, mario, ball, mask, necklace, control, holder, pool, skull, portable, cube, doctor

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Singular Systems

Singular Systems offers a range of mathematical software written in Java. Our main products are Jep and AutoAbacus which provide expression parsing and equation solving functionality for developers and end users.

solve, javacc, evaluation, evaluate, system, webcam, library, games, parse, parser, math, java, autoabacus, mathematics, expression, equation, formula, function

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JETIR- Journal of Emerging Technologies and Innovative Research

Journal of Emerging Technologies and Innovative Research is not limited to a specific field of engineering but is instead devoted to a wide range of subfields in the engineering sciences.

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Ray-Freeman.org | NMR Papers & More...

Nuclear magnetic resonance (NMR) detects tiny radiofrequency signals emitted by the nucleus of the atom when immersed in a strong magnetic field. The main aim of this website is to give access to Ray''s publications on high-resolution NMR, boiled down to a selection of 100, but a full list of titles and abstracts is also available.

pulse, pulses, coupling, decoupling, adiabatic, field, modulation, fourier, sampling, irradiation, relaxation, phase, coherence, suppression, excitation, spectra, transform, symmetry, peak, splittings, evolution, transfer, double, fast, hadamard, noise, composite, inadequate, algorithm, sidebands, receiver, computer, operation, cycling, anomalies, dante, methods, overhauser, scaling, frequency

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Formula Sheet

Search for formulas and instantly copy them to LaTeX or MS Word 2007+. Create and render formulas. Upload formulas and store them all in one place. Create and share lists and sheets full of formulas.

equation, formula, editor, sheet, share, render, store, search, upload, cheat, latex

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Home | Arm & Hammer Animal Nutrition

Animal First. Productivity Always. For the most important jobs you need to get done, Arm & Hammer Animal Nutrition can help keep you on the road to success. During each animal’s life cycle there are many unexpected turns along the way and we’ll help you deliver the right advice with the right products at the right time. We’ll help navigate so you can stay focused.

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Home

mathml, mathml equation editor, mathml activex control, render mathml, export mathml, equation editor, math authoring, authoring tools, scientific typesetting, mathematical typesetting, equation typesetting, math typesetting, typesetting software, mathml control, mathml activex, content mathml editor, presentation mathml editor, mathml editor, learning activities, tarsia, fjsw, activity template software, mathematical puzzle

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IT Staffing and Technology Solutions Company | Crystal Equation

Crystal Equation is a leading IT staffing services and technology solutions company. We’re the clear solutions for companies requiring talented engineers on a contingent or permanent basis. Learn more about our services today!

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Solving Quadratic Equations

Right from solving quadratic equations to solving quadratic, we have everything discussed. Come to Solve-variable.com and master quadratic equations, equations and plenty of other math subject areas

quadratic, equations, solving, equation, logarithmic, exponential

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Men's Clothing | Fashion Streetwear | Athleisurewear | Gym Sportswear – Golden Equation

Shop the latest mens clothing releases from British streetwear brand Golden Equation Clothing. We create modern male clothing including vests, t-shirts, shorts, hoodies & jackets for men across the world. Our contemporary streetwear is designed in the UK & comes with free standard delivery in the UK. #jointheequation

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NASS

NASS North American Sundial Society for sundials, gnomonics, history of sundials, theory of sundials, making sundials, using sundials, sundial education, teaching sundials, sundial curriculum, sundial construction, sundial design, sun and shadows, solar analemma, analemma calculation, equinox, solstice, and computing equation of time

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Francois Hurtaud Design

Francois Hurtaud is a French Industrial Designer currently based in Hong Kong. Francois sees design as an equation, trying to find creative solutions to balance between functionality & aesthetics, sustainability & profitability, viability & legitimacy.

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ACCUEIL AUTO PIÈCES

Equation réelle de Fermat - Démonstration de l''équation - Nombres et réalité - Les nombres dans l''Univers - Le dénombrable et le continu

theoreme, reelle, fermat, equation, leibniz, grand, dernier, galois, robinson, ptolemee, math, mathematique, dedekind

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ABS Trailers | Live Bottom Trailers ////////////////////////

ABS Trailers, manufacturer of live-bottom is always at the leading edge of technology, we innovate constantly, improve our products continuously, listen to our customers and build outstanding products that surpass their expectations. We believe our customers are a key part of the ABS equation: best idea + best response = best live bottom.

trailers, asphalt, bins, dump, live, bottom

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Buy Designer Women Kurtas, Trendy Salwar Kameez, Leggings, Indian Ethnic Jewellery & Fashion Handbags India - Fashion Equation

Fashion Equation is one stop fashion shop for women which offers designer kurtas, ready made salwar suits, printed patiala bottoms, indian jewellery.

template, shopify

4,718,966

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Solving Education Equation | Student Academic Consulting Solution – Virtue Analytic

Virtue Analytics offers analytics tools and consultancy to higher education institutions for financial, funding and enrollment management. Schedule an appointment with our representative.

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Unizor

Unizor contains educational material to help parents and supervisors to educate their students in advanced level subjects, starting with Mathematics. Parents and supervisors can control the educational process by enrolling their students into this or that program, check their scores on exams and accept or reject their results. Unizor provides invaluable capabilities for homeschooling as well as helps motivated students in their advanced selfstudy programs.

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Nutrimark.Net

Highest Quality Nutritional Supplements, HPF Hangover Prevention Formula, Prepair Anti-Fatigue Formula, Perfect Equation Multi-vitammin/Mineral.Phyto-Nutrient Supplement

hangover, prickly, headache, remedy, pear, alcohol, hangoverprevention, cure, exhaustion, prepair, formula, prevention, perfect, equation, fatigue, supplement, multivitamin

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Being simple | Just another mathematician. E-mail: [email protected]

Just another mathematician. E-mail: [email protected]

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Practice mental arithmetic — the arithmetic game

Kopfrechnen trainieren kostenlos und werbefrei. Practice mental arithmetic online. No ads and no charge.

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BEACON | An NSF Center for the Study of Evolution in Action

By: Dr. Wenying Shou - Fred Hutchinson Cancer Research Center Sometimes in science, a seemingly straightforward journey can take an enormous amount of time. Our paper in PLoS Biology (Hart et al., 2019) was one such journey. The question seemed easy enough: for a highly simplified microbial community — a community of two yeast strains engineered to help each other or "cooperate", could we predict how fast the community might grow? If you think that this question is esoteric, it is not. Cooperation is surprisingly common in biology: pathogenic bacteria cooperate with each other to launch infections; microbes in sewage treatment sludge cooperate to break down wastes. The faster a community can grow, the more likely it will survive perturbations or advance to new territories. Ultimately, a quantitative understanding of microbial communities will empower us to control and use communities as, for example, probiotics. One remarkable aspect of this work — the very long and turbulent gestation — is invisible from the data themselves. When responding to journal reviewers' critiques, I had the urge to write down this untold story of scientific discovery. A humble dream The project started when I was a postdoc about 17 years ago. To tie biology with mathematics, I joined a physicist's lab at the Rockefeller University in New York City. I wanted to see how interacting "parts" of a biological system might generate quantitative properties of the system as a "whole". All biological systems consist of parts. For example, an ecological community consists of interacting species, and the human body consists of different cell types. A quantitative understanding of how a biological system works can be very powerful. For example, it could help us predict what would happen if we were to perturb a part. A mathematical model consists of one or more equations. An equation describes how different quantities are linked to each other. For example, how fast population size changes equals how fast new members are added through birth, minus how fast the existing members die. The growth and death rates are examples of model parameters. Back then, people had been modeling biological systems such as ecological communities, gene regulatory networks, and the cell division cycle. Some models matched data beautifully. However, the renowned mathematician and computer scientist John von Neumann once stated "with four parameters I can fit an elephant, and with five I can make him wiggle his trunk." In other words, given enough "free parameters" — parameters one could freely choose rather than being constrained by reality from experimental measurements, a model can be made to fit any data. Although a fitting model can explain data, it does not mean that the model is correct or can predict new data. To avoid the "free parameter" problem, I decided to start with a very simple system. In such a system, I should know exactly how parts interact with each other. I could then write down the equations, know which parameters need to be measured, and measure all parameters. After much deliberation, I decided to engineer a highly simplified cooperative yeast community consisting of two strains, each supplying the other with an essential metabolite. My colleagues and I thought of a lovely name for it: CoSMO — Cooperation that is Synthetic and Mutually Obligatory. Unlike real-life communities where scientists often have trouble counting the number of species, CoSMO has two and only two strains. Unlike real-life communities where species influence each other by releasing many uncharacterized chemicals, in CoSMO each strain releases only one metabolite which is required and consumed by the partner. Moreover in CoSMO, the two strains coexist due to their inter-dependence, and thus I do not need to worry about losing any one of them. Now that I know how the two strains interact with each other, it should in principle be easy to predict community properties, such as how fast the community grows — or community growth rate. Community growth rate primarily depends on two traits of each strain: the metabolite release rate and the amount of metabolite consumed per birth. Thus, modeling community growth rate boils down to measuring four parameters. This is by no means ambitious! Mission aborted I measured all four parameters. I measured the metabolite release and consumption traits of each strain in the absence of its partner. I got rid of the partner so that the released metabolites would accumulate in the test tube for me to measure, instead of being immediately consumed by the partner. However, since the partner was not present, the measurement environment (called the "batch culture" environment) differed from the community environment. For example, to measure metabolite consumption in batch cultures, I would add a high dose of metabolite at the beginning of an experiment. In contrast, in communities, the consumed metabolite is constantly supplied by the partner at a low level. Measuring strain traits in a community-like environment would require a special experimental setup. So, I had to hope that the batch culture environment could approximate the community environment. After measuring the four parameters, I predicted community growth rate. However, my prediction was way off from the experimental results. I was disappointed. In theory, a mathematical model is useful when it fails, because failure suggests that we are still missing important pieces. In reality, I was far from being thrilled by the failure, because too many pieces could be missing, even in a system as simple as CoSMO. For example, the batch culture environment might not approximate the community environment; cells could be evolving… The problem immediately becomes monstrously messy and un-elegant — a devil. Eventually, I aborted the mission. I was forced to ask whether I could explain some other community property — the minimal total cell density required for the community to start to grow. That calculation required measuring more parameters — such as cell growth rates at various metabolite concentrations. I did not have the experimental setup for such measurements, so I gave in to free parameters. I did what was, and is still, commonly done: looking for literature values. The literature values varied over an order of magnitude, so I naturally chose the value that could explain my data. I felt guilty, but comforted myself by noting that at least, the free parameter I chose was not outrageous, and that at least, the fraction of free parameters in my model was far lower than most other models. This reasoning did not exonerate me, but helped to bring a closure to my postdoc project (Shou et al., 2007). Haunted by the devil When I started my lab at the Hutch, I promptly locked up the devil in a closet. I felt caught: on the one hand, grant reviewers kept punishing me because "CoSMO is too simple", yet on the other hand, I could not even understand a very basic property of the community. My modeling failure was indeed humiliating. There was no way I could rephrase the question in an exciting fashion to attract any one, possibly even including myself. My group started working on other more sexy problems, such as how the two cooperating strains might fend off cheaters who consume but do not contribute metabolites (Momeni et al., 2013b; Waite and Shou, 2012). Despite group members' successes, the devil kept haunting me. Babak Momeni, then a postdoctoral fellow in my lab, examined spatial patterning in CoSMO when CoSMO grew on an agarose pad. When we compared patterns predicted by our model versus patterns observed in experiments, they looked similar in a qualitative sense. However, the timing looked very different. This is not surprising given that we do not understand how fast the community grows. Fortunately, dynamics was not the focus of that paper, so we erased all time stamps from our simulations (Momeni et al., 2013a). Devil breaking loose Eventually, the devil of my past failure would not allow me to ignore it any further. Chi-Chun Chen and Jose Pineda, two talented group members, were quantifying metabolite release rates of evolved cells. They wanted to see whether cells could evolve to be more "generous" by releasing more. However, Chi-Chun and Jose were getting highly variable results despite their superb experimental skills. It seemed that we got stuck when the question turned quantitative. We suspected that the variable measurement results could be due to cell traits being highly sensitive to the measurement environment. To enable measurements in a community-like environment, David Skelding — a physicist in the lab — started to build devices called "chemostats". In chemostats, nutrients were supplied at a small dose (in small drops) but frequently (every tens of seconds), mimicking partner strain's slow but constant metabolite release rate. It took David a good year or more to ensure that chemostats worked reliably and precisely (Skelding et al., 2018). Taming the devil When Sam Hart joined my lab as a research technician, he inherited the problems I, Chi-Chun, and Jose had left behind. Initially, Sam continued to quantify strain traits in batch cultures, because after all, chemostat measurements are much harder and are limited by the number of chambers. However, at some point, we realized that without getting our fundamentals on a solid footing, we would be chasing after our tails: If we do not understand the two ancestral strains (i.e. why ancestral strains' traits cannot explain ancestral community's growth rate), there is no point trying to understand evolved strains. By that time, Sam had already invested a year or two. But Sam was unflustered because he understood the importance of asking the right, albeit inconvenient, question. Sam re-measured ancestral strains' metabolite release and consumption traits in David's chemostats. By controlling how slowly metabolites were supplied, Sam could force cells to grow at various slow rates observed in CoSMO. However, chemostats introduced their own devil: because of metabolite limitation, cells from both strains quickly evolved away from their original states while adapting to metabolite limitation. Sam then figured out ways to deal with this new problem. Eventually, Sam discovered that indeed, measurements of metabolite release and consumption traits could differ significantly in chemostats versus in batch cultures. Hanbing Mi, an undergraduate visiting student from China, figured out how to properly measure community growth rate when cells could evolve quickly. Once we took all these into consideration, we solved the puzzle (Hart et al., 2019). But only partially: we still do not understand CoSMO's initial phase of slower growth. Using the same quantification methodology that we have found to be trustworthy, Sam figured out what it means to be "generous" (Hart & Pineda et al., 2019), and which mutants evolved to be more generous (manuscript in preparation). Sam is now a graduate student at the University of Washington. Summary It takes a lot to do careful science. For science to advance, it must stand on a solid foundation. By demonstrating how to properly model a very simple living system, we have helped setting the standard for future modeling of more complex systems such as probiotic communities or infectious diseases. Acknowledgements I am very grateful to my lab members, particularly Sam Hart, Hanbing Mi, Jose Pineda, Chi-Chun Chen, and David Skelding, for doing high-quality work. Hart & Pineda, Chen, Chichun, Green, Robin, Shou W. 2019. Disentangling strictly self-serving mutations from win-win mutations in a mutualistic microbial community. eLife Accepted. Hart SFM, Mi H, Green R, Xie L, Pineda JMB, Momeni B, Shou W. 2019. Uncovering and resolving challenges of quantitative modeling in a simplified community of interacting cells. PLOS Biol 17:e3000135. doi:10.1371/journal.pbio.3000135 Momeni B, Brileya KA, Fields MW, Shou W. 2013a. Strong inter-population cooperation leads to partner intermixing in microbial communities. eLife 2:e00230. doi:10.7554/eLife.00230 Momeni B, Waite AJ, Shou W. 2013b. Spatial self-organization favors heterotypic cooperation over cheating. eLife 2:e00960. doi:10.7554/eLife.00960 Shou W, Ram S, Vilar JM. 2007. Synthetic cooperation in engineered yeast populations. Proc Natl Acad Sci USA 104:1877–1882. doi:10.1073/pnas.0610575104 Skelding D, Hart SF, Vidyasagar T, Pozhitkov AE, Shou W. 2018. Developing a low-cost milliliter-scale chemostat array for precise control of cellular growth. Quant Biol 6:129–141. Waite AJ, Shou W. 2012. Adaptation to a new environment allows cooperators to purge cheaters stochastically. Proc Natl Acad Sci 109:19079–19086. doi:10.1073/pnas.1210190109

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