We consider data from the Danish twin registry and aim to study in detail how lifetimes for twin-pairs are correlated. We consider models where we specify the marginals using a regression structure, here Cox’s regression model or the additive hazards model. The best known such model is the Clayton-Oakes model. This model can be extended in several directions. One extension is to allow the dependence parameter to depend on covariates. Another extension is to model dependence via piecewise constant cross-hazard ratio models. We show how both these models can be implemented for large sample data, and suggest a computational solution for obtaining standard errors for such models for large registry data. In addition we consider alternative models that have some computational advantages and with different dependence parameters based on odds ratios of the survival function using the Plackett distribution. We also suggest a way of assessing how and if the dependence is changing over time, by considering either truncated or right-censored versions of the data to measure late or early dependence. This can be used for formally testing if the dependence is constant, or decreasing/increasing. The proposed procedures are applied to Danish twin data to describe dependence in the lifetimes of the twins. Here we show that the early deaths are more correlated than the later deaths, and by comparing MZ and DZ associations we suggest that early deaths might be more driven by genetic factors. This conclusion requires models that are able to look at more local dependence measures. We further show that the dependence differs for MZ and DZ twins and appears to be the same for males and females, and that there are indications that the dependence increases over calendar time.


Welcome to Mrs. Szako's webpage.
I am the Math Interventionist here at Nichols Sawmill Elementary. During a typical school day, you will see me working with small groups of math students and helping in the math classes. Math has always been my favorite subject and I love helping students feel more comfortable and confident in their math abilities.
This will be my twenty-nineth year in education, where I have taught math in grades first through eighth. Before I came to NSE in 2012, I was a kindergarten through twelfth grade Math Specialist for Education Service Center Region 6 in Huntsville. I earned my bachelor's degree in Elementary Education in 1989 and my master's degree in Curriculum and Instruction in 2012 both from SHSU.
Ralph, my husband of seventeen years, and I have a son, Brody who is sophomre at MWHS this year. During our free time, my family enjoys watching baseball and fishing. Brody plays competitive baseball year round which keeps the family very busy.
If you have any questions, please feel free to email me at email@example.com or call me at 281-252-2133.


Springs Charter Schools has developed boxed set lesson plans for grades K-8 that offer multi-sensory and multi-media choices for students and parents to acquire essential skills. Each of the grade levels consists of weekly pacing guides, daily lessons, carefully chosen curriculum for the core subjects, and fun supplemental lessons to enrich your school experience. Your Education Specialist is here to support you in choosing the correct curriculum level and in enriching your school year with school-wide events, field trips, and learning center classes.
K – 2nd grades combine the well known Five in a Row series and All About Reading to create a balanced reading program of daily skills and literature based lessons integrating Science, Social Studies, Art & Music, and Geography. You can build math fluency and number sense in these early years with Right Start Math or Harcourt Math.
3rd – 8th grade blends carefully selected core curriculum, including 6+1 Traits of Writing and Daily Grammar Review, along with supplemental lessons and Novel Units to achieve current grade level expectations. The math options vary by grade level using Saxon, CGP, Harcourt and our own SCS developed Spring Into Math courses (grades 6 & 7 only).
As always, box set lesson plans are able to be modified and are meant to be a flexible tool to free you, the parent, up to focus your time and energy on teaching rather than designing school curriculum. We have done the work for you! Enjoy your school year.
Click here to learn more about the Math Path options. This Springs created path will help lead your child to math success!


A North Carolina man's love for math ending up winning him more than just good grades in school — he was the lucky winner of a nearly $200,000 lottery jackpot.
Jonathan Ruby, of Raleigh, recently tried his luck in the Cash 5 lottery games, purchased a $1 ticket from the Han-Dee Hugo's on Hillsborough Street for the Nov. 28 drawing, according to a release from the NC Education Lottery. The lover of math used a well known number — pi, or 3.1415 — to choose his ticket, a move that ended up winning him a third of the $578,823 jackpot, splitting the prize with two other lucky winners.
"I've always been an extremely big math person," said Ruby. "I picked my numbers based on pi."
Ruby told lottery officials that the lucky sequence has shown up in different ways throughout his life, so he took it as a sign to get his ticket.
"I kept seeing that number so my karma told me to use it," he said. "I even lived at a 314 address as a child."
Ruby had a good feeling about his ticket, sure that he had won something, but it wasn't until later that he realized just how lucky he was.
"I thought I won a dollar or two," Ruby said. "I was calm until I got home and checked the numbers and then I got very excited."
Ruby claimed his $192,941 jackpot at lottery headquarters on Monday (May 9), bringing home a total of $137,012 after taxes. When asked what he plans to do with his prize, the 64-year-old bartender told lottery officials he plans to pay some bill and save the rest for retirement.


The MSc Programme in Finance is a two-years course delivered entirely in English on financial applications, models and solutions from corporate, economic and quantitative perspectives. The programme covers the most important technical and quantitative aspects of finance in regular use in financial institutions.
The MSc in Finance program is intended to prepare students for a wide range of careers both inside and outside the financial industry, including advanced corporate finance, financial engineering and risk management, quantitative asset management, macroeconomic and financial forecasting, quantitative trading, and applied research.
This programme is dedicated to students who have a first degree (or equivalent) in economics or in subjects providing quantitative and financial skills.
The MSc in Finance will provide knowledge in three main fields:
- Quantitative Area. Students study in deep the methods used in financial markets to price financial securities: basic principles of stochastic calculus, no-arbitrage principle and risk neutral (martingale) pricing, derivatives pricing, interest rate derivatives, stochastic volatility models, financial econometrics.
- Economic Area. Students are exposed to the theoretical framework of modern financial economics: microeconomic models for business and finance, models with asymmetric information and decision under uncertainty, monetary economics and central banking approaches;
- Management Area. Our fundamental courses will provide the knowledge to study financial behaviour of financial and non-financial firms and financial markets.
Moreover, regulation of financial markets will be analysed in order to learn how financial players are subject to regulation constraints.
The programme provides several international mobility programs at qualified European (Erasmus), North American and Australian universities, as well as double degree programs with the European Business School (Frankfurt) and the University of Ljubljana. More double degree agreements are in progress.
Admission requirements depend upon the first level degree obtained by the student:
- Degree in business or economics: at least 12 ECTS (or equivalent) in mathematics for economics and finance and at least 8 ECTS in finance or corporate finance.
- Degree in science (including mathematics) or engineering: at least 18 ECTS (or equivalent) in mathematical methods and at least 8 ECTS in finance or corporate finance or, alternatively, at least 8 ECTS in financial mathematical modelling.
- Other degrees: at least 30 ECST (or equivalent) in economics, at least 8 ECTS in finance or corporate finance, at least 30 ECTS in mathematical methods. A final first level degree grade of at least 100/110 is also required.
All applicants must have English language skills at least at level B2 of the Common European Framework of Reference for Languages (CEFR), as well as computer skills at least equivalent to the ECDL core.
CAREER OPPORTUNITIES IN
Financial intermediation companies
Auditing and consulting
PROFESSIONAL PROFILES OF GRADUATES
Financial market analyst
Trader in financial markets
Manager in financial firms
Financial officer in non-financial firms
Componenti del Comitato per la Didattica:
- Prof. Giampaolo Gabbi
- Prof.ssa Costanza Consolandi
- Prof. Claudio Pacati
- Prof. Roberto Renò
Referenti Amministrativi dei Comitati per la didattica
- Sig.ra Elisabetta Bottiglioni
- Dott.ssa Carla Galardi


goal of this unusual game is not so unusual: it is to collect most points. There are 8 rounds
and in each of these rounds point cards are distributed. There are 8 tricks in each round. The
special features of this game are that each player takes exactly 2 tricks per round and a player
can secure a trick by calling "Meinz". At the end of a round, it is the sum of the numbers in each
player’s two tricks that determines the outcome of the round.


You can dive straight into using it or read on to discover how it works. In this article, we explain the arithmetic sequence definition, clarify the sequence equation that the calculator uses, and hand you the formula for finding arithmetic series sum of an arithmetic progression.
Sequences are useful in a number of mathematical disciplines for studying functionsspacesand other mathematical structures using the convergence properties of sequences. In particular, sequences are the basis for serieswhich are important in differential equations and analysis.
Sequences are also of interest in their own right and can be studied as patterns or puzzles, such as in the study of prime numbers.
There are a number of ways to denote a sequence, some of which are more useful for specific types of sequences. One way to specify a sequence is to list the elements. For example, the first four odd numbers form the sequence 1, 3, 5, 7. This notation can be used for infinite sequences as well.
For instance, the infinite sequence of positive odd integers can be written 1, 3, 5, 7, Listing is most useful for infinite sequences with a pattern that can be easily discerned from the first few elements. Other ways to denote a sequence are discussed after the examples.
Examples[ edit ] A tiling with squares whose sides are successive Fibonacci numbers in length. The prime numbers are the natural numbers bigger than 1 that have no divisors but 1 and themselves. Taking these in their natural order gives the sequence 2, 3, 5, 7, 11, 13, 17, The prime numbers are widely used in mathematics and specifically in number theory.
The Fibonacci numbers are the integer sequence whose elements are the sum of the previous two elements. The first two elements are either 0 and 1 or 1 and 1 so that the sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, Other examples of sequences include ones made up of rational numbersreal numbersand complex numbers.
In fact, every real number can be written as the limit of a sequence of rational numbers, e. This sequence does not have any pattern that is easily discernible by eye, unlike the preceding sequence, which is increasing. One such notation is to write down a general formula for computing the nth term as a function of n, enclose it in parentheses, and include a subscript indicating the range of values that n can take.
For example, in this notation the sequence of even numbers could be written as.In this example, to get from the position to the term, take the position number and add 4. If the position is, then the position to term rule is.. The nth term.
The th term of a sequence is the. th Term Rule Nth term rule – the equation that allows you to find any term in the sequence T n – the term in the “nth” position n – the position of the term of a sequence a Write an nth term rule for the following sequences. a. 11, 13, 15, 17, b. 5, , ,, .
The following geometric sequence calculator will help you determine the nth term and the sum of the first n terms of an geometric sequence. Guidelines to use the calculator If you select a n, n is the nth term of the sequence.
Write the equation for the nth term in a sequence using your newly found coefficients. Example: nth term in the sequence = n^3 + 2n^2 + 3n + 5 Plug in your desired value of n into the equation and calculate the nth term in the sequence. Write a rule for the nth term of the arithmetic sequence - 1.
Log in Join now 1. Log in Join now Secondary School. Math. 13 points Write a rule for the nth term of the arithmetic sequence Advertisement Ask for details ; Follow Report by Ramchandran Log in .
Two terms of an arithmetic sequence are a 8 = 21 and a 27 = Find a rule for the nth term. SOLUTION STEP 1 Write a system of equations using a n = a.


Mortgage Loan Calculator (PITI) Use this calculator to generate an estimated amortization schedule for your current mortgage. quickly see how much interest you could pay and your estimated principal balances. You can even determine the impact of any principal prepayments! Press the "Report.
Here’s how car loan payments are calculated, as well as a calculator that can do the hard part for you. How your car payment is determined (Loan Amortization 101) There are three major factors that.
Easily generate monthly and yearly amortiztion schedules for a proposed loan with our loan amortization calculator.
On your amortization calculator, your Continuous Amortization appears to be wrong in the sense that principle and interest do not continually increase and decrease respectively as well as the payment being completely wrong. I reworked the equations and found the expected results for both payment at the beginning of the loan and in arrears.
A loan calculator is a simple tool that will allow you to predict how much a personal loan will cost you as you pay it back every month. It’s quite simple: You provide the calculator with some basic information about the loan, and it does the math and spits out your monthly payment..
Loan Calculator Bankrate The mortgage calculator with taxes and insurance estimates your monthly home mortgage payment and shows amortization table. The loan calculator estimates your car, auto, moto or student loan payments, shows amortization schedule and charts.
This mortgage / amortization schedule calculator helps to find out the amortization schedule and rates for your loan in table / chart format for your annual, semi annual, monthly payments. Amortization is the process of gradually reducing a debt through installment payments of principal and interest.
For the full mortgage Rate Trend Index, go to http://www.bankrate.com/news/rate-trends/mortgage.aspx. To download the Bankrate Mortgage Calculator & Mortgage Rates iPhone App 2.0 go to.
Farm Credit Amortization Schedule Determines how to meet those needs and discusses the loan structure, including interest rates, collateral, amortization, payment schedule, etc., to optimize the outcome for the customer and farm credit illinois identifies loan opportunities ; credit analysis. 360 180 loan At the end of your loan term you will need to pay off your outstanding.
but government-backed loan programs may allow a higher percentage. NerdWallet’s prequalification calculator looks at back-end DTI while also considering other aspects of your credit profile, such as.
"Quick Federal Tax Calculator" for individual and corporation income tax; a simple loan amortization calculator based on monthly payments; a. As an example, let’s say you obtained a $250,000 30-year mortgage five years ago, and that your interest rate was 5.5%. According to an amortization calculator from Bankrate.com, your monthly.


Statistics Decision Tree
Complete the form below to find out what test you need to run. This is not a comprehensive statistical test repository. It can only tell you about the most common and basic statistical tests, such as, ANOVAs, Chi Squared, and t-tests. If you are making predictions or are comparing samples to a population, please go to the "Making Predictions & Comparisons section" further down on this page. Note: If you recieve a notice of "You should run a Unknown", please consult an advanced statistics book.


Bra Size Calculator
Formulae To Calculating Bra Size
|Breast Size = A
|Chest Size = B
A – B = Bra Size
Calculating Breast Cup Size
- Measure Your Chest: Using a tape measure, work out the length of just under your breasts, where the band of a bra would usually fit. When finding out the measurement of your chest you need to round this to the nearest inch.
- Measure Your Breasts: Applying the exact same method as above to your breasts will then give you your answer to this. Don’t forget to round it to the closest inch.
- Cup Size Calculation: Once you have got these two numbers you need to subtract your chest size from your breast size, this is your bra size. Once you have calculated this you can take a look at our table below to see where you are.


Objective of the course – aims of the course unit:|
The objecive of the course is to expand knowledge in the area of statistical tests and data sample processing, mastering the basics of operations research including the appplications in electrical engineering with the use of mathematical software.
Objective of the course – learning outcomes and competences:|
Ability to solve optimization and statistical problems from technological practice. Solving problems with the use of modern mathematical software.
The knowledge of the Bachelor´s and Master's degree level courses is requested.
Course contents (annotation):|
The course i s composed of three thematic units of common basis:
1) Probability and statistical processing of data, basic statistical tests and the possibilities of their use.
2) Characteristics of stochastic processes, Markov chains, staionary and ergodic processes.
3) Linear programming, transportation problem. Dynamic programming, models of stack resourses.
Teaching methods and criteria:|
Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.
Assesment methods and criteria linked to learning outcomes:|
Requirements for completion of a course are specified by a regulation issued by the lecturer responsible for the course and updated for every.
I. Statistics (5 weeks)
Basic notions from probability and statistics. Statistical sets. Point and interval estimates.Testing hypotheses with parametres (not only for normal distribution). Tests of the form of distribution. Regression analysis. Tests of good accord. Non-parametric tests.
II. Stochastic processes(4 weeks)
Deterministic and stochastic problems. Characteristics of stochastic processes. Limit, continuity, derivation and integral of a stochastic process. Markov, stationary, and ergodic processes. Canonical and spectral division of a stochastic process.
III. Operation analysis (4 weeks)
Principles of operation analysis, linear and nonlinear programming. Dynamic programming, Bellman principle of optimality. Theory of resources. Floating averages and searching hidden periods.
Specification of controlled education, way of implementation and compensation for absences:|
The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year. The student will be able to sit the exam only after a successful solution of a project has been presented.
Montgomery, D.C., Runger, G.C.: Applied Statistics and Probability for Engineers.
Third Edition. John Wiley \& Sons, Inc., New York 2003.
Miller, I., Miller, M.: John E. Freund's Mathematical Statistics. Sixth Edition. Prentice
Hall, Inc., New Jersey 1999. Předchozí vydání publikováno pod názvem Freund, J.E.:
Mathematical Statistics, Fifth Edition.
Taha, H.A.: Operations research. An Introduction. Fourth Edition, Macmillan Publishing Company, New York 1989.
Anděl, J.: Statistické metody. Matfyzpress, MFF UK Praha, 1993.
Zapletal, J.: Základy počtu pravděpodobnosti a matematrické statistiky. PC-DIR,VUT, Brno, 1995
Papoulis, A.: Probability, Random Variables and Stochastic Processes, McGraw-Hill, 1991.
Nagy, I.: Základy bayesovského odhadování a řízení, ČVUT, Praha, 2003
Škrášek, J., Tichý, Z.: Základy aplikované matematiky III. SNTL Praha, 1990


Thomas Yizhao and Chang Hou
Thomas Yizhao Hou is the Charles Lee Powell professor of applied and
computational mathematics at Caltech. He is one of the leading experts
in vortex dynamics and multiscale problems. His research interests are
centered around developing analytical tools and effective numerical
methods for vortex dynamics, interfacial flows, and multiscale problems.
He got his BA degree from South China University of Technology in 1982,
received his Ph.D. from UCLA in 1987, and joined the Courant Institute
as a faculty member in 1989. He moved to Caltech in 1993 and was named
the Charles Lee Powell Professor in 2004. Dr. Hou has received a number
of honors and awards, including Member of American Academy of Arts and
Sciences in 2011, an inaugural Fellow of Society of Industrial and
Applied Mathematics (2009) and Americal Mathematical Society (2012), the
Computational and Applied Sciences Award from US Association of
Computational Mechanics in 2005, the Morningside Gold Medal in Applied
Mathematics in 2004, the SIAM Wilkinson Prize in Numerical Analysis and
Scientific Computing in 2001, the Frenkiel Award from the Division of
Fluid Mechanics of American Physical Society in 1998, the Feng Kang
Prize in Scientific Computing in 1997, a Sloan fellow from 1990 to 1992.
He was also the founding Editor-in-Chief of the SIAM Journal on
Multiscale Modeling and Simulation from 2002 to 2007.
Yu-Chung Chang (Ph D, Mathematics) is currently an assistant professor in the Mathematics Division at Pasadena City College. Some of Dr. Chang’s professional interests are the theory and practice of Mathematics Problem Solving, and basic skill issues and strategies. One of her main efforts has been to use reading and writing to help students to understand Math problem solving and motivate their interests in studying Mathematics. She has participated in Service Learning, Writing Across Curriculum, and Reading Apprenticeship Group, led the FIG 3 (Faculty Inquiry Group for Intermediate Algebra), given Student Learning Outcomes Workshops on her case study WRAMPS (Writing and Reading Activities for Math Problem Solving), initiated Common Final Exams for Developmental Math, and organized an Algebra Learning Outcomes Workshop on faculty development for student success. The courses she has taught include Prealgebra, Beginning Algebra, Intermediate Algebra, College Algebra, Trigonometry, Precalculus, Calculus, Differential Equations and Linear Algebra.
Dr. Chang initiated Common Final Exam for Intermediate Algebra to help students achieving minimum standards before continuing transferable courses in 2007. She also started Pi Day Student Conference to encourage student ownership of Math learning in 2012.
Dr. Chang’s publications include “Eulerian Capturing Methods Based on a Level Set Formulation for Incompressible Fluid Interfaces” in Journal of Computational Physics, Vol. 124, pp. 449-464, (co-authored with T. Y. Hou, B. Merriman, and S. Osher, 1996), “How Writing and Reading Have Helped my Students to Achieve Critical Thinking SLOs in Mathematics” in SLO Newsletter, Pasadena City College, May 2006, and “No Longer Lost in Translation: How Yu-Chung Helps Her Students Understand (and Love) Word Problems” for the Advancement of Teaching website Windows on Learning of Carnegie Foundation.


It's a 4 player game, though I'm sure you could always use a little toy (maybe a Lego?) as a place marker if you wanted to play with a 5th person. There are 3 dice: two green dice with numbers 1-6, and 1 white operations die. There are also 4 player pieces are a rubbery material, so they won't slip out of little fingers. They are all swamp critters: a red snail, an orange alligator/crocodile, a purple dragonfly, and a green frog.
The game play is simple: You roll all 3 dice, and perform the addition or subtraction they create. You always subtract the smaller number from the larger number.
|This turn shows a roll that would be 5 - 2, so the player would move 3 spaces|
If you land on a stone that has a number on it, you roll the white operations die. If it is a +, you move forward the number on that stone. If it is a -, you would move backwards that same number. If you land on a stone that says "odds" or "evens", you roll a green number die. If the number that turns up is matches the stone you are on (so an even number for a stone that says "evens"), you move forward the number rolled. If you rolled an odd number when you landed on an "evens" stone, you simply stay where you are and it's the next person's turn.
The "endless loop" near the right side of the board is the only thing we alter the rules on. Players are supposed to land on the "exit" stone before they may exit the circle on their next roll. We play that once the first person actually exits, then everyone else may leave as well. The reason for this change is because it is so close to the end of the board that the first person out will almost always win without anyone else getting out of the loop. It would be better placed in the center of the board for that reason.
Bobble already enjoyed math before this game, but he didn't quite understand subtraction. Thanks to this game, he has become a wiz at subtraction as well as addition.
When this game gets boring for him (when his skills far surpass this game), I plan on introducing him to negative numbers, and letting him subtract the numbers in the actual order they land (making him go backwards spaces if it ends up being a negative number). This will keep the game fun for much longer!
Reading is not required for this game (pretty sure any child would quickly recognize the difference of the word "even" and "odd" and memorize which is which, even if they cannot read). Recognition of the numbers 1 through 6 are needed. Though you need to recognize which numbers (1-6) are even or odd, this is a skill they can learn while playing and not needed before hand.
Sum Swamp can be purchased at select retailers for about $20.
Disclaimer: Thoughts of Fluff is responsible for the content of this post. All opinions are my own and may differ from those of your own.


ML | K-Medoids clustering with solved example - GeeksforGeeks
May 17, · Step 1: Let the randomly selected 2 medoids, so select k = 2 and let C1 - (4, 5) and C2 - (8, 5) are the two medoids. Step 2: Calculating cost. The dissimilarity of each non-medoid point with the medoids is calculated and tabulated: Each point is assigned to the cluster of that medoid whose dissimilarity is less.
101 Machine Learning Algorithms for Data Science with
The algorithms have been sorted into 9 groups: Anomaly Detection, Association Rule Learning, Classification, Clustering, Dimensional Reduction, Ensemble, Neural Networks, Regression, Regularization. In this post, you'll find 101 machine learning algorithms, including useful infographics to help you know when to use each one (if available).
Machine Learning - Quick Guide - Tutorialspoint
Let us now discuss one of the widely used algorithms for classification in unsupervised machine learning. k-means clustering. The 2000 and 2004 Presidential elections in the United States were close — very close. The largest percentage of the popular vote that any candidate received was 50.7% and the lowest was 47.9%. If a percentage of the
NBA Data Analysis Using Python & Machine Learning | by
Jun 30, · NBA Data Analysis Using Python & Machine Learning. randerson112358. Jun 30, · 9 min read. Explore NBA Basketball Data Using KMeans Clustering. In this article I will show you how to explore data and use the unsupervised machine learning algorithm called KMeans to cluster / group NBA players. The code will explore the NBA players from
170 Machine Learning Interview Questions and Answer for
Jan 18, · 170 Machine Learning Interview Questions and Answer for . A Machine Learning interview calls for a rigorous interview process where the candidates are judged on various aspects such as technical and programming skills, knowledge of methods and clarity of basic concepts.
Clustering in Machine Learning - GeeksforGeeks
Jan 15, · Clustering Methods : Density-Based Methods : These methods consider the clusters as the dense region having some similarity and different Hierarchical Based Methods : The clusters formed in this method forms a tree-type structure based on
Machine Learning - Artificial Neural Networks
Machine Learning - Artificial Neural Networks. The idea of artificial neural networks was derived from the neural networks in the human brain. The human brain is really complex. Carefully studying the brain, the scientists and engineers came up with an architecture that could fit
Machine Learning for Data Analysis | Udacity
Aug 07, · Machine learning constitutes model-building automation for data analysis. When we assign machines tasks like classification, clustering, and anomaly detection — tasks at the core of data analysis — we are employing machine learning. We can design self-improving learning algorithms that take data as input and offer statistical inferences.
Agglomerative Methods in Machine Learning - GeeksforGeeks
4 rows · Feb 01, · The minimum value is 0.13 and hence we combine P3, P6 and P4. Now, form the clusters of elements
Machine Learning Tutorial for Beginners: What is, Basics of ML
Machine Learning is a system of computer algorithms that can learn from example through self-improvement without being explicitly coded by a programmer. Machine learning is a part of artificial Intelligence which combines data with statistical tools to predict an output which can be used to make actionable insights.
Classification And Clustering - XpCourse
Clustering and classification are machine learning methods for finding the similarities - and differences - in a set of data or documents. These methods can be used for such tasks as grouping products in a product catalog, finding cohorts of similar customers, or aggregating sets of documents by topic, team, or office.
Machine learning 4 kids Courses (46 New Courses
Machine Learning For Kids. Machine Machinelearningforkids.co.uk All Courses . 7 hours ago An educational tool for teaching kids about machine learning, by letting them train a computer to recognise text, pictures, numbers, or sounds, and then make things with it in tools like Scratch.. Website: https://machinelearningforkids.co.uk/ Category: Best online machine learning course 37 Used Show more
Top 40 Machine Learning Interview Questions & Answers
Aug 04, · 6. What is clustering in Machine Learning? Clustering is a technique used in unsupervised learning that involves grouping data points. If you have a set of data points, you can make use of the clustering algorithm. This technique will allow you to classify all
Machine Learning for Software Engineers - Learn Interactively
If you're a software engineer looking to add Machine Learning to your skillset, this is the place to start. This course will teach you to write useful code and create impactful Machine Learning applications immediately. From the start, you'll be given all the tools that you need to create industry-level machine learning projects. Rather than reading through dense theory, you'll learn
Machine Learning Concepts - Rubiscape Concept Dictionary
Machine Learning Algorithms. Machine learning algorithms are mathematical and logical programs which, when exposed to huge amount of data, can self-adjust to perform more efficiently and accurately. When an algorithm receives feedback on its previous output, it adjusts its parameters indigenously to perform better.
Machine Learning Tutorial Python -1: What is Machine
What is Machine Learning? This is an introduction to machine learning to begin the python machine learning tutorial series. This video describes what is mach


Ilse Nijensteen is a second year master student in Geoscience & Remote Sensing at Delft University of Technology. This master is about modelling, data analysis and data processing in the context of geosciences. She already completed bachelors in Applied Mathematics and Physics. As a part of her master, she is now a trainee at Weather Impact, contributing to the development of the ‘Waarschuwing voor WaterOverlast’ (W2O) project. This innovative service will use a combination of satellite data, weather predictions, hydrological models and algorithms to make better flooding predictions.


Sample size calculator for two sample t test
Assuming two independent groups and a Normally distributed measurement, how many observations are needed to detect the difference that you specify, at the power that you specify, with the type I error rate that you specify?
The minimum required sample size per group is:
Histograms of how the data might look (if your measurement follows a Normal distribution):
The small superimposed curves show the sampling distribution of the group means, using the recommended sample size given above. The power and type I error rate dictates how much these curves should overlap, and the sample size controls how "peaked" or "flat" they are.
If you increase the SD the curves are "flatter" and therefore overlap more; N increases to compensate
If you increase the difference in means, the curves are further apart; N decreases to compensate.
Please e-mail me with issues, bugs, or feature requests


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Counting money is the next step when students know basic monetary values and can use skills like skip counting to figure out how many bills add up to a particular dollar value. The worksheets on this page start with a certain number of specific bills, then progress to mixed bills and finally to combinations of bills with coins.
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Here, you will find free phonics worksheets to assist in learning phonics rules for reading. These free worksheets are printable and designed to accommodate any lesson plan for reading that includes phonics. Conveniently organized by the skills covered, these worksheets come with answer keys. Feb 10, 2017 · Worksheet 2. Worksheet 2 Addition and Subtraction of Money. Worksheet 3. Worksheet 3 Addition and Subtraction of Money . Worksheet 4. Worksheet 4 Addition and Subtraction of Money
Money Worksheets with solutions and Printables, A collection of money games that teach or Money Worksheets and Printables. We have added some free games that can be played on PCs, Tablets...
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Money Worksheets. Want to help support the site and remove the ads? Become a patron via patreon or donate through paypal. Each worksheet has 5 problems finding the sum of the money shown.
Money. Level. Low to mid-intermediate. Time. 90 minutes. Materials. Lesson plan: guide for teacher on procedure including worksheet tasks Download lesson plan 24 kb. Worksheets: five downloadable worksheet exercises Download worksheets 21 kb. The plan and worksheets are downloadable and in pdf format.
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The rounding money worksheet maker creates worksheets from a randomly generated set of values. Randomly generating the numbers allows you to create multiple worksheets without repeating the same problems. You can simply select the number of problems that you want on the worksheet and the type of rounding that you want the student to do. Use this worksheet to weigh needs versus wants, and to evaluate how these fit into your budget. WORKSHEETS. Managing Your Money. A worksheet to help you control your spending.Money Worksheets. Money worksheets are an excellent resource for parents and teachers teaching kids about money. Check our JumpStart's collection of free and printable money worksheets for kids.
Help your teenager organize his expenses and save his money with this FREE teen budget worksheet. Download the worksheet and save it to your desktop. Your teen can type in his monthly expenses and income, and the worksheet will calculate his budget
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Displaying top 8 worksheets found for - Money Management Skills. Some of the worksheets for this concept are S134g essential living skills money management, Module 1 money home and food management, A guide to money management for people with disabilities, Budget module wd, Money station curriculum guide sample, Effective strategies for personal money management, The complete money workbook ...
Here, you will find free phonics worksheets to assist in learning phonics rules for reading. These free worksheets are printable and designed to accommodate any lesson plan for reading that includes phonics. Conveniently organized by the skills covered, these worksheets come with answer keys.
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Money Worksheets provides FREE math printable note and coin money worksheets for learning and study. Kindergarten money worksheets, money games, change worksheets and more!Facebook Twitter Pinterest If your kids need some help learning about money you should check out this free printable packet. This free printable pack has tons of fun money activities. There are 25 pages with 3-part cards, matching activities, handwriting and games, it hardly feels like math at all. Your kids will really feel likeRead More
Money Worksheets. This set also includes fun money worksheets with all kinds of activities to practice coin recognition, both heads and tails. It covers the value of coins from pennies to quarters. Here’s a quick peek at some of the money worksheets in this set. Time Worksheets. Time worksheets also come with this set.
Use this worksheet to weigh needs versus wants, and to evaluate how these fit into your budget. WORKSHEETS. Managing Your Money. A worksheet to help you control your spending.
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Oct 21, 2019 · This money themed activity is a great way to sneak in some coin recognition to supplement your pre k, kindergarten, and first grade students. Whether you are a parent, teacher, or homeschooler – you will love this money activity and money worksheet to add to your farm them, math center, extra practice, or summer learning. Kindergarten Money
Aug 30, 2013 · Identify Coin Values with Free Printable Money Worksheets One of the most popular worksheets we have is the sheet that teaches children how to identify coin values . By clicking on the link, you can see that the sheet is in full color with extremely accurate depictions of the quarter, nickel, dime and penny.
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Over 200 Scholastic Teachables' Free Printable Worksheets span a variety of subjects and topics from Pre-K through Grade 8. Sign up today, and you'll have access to Scholastic's more than 30,000 award-winning printables for all subjects and grades, including worksheets, lesson plans, practice pages, and more.
1 day ago · Money worksheets printables understanding how math intersects with money is at the heart of our money worksheets. Print as many of these free printable money worksheets as you will need. These free printable pdf money worksheets cover topics appropriate for early grade kids who are learning how to identify count and compare physical money.
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Money Worksheets provides FREE math printable note and coin money worksheets for learning and study. Kindergarten money worksheets, money games, change worksheets and more!View U.S. Money worksheet (1).pdf from ECON 101 at LIM College. U.S. Money Quiz: Eow Well Do You Know Your Money? 1. When did the first printing of U.S. cuffency occur? 2. What was the first U.S.
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Your kids from Kindergarten up through sixth grade will love using these math worksheets. New math workbooks are generated each week to make learning in the classroom fun. Word problems are emphasized for a deeper understanding of how math works, along with reinforcing basic math facts.
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Print this worksheet and fill out the expenses and income sections to see if you have a realistic budget. Multiply the monthly amounts by the number of months you'll have the expense to get a yearly amount for each category. Money Adding Worksheets Adding Money Worksheets will teach children of all ages how to add money together. *Numbers in the sheet link names indicate how many coins need to be added together per line* Money Add 3A Worksheet Money Add 3B Worksheet Money Add 3C Worksheet Money Add 4A Worksheet Money Add 4B Worksheet
Money Worksheets and Resources. Printable math worksheets that help students learn how to count and use money. We work on basic operations and word problems with various denominations of currency. We include skills with the American and Canadian Dollar. We also include Euros. Counting Money
Money word problems #3 In this money math worksheet, your child will solve word problems that involve doing addition and subtraction with dollars and cents. MATH | GRADE: 2nd, 3rd Displaying top 8 worksheets found for - Money Management Skills. Some of the worksheets for this concept are S134g essential living skills money management, Module 1 money home and food management, A guide to money management for people with disabilities, Budget module wd, Money station curriculum guide sample, Effective strategies for personal money management, The complete money workbook ...
Counting money worksheets teachers can print for free to help students in first grade count money. Find here some good counting money worksheets that can help students learn how to count money.
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This money management worksheet allows you or someone close to you to locate your financial accounts. For anyone who has ever had to execute a will, not knowing where to locate money or who...Facebook Twitter Pinterest If your kids need some help learning about money you should check out this free printable packet. This free printable pack has tons of fun money activities. There are 25 pages with 3-part cards, matching activities, handwriting and games, it hardly feels like math at all. Your kids will really feel likeRead More
L'infâme Ratty et son gang sont sur le point de cambrioler la Banque de Grande Bretagne. La police n'en sait rien. Spycat le chat espion pourra-t-il arrêter Ratty à temps?
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Money ESL Worksheets. Elementary (A1-A2). Pre-intermediate (A2). Intermediate (B1). Easy Money. ESL Money Worksheet - Reading, Matching and Writing Activity - Elementary (A1-A2) - 30 minutes.
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Americans can leave 2020 money in their FSAs and Dependent Care FSAs and spend it in 2021 if the stimulus bill is signed into law. Dec. 24, 2020 at 11:03 a.m. ET by Alessandra Malito Feb 19, 2017 · grade 3 maths worksheets word problems on money. Word Problems on Money These Grade 3 Worksheets have answers also given in the downloadable links below.
See more ideas about money worksheets, worksheets, money math. Here is a selection of printable money worksheets to help kids learn to count up money amounts and solve money...
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Grade 3 Money Math Worksheets. Choose category of money math worksheets you wish to view below.
Your Money Makeover: Budgeting Worksheet Total Spendable Income minus Total Expenses Homeowner’s Association, Fitness, etc. Set money aside each month for annual expenses Set money aside each month for future and/or unexpected expenses
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Free Printable Money Worksheets Are Ideal . The free money worksheets that we offer are of high quality. You don’t want to miss out on getting them for your class or for your own children. They truly make learning more fun, and your kids or students will appreciate that a lot. Change Money Worksheets. This is a fantastic bundle which includes everything you need to know about change money across 28 in-depth pages. These are ready-to-use Change Money worksheets that are perfect for teaching students about the calculating change money which is a very important skill and will be used in all parts of life.


Custodian of Policy: Registrar
Relevant Minnesota State System Policy: Minnesota State System Policy 3.3Relevant Procedures: Minnesota State System Procedure 3.3.1Effective Date: Spring 2020Last Review: Fall 2016Next Review: Fall 2022
English Placement Policy
In order to be considered valid for placement purposes, ACT/SAT scores and ACCUPLACER scores must have been earned within five years from the start of the class. High school GPA must be within the last ten years. The English Placement policy will be reviewed every two years.
English Placement for International Students who do not have English as their first language.
Math Placement Policy
Two sets of Accuplacer placement scores are available:
ACT Math and SAT Math Scores Comparison: ACT 19 = SAT 510; ACT 22 = SAT 540; ACT 23 = SAT 560; ACT 24 = SAT 580.
ACT, MCA and SAT scores are valid for 5 years. Accuplacer scores are valid for 2 years.
*MCA, Minnesota Comprehensive Assessment, Mathematics score will be used for only MATH105, MATH134, and MATH127 placement.
The purpose of this policy is to improve student success in college and university courses through student assessment and course placement that addresses reading comprehension, written English, and mathematics knowledge and skills.


Evil Shaunevil is in the house!
This weekend, I'm proving everyone wrong, EVERYONE!
Ever since I've moved into my new place, my talk of throwing a baseball from my balcony onto the roof of the office building across the street has been ridiculed. Due to the possibility of me going over the edge of my glass balcony while throwing a ball, I've decided to no longer attempt my throw of a baseball.
Instead, I brought up the idea of sling-shotting a small rubber ball onto the roof of the building. Again, the idea was shot down.
"No way, it's impossible..."
"Can't be done Shaun..."
"You might hit the side of the building but it's not landing on the roof"
"Are you retarded?"
Well. Fuck all of y'all doubters. I did the math. An average street lane is 12.6 feet in width. The distance from the base of my building to that building is about 23 car lanes across (What? You actually thought I'd stand outside with a frigging yard stick measuring? Gimme a break. This is 2006 son. I'm fucking smart...
That works out to about 290 feet. Anyone know the distance from left field to home place on a baseball diamond? The field I played at as a kid was 300 feet. My slingshot should clear 300 feet with no problem!
To add heights into equations I'm on the 29th floor -- about 348 feet high -- shooting down onto a building that's probably about 200 feet lower than I am now. My shot should be about 145 feet higher than I am now (~500 feet) at about 145 feet out assuming I fired my shot at a 45 degree angle and that the shot had just enough energy to go the 290 feet.
For simplicity we won't tack on gravity, coefficient of drag, wind velocity, etc etc. Yes, yes, all those goodies. This ain't school!
See equation above, but please note, I botched a number on the left for all you math correcters out there so the trajectory shown beyond the 290 ft isn't correct or to scale (And if you're correcting my scribble of a equation that took me two seconds, you're lame... ) .. and all you high school / college drop out types who have no idea what an equation is, I didn't forget you guys: Click here, for something you can understand.
I got this one kids, I got this one.
How could I miss? Start placing your bets cuz I'm taking all your money! This is EASY... and for my next trick... ahh there's no next trick.. I've got a date! I'm out...
Above: The distance my "shot" must travel. Piece of cake!
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Calculator for the optimal diameter of a diseased bi/tri-furcation
When stenting a diseased artery segment in a bifurcation or trifurcation, it is important to ensure diameters that will achieve optimal blood flow to prevent risks of restenosis. The interface below allows the determination of the optimal diameter for a diseased segment knowing the diameters of the other two or three segments in a bifurcation or trifurcation, respectively.
Do you want to calculate the optimal diameter of a diseased segment in a bifurcation or a trifurcation?
Provide the units used for the diameters:
Enter two of the three available diameters:
Dm - Diameter of the mother segment
D1, D2 - Diameter of the daughter segments


WINTER 2021 LESSON STUDY
Cultivating students' confidence in math discussions
How can we cultivate students’ confidence in math discussions and group work so they are willing to share their thinking and support one another?
THEORY OF ACTION
If we as teachers provide students with UDL structures such as sentence stems, group work roles, and multiple modes of access to communication (chat, sharing screen, using pictures, and verbal), then students will feel empowered and willing to lead discussions in math, resulting in deeper discussions and more positive math identities.
REFLECTING ON THIS LESSON STUDY
Dismantling the power structure of the teacher being the sole holder of knowledge and letting students lead discussions in math classes helps recognize the brilliance within children, helps them build on the prior knowledge they have, connects the students to their classroom community, and demands critical thinking for students to access skills they are developing.


Twenty juniors and seniors from Hillsboro High School attended the Donald L. Bruyr Mathematics Competition at Emporia State University on October 23. There were approximately 25 teams in our division and over 60 individuals in each of the individual competitions. Congratulations to Dillon Boldt on placing 5th in the individual geometry competition! All students who competed represented Hillsboro well.
Geometry Individual Competition Results
Dillon Boldt- 5th
Sarah Paulus- 9th
Collin Brown- 17th
Algebra Individual Competition Results
Callie Arnold- 23rd
Millie Secrhist- 26th
Team Competition Results
Caleb Diener, Henry Hein, and Charlie Major finished 9th place in the algebra team competition.
Surinda Bell, Jessi Dalke, and Kyla Isaac finished 8th place in the geometry team competition.
Jacob Denholm, Carson Linnens, and Jessica Saunders finished 6th place in the math scramble team competition.


The Team Behind Ako Maps
Ako Maps is a proud product of Cognitive Performance Labs, a Kiwi company founded in 2018 and based in Auckland, New Zealand.
Dr Kerry Spackman, our CEO and co-founder, was inspired to develop Ako Maps from his experiences as a maths teacher and from studying maths at the University of Auckland. At the time, he mapped out every concept he learned on sheets of brown paper – so big they covered the entire kitchen table! Kerry won the Senior Prize in Applied Mathematics, and years later this study technique was modernised as Ako Maps.
Meet the Team


Presently take these five chances addressing the five winning numbers (1/56, 1/55, 1/54, 1/53, and 1/52). The “1” on top of the part addresses your solitary opportunity to effectively coordinate with the drawn anime-168.com.
Presently you take your adding machine and increase every single top number (1x1x1x1x1) equivalent one (1). Next you duplicate every one of the base numbers (56x55x54x53x52). Effectively entered and increased you find the complete is 458,377,920. The new part gets 1/458,377,920. This is a 458 million to one opportunity to win. On the off chance that you were needed to pick the numbers all together very much like they are drawn, at that point these eventual the chances against you to win this Pick 5/56 ball lottery game.
Luckily or tragically, you are not needed to pick the numbers in the specific request they are drawn. The second step of the recipe will decrease the chances, which permits you to coordinate with these five winning numbers in any request. In this progression you will increase the quantity of balls drawn – five (1x2x3x4x5). With adding machine close by you see that the absolute equivalents 120.
To give you the option to pick your five coordinating with numbers in any request, you make these chances by partitioning 120/417,451,320. You unquestionably need a number cruncher for this one. 120/458,377,920 lessens your chances of winning this lottery to 1/3,819,816. These are over 3.5 million to one chances against you of winning this Pick 5/56 ball lottery game.
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為了改善滾珠螺桿進給系統的加工精度，在本研究中建立一個數學模型來模擬滾珠螺桿進給系統的溫度分布和熱變位。首先利用雷射干涉儀來取得滾珠螺桿進給系統在各種工況條件下的定位精度，然後校準熱模型中的熱變形量直到與實驗結果相互吻合，再通過複雜的工況條件進行驗證。在此熱模型中也探討各項係數及操作條件下對於模擬結果的影響，包含環境溫度、熱對流係數、潤滑油黏溫關係式、螺帽速度及加速度係數等。而模擬結果顯示滾珠螺桿進給系統之發熱量在螺帽速度10 mpm下大約為700 W/m2，在螺帽速度5 mpm下大約為400 W/m2，單一工況之模擬結果誤差為4 μm，而在複雜工況條件下的誤差為7 μm。 In order to improve the machining accuracy of a ball screw drive system, in this study a mathematical model is developed to simulate the temperature distribution and thermal displacement of the ball screw drive system. Firstly, the position accuracy of a ball screw drive system is obtained using a laser interferometer at various working conditions. Then simulated thermal deformations are calibrated to match experimental results. Then the model is verified by complex working conditions.The effects of various coefficient and operating conditions are also investigated in this model, including ambient temperature, heat convection coefficient, lubricant viscosity relationship, nut speed and acceleration coefficients. The result show that the heat generation in the ball screw drive system is around 700 W/m2 at the nut speed of 10 mpm, whereas 400 W/m2 at 5 mpm. The position accuracy predicted by this model is 4 μm in simple working conditions, whereas 7 μm in complex working conditions.


A history of mathematics new york: harpercollins, 1993  mcclenon, r b leonardo of pisa and his liber quadratorum american mathematical monthly. Leonardo of pisa, better known today as fibonacci, is largely responsible for the for the most part, the story of numbers was easy to discover is known today as the hindu-arabic system, a name that reflects its history. Until recently, history had relegated leonardo to a footnote indeed, his name is known today primarily in connection with the fibonacci. He is a renowned mathematician from the late 1100's through the early to mid 1200's during question: mr fibonacci, what year were you born 1 answer:. Fibonacci was not given his famous nickname until years after his death the ratio works out to be 1:1618 which painters used to proportion their work.
Leonardo fibonacci discovered the sequence which converges on phi this sequence was known as early as the 6th century ad by indian i am very curious about the “sequence” and how it affects us as people in our daily lives fractions or even negative numbers, in any combination, will work. His work is largely responsible for the dominance of the death, 1250 (aged 79–80) how famous was leonardo “fibonacci” pisano yes no what was. The commemorative tablet to leonardo fibonacci in pisa for further details of the life and works of leonardo, see my 2011 book the man i'll be giving at the maa's history of mathematics group meeting (homsigmaa) at. This fun picture book is a fictionalized story of the real-life mathematician leonardo of pisa he journeyed to northern africa to work in his father's business more than 800 years ago he was surprised to buy blockhead: the life of fibonacci.
Sometime about 1225 ad, fibonacci—or leonardo of pisa, as he was known until relatively recent indeed, a study of his writings reminds one of the history. The fibonacci sequence is the series of numbers: history fibonacci was not the first to know about the sequence, it was known in thank you leonardo. Fibonacci, also known as leonardo of pisa, was born in pisa, home of the famous the mathematical writings of fibonacci known to us and their dates are . Its history, significance, and manifestations in nature the mathematician leonardo of pisa, better known as fibonacci, had a significant impact on. Leonardo pisano is better known by his nickname fibonacci he was the son of guilielmo and a member of the bonacci family fibonacci himself sometimes.
Fibonacci leonardo of pisa, leonardo pisano bigollo fact despite his the history of fibonacci is not a hard one to find- fibonacci was born in. The fibonacci sequence has other interesting mathematical properties - the ratio greek architects used the ratio 1:phi as part of their design, the most famous. Grade 2–5—leonardo does his math problems so quickly that he has plenty of the story of fibonacci starts in his childhood and explains that his peers and. By charles burnett, professor of the history of islamic influences in europe text of the middle ages—the liber abbaci of leonardo of pisa, known as fibonacci. Here is a short biography of the 13th-century mathematician life and works of the italian mathematician it is believed that leonardo pisano fibonacci was born in the 13th century, in 1170 (approximately), and that he.
This biography of leonardo fibonacci provides detailed information about his childhood, life, achievements, works & timeline. In the modern era the fibonacci sequence recalls a possible aspect of leonardo's math life arithymetic in the course of his work leonardo was born in pisa (then its own sovereign republic, now part of italy) but spent his. Born on april 15, 1707, in basel, switzerland, leonhard euler was one of math's most pioneering of mathematics and engineering, with his work highlighted by the mathematical association of america blaise-pascal-wc-9434176-1-402. Leonardo fibonacci was born in pisa in about 1180, the son of a member of the life and work of leonardo da vinci leonardo da vinci had a powerful mind.
Leonardo da vinci (1452-1519), florentine artist of the renaissance (the period of western european history stretching from the early 14th century to the mid to. Little is known about the life of leonardo of pisa, also called fibonacci to produce a number of writings that laid the foundation of a new beginning of applied. In 1202, italian mathematician leonardo pisano (also known as fibonacci, rabbits can't reproduce until they are at least one month old, so for the first month ,.


The Early Life of Ada Lovelace
Ada Lovelace, born Augusta Ada Byron, is widely regarded as the world's first computer programmer. She was born on December 10, 1815, in London, England. Ada had a fascinating upbringing, being the daughter of Lord Byron, the famous poet, and Anne Isabella Milbanke, a mathematician.
Despite her parents' separation when she was just a few weeks old, Ada's mother ensured that she received a well-rounded education. At an early age, Ada developed a keen interest in mathematics and science, showing exceptional aptitude in these subjects.
Ada's passion for numbers and calculations grew as she delved deeper into her studies. She was tutored by some of the best mathematicians and scientists of her time, including Augustus De Morgan and Mary Somerville. These mentors recognized Ada's brilliance and nurtured her love for mathematics and logical reasoning.
Ada's Introduction to Charles Babbage
Ada Lovelace's interest in mathematics and science was further nurtured by her mother, who introduced her to prominent mathematicians and scientists of the time. At the age of 17, Ada met Charles Babbage, a renowned mathematician and inventor. Babbage's invention, the Analytical Engine, is considered the precursor to modern computers. This encounter would prove to be a turning point in Ada's life.
Charles Babbage recognized Ada's exceptional mathematical abilities and intellect. He became her mentor and close collaborator, fostering her interest in the world of computing and laying the foundation for her groundbreaking work in computer programming.
The Collaboration Between Ada and Charles Babbage
Ada Lovelace's collaboration with Charles Babbage was instrumental in shaping her legacy as the pioneer of computer programming. She translated and annotated an article written by Italian engineer Luigi Menabrea about Babbage's Analytical Engine. Ada's annotations, which were three times longer than the original article, included a method for calculating Bernoulli numbers using the Analytical Engine.
What set Ada's annotations apart was her visionary insight. She recognized that the Analytical Engine had the potential to do more than just calculations. She envisioned it as a general-purpose machine that could be programmed to perform various tasks beyond number crunching. Ada's notes included algorithms for generating complex graphics and music, making her the first to articulate the concept of software.
Ada's work on the Analytical Engine demonstrated her deep understanding of its potential and laid the foundation for modern computer programming. Her ideas were far ahead of her time, anticipating the development of computer programs and the possibilities they could unlock.
Lovelace's Vision for the Analytical Engine
Ada Lovelace's vision for the Analytical Engine went beyond mere calculations. She saw its potential for creating not only numerical results but also generating complex graphics and music. Her foresight in recognizing the capabilities of the Analytical Engine as a general-purpose computing machine laid the foundation for modern computer programming.
Ada's notes on the Analytical Engine were published in 1843, in an English science journal. However, due to the prevailing gender biases of the time, her work received little attention and was not widely understood or acknowledged.
It was not until the late 20th century that Ada Lovelace's contributions to computer programming were fully recognized. Computer scientists and historians revisited her work and acknowledged her as the world's first computer programmer. They marveled at her ability to grasp the potential of computing machines and her visionary ideas that remain relevant even today.
The Legacy of Ada Lovelace
Ada Lovelace's contributions to the field of computer programming were ahead of her time. Unfortunately, her work went largely unnoticed during her lifetime. It was only in the mid-20th century that her notes on Babbage's Analytical Engine were rediscovered and recognized for their significance.
Today, Ada Lovelace is celebrated as a pioneer and visionary in the world of computer science. Her insights and ideas continue to inspire generations of programmers and technologists. The second Tuesday of October is observed as Ada Lovelace Day in her honor, to recognize the achievements of women in science, technology, engineering, and mathematics (STEM).
Ada Lovelace's remarkable contributions to computer programming laid the groundwork for the digital revolution that followed. Her visionary ideas and analytical prowess continue to shape the world of technology today. Ada Lovelace will forever be remembered as the pioneer who paved the way for future generations of programmers.
Ada Lovelace's remarkable journey from being the daughter of a famous poet to becoming the pioneer of computer programming is a testament to her brilliance, determination, and forward-thinking mindset. She overcame societal barriers and made invaluable contributions that continue to shape the world we live in. Ada Lovelace's legacy serves as an inspiration for aspiring programmers, reminding us of the power of ideas and the impact one person can make on the world.


(updated for 2013)
We will use the notation from Spitzer (1978). See also Draine, Ch. 3. We represent the density of a state j as
- n: particle density
- j: quantum state
- X: element
- (r): ionization state
- For example,
In his book, Spitzer defines something called “Equivalent Thermodynamic Equilibrium” or “ETE”. In ETE, gives the “equivalent” density in state j. The true (observed) value is . He then defines the ratio of the true density to the ETE density to be
This quantity approaches 1 when collisions dominate over ionization and recombination. For LTE, for all levels. The level population is then given by the Boltzmann equation:
where and are the energy and statistical weight (degeneracy) of level j, ionization state r. The exponential term is called the “Boltzmann factor”‘ and determines the relative probability for a state.
The term “Maxwellian” describes the velocity distribution of a 3-D gas. “Maxwell-Boltzmann” is a special case of the Boltzmann distribution for velocities.
Using our definition of b and dropping the “r” designation,
Where is the frequency of the radiative transition from k to j. We will use the convention that , such that .
To find the fraction of atoms of species excited to level j, define:
as the particle density of in all states. Then
Define , the “partition function” for species , to be the denominator of the RHS of the above equation. Then we can write, more simply:
to be the fraction of particles that are in state j. By computing this for all j we now know the distribution of level populations for ETE.


A deterministic finite automaton (DFA) is a 5-tuple, , consisting of
- a finite set of states
- a finite set of input symbols
- a (partial) transition function
- an initial state
- a set of accept states
An isomorphism between two DFAs and is a bijection such that , and .
Isomorphism of DFA is GI complete
Without further restrictions, the problem of testing whether two DFAs and are isomorphic is as difficult as testing whether two graphs and are isomorphic, i.e. the problem is GI complete. A simple construction shows that the problem of testing whether two digraphs and are isomorphic reduces to DFA isomorphism testing.
For a digraph , construct the DFA with , , , and defined for by , and for by .
Obviously, the digraphs and are isomorphic iff the DFAs and are isomorphic.
A canonical labeling technique
A reasonable restriction is to require that every state in is reachable from . Let . Then a unique labeling of can be produced by a breadth first search of starting at as follows: You have a queue (first-in, first-out store), initially containing only . Repeatedly do this: remove the state at the head of the queue, say , then push into the queue (at the tail) those of (in that order) which have never previously been put into the queue. Since every state is reachable from , every state is put into the queue eventually. Stop when that has happened and define to be the order in which states were put into the queue. Since this labeling is independent of any ordering or labeling of , it fixes the only bijection between and that can possibly lead to an isomorphism between and . It is easy then to check whether they are actually isomorphic.
Attributing that algorithm to Brendan McKay would be misleading, because it is so obvious. For example J.-E. Pin described the same algorithm (using depth first search instead of breadth first search) earlier, as an answer to a question about finding an isomorphism between finite automata.
Brendan McKay’s canonical labeling technique
The context in which Brendan McKay described his canonical labeling technique was actually slightly more complicated, because there was no distinguished state , and the state space of the automaton wasn’t required to be weakly connected. But instead, was injective for all . If we drop the requirement that is a total function and allow it to be partial, then we end up exactly with the reversible deterministic finite automata, described earlier on this blog. Brendan McKay’s technique generalizes effortlessly to this setting, as does the original context (where group actions are replaced by inverse semigroup actions).
Above are some colored digraphs corresponding to reversible deterministic finite automata (the initial state and the final states are ignored). We continue to describe the canonical labeling technique in terms of deterministic finite automata. For each state , we can produce a unique labeling (of the weakly connected component containing ) by a breadth first search of starting at as above, expect when we remove the state from the head of the queue, (instead of ) we have to push into the queue (at the tail) those of (in that order) which are defined and have never previously been put into the queue.
But how can we create a canonical labeling of from the unique labelings ? Just take (one of) the lexicographically smallest labelings of each block, and sort the block lexicographically based on those labelings. The lexicographical order in this context is defined by encoding a labeled block in some reasonable (unique) way as a string, and comparing those strings lexicographically. It’s a good idea to modify this lexicographical order to first compare the lengths of the strings, but this is already an optimization, and there are more possible optimizations, as described in Brendan’s answer. These optimizations are the context of the following remark at the end of his answer:
The graph is actually a deterministic finite automaton (at most one edge of each colour leaves each vertex). There could be faster isomorphism algorithms out there for DFAs, though I’m dubious that anything would work faster in practice than a well-tuned implementation of the method I described.
This remark was actually the main motivation of this blog post, i.e. to investigate the relation of Brendan’s technique to isomorphism testing for DFAs. If there were really faster isomorphism algorithms out there for DFAs, then either they would not be applicable to the problem which Brendan had solved there (if they rely on reachability from ), or they would also solve GI itself in polynomial time (which is highly unlikely).
The truth is I have been yak shaving again, even so I explicitly told vzn that I didn’t want to get too involved with GI. How did it happen? Fahad Mortuza (aka Jim) asked me for help refuting his attempts to solve GI in quasipolynomial time. (This is completely unrelated to the recent breakthrough by László Babai, except maybe that he triggered some people to spend time on GI again.) While working with him, I realized that permutation group isomorphism might be more difficult than group isomorphism, and asked some questions to get a better feeling for the relation of permutation group isomorphism to GI. The idea to consider the case where the group is fixed came from reading an introduction to category theory, because those morphisms of left -sets felt like cheating (or oversimplifying) to me. So I guessed that this case should be easy to solve, if I would only understand how Brendan McKay handles automorphisms of graphs efficiently. Then Brendan McKay himself explained his technique (for this case) and I discovered the interesting connection to inverse semigroups and finite automata, so I decided I had to write a blog post on this. Now I have written this post, just to avoid having another item on my ToDo list which never gets done.


What is tree?
A tree is an undirected graph in which two vertices are connected together by exactly one path. A tree with N number of vertices contains (N−1) number of edges.
The edges of a tree are known as branches.
Elements of trees are called their nodes.
The nodes without child nodes are called leaf nodes.
A labelled tree diagram with 6 vertices and 5 edges
Spanning Tree: Spanning tree is the subtree of the graph that contains all the vertices of that graph. The edges of spanning tree are called Branches.
Forest: A forest is an undirected graph in which all the connected components are trees. For every tree number of vertices (V) – number of edges (E) = 1, we can count the number of trees that are within a forest by subtracting the difference between total vertices and total edges.
Figure showing difference between Tree and Forest
Polytree: A Polytree also known as Oriented tree is a directed acyclic graph whose underlying undirected graph is a tree. If we replace the directed edges with undirected edges, undirected graph is obtained.
Rooted Tree : A rooted tree is a tree in which one node is designated as root. The edges of the rooted tree can have orientation either away from the tree or towards the tree.
When the edges of rooted tree are directed away from the tree than it is known as arborescence, branching, or out-tree and when the edges of rooted tree are directed towards the root than it is known as anti-arborescence or in-tree.
Properties of graph :
- Every tree is a median graph and bipartite graph
- In every connected graph G there is a spanning tree .
- For any three vertices in a tree the path between them has exactly one vertex in common .


Compound interest is a powerful tool in investing that builds wealth overtime. In this article, we will explain what compound interest is, how it works, and why it is important to start investing early.
What is Compound Interest?
Compound interest is the interest that is earned not only on the principal amount but also on the accumulated interest. In simple terms, it is the interest you earn on the interest you have already earned. Unlike simple interest, which only earns interest on the principal amount, compound interest allows your investments to grow exponentially over time.
How Does Compound Interest Work?
To understand how compound interest works, let’s consider a simple example. Suppose you invest $10,000 at an interest rate of 5% per year. After the first year, your investment would be worth $10,500, including the $500 in interest earned. However, if you reinvest the $500 back into your investment, your new principal balance would be $10,500, and the interest earned in the second year would be calculated based on that amount. This process continues year after year, leading to exponential growth in your investment.
Why is it Important to Start Early?
The power of compound interest lies in time. The longer you allow your investment to grow, the more significant the impact of compound interest will be. The earlier you start investing, the more time you have for your investment to compound and grow exponentially.
A popular — and completely hypothetical — example involves two brothers investing $100 each month starting at age 25. Brother 1 averages a 1% positive return each month, compounded monthly over 40 years. Brother 2 invests $1,000 a month but doesn’t start until 30 years later, and they get the same positive return over 10 years.
After 40 years, Brother 1 has $1.15 million while Brother 2, who invested more each month, has $235,855. Early and consistent contributions will yield higher returns once it’s time to retire.
Compound interest is a powerful tool and can help you build wealth overtime. By reinvesting your interest earnings, you allow your investment to compound and grow exponentially. Starting early gives you the advantage of time and allows you to benefit from power of compound interest.
“What is Compound Interest?” The Balance, accessed May 4, 2023, https://www.thebalancemoney.com/compound-interest-4061154
“The Life-Changing Magic of Compound Interest,” Forbes, accessed May 4, 2023, https://www.forbes.com/advisor/investing/compound-interest/
“The Power of Compound Interest,” Investopedia, accessed May 4, 2023, https://www.investopedia.com/terms/c/compoundinterest.asp
“Aligning Your Philanthropic Operating Model with Your Goals”, Harvard Business Review, accessed May 4, 2023, https://hbr.org/2023/01/aligning-your-philanthropic-operating-model-with-your-goals
The content in this article is provided for informational purposes only and should not be relied upon as recommendations or financial planning advice. We encourage you to seek personalized advice from qualified professionals regarding all financial decisions.


There is a branch of mathematics, topology, which can be described as the study of the possible “shapes of space”, referring to the 3-dimensional space as we experience it in the world, as well as 4-dimensional space-time and other more abstract spaces (such as those of higher dimensions). It is the study of structure at a more basic level than geometry because it contains no notion of distance or angles. It is sometimes dubbed “rubber sheet geometry”, for reasons which will be clear shortly.
Topologically speaking, a brick is the same as a ball and a coffee cup is the same as a doughnut. In both cases each could be morphed into its counterpart smoothly with only stretching, squeezing, folding or twisting allowed, but not tearing, breaking or hole-filling (assuming the objects were made of pliable enough material), or in the jargon of mathematics “remaining invariant under homeomorphic deformation”. Topology is also concerned with the definition of regions and their connectedness (within and between), for example the notions of “inside” and “outside”.
There is one aspect of topology that I think is relevant to philosophy, particularly Merleau-Ponty’s phenomenology. That is the concepts of intrinsic and extrinsic points of view. The intrinsic viewpoint is from the perspective of the mathematical object itself (or a being living on it). For example, for a 2-dimensional being living on a torus (the surface of a doughnut) the universe is just the surface. Nothing else exists. That is the intrinsic viewpoint. This being can carry out experiments which will confirm that its universe conforms to a Euclidean geometry (for example the angles of triangles add to 180° and the circumference of a circle = 2πR).
It would also be possible in principle for the being on the torus to verify that travel in a straight line in either of two orthogonal directions would result in return to the same place, and that some loops cannot be contracted to a point (the loops that from the extrinsic viewpoint are snagged around the inner “hole”). From the intrinsic viewpoint there is no “hole”. The world is complete in itself. From the extrinsic viewpoint on the other hand, the torus is situated in an ambient 3-dimensional space. Travel paths that from the intrinsic viewpoint are geodesics (shortest possible routes or straight lines) are from the extrinsic viewpoint curves (such as circles).
The analogous situation arises for a being on a sphere (the 2-dimensional surface of a ball). From the intrinsic point of view the surface is the whole universe. The angles of triangles will add up to more than 180° and the circumference of circles will be less than 2πR, hence the geometry is non-Euclidean.
The point is that due to a theorem Theorema Egregium (Remarkable Theorem) proved by Gauss, the curvature of the “world” (curvature being a purely theoretical notion since as far as the resident being is concerned the world is perfectly flat and curvature has no physical meaning – curved through what?) can be measured purely on the surface (“in the world”) alone, which will determine the appropriate geometry of “the world” (Euclidean or non-Euclidean) without recourse to a mystical “3rd dimension”.
I am thinking that perhaps topology might be fruitful in somehow shedding light on those terms, such as connectedness, boundary, inside, outside etc. which also crop up in philosophy and related disciplines, and I am not the first to have this idea.
Philosophers such as René Descartes and Jacques Lacan, for example were very interested in topology. Descartes was a pioneer in the field, discovering what became known as Euler’s characteristic more than 100 years before eminent mathematician Leonhard Euler did so in 1752. Lacan is another kettle of fish entirely, however. But while someone like physicist Alan Sokal (perpetrator of the “Sokal hoax” resulting from the publishing of this paper) would no doubt mock Lacan’s use of examples from the field of topology to illustrate points in the fields of philosophy and psychoanalysis, I have a more charitable view. At the very least, the contemplation of such wonderful objects as the Möbius strip, the Klein bottle and Borromean Rings (employed by Lacan as described here and here ) should be encouraged to help us think more imaginatively and less dogmatically about concepts such as connectivity and inside/outside-ness.
Topology abounds in even more astoundingly intuition-defying objects, for example fractal objects such as the Koch snowflake (which has finite area but infinite length perimeter) and Alexander’s Horned Sphere.
Rather, the inside is, but the outside is not, because it is not simply connected (some loops cannot be contracted to a point).
My point with these curious topological oddities is this. If the (apparently) two sides of a surface can in fact sometimes be just one side and if sometimes the regions of inside and outside are unable to be cleanly distinguished, then perhaps the apparent Cartesian dualism split (“mind is interior and matter is exterior and never the twain shall meet”) might turn out not to be so hopelessly clearcut, with tendrils of each realm ambiguously and inextricably embracing the other, taking the form of a topological entity. I am attracted to the phenomenology of Merleau-Ponty for just that reason. And, after all, the fractal objects of pure mathematical thought have turned out to be highly useful in modelling natural systems, so why not consider topology as one more tool for modelling ontology?
I know this post has been pretty far out there in the speculative stratosphere for me, but it was good to indulge my passion for topology and mix it up with my new found interest in phenomenology. I expect the next few posts will be more down to earth.


City Summer Youth Academy is for students ranging from incoming 6th graders through currently enrolled high school students. CSYA is underwritten by a generous grant from the Wells-Fargo Foundation.
Math - Applied Precalculus
Monday-Friday, 6/13-6/24/2022, 9:30am-12:00pm
Instructor: Alex Roberts
Description: Review or learn important functions such as polynomial and rational functions, exponential and logarithmic functions, trigonometric functions, polar and parametric functions and systems of equations leading into vectors and matrices. Learn about conic sections, sequences, probability and limits. Apply your understanding to model real physical systems and test your knowledge with challenging number theory problems.
Class format: Google Jamboard/on the blackboard via Zoom or the like
Prerequisites: able to understand graphs of linear functions
Includes Classroom Exercises/Suggested Homework
This will be a live synchronous course. Students will need a computer or smart phone with webcam and microphone, internet and web streaming capacity, and the Zoom application installed to their device.


The best online roulette is the one that allows the player to win, that is, a licensed game in which the RNG is honestly tuned. Although the power of chance plays a great role, users should not forget that they need to play online roulette following mathematical laws. A properly selected online casino roulette strategy allows maximizing the player’s advantage and win. Before practicing online roulette strategies, it is vital to make sure that players choose a licensed casino site.
Casino Roulette Strategy: The Most Popular Ones
An inexperienced person often thinks that they win at roulette solely due to luck, but this is far from the case. The game has many undercurrents, so live casino roulette strategy will help the participants to distribute all the bets to finish the game with minimal losses.
- In a fixed betting strategy, players bet the same amount anyway. The rate never changes. James Bond’s roulette strategy belongs to this category. They say that this famous hero used it. The essence of this roulette system is to cover 25 out of 37 numbers to increase the chances of winning;
- In the Fibonacci sequence numbers, each of which is the sum of the previous two. The result is 1, 1, 2, 3, 5, 8, 13, 21, 34, etc. Each time, to find the continuation of the sequence, players should add the last two numbers. Playing, according to this winning casino roulette strategy, involves raising and lowering rates in this sequence;
- If gamblers have been looking for an effective betting system for roulette for a long time, they will probably want to give preference to the Dutch one. Recently, this variation of the reverse progression has proven itself well among gamblers. The progression of the Dutch system is 1-3-5-7-9, considering that the bets are made at $ 1. So, by increasing the number of bets in progression, the numbers will change.
No online casino roulette strategy can give a 100% guarantee of a big win, but at the same time, it will help to keep the losses to a minimum.
Red-Black Strategy To Win Casino Roulette
Even before the roulette wheel was not started, the probability that one of the zones, either red or black, will fall out is equal to 0.486, and that the ball will fall into the zero sector is 0.027.
- In a situation when, after starting the roulette wheel, the ball falls into the black field, the chances of falling out of the red zone the next time increase significantly;
- When the following situation occurs, black falls out two times in a row, then, accordingly, the chances of the ball hitting the red zone increase significantly;
- Of course, no players can be 100% sure, so the fact that their chances of getting a victory, due to the best casino roulette strategy, are great is a fact. As statistics show, one sector can drop out no more than ten times.
The players should adhere to the basic tactics of red-black casino roulette strategy, the essence of which is that they need to bet only on the number that is most likely to come up. To predict a sector or a number correctly, they need to know the statistics of drops.


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April 14, 2020 @ 10:00 am - 5:00 pm
An event every week that begins at 10:00 am on Monday, Tuesday, Wednesday, Thursday and Friday, repeating until May 15, 2020
Get those pencils sharpened! Former math teacher, Phyllis, can help to answer all of your math questions, from kindergarten to calculus. You can schedule a time to work with Phyllis from your own home. Just reach out to her and you can decide together the best way to work (Zoom, FaceTime, etc). By appointment only: 845-688-2214 or email@example.com.


C(q) is the least amount of money needed to buy inputs that will produce output q. It is the cost function.
FC are fixed costs, the costs incurred even if there is no production. FC = C(0).
VC(q) are variable costs. VC(q) = C(q) - FC.
AC(q) is average cost. AC(q) = C(q)/q.
AVC is average variable cost. AC(q) = VC(q)/q.
AFC is average fixed cost. AFC(q) = FC/q. AFC(0) is infinite and AFC(inf.) is zero. (yes, I should have said that the limit as q approaches infinity of AFC is zero, but I am sure you can tolerate the short hand.)
MC(q) is marginal cost. It is the cost of making the next unit. MC(q) is approximately C(q+1) - C(q). Put the other way, C(q+1) is approximately C(q) + MC(q). The cost of making q+1 units is the cost of making q units plus marginal cost at q. A Diagram.
Assuming that FC are not zero, AC(0) will be infinite and AC(inf) = AVC(inf)
Whenever AC is increasing, MC is above AC. When decreasing MC is below AC.
AC(q+1) - AC(q) = c(q+1)/(q+1) - c(q)/q = c(q)/(q+1) + mc(q)/(q+1) - c(q)/q
= -c(q)/(q(q+1) + mc(q)/q+1)
= (1/(q+1)) (mc(q) - ac(q) ) so mc greater than ac means ac(q+1) > ac(q) or ac increasing.
This means that MC goes through the minimum point of AC. Note that MC = VC(q+1) - VC(q). (why?) so the above proof also shows that MC goes through the minimum point of AVC.
Firms maximize profits. p = p q - c(q) = q (p - ac(q) ).
A necessary condition for maximizing profits is that p = mc(q). We assume mc slopes up.
Part of a proof: We will show that if p = mc(q*) then profits go down if one decreases q* by one unit. One can show, but we will not, that increasing q above q* will also decrease profits. Thus q* is a local profit maximum. Our claim is that
p(q*) - p(q*-1) is positive. Now p(q*) - p(q*-1) =
[pq* - c(q*)] - [ p (q*-1) - c(q*-1)]
= p - [ c(q*) - c(q*-1) ]
= p - mc(q*-1)
which is positive because mc slopes up and equals p at q*. (draw the picture)
(at home construct the same argument for for q*+1 and q*+2. do you see the problem with the discrete approximation of mc as c(q*+1) - c(q*) rather than the calculus answer of mc is limt -> 0 [c(q+t) - c(q)]/t.)
The shutdown point is given by p = minimum point on avc. When p = min avc = mc , profits will be exactly - FC. p = q ( p - ac) = q ( p - avc) - fc but p = avc so p = -fc. Profits would be less if p were less so p less than min avc = mc, best policy is shutdown.
The supply curve is mc above avc.


|Jennifer Franklin of Ottawa, Canada was the first to solve this puzzle. Franklin submitted her solution on October 29, 1998. This page was created in March 1997. I'm surprised that a year and a half elapsed before someone found a correct answer!|
Self-referential sentences are sentences that comment on their own characteristics, structure, and function. For example, this sentence is self-referential because it asserts its self-referential nature.
My puzzle is a system of four numerical self referential sentences; each sentence in the set refers to its digital or numerical contents and/or the digital or numerical contents of other sentences in the set. This particular system of sentences is different than typical systems of self-referential sentences because all the numbers are in base three.
Base three numbers are the same as familiar decimal numbers except that they are written with only three different digits instead of ten. Each digit in a number represents that multiple of the number's base to a power determined by the digit's position in relation to the number's decimal point. An entire number is equal to the sum of these digital multiples of successive powers of the base. For example, the base ten number 5372 = 5 × 103 + 3 × 102 + 7 × 101 + 2 × 100. It's easy to convert numbers of any base to base ten. You simply multiply each digit by the appropriate power of the base and add up the results. For example, the base three number 2201 = 2 × 33 + 2 × 32 + 0 × 31 + 1 × 30 = 73. It is also fairly simple to obtain a base three number from a base ten number by dividing the number by three, generating a digit from the remainder, and repeating the process with the integer of the quotient to obtain successive digits. For example, we could reverse the example shown above (R stands for remainder):
73 ÷ 3 = 24 R 1
24 ÷ 3 = 8 R 0
8 ÷ 3 = 2 R 2
2 ÷ 3 = 0 R 2
The base ten number 73 is thus converted back to the base three number 2201.
The object of this puzzle is to fill in the fields in each sentence with positive base three numbers so that all of the sentences are true. Remember that all the numbers already in the sentences are also in base three. The red numbers serve simply to number the sentences in base three from one to four and should not be considered part of the sentences. When a sentence refers to the number of 0s, 1s, or 2s in a sentence or a set of sentences, it means the number of occurrences of that particular digit, not the number of occurrences of that particular number. So in its initial state sentence 1. has five (written "12") 1s, not two.
This puzzle may have more than one solution. See if you can find a solution other than the one on the solutions page.
Check out David Dewey's home page!


A linear model is a type of analysis that enables a business to test individual variables to determine their impact on their overall sales.
Any given business — especially omnichannel businesses — has multiple factors that drive sales. In the ecommerce space, that’s magnified with social media, paid online ads, organic search traffic, and more guiding consumers into ecommerce websites. A linear model allows a business to test these and other independent variables to determine their impact on a business goal (usually sales).
More specifically, a linear model is a mathematical equation that many analytical systems can run automatically to see how a factor influences a dependent variable, such as sales growth, conversion rates, or newsletter signups.
Linear models are useful for determining where to place marketing spend because they give a business detailed data on what’s driving business success. With this information, the business can adjust strategies that aren’t working, invest more in strategies that are, and better understand the nuances of their sales cycles and channels.