From EP 4, we could know all 3 types of Linear regression. Linear regression is just one of 4 Machine Learning (ML) algorithms.
Supervised Learning is ML on labeled output and we use the label to train our models. For example, we have data of age and income. We want to predict income at any age as labeled output is income.
In other hand, Unsupervised Learning is working on unlabeled output that means we have no initial result data to train models. We will talk about this later.
And Continuous means quantitative output as Discrete means qualitative output.
As the figure above, there are main 4 ML algorithms:
Discrete Supervised Learning. This is for predicting group in limited values. For example, we want to predict which group of interests for a customer when we have customer data as ages, occupations, genders, and interests.
Continuous Supervised Learning. This is to predict output as it can be any values. The example is the previous episode.
Discrete Unsupervised Learning. It is to group our data. For example, we want to group customers into 8 types leading to the hit advertisements from customer data.
- Dimensionality reduction
Continuous Unsupervised Learning. This is working on data optimization. One day we will have tons of data in thousands columns, and Dimensionality reduction helps us find the most important columns to deal with in terms of data processing.
And this time, I am proud to present…
Logistic Regression predicts the probability. Despite its name, its algorithm is classifier as the result is a member of labeled output.
Now it’s the time.
We reuse Titanic data again. Assign
x as “Pclass”, “is_male” that is calculated from “Sex”, “Age”, “SibSp”, and “Fare”.
y as “Survived”. We are going to predict the survivability.
Utilize the module
sklearn.linear_model.LogisticRegression() and run
solver='lbfgs' to avoid a warning.
fit(). Just peeking
coef_ and find the second column, “is_male”, has negatively impact on “Survived”.
Once we get the model then go to test. We create a crew with “Pclass” is 30, male, no “SibSp”, and paid 25 as “Fare”.
Our model predicts he was dead (“Survived” is 0). Please mourn for him 😢.
.predict_proba() and we realize his survivability is just 10%.
Ok. Let’s see the correctness of the model. We create a
DataFrame to combine “Survived”, predicts, and a correction flag as “is_correct”.
Average correctness of our model is 83%. Quite great.
Besides, we shall meet Dummy Classifier. This one provides the “baseline” classification model. It means we can apply this as a standard to evaluate our model.
Dummy Classifier run the model with simple rules and we can define the rule by the parameter
strategy. This time is “most_frequent” that is to predict base of frequent values of the training set.
Now we check the baseline correctness as it is just 52.7%. Our Logistic Regression model above works.
Classifiers is useful for data categorizing works and I hope this blog can be great for you to understand ML overview.
Let’s see what’s next.


Board of Secondary Education (BSE) on Monday released the timetable for the Matric exam (Summative-II).
According to the BSE, the examination would be of 80 marks for each subject (50 objective and 30 subjective). Two-hour exam will be held for every subject, barring Mathematics where students will get extra 15 minutes.
Exam will start at 8 AM from April 29-May 7.
April 29: Second Language English/Hindi (8-10 am)
May 2: Mathematics (8-10.15 am)
May 4: Science (8-10 am)
May 5: First Language Odia/Bengali/Hindi/Urdu/Telugu/ alternative English (8-10 am)
May 6: Third Language (8-10 am)
May 7: Social Science


How do I interpret the test results?
These tests are for potency and the units are mg/g or mg/1000mg. So, if you’re interested in the percentage of cannabinoid in a given product, you just move the decimal over three spaces. Ex: 2.6mg/g = .0026g/g or 0.26%.
To calculate the amount of CBD in your product, you multiply the mg/g by 29g/bottle (oil is less dense than water so 30ml weighs 28.8g). So for our Calm tincture, 37.2mg/g x 28.8g = 1071mg CBD.
In our high-potency tinctures, one bottle contains ~1000mg CBD which translates to 1.2mg CBD per drop (there are slight variations in drop size depending on the viscosity of the oil).
Our products are high potency, full-spectrum and all guaranteed to be below 0.3% THC.
Start low and go slow. Begin with 4 drops-1/4ml (5-8mg CBD) and slowly work your way up to what is ideal for you.


Moose Math for Apple iOS [Free for Limited Time]
Moose Math engages kids in a mathematical adventure and teaches counting, addition, subtraction, sorting, geometry and more. While playing 5 multi-level activities in the Moose Juice Store, Puck’s Pet Shop and Lost & Found, kids can earn rewards to help build their own city and decorate buildings. Moose Math introduces a new whimsical group of Duck Duck Moose characters, The Dust Funnies, who help with mastering math skills. Moose Math is aligned with Common Core State Standards for Kindergarten and 1st Grade and includes a Report Card section where parents and teachers can monitor progress and find additional skill-building activities. AGES: 3-7.
Moose Math features 5 engaging math activities:
1) MOOSE JUICE: Make smoothies while practicing counting, addition and subtraction
2) PAINT PET: Match the pets by counting the number of dots
3) PET BINGO: Solve addition, subtraction and counting problems to get BINGO
4) LOST & FOUND: Learn and sort through shapes and colors
5) DOT TO DOT: Help the Dust Funny find his way home by joining the dots
Kids will learn the following math skills based on Common Core State Standards:
– Understand the relationship between numbers and quantities
– Solve word problems and algebraic thinking
– Practice number pattern recognition
– Count by 1’s, 2’s, 5’s and 10’s
– Master counting to 100
ADDITION & SUBTRACTION:
– Add and subtract by 1’s, 2’s, 5’s and 10’s
– Add and subtract up to 20
– Learn to add and subtract with numbers, dice and rekenrek racks
– Master geometry at Kindergarten and First Grade levels
– Learn to identify and recognize shapes
– Understand and compare lengths
PARENT REPORTING: Includes a Report Card section where parents and teachers can monitor progress for each child and learn about new skill-building activities.
DEVELOPED WITH EDUCATORS:
– Developed in conjunction with Stanford University Educator, Jennifer DiBrienza, PhD in –
Early Elementary Education and former NYC public school teacher (K-Grade 2)
COMMON CORE STANDARDS: K.CC.1, K.CC.2, K.CC.4, K.CC.6, K.OA.1, K.OA.2, K.OA.5, K.MD.2, K.MD.3, K.G.2, K.G.3, K.G.4, 1.OA.1, 1.OA.2, 1.OA.6
ABOUT DUCK DUCK MOOSE
(A wholly-owned subsidiary of Khan Academy)
Duck Duck Moose, an award-winning creator of educational mobile apps for families, is a passionate team of engineers, artists, designers, and educators. Founded in 2008, the company has created 21 top-selling titles and has received 21 Parents’ Choice Awards, 18 Children’s Technology Review Awards, 12 Tech with Kids’ Best Pick App Awards, and a KAPi award for “Best Children’s App” at the International Consumer Electronics Show.
Compatibility: Requires iOS 6.0 or later. Compatible with iPhone, iPad, and iPod touch.


The Statistical Society of Australia (SSA) will host the Early Career & Student Statisticians Conference (ECSSC) 2021 virtually from July 26th to August 1st 2021. As part of the conference, we have set side a day (July 31st 2021) for our future budding statisticians! High school students (year 7 – 12), or teachers of high school and primary students are encouraged to join in the conference.
Workshop: An introduction to statistical programming and analysis
The day will begin with a hands-on workshop were students and teachers will be introduced to the freely available software package R and learn the fundamentals of statistical programming (no experience required!). Participants will have opportunities throughout the workshop to implement what they learn as they work through a statistical problem, from data exploration to data visualisation and more. Our workshop presenters are experienced R users and statisticians, spanning industry and academic researcher.
- Dr. Emi Tanaka, Department of Econometrics and Business Statistics, Monash University
- Dr. Kevin Wang, Statistician at CSL Behring
- Patrick Robotham, Nimble Australia Pty Ltd
- Daniel Fryer, Department of Mathematics and Physics, The University of Queensland
High School Day Career Panel
Following the workshop, a careers panel will provide information on the many possible career pathways in statistics and how to navigate statistical learning. Hear from recent statistics graduate and early career statisticians on there experiences studying statistics at varying levels of education, and how they use data in their everyday work to solve a wide variety of problems.
Soraya McPhail is a current methodology graduate at the Australian Bureau of Statistics, ABS. She completed a Bachelor’s degree in Economics, Mathematics and Statistics at the University of Western Australia in 2020. At the ABS, Soraya works within the Statistical Methodology Branch, where she assists her team in providing statistical and sampling advice to ABS Business Surveys. Over her short time at the ABS, Soraya has worked on a wide range of projects including investigating the feasibility of using administrative data for ABS publications, confrontational analysis, sample design and estimation support for internal ABS clients.
Ever since graduating from Macquarie University in 2018, I have had the opportunity to work across multiple sectors, industries and organisational scales. From being an analyst at Australia’s largest debt purchaser to catching internal fraud for Westpac, and now with NSW Health as a Trainee Biostatistician. Let me just tell you, I’ve been in the trenches and I’ve seen some things. So, if you got what it takes, let me share my insights about this wild world.
Dr. Elena Tartaglia
Dr. Elena Tartaglia is a Research Scientist at CSIRO’s Data61. She is part of the Analytics and Decisions Sciences program and mainly works on consulting projects with external clients. Elena completed her PhD in Mathematics at the University of Melbourne in 2016 and moved into data science three years ago. Since joining Data61, she has used statistics and data science to solve problems in manufacturing, education, risk management and bushfire prevention.
Registration is free of charge for school students. Simply upload a copy of your student ID at the time of registration as proof of your student status. As part of your registration, you will also have access to all other conference days which include an amazing line-up of keynote speakers from all occupations, and a diverse range of selected talks from early career & student statisticians.
Register for the conference!
Online registration and information on the conference, keynote speakers, workshops, and abstract submissions are available at: http://ecssc2021.com.au/.
A number of door prizes will be drawn during the High School Career Day, courtesy of the Australian Research Council Centre of Excellence for Mathematical & Statistical Frontiers (ACEMS). These will include some introductory statistical textbooks and book vouchers to help foster your learning in statistics!
If you have any questions, concerns, or feedback, please contact the ECSSC Chair via email at firstname.lastname@example.org.
We look forward to welcoming you to our conference!


Muswell Hill Primary School’s vision for Mathematics is that each child will possess a confidence and positive attitude to the subject regardless of their gender or background.
Each child will move onto the next stage in their learning with a secure base of fluency and knowledge of key number facts. This knowledge will allow them to explore and solve mathematical challenges in everyday situations as maths is seen as an integral part of life.
At Muswell Hill Primary School the teaching of Maths is based on a mastery approach. The approach ensures that children learn the strategies and concepts on a deeper level rather than rushing through the objectives. Attention is paid to reinforcing their knowledge. Teachers use a teaching for mastery approach. At our school this means that the whole class will work together in some lessons, particularly those that introduce and explore a new concept. Teachers will focus on small steps, key representations, questions and misconceptions to introduce a concept, aiming for all children to become secure in the concept. In other lessons, it might be effective for the class to spend more time working in smaller groups or on independent practice; this will be based on the teacher’s assessment, from the previous lesson. Teachers will, informed by their assessments, adjust lessons and activities so that they are pitched at appropriate levels of challenge and provide the right ‘next step’. Best practice at our school is keeping the whole class working on the same concept, taking small steps to master this but also assessing progress and using ‘flexible grouping’: grouping that is informed by day to day marking and assessment of misconceptions. When appropriate, throughout the lesson, the children will be drawn together to learn from each other and share misconceptions so they can progress as a class. Children with special educational needs may well be working to an individual plan and teachers will differentiate their work, ensuring they are included in the theme of the lesson. Whatever their level of attainment, children should not experience repeated failure or effortless success; success should be encoded.
Lessons are planned from a balanced mathematics curriculum based on the National Curriculum with a strong emphasis both on fluency in number facts, calculations and place value and applying all areas through reasoning and problem solving. Teachers are expected to use precise explanations in order for children to clearly understand key concepts and strategies and assess pupils regularly to identify those requiring intervention, so that all pupils are supported in keeping up – diminishing differences and disadvantages. Specific, differentiated and deep questioning in lessons are key in order to test conceptual and procedural knowledge, as well as supporting and stretching pupils according to their needs.
Teachers at MHPS base their pedagogy on evidence from bodies such as the NCETM, NRICH and Whiterose, they gather, develop and share great lesson ideas which make maths relevant as well as those which promote problem solving with pure number. Games, reasoning and problem solving are cornerstones of our teaching and learning of mathematics. The school has worked in partnership with NCETM in recent years and is committed to approach.
The curriculum is planned so that children have regular opportunities to embed their understanding of key maths skills; such as number bonds, knowledge of +, -, x and division/multiplication tables. The progression of written methods for calculations follow the CPA approach – from concrete (actually ‘doing’ with real objects) to pictorial representations – moving to abstract concepts only when children are ready and have a secure conceptual understanding. The calculation policy with the progression of methods used across the school is attached here.
Maths @ Home
To consolidate and reinforce the maths learning carried out in school, teachers are now able to allocate online activities via the Topmarks online homework resource IXL. The children have been given their individual log in details and once logged in can access and complete their maths homework each week.
Staying Safe Online
DLC and the Internet have become integral to teaching and learning within schools, providing pupils and staff with opportunities to improve understanding. However, whilst this technology has many benefits for Muswell Hill Primary School, we recognise that clear procedures for appropriate use and the education of staff and pupils about online behaviour and potential risks are essential. Please click here to see our Online Safety Policy.
Here are a list of a few useful websites to help the children with their maths learning at home:
1) Top Marks Hit the Button: this is great for quick fire times table and number fact practice to develop the children’s fluency:
2) TT Rockstars: In KS2 each pupil has been set up with their own individual log in, which means they can access this exciting online resource at home as well as at school.


Michael Lacey is a highly-honored mathematician who currently serves as a full professor and associate chair of faculty at the Georgia Institute of Technology. Michael Lacey first came to the Georgia Institute of Technology in 1996 with the rank of associate professor. He became a full professor in 2001, and he moved to his current role in 2017.
Michael Lacey earned a BS degree in mathematics from the University of Texas in 1981. In 1987, he earned a Ph.D in mathematics under the direction of Walter Philipp. His thesis was in the area of probability theory.
Before coming to the Georgia Institute of Technology, Michael Lacey was an assistant professor at the University of Louisiana. From there, he moved to the same position at the University of North Carolina. From 1989 through 1996, Michael Lacey served as an assistant professor at the University of Indiana.
Dr. Lacey has received a number of honors in his field. In 1997, he was awarded with the Prix Salem for his work in phase space analysis. Dr. Lacey followed this by receiving a Guggenheim Fellowship in 2004. This prestigious honor is given to no more than four mathematicians in any given year.
In 2008, Dr. Lacey was awarded a Fulbright Fellowship, and spent time in Buenos Aires, Argentina. The American Mathematical Society accepted Dr. Lacey as a fellow in 2013. That organization stated that Dr. Lacey had made, “outstanding contributions in the advancement of mathematics”.
In his current teaching role, Dr. Lacey teaches a number of different courses on a rotating basis. In the past he has taught courses that include the Foundation of Math Proofs, Vector Calculus, Linear Algebra and Harmonic Analysis.
Dr. Lacey continues to be an adviser to graduate students and those in the Ph.D program at the Georgia Institute of Technology. He has worked with several students in postdoctoral programs as well.


Special pricing subjects are subjects which require a great deal of preparation by the tutor. These are subjects that are rarely asked for by students. Generally for every hour spent with the student, the tutor will spend three or more hours without the student. Because these are so labor intensive, I generally will only take on one special price situation in a semester - two at the most. The cost rate for the student can be significantly lowered from the prices show below if a digital unlocked pdf copy of the book is sent to me by the student, or if the student purchases a book for me (which I keep).
Having students come to my home allows me to schedule sessions both before and after any particular student. This allows me to reduce my fees in these cases. I am located near 40th and Old Cheney. (See a map. Click your browser's back button to get back to this page.)
One Person Rate
The rate for one person is $60 per hour.
An individual's group rate is calculated using the formula (n + 1) R / (2n) where n is the number of people in the group and R is a person's single-person price rate (including any promotional discounts). So the individual rate for two people (using the regular rate of $60/hr as an example) would be (2 + 1)($60 per hour) / 4 = $45.00 per hour, three people would be (3 + 1)$60 / 6 = $40 per hour, and so on. Promotions that lower an individual's single-person rate are applied before the group rate formula is used.


Comparing stock investments
Students learn how calculating capital gains and capital losses can help them evaluate stock investments.
To measure a stock’s past performance, you’ll need to calculate that investment’s gains and losses.
- How do you calculate a capital gain or capital loss?
- How can you use percentages to evaluate a stock’s past performance?
- Calculate capital gains and capital losses for stock transactions in terms of dollars and percentages
- Understand how these calculations can help evaluate a stock’s past performance
What students will do
- Calculate capital gains and capital losses in terms of dollars and percentages for specific stock transactions.
- Determine which stock transaction had the greatest capital gain in terms of dollars.
- Determine which stock transaction had the greatest gain in terms of percentages.
Note: Please remember to consider your students’ accommodations and special needs to ensure that all students are able to participate in a meaningful way.


Welcome to Year 1
Firstly thank you so much to everyone for coming to join in with our Harvest celebrations on Friday. We hope you enjoyed it as much as we did.
Next week in Maths we will be ordering 3 groups of numbers from the smallest to the greatest and vice versa. We will then be ordering these numbers on a blank number line. In English we are revisiting the Three Little Pigs and thinking in particular about the Wolf who has gone missing! We will be planning and making our own missing wolf posters focusing on adjectives and descriptive phrases. In Art we will be taking a closer look at Autumn and will use leaves, pastels, paint and other media to create an Autumn scene. We will be looking at high and low pitch in Music, practising our computing skills using bug club and learning more about our value of the month - Happiness.
Maths at home
- Writing numbers 0-10 the correct way round. All numbers are written starting from the top.
- Use the vocabulary, greater than, more than, fewer than, less than and equal to and discuss what each mean.
- Practise ordering 3 numbers from 0 - 10 from smallest to biggest and vice versa. Where possible use every day objects eg pasta to help with representing each number first before ordering.
Don’t forget Infants parents evening this week. Tuesday 3.15 - 6pm and Thursday 5.00pm - 8.00pm
Thank you for your continued support.
Year 1 Team
Curriculum evening handouts:


A downloadable game for Windows, Linux, and Android
Merge as many equal numbers as you can before you run out of actions!
Unlock 20+ different levels and optimize your score in this simple, but addictive logic puzzle.
- 4 difficulty options
- 24 levels
- translations: English and German
In order to download this game you must purchase it at or above the minimum price of $1 USD. You will get access to the following files:
Also available on
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The third edition of this highly acclaimed undergraduate textbook is suitable for teaching all the mathematics for an undergraduate course in any of the physical sciences. As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. Further tabulations, of relevance in statistics and numerical integration, have been added. In this edit.
A Course of Pure Mathematics is a classic textbook in introductory mathematical analysis, written by G. H. Hardy. It is recommended for people studying calculus. First published in 1908, it went through ten editions (up to 1952) and several reprints. It is now out of copyright in UK and is downloadable from various internet web sites. It remains one of the most popular books on pure mathematics.
An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities by George Boole, published in 1854, is the second of Boole's two monographs on algebraic logic. Boole was a professor of mathematics at what was then Queen's College, Cork (now University College Cork), in Ireland.
Calculus Made Easy is a book on infinitesimal calculus originally published in 1910 by Silvanus P. Thompson. The original text continues to be available as of 2008 from Macmillan and Co., but a 1998 update by Martin Gardner is available from St. Martin's Press which provides an introduction; three preliminary chapters explaining functions, limits, and derivatives; an appendix of recreational calculus problems; and notes for modern readers. Gardner changes "fifth form boys" to the more American sounding (and gender neutral) "high school students," updates many now obsolescent mathematical notations or terms, and uses American decimal dollars and cents in currency examples.


The Ultimate Restaurant Break-Even Formula Guide: How to Calculate Your Break-Even Point
Knowing your numbers, including your break-even point, is a critical part of running a financially viable restaurant. Your restaurant can have a James Beard Award and tables filled with customers, but if it’s spending more than it’s bringing in, the business will inevitably fail.
Novice restaurateurs may be surprised to learn just how much math is involved in running a successful restaurant. You have to calculate the cost of goods sold to set menu prices. You have to keep an eye on labor spending to ensure overtime isn’t biting into your profits. You also have to run a break-even point analysis to ensure your restaurant is financially healthy.
In this guide to the break-even formula, we’re explaining:
Why doing a restaurant break-even analysis is vital
Common terms related to the break-even point formula
How to calculate a break-even point for your restaurant
How to use a break-even analysis to make business decisions
Break-Even Formula 101: Why Knowing Your Break-Even Point Is Crucial to Restaurant Success
Conducting a restaurant break-even analysis helps you determine how much you need to sell so that your business’ expenses match its revenue. This is one of the most critical restaurant KPIs to measure, because your break-even point enables you to understand how well your restaurant is doing financially.
Your restaurant could be generating $100,000 each month in revenue, which sounds impressive. But if you do a break-even analysis, you might find out that your restaurant spends $200,000 each month and needs to double or triple its revenue to be profitable.
When you know your restaurant’s break-even point, you can set realistic prices and sales goals to make up for your spending and turn a profit.
Break-Even Formula Glossary
Here are several terms you need to know to use the break-even formula successfully.
What is a break-even point?
A break-even point is the spot at which a business earns as much money as it spends. In other words, a restaurant reaches its break-even point when it has a $0 net profit; thus, its revenue and expenses are equal.
What is a break-even analysis?
A break-even analysis is the exercise of calculating your break-even point to find out how much money your business needs to generate or how many units it must sell before it starts becoming profitable.
What is the break-even formula?
The break-even formula helps you find your restaurant’s break-even point. You can calculate it in units sold or sales dollars generated.
The formula for break-even point by units sold is:
Break-Even Point by Units Sold = Sum of Recurring Costs / Contribution Margin
And the formula for break-even point by sales dollars is:
Break-Even Point by Sales Dollars = Sum of Recurring Costs / Contribution Margin Ratio
We’ll break these formulas down in the next section.
How to Calculate Your Restaurant’s Break-Even Point
Here’s how to use the two break-even point formulas to uncover critical business insights.
Pro tip: Use your POS reports to find key components of these formulas, instead of calculating them manually.
How to Use the Break-Even Formula to Find Your Restaurant’s Break-Even Point by Units
So, what do we mean by break-even point by units?
This figure reveals how many units of a specific menu item (e.g. scoops of ice cream) you have to sell to reach a $0 net profit. Calculating break-even point by units, rather than by sales dollars, is most useful when your menu has only a few items on it.
Sandwich shops, pizza parlors, and ice cream shops are examples of venues that might use the formula for break-even point by units.
Choose a period of time over which you’d like to know your break-even point. For example, if you calculate your monthly break-even point, you’re learning how many units you have to sell in one month to earn as much as you spend in one month.
Break-Even Formula by Units Sold = Sum of Recurring Costs / Contribution Margin
Expanded Formula: Recurring Costs / (Revenue Per Unit – Cost Per Unit)
To find your sum of recurring costs, add up regular expenses your restaurant owes, like rent or mortgage payments, salaries and wages, restaurant insurance, inventory, and utilities. Check your POS reports to find these expenses more easily. If you’re calculating your monthly break-even point, determine how much you spend on these things during a month.
To find your contribution margin, subtract your cost per unit from your revenue per unit. Revenue per unit is how much you charge customers for the item that you’re calculating a break-even point for, like a scoop of ice cream. Cost per unit is how much that item costs you to make. You can find your cost per unit in your POS reports. To calculate this figure manually, add up the ingredients’ costs for one unit of the menu item in question.
Let’s put this formula into practice. You own a sandwich shop and want to figure out how many sandwiches you need to sell each month to break even.
First, you find your recurring costs per month. After adding up your monthly inventory costs, rent, utilities, labor, and other expenses, you discover that your restaurant has $25,000 in monthly expenses.
Next, you identify your revenue per unit and cost per unit to calculate your contribution margin. You charge customers $10 for a sandwich, so that’s your revenue per unit. You look up your per-unit costs POS report and find that two slices of bread, three ounces of deli meat, two slices of cheese, and a dollop of mayo costs your shop $3. You subtract the cost per unit cost from revenue per unit ($10 – $3) and find out that your contribution margin is $7 per sandwich.
Then you divide your recurring monthly expenses by your contribution margin ($25,000 / $7) and learn that you have to sell 3,571 sandwiches each month to break even.
25,000 / (10 – 3) = 25,000 / 7 = 3,571
How to Use the Break-Even Formula to Calculate Your Restaurant’s Break-Even Point by Sales
The break-even point by sales dollars formula reveals how much revenue your restaurant must generate to break even. This exercise is more useful than finding out how many units you need to sell if your restaurant has a varied menu.
Break-Even Point by Sales Dollars = Sum of Recurring Costs / Contribution Margin Ratio
Expanded formula: Recurring Costs / [(Average Revenue Per Unit – Average Cost Per Unit) / Average Revenue Per Unit]
Just like in the previous formula, to find the sum of recurring costs, you need to add up your restaurant’s regular expenses, like rent, wages, and inventory costs.
Don’t confuse contribution margin with contribution margin ratio.The contribution margin ratio involves dividing the contribution margin by revenue per unit.
To find your contribution margin ratio, you’ll first need to calculate your contribution margin. You’re going to calculate contribution margin differently than you did for the break-even point per sales dollars formula.
You’ll use the average revenue per unit and the average cost per unit, rather than revenue per unit and cost per unit, because you want to know cost and revenue for the entire menu, rather than just for one item. Look at your POS reports to find these figures.
So, find your contribution margin by subtracting the average cost per unit from the average revenue per unit. Next, find your contribution margin ratio by dividing your contribution margin by your average revenue per unit.
Let’s apply the break-even formula per sales dollars to the sandwich shop example. You want to find out how much revenue you need to generate each month to break even.
You already know from the last example that your sandwich shop’s monthly recurring expenses are $25,000.
Besides sandwiches, your shop also sells chips and drinks. You look at POS reports and learn that your average revenue per unit is $7 (your average menu price), and your average cost per unit is $2 (the average amount it costs your shop to make sandwiches or purchase chips and drinks).
Now you can plug those numbers into the break-even formula per sales dollars:
You find out that you need to generate $35,000 in monthly sales to break even.
4 Ways to Use a Restaurant Break-Even Analysis
Knowing your restaurant’s break-even point can help you set goals to reach your break-even point and eventually make a profit.
Here are four ways to use a break-even point restaurant analysis to achieve business success.
1. Set Sales Goals
Knowing your break-even point can help you set sales goals based on data rather than just a gut feeling or historical sales figures. For example, if you sold 10,000 sandwiches this time last year, but your expenses have since gone up, then setting a goal to sell 10,000 sandwiches isn’t useful.
While the sandwich shop examples mentioned earlier calculated the break-even point on a monthly basis, you can also calculate it on a weekly, quarterly, or annual basis to set sales targets.
2. Set Menu Prices
Conducting a break-even analysis reveals how many units or sales you need to make to break even. If your sales goals seem unattainable, there’s no need to fret. Rather than increasing the number of units you sell, you can also increase your menu items’ prices or decrease the cost per unit.
For example, rather than selling sandwiches for $10, you could charge $13 for them, which will bring you closer to your revenue goals. And if you decrease your cost per unit from $3 to $2 by reducing portion sizes or finding cheaper vendors, you can reach your break-even point even faster.
Suppose you run a per unit break-even analysis with $13 as your revenue per unit and $2 as your cost per unit with $25,000 in recurring expenses. In that case, you have to sell 2,272 sandwiches rather than 3,571 sandwiches (based on when your revenue per unit was $10 and your cost per unit was $3) each month to break even. That’s nearly 1,300 fewer sandwiches you have to sell each month!
3. Manage Expenses
Another way to break even more quickly is to reduce your recurring expenses. While some costs are fixed, like rent payments, others are varied. Audit your most significant variable expenses and find ways to reduce those costs.
For example, labor is one of the greatest variable expenses for restaurants. Restaurants typically spend 30.5% of their revenue on salaries and wages.
Look at your POS to audit your labor spending. How often are you overstaffed? Can you cut down on overtime? Can you give servers side duties that can make you spend less on back of house staff?
When you decrease your recurring expenses, you can reach your break-even point more quickly.
A restaurant is first and foremost a business and needs to be treated as such to stay open for the long term. A break-even point restaurant analysis can unlock powerful insights into your business’ financial health and help you plan for its longevity.
Dana is the former Content Marketing Manager at TouchBistro, sharing tips for and stories of restaurateurs turning their passion into success. She loves homemade hot sauce, deep fried pickles and finding excuses to consume real maple syrup.


L. Aiken, Attitudes toward mathematics, Review of Educational Research, 40 (1970) 551-596.
 L. Aiken, Update on Attitudes and other aﬀective variables in learning mathematics, Review of Educational Re-search, 46 (1976) 293-311.
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of mathematics, Nordic Studies in Mathematics Education, 17 (2012) 101-118.
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the cognitive in pre-university students, inProceedings of the 24th Conference of the IGPME, T. Nakahara and M.
Koyama, eds., 2000, 217-224.
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of the 23rd Annual Conference of PME, O. Zaslavsky, ed., 1999, 249-246.
 P. Di Martino and R. Zan, ‘Me and maths’: Towards a deﬁnition of attitude grounded on students’ narratives,
Journal of Mathematics Teacher Education, 13 (2010) 27–48.
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Systems in Mathematics Education, B. Pepin and B. Roesken-Winter, eds., Springer, Switzerland, 2015, 51-72.
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Education, G. C. Leder, E. Pehkonen, and G. Törner, eds., Kluwer, Dordercht, 2002, 59-72.
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and Learning, D. A. Grouws. ed., Macmillan, New York, 1992, 3–38.
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Norwood, 1980, 265-295.
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 R. Skemp, Relational understanding and instrumental understanding, Mathematics Teaching, 77 (1976) 20–26.


Songs I Never Skip is a collection of my favourite songs.
I am Craig Barton. I am a secondary school maths teacher, based in the North West of England. I am the Maths Adviser to the TES, the creator of mrbartonmaths.com, host of the Mr Barton Maths Podcast, and the co-founder of diagnosticquestions.com. I also run the (non maths!) blogs 555words.com and the Just the Job Podcast. My novels are Secrets and Mince Pies, Tell me a Story and The Cambridge Diaries: A Tale of Friendship, Love and Economics. On Twitter I am @mrbartonmaths.


Geometric shapes - unique plant pictures
Who says mathematics is boring? Such geometric shapes as these look too perfect to be real. But they exist in nature and in a special case in plants. We tend to believe that perfect geometry can only be created by human hands.
That is a complete mistake. Even Galileo Galilei writes in his Il Saggiatore: "The universe was written in the language of mathematics - its characteristics are triangles, circles and other geometric figures". Real artists know that there is an embroidered order in nature. They first observe the natural creations for hours in order to imitate them perfectly.
The perfect spiral of Drosophyllum Lusitanicum
For millennia, human civilization has sought to understand the perfect geometry in nature. So Plato in the 4th century BC. BC believed that symmetry in nature was a proof of the existence of universal forms. The famous British logician and mathematician Alan Turing has explained in his contributions on theoretical biology the way in which the geometric patterns were formed in nature.
Already as children we admired the beautiful structures of the snow crystals. It's like a real magic. Perfect fractals, exact symmetry - how does nature manage to achieve such perfection in the forms?
Marvel! Take a look at these beautiful plant mandalas that we have collected for you here. Next time you are in nature, try to find geometric shapes. You will be surprised what a variety unfolds before your eyes.
Exotic porcelain flower - Hoya aldrichii
Spiral Aloe Polyphylla
Perfect Geometry in Purple - the Amazon Lily Leaf
Stable nature construction
Majestic Dahlia in violet
Ginkgo tree - close-up
The three-dimensional Hygrophila Corymbosa
Green nature mandala - the lobelia
The whimsical Pelecyphora Aselliformis
Magnificent camellia flower
The secret of red cabbage
The perfection of the sunflower blossom
Prickly succulent spiral
Delicate white flowers in circle
Nature Geometry in the Water - Sedum-like Ludwigie


My name is Lindsay Perro and I am an educational writer and content developer.
After spending 8 years as a Middle School Math Teacher, I am now following
my passion and focusing on creating quality educational resources to make
your job easier and keep students engaged and excited about math!
My last teaching position was in Math Intervention. In this position I worked with at-risk math students in grades 6-8. I quickly realized how bored they were by traditional textbooks and traditional ways of teaching. Since I didn't have a specific curriculum to follow I was able to work based on what the students needed. That flexibility really helped me embrace the idea of creating my own curriculum and resources. I discovered that students might hate worksheets, but will jump at the chance to practice fraction operations if it was a coloring activity. Yes, even middle school students love to color! I started to go by the thinking, "If I'm bored making the answer key, they'll be bored doing the work too!" That drastically changed the way I taught.
I've been blessed with two wonderful children and the opportunity to take time away from the classroom to focus on being a Mommy to them, while working from home doing what I love!
My goal is to help math teachers bring their students out of the math textbook and into a hands on, interactive and fun learning environment. By taking students beyond the worksheet and into things like board games, coloring pages, stations, riddles and more, we are able to allow them to have fun while learning.


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.


<insert slideshow here>
A special Thank You to the Oregon Coast STEM Hub for their support of Siuslaw School District this year. They have provided teachers with a variety of professional development opportunities. Siuslaw teachers have been taking advantage of the PD offered and are engaging students throughout the district in Science, Technology, Engineering, Art and Math education.
The Oregon Coast STEM Hub promotes integrated science, technology, engineering and math education and serves coastal teachers, students and communities. It is one of six Regional STEM Hubs funded in 2014-2015 by the Oregon Department of Education. The Oregon Coast STEM Hub is centered at OSU's Hatfield Marine Science Center in Newport and serves the entire Oregon coast region.
Marine Advanced Technology Education, Remotely Operated Vehicles is a program here students use STEAM curriculum to solve real world problems. In this unit, student will work in cooperative learning teams to engineer and build an underwater robot to solve real-world problems underwater.
Check out their official website.


The Project Maths Performance was a collaborative project between Music Generation Wicklow, Music Generation and the Department of Education and Skills. The idea from this project evolved from the established correlation between Maths and Music. From metre, rhythm, random selection, harmonics, repetition, built chordal patterns the possibilities are endless! The Department of Education through Music Generation has given us this opportunity to celebrate this relationship between maths and music and provide a really exciting and accessible experience for the young people of Scoil Chonglais, Baltinglass.
Composer Andrew Synnott conducted workshops and exploration sessions with the students from Scoil Chonglais, supported by five Music Generation Wicklow tutors. Together they explored the connections between maths and music, and selected a notion on which the composition could be based. The students were invited to perform at a National Conference for Project Maths held in the National University of Ireland, Maynooth on Friday 15th November 2013. Forty Students from Scoil Chonglais and five professional musicians from Music Generation performed the original composition which was attended by the Minister for State Sean Sherlock.


The t-shirt fundraiser was great, kids and adults from all the grades ordered shirts. I will place the order for the shirts Monday (Today) afternoon.
Super Power of the week- Virtue of Unity. Working together we can do anything!
So exciting, Mrs. Harrison and I are working together in P.E. to teach these first graders how to play kick ball. We are starting very basic and having a lot of fun!
Social Studies- This week we will finish up our unit on Needs, wants, money and jobs. I am very excited to start science again. We will study sound and light!
Math- We are continuing to work on place value with 1s and 10s. We also introduced using the number chart as a math tool. I am sending home a sheet on Xtramath. This is a great web site/app we are using in class that gives great practice with math facts and also great information on how each student is doing. I strongly encourage students to practice at home with it daily. It only take 5-10 min.
Homework-Extra math, 2 Math pages, Star reading, 8 stars are required with 4 sentences. These sentences should summarize what they read. This is a great writing practice for our first graders. It is also great comprehension practice.
Have a great week,
4/27 Talent Show
4/30-5/11 Kick ball tournament.
5/4 Dace Evolution Field trip 9:40-11:20
5/11 STAFF AND PARENT KICKBALL GAME


Dr Antonie Kotze (Pr.Phys)
Antonie holds a Ph.D. in Theoretical/Mathematical Physics from the University of the Witwatersrand where Quantum Chaos Theory was his field of interest. He is a registered professional physicist (http://www.saip.org.za/index.php/news-and-events/opportunities/287-register-as-professional-physicist-pr-phys-with-saip). With more than 23 years' experience as a quantitative analyst in the South African and African financial and derivatives markets, he is a renowned expert in financial mathematics, modelling and training. Antonie is a former Rand Afrikaans University (currently the University of Johannesburg) faculty member who has facilitated many successful training workshops throughout Africa. He has recently been appointed Senior Research Associate in the department of Quantitative Finance at the University of Johannesburg and and as Extraordinary Senior Lecturer in the Department of Mathematics and Applied Mathematics at the University of Pretoria.
With his one foot firmly planted in academia, he bridges the gap between academic research and the practicalities of the trading floor and risk management within trading houses.
The span of Antonie's derivative experience includes capital, interest rate, foreign exchange, commodity (hards and softs), credit and equity markets. He has hands-on knowledge of trading derivatives, statistical analysis, Monte Carlo simulations, stress testing and scenario analysis, option trading and risk management systems, basket and relative arbitrage, futures curves, equity linked and interest rate derivative structures, foreign exchange futures, derivatives clearing and collateralised finance - the gains of working in a front office quantitative position. He is also a registered Safex and YieldX derivatives dealer.
He has been an independent derivatives pricing, valuation and model validation specialist and expert since 2003. He also conducts and facilitates specialist training courses and workshops on all topics relating to the financial markets, trading, risk management, Basel regulations and derivatives pricing and modeling.
Antonie's career history includes close work with institutional clients and hedge funds to devise investment, hedging and gearing strategies utilising complex optionality. He has developed highly sophisticated mathematical models and computer systems used by traders, risk managers, fund managers and corporate financiers. As a derivative expert he assists companies and audit firms in the structuring, modelling and valuation of complex mergers, acquisitions, take-overs, lending agreements between companies, BEE structures, structured transactions and employee share incentive schemes.
Antonie held positions as a quant at Standard Bank, RMB, Mercury Structured Products and Absa Corporate and Merchant Bank (now Absa Capital and part of Barclays Capital) before he incorporated Financial Chaos Theory (FCT) in 2003. FCT is proud to be an independent valuation service provider or pricing vendor.


An unfingered guitar string is 0.70 m long and is tuned to play E above middle C (330 Hz). How far from the end of this string must the finger be placed to play G# above middle C (415 Hz)?
I’m stuck on this one can someone help me out?
For a string fixed at both ends the fundamental frequency is f1 = v/2L
So v/2 = L1*f1 Since the wave speed is constant
we obtain for the second frequency
v/2 = L2*f2
Putting these together L1*f1 = L2*f2 or L2 = L1*f1/f2 = 0.70m*330/415 = 0.56 m
So you must finger the string at 0.70-0.56 = 0.14m from the end


Table of Contents :
Top Suggestions 1st Grade Counting Coins Worksheet :
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In the dynamic realm of mathematics, where precision and efficiency are paramount, the need for expert solutions in seconds has become increasingly crucial. As students, educators, and professionals grapple with mathematical challenges, a distinguished ally steps into the spotlight – the “Mathematics Maestro Solver.” This article delves into the significance of the Mathematics Maestro Solver, a tool designed to provide expert solutions with unprecedented speed and accuracy.
Rising Demands in the World of Mathematics:
The contemporary landscape of academia and professional pursuits demands swift and accurate solutions to mathematical problems. As the complexity of mathematical challenges continues to grow, the pressure to obtain expert solutions in a matter of seconds has become a defining characteristic of success in various fields. The Mathematics Maestro Solver stands at the forefront, ready to meet these rising demands head-on.
Features of Mathematics Maestro Solver: Navigating its Capacities:
The Mathematics Maestro Solver distinguishes itself through a suite of features meticulously designed to address the diverse needs of users engaged in mathematical problem-solving. Its advanced algorithms, instantaneous functionality, and commitment to precision make it an indispensable tool for those seeking expert solutions within seconds.
Advanced Algorithms: Harnessing Computational Power:
At the heart of the Mathematics Maestro Solver are advanced algorithms that harness the full spectrum of computational power. These algorithms are crafted to unravel complex mathematical problems with speed and accuracy, ensuring that users can obtain expert solutions without compromising on precision. The synergy of mathematical expertise and cutting-edge algorithms positions the Mathematics Maestro Solver as a powerhouse in the world of mathematical tools.
Instantaneous Functionality: Speed Redefined:
One of the defining features of the Mathematics Maestro Solver is its instantaneous functionality. In a world where time is of the essence, users can input mathematical challenges and receive expert solutions in a matter of seconds. This real-time capability not only sets the Mathematics Maestro Solver apart but also caters to the urgent needs of students, professionals, and anyone engaged in time-sensitive mathematical tasks.
Versatility Across Mathematical Realms: From Basics to Complex Challenges:
The Mathematics Maestro Solver’s versatility shines as it seamlessly navigates through a wide array of mathematical realms. Whether users are tackling fundamental arithmetic problems, algebraic equations, or intricate calculus challenges, the solver adapts to the complexity of each task. Its versatility positions the Mathematics Maestro Solver as a comprehensive tool catering to users with diverse mathematical problem-solving needs.
User-Friendly Interface: Accessibility Redefined:
Despite its computational prowess, the Mathematics Maestro Solver maintains a user-friendly interface. Accessibility is paramount, and the tool is designed to cater to users across different proficiency levels. The intuitive interface ensures that individuals, regardless of their mathematical background, can effortlessly engage with the solver and obtain expert solutions within seconds.
Precision at Every Step: Ensuring Accuracy in Results:
While speed is a hallmark of the Mathematics Maestro Solver, it does not compromise on precision. Each solution generated by the solver is meticulously crafted to uphold accuracy and correctness. This commitment to precision ensures that users can rely on the Mathematics Maestro Solver for dependable and trustworthy mathematical solutions, a crucial attribute in academic and professional settings.
Plagiarism-Free Solutions: Upholding Academic Integrity:
Maintaining academic integrity is a core value embedded in the functionality of the Mathematics Maestro Solver. The tool provides plagiarism-free solutions, ensuring that each response is generated based on the user’s input. This commitment to authenticity and originality reinforces the Mathematics Maestro Solver’s credibility as a reliable educational resource.
Customization for Individual Preferences: Tailoring the Experience:
Recognizing that every user has unique preferences, the Mathematics Maestro Solver offers customization options. Users can tailor settings to align with their preferred learning style, adjusting the complexity of solutions, formatting preferences, and more. This customization ensures that the Mathematics Maestro Solver caters to individual needs, enhancing the overall user experience.
Feedback Mechanism for Continuous Improvement: Evolution in Excellence:
To ensure that the Mathematics Maestro Solver remains at the forefront of technological excellence, it incorporates a feedback mechanism. Users can provide input on the effectiveness of solutions, user interface features, and overall user experience. This feedback loop facilitates continuous improvement, allowing the Mathematics Maestro Solver to evolve based on the evolving needs and preferences of its user base.
Educational Support and Enrichment: Beyond Solutions to Understanding:
The Mathematics Maestro Solver goes beyond being a solution provider; it serves as an educational ally, offering support and enrichment. It acts as a virtual tutor, providing additional insights, explanations, and alternative approaches to mathematical challenges. Users, whether students or professionals, can leverage this support to deepen their understanding of mathematical concepts and enhance their overall proficiency.
Continuous Learning and Adaptability: Navigating the Mathematical Landscape:
The Mathematics Maestro Solver embodies a philosophy of continuous learning and adaptability. It recognizes that the landscape of mathematical challenges is ever-evolving, with new complexities and nuances emerging regularly. By promoting a mindset of continuous learning and adaptability, the Mathematics Maestro Solver ensures that users remain agile and well-equipped to navigate the dynamic world of mathematical problem-solving.
The Mathematics Maestro Solver emerges as a transformative tool in the realm of mathematical problem-solving, providing expert solutions in seconds. Its advanced algorithms, instantaneous functionality, and commitment to precision redefine the landscape of mathematical tools. As users embrace the Mathematics Maestro Solver, they unlock a gateway to rapid and accurate mathematical solutions, empowering themselves to navigate the challenges of mathematics with unparalleled speed and expertise. In a world where time is a precious commodity, the Mathematics Maestro Solver stands as the key to unlocking a new era of expert solutions in the blink of an eye.


The NO MATH solution for customizing your knitting patterns.
Shorten or lengthen your cardigan and calculate the perfect band pickup.
Add darts to any pattern for improved fit.
Accurately increase or decrease a large number of stitches across a row.
Design your own rectangular items using any yarn and any stitch pattern.
Easily modify the number and size of buttons to personalize a cardigan.
Substitute yarns for any knitting pattern with a little math.
Adjust the length of any shaped piece. Perfect for modifying sleeve lengths.
Shape a large number of stitches over a smaller number of rows. Shape shoulders for better fit.
This app is available on iOS and Android devices, download today and start customizing your patterns.
(iPad version in the works)


FIXED INCOME STATISTICS
Average Price is a price of bond's interest- rate sensitivity based on the average of the price over which a bond's cash flows accrue to the bondholder.
Source: Thompson, Siegel & Walmsley LLC
Average Maturity is computed by weighting the maturity of each security in the portfolio by the market value of the security, then averaging these weighted figures.
Average Duration is a time measure of a bond's interest-rate sensitivity, based on the weighted average of the time periods over which a bond's cash flows accrue to the bondholder.


Thursday, April 18, 2013
According to a recent theory the Universe could be a dodecahedron. It is surprising that Plato used a dodecahedron as the quintessence to describe the cosmos. Plato (c. 427 BC – c. 347 BC) also stated that time had a beginning; it came together with the universe in one instant of creation.
Plato held the view that mathematical objects really existed so that they are discovered by mathematicians (in the same way that new continents are discovered by explorers) rather than invented. Plato believed that mathematics provided the best training for thinking about science and philosophy. The five regular solids are named Platonic Solids today after Plato.
Of the 5 solids, the tetrahedron has the smallest volume for its surface area and the icosahedron the largest; they therefore show the properties of dryness and wetness respectively and so correspond to Fire and Water. The cube, standing firmly on its base, corresponds to the stable Earth but the octahedron which rotates freely when held by two opposite vertices, corresponds to the mobile Air. The dodecahedron corresponds to the Universe because the zodiac has 12 signs (the constellations of stars that the sun passes through in the course of one year) corresponding to the 12 faces of the dodecahedron.
“To earth, then, let us assign the cubic form, for earth is the most immovable of the four and the most plastic of all bodies, and that which has the most stable bases must of necessity be of such a nature. Now, of the triangles which we assumed at first, that which has two equal sides is by nature more firmly based than that which has unequal sides, and of the compound figures which are formed out of either, the plane equilateral quadrangle has necessarily a more stable basis than the equilateral triangle, both in the whole and in the parts. Wherefore, in assigning this figure to earth, we adhere to probability, and to water we assign that one of the remaining forms which is the least movable, and the most movable of them to fire, and to air that which is intermediate. Also we assign the smallest body to fire, and the greatest to water, and the intermediate in size to air, and, again, the acutest body to fire, and the next in acuteness to air, and the third to water. Of all these elements, that which has the fewest bases must necessarily be the most movable, for it must be the acutest and most penetrating in every way, and also the lightest as being composed of the smallest number of similar particles, and the second body has similar properties in a second degree, and the third body, in the third degree. Let it be agreed, then, both according to strict reason and according to probability, that the pyramid is the solid which is the original element and seed of fire, and let us assign the element which was next in the order of generation to air, and the third to water.We must imagine all these to be so small that no single particle of any of the four kinds is seen by us on account of their smallness, but when many of them are collected together, their aggregates are seen. And the ratios of their numbers, motions, and other properties, everywhere God, as far as necessity allowed or gave consent, has exactly perfected and harmonized in due proportion.“
Plato: Timaeus (55d-56c) p 1181
The posters visualize the five solids in space creating a surreal depiction of Plato’s Universe.


Ph.D. in Applied Mathematics, May 2012, New Jersey Institute of Technology, USA
Dissertation: Instabilities in Newtonian films and nematic liquid crystal droplets.
Advisors: Dr. Lou Kondic and
Dr. Linda J. Cummings
M.S. in Applied Mathematics, National Chung Cheng University, Taiwan
Thesis: Numerical methods for the nonlinear Schrodinger equation
Advisor: Dr. Ming-Chih Lai
B.S. in Mathematics, National Chung Cheng University, Taiwan
2012.12--2014.07 Research Associate, Loughborough University, UK
2012.06--2012.12 Marie Curie Experienced Researcher, Loughborough University, UK
Coherent structures in non-local dispersive active-dissipative systems T.-S. Lin, M. Pradas, S. Kalliadasis, D. T. Papageorgiou and D. Tseluiko,
Modeling flow of nematic liquid crystal down an incline
M. A. Lam, L. J. Cummings, T.-S. Lin and L. Kondic, J. Eng. Math., in press.
Numerical study of a non-local weakly nonlinear model for a liquid film sheared by a turbulent gas T.-S. Lin, D. Tseluiko and S. Kalliadasis, Procedia IUTAM, 11, 98 (2014).


Pyongyang, May 25 (KCNA) — It was in 1343 that the astronomy-related book “Susiryokchopbopripsong” written by Kang Bo, a civil official and mathematician in the period of Koryo (918-1392), was brought out.
Carried in the book are numeration tables for making calendar and astronomical data.
The book has three sections, which deal with the theories on movements of the sun and the moon and a theory on Mercury, Venus, Mars, Jupiter and Saturn, together with an appendix to mathematical theories on multiply and division.
The book is of great significance as it is a collection of astronomical calculations made in a peculiar way and shows the astronomical achievements gained by the then Korean people.
Image credit: https://www.flickr.com/photos/ninjawil/2299529701/


Easy to use, myRandom is a random number generator. Based on a given range, it generates a random number (or a set of random numbers) for you! You can use it to raffle gifts, on events, promotions and much more!
Here are some of myRandom features:
- Generates as many random numbers (or sets) you want.
- Keeps track of the numbers you've generated.
- Generated sets can be shown in ascending, descending or random order.
- Generated numbers can be copied and pasted into an e-mail, text message or any other app.


Are you curious about how many milliliters are in half a pint? Well, we’ve got the answer for you! In the US customary system of measurement, there are 236.588 milliliters in half a pint. That’s a precise conversion that can come in handy when working with recipes or understanding liquid volumes.
Converting Pints to Milliliters
Let’s dive into the world of conversions and explore how pints can be converted into milliliters. Understanding these conversions can come in handy when you need to switch between different measurement systems or work with recipes that use different units of volume. So, let’s get started!
- The Conversion Factor:
To convert pints to milliliters, we need to know the conversion factor. A pint is equal to 473.176 milliliters (ml). This means that for every pint, there are approximately 473 ml.
- Converting Pints to Milliliters:
Now that we have our conversion factor, let’s put it into action. To convert a given number of pints into milliliters, simply multiply the number of pints by 473.176.
- If you have 2 pints, multiply 2 by 473.176: 2 x 473.176 = 946.352 ml
- If you have half a pint, which is equivalent to 0.5 pints: 0.5 x 473.176 = 236.588 ml
- Practical Examples:
Understanding conversions becomes easier when we see how they apply in real-life scenarios.
a) Cooking: Imagine you’re following a recipe that calls for half a pint of milk but your measuring cup only has milliliter markings. By using our conversion factor, we know that half a pint is equal to approximately 236 ml of milk.
b) Bartending: Aspiring mixologists often encounter recipes in both pints and milliliters when crafting delicious cocktails at home or behind the bar counter. Knowing how to convert between these units allows them to accurately measure and create their signature drinks.
How Many ML in Half a Pint
When it comes to understanding measurements, it’s important to have a clear grasp on the conversion factors between different units. In this section, we’ll focus on clarifying how many milliliters (ml) are in half a pint. By breaking down the numbers and providing relevant examples, we aim to make this topic easier for you to comprehend.
To begin with, let’s establish the basic conversions. One pint is equal to 473.176 milliliters (ml), while half a pint is simply half of that amount, which gives us 236.588 ml. It’s worth noting that these values may vary slightly depending on rounding conventions or regional differences in measurement standards.
Understanding these conversions can be particularly useful when dealing with recipes or beverage servings. For instance, if a recipe calls for half a pint of water and you prefer measuring ingredients in milliliters, you’ll need approximately 236.588 ml.
So, next time you’re faced with a recipe that calls for half a pint and want to convert it into milliliters, remember this: there are 236.588 milliliters in half a pint according to the US customary system of measurement. Armed with this knowledge, you’ll be able to confidently tackle any culinary endeavor that comes your way!


Omar Abdul Halim, Master’s Student (started in Fall 2020; defended: February 2022 — UNBC).
Thesis: Dynamics of integrodifference and reaction-diffusion equations in heterogeneous media. (Omar’s Thesis is available at UNBC Library Reserves)
Thomas Peterson (NSERC-USRA, Summer 2022). Project: Nonlinear integral equations: deterministic and numerical analysis.
Katherine Saunderson (NSERC-USRA, Summer 2021). Project: Integrodifference equations and dynamics in patchy landscapes.


About FOSSEE Animations
The FOSSEE Animations Project works on making seemingly complex Science and Mathematics topics feel natural and approachable through animations.
The animations are created by students across the country. The students work with a mentor in creating a library of visualizations.
FOSSEE Animations is a part of the FOSSEE
project at the Indian Institute of Technology, Bombay
. The FOSSEE project is funded by the National Mission on Education through ICT, MHRD, Government of India.
All animations are made with open-source toolkits and are freely available under a Creative Commons Attribution-ShareAlike 4.0 International License. The animations themselves are open-source. You may find them here
Anyone can contribute to this project! You may read the Guidelines page
for detailed instructions on how you can contribute.
Math Internships and Workshops (on Visualizing Math with Open-Source toolkits) are conducted throughout the year. Visit our Outreach
page for more details on the same.
Internships are from selected topics in Mathematics, like Real Analysis, Linear Algebra and Calculus. Our focus lies primarily on an undergraduate level of Mathematics. To view our repository on Mathematics topics, visit math.animations.fossee.in
We also conduct workshops in colleges and universities across India. You can write to us at firstname.lastname@example.org
to request a workshop at your college.


Logic Cards Yellow is the second edition of Logic Cards with all new challenges – a set of logic, geometry, and mathematical tasks to tease your brain. It comes with an augmented reality app, that shows you animated solutions for each challenge. The challenges have various difficulty levels to choose from. The pack fits in your pocket and you can take it anywhere with you. It’s educational, it’s math, it’s smart, and it’s a maze of IQ boosting fun! Enjoy yourself! Logic Cards Yellow includes 53 cards with number, logic or geometry challenges in 5 difficulty levels, instructions, answers and a solutions app.


Karvonen Equation for Target Heart Rate Range Calculation
The Karvonen Formula is a mathematical formula that helps you determine your target heart rate zone. Staying within this range will help you work most effectively during your cardio workouts.
The typical way we calculate MHR is with the formula 220-age. This formula is a bit controversial because it doesn’t reflect the differences in heart rate according to age;
the formula overestimates the max heart rate for younger athletes, and underestimates the max heart rate for older athletes.
A more accurate formula, offered in a study published in the journal, Medicine & Science in Sports & Exercise, is
206.9 – (0.67 x age)
THR= [(MHR – RHR) X % intensity] + RHR
THR =Target Heart Rate
MHR =Maximum Heart Rate 206.9 – (0.67 x age)
RHR =Resting Heart Rate (bpm when at rest)
BPM =Beats Per Minute
HRR =Heart Rate Reserve (Difference between MHR and RHR)
% Intensity =Usually 60 and 80 percent
Here is an example of the Karvonen formula for a 23 year old person with a resting heart rate* of 65 beats per minute (*to get your resting heart rate, take your pulse for one full minute when you first wake up in the morning or after you’ve been resting for a while).
206.9 – (0.67 x 23 (age)) = 191
191 – 65 (resting heart rate) = 126 (heart rate reserve)
126 * 65% (low end of heart rate zone) OR 85% (high end) = 82 OR 107
82 + 65 (resting heart rate) = 147
107 + 65 (resting heart rate) = 172
The target heart rate zone for this person would be 147 to 172
You only have one life, choose to live it.
KARVONEN FORMULA WORKSHEET
Take your heart rate first thing in the morning in a lying position before rising.
Count how many beats in one minute. Do this for 5 consecutive days.
Total of all 5 days___________ divide by 5 = _________________________
Your Resting Heart Rate
Now, (206.9 – (0.67 x 23 (age)) = _____________________
Your Maximum Heart Rate
____________________ minus ____________________ = ______________________
Your Maximum Heart Rate Your Resting Heart Rate Your Heart Rate Reserve
_________ x .50 = _________ + _________ = __________ (Your Target Heart Rate at 50%)
Your HRR Your RHR
x .65 = _________ + _________ = ________ (Your Target Heart Rate at 65%)
x .70 = _________ + _________ = ________ (Your Target Heart Rate at 70%)
x.75 = _________+ _________ = ________ (Your Target Heart Rate at 75%)
x .80 = _________ + _________ = ________ (Your Target Heart Rate at 80%)
x .85 = _________ + _________ = ________ (Your Target Heart Rate at 85%)
x .92 = _________ + _________ = ________ (Your Target Heart Rate at 92%)
Finding Your Daily Caloric Needs:
Calculating your Basal Metabolic Rate (BMR) Total Daily Energy Expenditure (TDEE)
Men: BMR = 66.5 + (13.75 X wt in kg) + (5.003 X ht in cm) – (6.775 X age in years)
Women: BMR = 655.1 + (9.5663 X wt in kg) + (1.85 X ht in cm) – (4.676 X age in years)
Note: 1 inch = 2.54 cm. — Height in inches x 2.54 = Height in centimeters 1 kilogram = 2.2 lbs. — Weight in pounds / 2.2 = Weight in kilograms
You are female, You are 30 years old, You are 5′ 6 ” tall (167.6 cm) You weigh 120 lbs. (54.5 kilos)
Your BMR = 655.1 + 521.36 + 310.06 – 140.28 = 1346.24 -or- 1346 calories/day
Now that you know your BMR, you can calculate TDEE by multiplying your BMR by your activity multiplier from the chart below:
Sedentary = BMR X 1.2 (little or no exercise, desk job)
Lightly active = BMR X 1.375 (light exercise/sports 1-3 days/wk)
Mod. active = BMR X 1.55 (moderate exercise/sports 3-5 days/wk)
Very active = BMR X 1.725 (hard exercise/sports 6-7 days/wk)
Extr. Active = BMR X 1.9 (hard daily exercise/sports & physical job or 2X day training, i.e marathon, contest etc.)
Example: Your BMR is 1346.24 calories per day Your activity level is moderately active (work out 3-4 times per week) Your activity factor is 1.55
Your TDEE = 1.55 X 1346.24 = 2086.67 -or- 2087 calories/day
Katch-McArdle formula (BMR based on lean body weight)
If you have had your body composition tested and you know your lean body mass, then you can get the most accurate BMR estimate of all. This formula from Katch & McArdle takes into account lean mass and therefore is more accurate than a formula based on total body weight. The Harris Benedict equation has separate formulas for men and women because men generally have a higher LBM and this is factored into the men’s formula. Since the Katch-McArdle formula accounts for LBM, this single formula applies equally to both men and women. BMR (men and women) = 370 + (21.6 X lean mass in kg)
You are female You weigh 120 lbs. (54.5 kilos)
Your body fat percentage is 20% (24 lbs. fat, 96 lbs. lean)
Your lean mass is 96 lbs. (43.6 kilos)
Your BMR = 370 + (21.6 X 43.6) = 1312 calories
To determine TDEE from BMR, you simply multiply BMR by the activity multiplier:
Your BMR is 1312
Your activity level is moderately active (work out 3-4 times per week)
Your activity factor is 1.55 Your TDEE = 1.55 X 1312 = 2033 calories
Take the guesswork out of your calculations and take control of your life! There are too many variables in our daily fitness lives to leave something simple and easily determined, to chance.
Visit us at Imprint Fitness if you have any questions and to contact us directly.
Happy calculating & I’ll see you around the gym!


Q: What courses should be taken during the first year?
Analytical, computational and technological skills have become increasingly important in many disciplines and professional careers. We therefore encourage students to improve and further develop those skills, independent of their intended majors, by taking courses in Mathematics and Computer Science in their first year in college.
To enroll in an introductory mathematics course, students (with the exception of those with advanced-placement credit in calculus) must take the Mathematics Placement Test given during preregistration. Based on placement test scores, students are place into Precalculus, Calculus, or Honors Calculus. Students are encouraged to enroll in the course according to their placement . Students may challenge their placement by taking a backup placement test once.
Two Calculus tracks are open to students with appropriate scores in the Mathematics Placement Test: the regular track MATH 120-MATH 121, and the Honors track MATH 124-MATH 125. Both tracks start in the Fall. Students who do not place into Calculus, but place into Precalculus (MATH 119), can start with MATH 119, to prepared for Calculus and continue with MATH 120 the following year.
The regular track is the less theoretical Calculus sequence (MATH 120-MATH 121). It is geared toward students interested in the natural and social sciences, as well as Computer Science. Many of those studetns will not continue with upper level mathematics classes. Students in this sequence who plan to continue to study mathematics in the future are encourage to take MATH 121 in the Spring semester of their first year.
Honors Calculus (MATH 124-MATH 125) is the more theoretical track and prepares students for intermediate and upper level mathematics classes. It is therefore recommended that students with a strong mathematical background, who intend to take higher-level mathematics classes in the future, start with MATH 124-MATH 125. Those students are usually interested in Mathematics, Physics, Computer Science, and Economics.
Students with a sufficiently high score on the AP (AB) Calculus test receive credit for MATH 120. This credit fulfills the prerequisite for MATH 121, but not for MATH 125. It is recommended that these students start with MATH 124 and continue into MATH 125 if they are interested in taking higher-level mathematics classes in the future.
Students with a sufficiently high score on the AP (AB/BC) Calculus test receive credit for MATH 121 and may continue with MATH 130. In the exceptional circumstances, first-year students without credit for MATH 121 may enroll in MATH 130 with permission fo the instructor.
Q: What courses should first year students steer clear of?
Most mathematics courses have to be taken in a particular sequence. Students are not allowed to register for courses without fulfilling the necessary prerequsities first. For this reason, a mathematics major cannot be completed in less than three years.
Q. Does the deparment offer a First-Year Intensive course?
The department offers 2 FYI courses: 1) Diving into Mathematics Research (MATH 110); 2) Diving into Computer Science Research (CSci 110). It is a 5th class for all students, and it is spread over the course of the year with 0.5 credits per semester. It gives first-year students a unique opportunity to work with faculty and peers on interesting current research projects and to become a part of an intellectual and social community of students with similar interests. Both courses are by permission only and there is a limited number of spaces. With few exceptions, only students with a strong background in Mathematics who register for Honor Calculus or have credit for Calculus with be allowed to join in the class. Students interested in Mathematics research should contact Professor Gideon Maschler (firstname.lastname@example.org). Students interested in Computer or Computational Science should contact Professor Natalia Sternberg (email@example.com).
Q: Where should students or faculty go for more information?


Monday, October 15, 2012
Third World Farmer
After looking at various games, I chose Third World Farmer. I think this game gives the student the opportunity to problem solve and by the choices made, they will either succeed or fail. I have played this game five times and I have to admit I was horrible at first! But, each time I am getting better and better! This game really forces the student to understand world problems and to use cognitive skills.
Using Third World Farmer, I would have my students keep of log of how much money they have, what they spend for the year and how much they made, repeating this every year. The objective would be for the students to understand adding and subtracting figures in a non-traditional math way (solving equations). This would ready them for their own life, learning how to manage money. They would have to present the log that they have kept and explain to the class what money they used and what they made each year and if they had enough left over for the following year and the outside factors that affected this.
I could also use this game as a history/geography lesson. The objective would be to understand and discuss how resources affects life in third world countries. They will also be able to compare and contrast our own life with those in a third world, like Africa. Working in small groups, students can compare and contrast their own life to that of Africa's. Then, as a class, we can discuss the results before having the students write their findings. Talking in a small group (where some may feel more comfortable talking) and then in a larger class group will give the students plenty of ideas and time to ask questions before having to work on their own and write their conclusions.


Rate Group Test Worksheet Report
Normal and MVAL EBARS
The normal accrual rate for an employee for the plan year is the increase in the employee’s accrued benefit (within the meaning of section 411(a)(7)(A)(i) during the measurement period.
The most valuable optional form of benefit used to determine the most valuable accrual rate reflects the value of all Optional Forms of Benefits accrued or treated as accrued that are payable in any form and at any time under the plan.
What is a Rate Group?
A Rate Group consists of one HCE and all other employees whose Normal and MVAL EBARS are equal to or greater than the EBARS of the HCE.
In order to determine whether a plan satisfies the general test, the plan is broken down into rate groups, or “mini plans”. Each HCE who receives an allocation or an accrual rate forms a rate group. Every other participant who has an equal or greater allocation rate or accrual rate than the HCE is a member of that rate group.
In our example, the first Rate group consists of Brian HCE3 only because there are no other employees with a Normal and MVAL EBARS greater than Brian.
Rate Group 2 consists of Kyle HCE2 and Brian HCE3. That’s because Brian’s Normal and MVAL EBARS are greater than Kyle.
Rate Group 3 consists of Chad HCE1 and Jamie, Kyle and Brian.
To simplify things, this report, is sorted by both Normal and MVAL EBARS in descending order.
Now, it should be easy to see that Rate Group 4 consists of Rick HCE4 and all the employees above Rate Group 4.
Finally, Rate Group 5 consists of Frank HCE5 and all the other employees.
What is a Ratio Percentage?
A Ratio Percentage must be calculated for each Rate Group. This calculation is done in three steps:
Step 1: Count the number of NHCE's in each Rate Group and divide this by the total NHCE's in the Plan.
Step 2: Count the number of HCE's in the Rate Group and divide this by the total HCE's in the Plan.
Step 3: The Ratio Percentage for a Rate Group is Step 1 divided by Step 2.
Look at Rate Group 3 in the example below:
The Ratio Percentage of Rate Group 3 is 1/3 (one out of 3 NHCE's) divided by 3/5 (3 HCE's out of 5 HCE's) equals 55.56%.
If the Ratio Percentage for all Rate Groups is 70% or more, the plan automatically passes the Rate Group test.
In this example, our Ratio Percentages are all lower than 70%.
However, if the Plan passes the Average Benefit Percentage Test, the Ratio Percentages must only be greater than the Mid-Point Percentage of 45% to pass.
But since Rate Group 1 and Rate Group 2 are both zero, we fail.
The worksheet below, shows that we only need 1 NHCE to have Normal & MVAL EBAR greater than Brian & Kyle’s EBARS to pass. You should then go to the Classes and increase the Profit sharing for the NHCE's until it passes the Rate Group Test.


August 16, 2017 by johnston00
However, the proportion of students at ordinary level who are struggling and failing to secure any CAO points for their subjects has jumped dramatically in some subjects.
Unlike higher level, a score of below 40 per cent at ordinary level does not attract any CAO points.
At ordinary-level maths, for example, the proportion failing to get any CAO points has now reached 10 per cent.
This means more than 3,000 students, in effect, failed their maths, posing real difficulties in accessing a range of college course.
Some of the most dramatics increases in the proportion of students failing to secure CAO points for ordinary level subjects were in English (up 42 per cent) and Irish (up 64 per cent).
Much of this increase may well be down to a higher concentration of less-able students remaining in ordinary-level courses.
But the figures are also likely to point to concerns over teaching quality and difficulties accessing foundation-level classes in smaller schools.