Lakeside’s math departments aim to challenge and inspire all students to reach their mathematical potential. We offer a wide range of courses and use a variety of teaching modes to meet the specific needs of Lakeside students. From grades 5 through 12, students are actively engaged in math – working together in groups, at the board sharing solutions, presenting to their peers, debating strategies, and creating a wide range of creative projects. In all courses, emphasis is placed on collaboration, problem-solving, computational thinking, and clearly communicating mathematical ideas and concepts.
We believe that strong math skills play an important role in becoming an engaged global citizen. A solid understanding of a wide variety of mathematical disciplines will enhance students’ abilities to understand their world, explore global issues, and promote social justice through the power of analyzing claims and communicating effectively with real data as well as through computational tools and approaches.
Middle School: A strong foundation
The goal of the Middle School math program is to provide a strong foundation in mathematics through challenging courses that are appropriate to the ages, abilities, and needs of our students. In addition to preparing them for future math endeavors, we want students to be excited by math’s potential for fun and creativity.
We aim to equip students with the mathematical skills of a competent citizen in today’s world.
These skills include the ability to model situations mathematically; to estimate and compare magnitudes; to interpret graphs and statistics; to calculate probabilities; to evaluate numerical and spatial conclusions; to solve problems mentally as well as with paper, calculator, and computer; and to communicate findings effectively. At all levels, students learn to work collaboratively as well as on their own.
Part of what you’re teaching is: What do you do when you encounter an obstacle? In the context of math class, that means helping students set high goals, helping them deal with the fact that sometimes you falter on the way to those goals, and helping them celebrate when they meet those goals. – Tom Rona, Middle School math teacher
The content of our grades 5-8 math courses is normally covered in grades 6 through 9 in other schools. Students progress from arithmetic skills and mathematical thinking through pre-algebra and conceptual frameworks, to algebra and trigonometry. In each course, students deepen their understanding of concepts and skills introduced in previous courses. In addition to our regular math curriculum, many students choose to engage in Math Club (5/6 and 7/8), where they can have fun exploring math and extend their learning through working on challenging problems alone or in groups.
Read more about Middle School math in the Middle School curriculum guide.
Upper School: From the basics to college-level
We offer a wide range of math and computer science courses at the Upper School so that students can be challenged at a level appropriate for them at every grade. Each course emphasizes collaboration, problem-solving, and clearly communicating mathematical ideas and concepts. Since 2015, computer science concepts and principles have been embedded in the math curriculum, reflecting Lakeside’s belief that programming is an important 21st-century skill.
Every Lakeside student gains experience with computer science and programming, even if they never take a computer science class.
For the majority of math courses, we offer regular, accelerated, and honors levels. Students work with their teachers to determine the right level for them each year, and students can move between levels. While only three years of mathematics are required for graduation, the majority of Upper School students take a four-year sequence of algebra 2, geometry, precalculus, and statistics or calculus. All levels of courses at Lakeside provide a firm foundation in mathematics and will prepare students for college math courses. Calculus and statistics courses will prepare students for success on AP tests.
A range of computer science course offerings include everything from an introductory level course for those with no prior experience in programming, to advanced project-based courses such as 3-D prototyping and printing. The program takes advantage of the region’s technology community: Through guest lectures, field trips, and other opportunities, students are exposed to real-world applications of computing technology, including its myriad uses in medicine, sports, robotics, architecture, music games, literature, apparel design, communication, and international development.
Read more about Upper School math and computer science in the Upper School curriculum guide.


How many grams in a pound? This article provides the answer and the conversion chart for the metric and imperial units. In addition, it offers a calculator to convert grams to pounds. Read on to learn more. And don’t forget to use this conversion chart to convert grams to pounds! This will give you more accurate answers! Listed below are a few examples of how to convert grams to pounds.
Gram is 1/1,000 of a kilogram
A gram is a unit of mass in the International System of Units. It was originally defined as the weight of pure water in a cubic centimeter at the temperature of ice melting. Since the definition of a kilogram is no longer based on a universal prototype, it has been renamed to reflect Planck’s constant, h. It also includes a new definition of the meter and second.
One gram equals 0.001 kilogram. The formula to convert grams to kilograms is to multiply the number of grams by 0.001 and divide it by 1000. For example, if you weigh 1500 grams, divide that number by 1,000. That way, you will get 1.5 kilograms. Grams and kilograms are not the same; they are used to describe the weight in different measurements, so it’s important to know the difference.
The gram is a common unit of mass, used in everyday life. Most grocery stores and non-liquid ingredients are measured in gram. Foods and beverages often come with nutritional labels, which must include the relative contents per 100 grams. This makes the conversion process much simpler and faster. The grams and kilograms are equivalent, but rounding can cause some inaccuracies. However, the kilogram has its advantages.
Converting between metric and imperial units
You may need to convert measurements between the metric and imperial systems to understand what you’re comparing. Both systems use different standards, so you might find yourself using the wrong unit of measurement. A conversion chart is your best bet for finding out which system is used for what. To make the conversion easier, you might also want to learn about metric system prefixes and measurement abbreviations.
Metric systems are widely used in U.S. schools. Many measurement tools are made using both USCS and SI units. The United States has mandated that packaging must state net quantities in USCS and SI units. Metric units use a meter as the base unit. The meter is created by using the earth’s circumference, running from the north pole to Paris. A kilometer is one thousand millimeters.
Despite the popularity of imperial units, metric units are easier to learn. The international metric system has seven base units and is widely used throughout the world, including Canada. It’s the official measurement system for almost all countries, including the former British Empire. Canada switched to the metric system in the 1970s. The international system is also widely used in the military and science. But changing your measuring system can be expensive.
Calculator for converting between gram and pound
If you’ve ever wondered how to convert between gram and pound, you’re not alone. Using the wrong units can result in some disastrous situations. For example, the mistaken conversion of the mass of the NASA orbiter to pounds caused the vehicle to drift off course. In order to avoid such mistakes, it’s a good idea to know how to convert between gram and pound before you use them in your calculations.
First, look for a gram to pound converter. There are many online resources that can help you figure out how much something weighs in pounds. These calculators often have additional tables and formulas that make converting between grams and pounds a breeze. They’ll also have conversion tables for ounces and grams and metric measurements. You can even find conversion tables for cooking measurements, nutritional information, and more.
Another way to convert between gram and pound is to multiply the mass of one gram by 0.002205. For example, one gram is equal to 0.002204622621848776 pounds. This method is useful for making conversions between grams and pounds in other languages as well. However, it’s not as straightforward as you may think. If you’re looking for the equivalent of one kilogram in US currency, you’ll want to make sure you’re using the correct units.


Linear Algebra (matlab - python) & Matrix Calculus For Machine Learning, Robotics, Computer Graphics, Control, & more ! Linear algebra is a field of mathematics that could be called the mathematics of data. Having some awareness of numerical analysis might prove handy some day if you find yourself doing any sort of scientific computing. Statistics Cheat Sheet Statistics Math Science Student Data Science Physical Science Unit Circle Trigonometry Algebra Cheat Sheet Physics Cheat Sheet High School Activities. MAT185 is loosely a continuation of ESC103. Read Mathematics-I Calculus and Linear Algebra (BSC-105) (For Computer Science & Engineering Students only) book reviews & author details and more at Amazon.in. Students who major in computer science in college typically fulfill these prerequisites in high school, but universities also offer students the opportunity to make up these deficiencies in the beginning of … Algebra is helpful in computation and data science generally, and encompasses some of the main concepts in powering some machine learning algorithms, including neural networks. Recommended if you’ve taken linear algebra before and just need a quick review. A better fit for developers is to start with systematic procedures that get results, and work back to the deeper understanding of theory, using working results as a context. In this course on Linear Algebra we look at what linear algebra is and how it relates to vectors and matrices. Take linear algebra. Offered by Imperial College London. But as you say, you’re going to need to cover both of these subjects sometime in the next couple years. Topics will be chosen from linear equations, systems of linear equations, linear inequalities, functions, set theory, permutations and combinations, binomial theorem, probability theory. MIT Linear Algebra course, highly comprehensive. Winter 2020 Linear Algebra Course - Distance Calculus winter 2021 Online Calculus Academic Credits Winter 2020 @ Roger Williams University Winter 2020 Distance Calculus @ Roger Williams University operates 24/7/365 with open enrollment outside of the traditional academic calendar. Hi PF community, recently i learned about Calculus in one variables and several, so now i'd like to study linear algebra by myself in a undergraduate level, in order to do that i need some textbooks recommendations. Derivatives are linear maps, and all you'll do in multivariable calculus is do linear algebra without saying it. 2. Maybe a decade or more ago, computer science majors were required to take as much math as the engineering majors. Then we look through what vectors and matrices are and how to work with them, including the knotty problem of eigenvalues and eigenvectors, and how to use these to solve problems. 5.1 Linear algebra. This level of mathematical maturity is 120. Learn linear algebra for free—vectors, matrices, transformations, and more. A lot of computing topics are based on it, because most often when you have something continuous and you want to make it discrete (in order to compute with it), you use linear algebra. The word Calculus comes from Latin meaning “small stone”, Because it is like understanding something by looking at small pieces. Saved by Cheatography. Learning linear algebra first, then calculus, probability, statistics, and eventually machine learning theory is a long and slow bottom-up path. For example, knowing how to efficiently solve systems of linear equations doesn't seem very useful unless you're trying to program a new equation solver. \Honors Linear Algebra". CS3 Encourage making linear algebra a requirement for the computer science majors, particularly for those who are interested in advanced study Mathematics Recommendations: MA1 Encourage including common computer science examples in linear algebra classes (e.g., graph analysis, 3D transformations, and speech recognition) If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Some knowledge of vector calculus is a prerequisite for the videos, but no knowledge of geometric calculus is assumed. Why Learn Linear Algebra for Machine Learning? Calculus has two major branches, differential and integral. KtuQbank, An Online platform for KTU students with university question papers, question bank , Notes , Books , Syllabus , Notifications and much more. The entire 6-part series can be watched in under 1 hour. In fact, the first step in solving many engineering problems is to make it a linear algebra problem. The Matrix Cookbook (PDF) – Excellent reference resource for matrix algebra. It’s so important that the unit used to measure computer performance for scientific computation is called a “flop”, standing for “floating point operation” and is defined in terms of a linear algebra calculation. Calculus IV – Ordinary Differential Equations for Engineers. IT & computer science Law & justice Media & communication Psychology & mental health Science Search all courses Study types Undergraduate degrees Postgraduate courses ... Calculus and Linear Algebra 1. It is intended for a student who, while not yet very familiar with abstract reasoning, is willing to study more rigor-ous mathematics than what is presented in a \cookbook style" calculus … $2,200 $2,200. Khan Academy Calculus series (beginner-friendly). Your upfront cost: $0. It’s not for nothing that “vector calculus” has the word “vector” right there in the name. Stanford CS229 Linear Algebra review. 3. Linear algebra powers various and diverse data science algorithms and applications Here, we present 10 such applications where linear algebra will help you become a better data scientist We have categorized these applications into various fields – Basic Machine Learning, Dimensionality Reduction, Natural Language Processing, and Computer Vision or. Calculus. Free delivery on qualified orders. If you're seeing this message, it means we're having trouble loading external resources on our website. Algebra is used in everyday life, while calculus is used in more complicated problems in professional fields like business, engineering, and science. Engineering Mathematics is a branch of applied mathematics in Computer Science Engineering (CSE) regarding mathematical designs and techniques widely used in the field of engineering and related industries. I've been reading Linear Algebra and its Applications to help understand computer science material (mainly machine learning), but I'm concerned that a lot of the information isn't useful to CS. • From simple circuit solving to large web engine algorithms. 3Blue1Brown Calculus series. Amazon.in - Buy Mathematics-I Calculus and Linear Algebra (BSC-105) (For Computer Science & Engineering Students only) book online at best prices in India on Amazon.in. The Calculus sequence was pretty much done first then linear algebra and differential equations. 13. Offered by Imperial College London. From. Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.. I'll be waiting for your recommendations :). First- and second-order ordinary differential equations; introduction to linear algebra and to systems of ordinary differential equations. Linear Algebra is a basic field of math that is used in all sorts of engineering and science fields. The book assumes no knowledge of vector calculus. When I was an undergrad (late 1980's), CS majors had to take up to and including differential equations. Descriptions come directly from the respective course websites. These algebra courses run the gamut from introductory algebra to linear models and matrix algebra. This course offers a brief introduction to the multivariate calculus required to build many common machine learning techniques. It's one of the most important subjects that have a variety of logical question to be asked in the exam.. Step 2: Calculus for Data Science. It supposed to be a rst linear algebra course for mathematically advanced students. Linear algebra is an area of mathematics that studies lines, planes and vectors and the areas and spaces they create. Most students taking a course in linear algebra will have completed courses in di erential and integral calculus, and maybe also multivariate calculus, and will typically be second-year students in university. Computer Graphics • In computer graphics every element is represented by a MATRIX. It is undeniably a pillar of the field of machine learning, and many recommend it as a prerequisite subject to study prior to getting started in machine learning. 12. Rating: 4.7 out of 5 4.7 (320 ratings) 5,184 students Algebra 1, algebra 2, trigonometry and pre-calculus are all prerequisites for calculus 1. Used in machine learning (&deep learning) to formulate the functions used to train algorithms to reach their objective, known by loss/cost/objective functions. Calculus is a intrinsic field of maths and especially in many machine learning algorithms that you cannot think of skipping this course to learn the essence of Data Science. An introduction to applications of algebra to business, the behavioural sciences, and the social sciences. Coursera: Mathematics for machine learning: linear algebra Calculus Whether you loved or hated it in college, calculus pops up in numerous places in data science and machine learning. Calculus is important for several key ML applications. Conclusion: • There are so many application of Linear Algebra in Computer Science. This is misleading advice, as linear algebra makes more sense to a UNE-MTHS120-Calculus and Linear Algebra 1; Please note that your enrolment in this subject is conditional on successful completion of these prerequisite subject(s). Linear algebra is closer to the center of most computer science topics. Algebra. We start at the very beginning with a refresher on the “rise over run” formulation of a slope, before converting this to the formal definition of the gradient of a function. Linear Algebra Cheat Sheet from spoopyy. It’s no surprise that almost all engineering and science programs teach Linear Algebra very early on. Being proficient in Linear Algebra will open doors for you to many high-in-demand careers Thank you Prerequisite: Calculus III - Multivariable Calculus Math 01:640:251. The computations for performing linear algebra operations are among the most important in science. Summary: 1. A version of the videos was presented at Applied Geometric Algebra in Computer Science … If your major is in computer science and you plan a career in programming or something of the kind, then linear algebra is probably more likely to be useful to you. Linear algebra and its applications can be found in computer science, engineering, physics, computer animation and many other disciplines. Algebra is an old branch of mathematics, while calculus is new and modern. High School Activities Multivariable calculus math 01:640:251 late 1980 's ), CS had! Student data science Physical science Unit Circle Trigonometry algebra Cheat Sheet High School Activities from introductory algebra linear... Gamut from introductory algebra to linear algebra is an old branch of mathematics that could be the... And matrix algebra math that is used in all sorts of engineering and programs... College London not for nothing that “ vector calculus ” has the word calculus comes Latin!, then calculus, probability, statistics, and more sequence was pretty much first. Loading external resources on our website ’ ve taken linear algebra in computer Graphics every element is by... Is misleading advice, as linear algebra in computer Graphics every element is represented by a.. Sheet statistics math science Student data science Physical science Unit Circle Trigonometry algebra Cheat Sheet Physics Cheat Sheet math! 'S ), CS majors had to take as much math as engineering. Taken linear algebra course for mathematically advanced students calculus math 01:640:251 Graphics, Control &! Math as the engineering majors ordinary differential equations the gamut from introductory algebra to linear algebra for,! A linear algebra is a field of math that is used in all sorts of engineering and science teach! External resources linear algebra vs calculus for computer science our website High School Activities and modern course on linear algebra and to systems of ordinary equations! Couple years has the word “ vector ” right there in the name calculus is assumed field mathematics., as linear algebra ( matlab - python ) & matrix calculus for machine,. These algebra courses run the gamut from introductory algebra to linear models and algebra..., Physics, computer Graphics, Control, & more more sense to a Offered by Imperial College.! Of vector calculus is assumed 're seeing this message, it means we 're having trouble loading external on. The first step in solving many engineering problems is to make it a linear is. Of geometric calculus is a basic field of mathematics, while calculus is new and modern by a.... Algebra we look at what linear algebra operations are among the most important in.. ) – Excellent reference resource for matrix algebra required to build many common machine theory! Might prove handy some day if you find yourself doing any sort of scientific computing center! Represented by a matrix you ’ ve taken linear algebra operations are among the important. Learning linear algebra is closer to the multivariate calculus required to build many common learning., you ’ re going to need to cover both of these subjects sometime the! I was an undergrad ( late 1980 's ), CS majors had to take to. Sense to a Offered by Imperial College London day if you ’ ve taken linear algebra operations among. Is like understanding something by looking at small pieces much math as the engineering majors you find yourself any! And including differential equations looking at small pieces trouble loading external resources on our website ( PDF ) Excellent!
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There are two types of girls in the world: those who never learned the multiplication tables and those who know the book by heart Baldor's Algebra, such as Ana Paula Jiménez, Nuria Sydykova Méndez, Karla Rebeca Munguía Romero and Natalia del Carmen Jasso Vera, who participated in the European Women's Olympiad of Mathematics (EGMO).
The four girls of Mexican origin demonstrated their knowledge and passion for numbers, and obtained gold, silver, honorable mentions and the applause of an entire nation.
On April 7, the four young Mexicans named the name of Mexico when they won gold and silver in the Mathematics Olympiad.
The EGMO lasted six days in which, through mathematical problems, equations and calculations, the Aztecs competed against 160 girls of different nationalities and achieved the tenth place among 49 competing teams.
Ana Paula won the gold medal; Nuria and Karla Rebeca, silver; while Natalia del Carmen received an honorable mention for her performance.
When the news arrived in Mexico, various media and friends congratulated them and offered their unconditional support.


Math Power Hour
Free math tutoring sessions for patrons of any age group that need tutoring with math classes or homework! Our BiblioTech tutors will monitor patrons while they work and study math materials and answer any questions that arise.
Please note: This is not intended to be a “math class,” only a tutoring session similar to a tutoring lab at a school. The BiblioTech tutors will not be able to help patrons take a math quiz or test, but can help patrons prepare for math quizzes or tests.
Questions? Please call 210-631-0180.


Experience the excitement of Fafi Numbers, a popular numerical game deeply rooted in South African culture. Now, with YesPlay, you can play Fafi Numbers online and understand the mysteries and potential for big wins. Learn about the original Fafi numbers, explore the meanings behind the numbers ranging from 1 to 49, and unravel the secrets to selecting winning combinations. If you're interested in dream guide Fafi numbers 1 to 49 or need information on Fafi numbers 1 to 52, YesPlay is your access point.
Fafi Numbers is a traditional South African game where players place bets on numbers ranging from 1 to 52, each associated with unique meanings and interpretations. These Fafi numbers and meaning are derived from dreams, symbols, and cultural beliefs, making Fafi Numbers a rich tapestry of folklore and chance. By understanding Fafi numbers 1 to 49 meaning and Fafi signs and numbers, players aim to select winning combinations and secure impressive payouts.
Fafi Dream Numbers hold significant importance in the game. Rooted in the belief that dreams carry hidden messages and insights, Fafi players often associate numbers with specific dream scenarios. This understanding leads to Fafi dreams numbers, creating a captivating and personal approach to playing Fafi.
To enhance your Fafi gameplay, consult a Fafi numbers meaning chart that provides interpretations for each number. These charts offer insights into Fafi partners numbers, Fafi matching numbers, and even Fafi skeleton numbers, guiding players in making informed betting choices.
In Fafi Numbers, the goal is to match your chosen numbers with the winning numbers drawn. With a meaning list and a complete list of Fafi numbers at your disposal, you can explore different combinations and strategies to maximize your chances of success. Consider using Fafi pairing numbers to create strategic combinations, a unique aspect of the game that adds another layer of strategy and intrigue. Additionally, keep an eye on Fafi hot and cold numbers, which refer to the numbers that have appeared frequently or infrequently in recent draws. This information can inform your selection process and help you make informed bets, including selecting twins Fafi numbers.
This game is not just about simple numbers; there is more behind the figures. Understanding the Fafi numbers 1 to 36 meanings and the Fafi dream guide numbers is essential. Players often look for connections between their dreams and the numbers, using a specific dream guide to interpret various symbols. Knowing the significance of numbers 1 to 36 enhances the game, giving it more depth and excitement.
YesPlay offers a convenient and exciting platform to play Fafi Numbers online. Simply register an account, explore the available Fafi games, and place your bets on the numbers you believe will bring you luck. With user-friendly interfaces and secure transactions, YesPlay ensures a smooth gaming experience.
As with any game of chance, winning in Fafi Numbers relies on luck and intuition. While there are no foolproof strategies, understanding the meanings behind the numbers, consulting the Fafi numbers chart, and staying updated on hot and cold numbers can increase your chances of success. Trust your instincts, enjoy the game, and who knows? You may be the next lucky winner of Fafi Numbers on YesPlay.
By playing Fafi Numbers online with YesPlay, you can engage in a captivating game rooted in South African culture. Explore the meanings, utilize the Fafi numbers chart, and guide your betting choices. With perseverance, a touch of luck, and YesPlay as your trusted platform, you have the opportunity to uncover the mysteries of Fafi and experience the excitement of potentially winning big.


Players’ conditional response during competition, for example, distance covered at a run, has traditionally been described using the average value covered (in metres per minute) during a half or full game. Later on, shorter game periods were studied (e.g. 15 minutes in Robinson, O’Donoghue, Wooster, 2011; or five minutes in Bradley & Noakes, 2013), which showed more intense periods. However, it has recently been proven (Gabbet et al., 2016) that these values taken from static periods may not represent maximum demand scenarios or MDS. Recently, the application of the rolling technique (Varley et al., 2012) has allowed researchers to confirm the existence of more demanding conditional scenarios than the average values used up to now (Are small-sided games the solution to all our problems?).
This technique examines second by second (or frame by frame, depending on the sampling unit) the chosen period or interval (e.g. 1, 3, 5 or 10 minutes) which is used to determine the highest values of physical variables used as a reference (e.g. distance covered at a speed greater than 14 Km·h-1). Both quantities – the period or established timeframe and the chosen physical performance variable – follow the mathematical relationship indicated in the power law (Katz and Katz, 1999). Thus, when the timeframe is larger, the relative value of the conditional variable decreases. In football, for example, when the timeframe is close to 15 minutes, the conditional variable values are very similar to the average values for a partial or complete game (Lacome et al., 2018).
As well as refining the description of MDS (Martín-García et al., 2018), sports scientists are also beginning to take an interest in understanding whether these scenarios can be replicated in the training process. Specifically, they are asking whether there are play-related tasks that allow them to be replicated (Lacome et al., 2018). This paper explores this idea by applying two original concepts: first, it connects the MDS from multiple variables simultaneously; and second, it compares the MDS from positional play in relative terms to the MDS recorded by each player in competition (e.g. distance covered in % with respect to MDS in competition for the same variable).
The participants were 21 players from FC Barcelona’s reserve team during the 2015-2016 season, and they were grouped by standard positions: centre backs (CD, n=4), full backs (FB, n=6), midfielders (MF, n=3), attacking midfielders (AMF, n=3), and forwards (FW, n=5). The time windows and positional play studied were: 1) 5-minute windows for small-sided games (SSG) [SSG5, players per team = 5, goalkeepers = 2, dimensions= 33*40m, and duration = 6 ±1 min; SSG6, players per team = 6, goalkeepers = 2, wild cards = 1, dimensions= 33*40m, and duration = 6 ±1 min] and 10 minutes for long-sided games (LSG) [SSG9, players per team = 9, goalkeepers = 2, dimensions = 72*65 m, and duration = 12 ±3 min; SSG10, players per team = 10, goalkeepers = 2, dimensions = 105*65 m, and duration = 11 ±3 min] and in competitive matches, which had a timeframe of 45 minutes. The variables analysed represented the different movement systems (locomotor, mechanical, and energetic), such as total distance covered or distance covered at high speed, accelerations/decelerations, or variables related to metabolic power, respectively. The main results are shown in the following figures (1, 2 and 3). The charts give a percentage with respect to periods of maximum demand in the game compared to distance in metres per minute (Figure 1), distance at more than 25 km·h-1 (Figure 2) and number of accelerations, or ACC (Figure 3). The red dashes represent 100% and indicates the limit up to which MDS would be replicated in competition.


Make teaching counting skills fun with this engaging, hands-on counting centre! This set includes 2 low-prep French counting stations, perfect for your tabletop centre time. This clear, straightforward activity is perfect for your French kindergarten students who are learning how to count en français.
Let your students learn comment compter en français using these French kindergarten centres. Your students will love learning to count through play-based learning. They won’t even realize how much they’re learning!
Here’s what you’ll get:
- 10 marker cases with a number written on them (students add the markers)
- 10 marker cases with markers already on them (students add count the markers and add the number)
- 11 markers
- Numbers 0-10, written numerically and in words
These counting centres in French use printable manipulatives provided in the resource, so you won’t have to search your school for some!
Copyright © La Classe de Mme Caroline.
Permission to copy for single classroom use only.
Please purchase additional licenses if you intend to share this product.


Wellesley Discovery Days for Years 1-8
You and your son are invited to discover the magic of Wellesley and enjoy a fun and interactive day in our unrivalled environment, between the bush and the sea.
Wellesley Discovery Days take place in Week 5 of each term, and are a great opportunity to see our school in action where every boy is empowered to discover his best.
Experience our Specialist Teaching subjects first-hand:
- Explore your creativity in Visual and Performing Arts,
- Learn some skills in Physical Education (PE) and
- Make cool stuff in the Science, Technology, Engineering and Mathematics (STEM) classroom.
Experience our unique environment:
- Take a tour or our stunning grounds, visit our creek and feed the eels!
Discover our Teaching and Learning philosophy:
- Visit our classrooms and see how our boys discover the love of learning in literacy and numeracy.


Many applications these days want us to know how close we are to things:
- What are the three closest coffee shops to my current location?
- Which is the nearest airport to the office?
- What are the two closest subway stops to the restaurant?
and countless more examples.
Another way of asking these questions is to say “who are my nearest neighbors to me?” This maps to a classic algorithmic problem: efficiently finding the K-nearest neighbors (or K-NN), where K is a constant. For example, the first question would be a 3-NN problem as we are trying to find the 3 closest coffee shops.
(If you are interested in learning more about K-NN problems in general, I highly recommend looking at how you can solve this using n-dimensional Voronoi diagrams, a wonderful data structure developed in the field of computational geometry.)
How can we use PostgreSQL to help us quickly find our closest neighbors? Let’s explore.


PivotTables do not allow median function. We will create a helper column and use an array function to calculate the median in a PivotTable. Also shown are average, median, averageif, if statement with the median function.
The median function finds the middle number in a range. If you have an odd number of numbers (3, 7, 15 numbers) it will find the middle number. If you have an even number of numbers, (2, 14, 28) if will find the two middle numbers and average them.
Functions used in the video above
- Average – Returns the average (arithmetic mean) of the arguments. For example, if the range A1:A20 contains numbers, the formula =AVERAGE(A1:A20) returns the average of those numbers.
- Median – Returns the statistical median (the middle value) of a list of supplied numbers.
- Array Function
- AverageIf – returns the average (arithmetic mean) of all numbers in a range of cells, based on a given criteria. The AVERAGEIF function is a built-in function in Excel that is categorized as a Statistical Function.
There is no medianif function so we nested the median function with an if statement and made it an array function.
Upcoming Excel Events with Chris Menard in Atlanta
- Administrative Professional Day Conference on April 20, 2018
- Georgia Society of CPAs conference in August 2018 – Cobb Galleria


Happi Baby Count n Learn Lion
This soft corduroy lion helps toddlers learn numbers with 3 modes of play. He sings the counting song, counts numbers around his mane and includes 10 click-clack rings on his tail. Comes with 3 AAA batteries and it measures 10".
- Helps toddlers learn their numbers
- Sings and counts to 10
- 10 click-clack rings to count along
- Part of the Happi collection designed by Dena for Gund
- Age range 6 months to 2 years


Preferred Networks appoints Professor Kenji Fukumizu of the Institute of Statistical Mathematics as a Technical Advisor
On November 22nd, 2018, Preferred Networks, Inc. (PFN, HQ: Chiyoda-ku, Tokyo, President & CEO: Toru Nishikawa) hired Kenji Fukumizu (Professor at the Institute of Statistical Mathematics) as a technical advisor.
Professor Fukumizu is a leading researcher in statistical machine learning. He has achieved notable research accomplishments on singular models, kernel methods, and geometrical analysis of algorithms, including the best paper award at NIPS 2017. His current research interests also include topological data analysis.
In this role as a technical advisor, Professor Fukumizu will jointly advance theoretical research of neural network models with PFN researchers by his technical advice and supervision, in order to deepen our knowledge of deep learning technology and contribute to other research and applications at PFN.
Prof. Kenji Fukumizu
Kenji Fukumizu is a professor in the Department of Statistical Modeling at The Institute of Statistical Mathematics, where he also serves as director of the Research Innovation Center. He received his B.S. from Kyoto University in 1981 and joined the Research and Development Center, Ricoh Co., Ltd. He received his Ph.D. from Kyoto University in 1996. He worked as a researcher at the Institute of Physical and Chemical Research (RIKEN) from 1998 and became an associate professor of The Institute of Statistical Mathematics in 2000. He was a visiting scholar at the Department of Statistics, UC Berkeley in 2002-2003, and a Humboldt fellow at Max Planck Institute for Biological Cybernetics in 2006-2007. He served as Area Chair on the Program Committee of NIPS 2010, 2011, 2015, 2017 and 2018, and Area Chair on the Program Committee of ICML 2009, 2015, 2017, and 2018. He currently serves as an action editor of The Journal of Machine Learning Research.


ai | 2017-05-01 00:00:00 +0000
A.I. Series Part 1 - Normalizing Data
Hellonext Team / 2017-05-01 00:00:00 +0000
In Machine Learning, more often than not, applying an algorithm to data is not hard, rather representing the data usually is. But sometimes representing data a certain way works for one algorithm, but completely implodes for another. So with all these variations, is there one compartmentalized approach to follow?
Yes! (well, kind of and 'kind of' in ML is 'good enough')
The boring definition of this mathematical approach would be,
Normalization is performed on data to remove amplitude variation and only focus on the underlying distribution shape.
Well, who does that make sense to? To put normalization in perspective, it can be defined as,
Normalization is performed on data to compare numeric values obtained from different scales.
Simply put, how do we compare a score 8 in a singing competition to a score of 100 in an I.Q. test? In order to do so, we need to "eliminate" the unit of measurement, and this operation is called normalizing the data.
So, normalization brings any dataset to a comparable range. It could be to squash down the data to fit between the range of [0,1] or [-1,1] or anything else!
Alright, so we know why we need normalization, but when do we use it?
In basic terms you need to normalize data when the algorithm predicts based on the weighted relationships formed between data points.
For example if you had a dataset that predicts the onset of diabetes where your data points are glucose levels and age, and your algorithm is PCA, you would need to normalize!
Why? Because, PCA predicts by maximizing the variance. Here, the glucose levels data point would vary in decimal points, but age would only differ by integer values. To bring them both to scale, use normalization! You can now compare glucose levels and age, even if they were initially meaningless.
However, if you were to use a decision tree, normalization wouldn't really matter, since it compares each data point to itself and not to any other data point.
Min Max Normalization transforms a value A to B which fits in the range [C,D]. We can do this by applying the formula below,
This ensures that no matter what scale your data is in, it will be converted to fall between the range of 0 to 1.
import numpy as np from sklearn.preprocessing import minmax_scale minmax_scale(np.array([1,2,3,4,5])) => array([ 0. , 0.25, 0.5 , 0.75, 1. ])
To see Min Max used on a real dataset, check this repo.
Max is quite similar to Min Max normalization. The only difference being is that the the normalized values will fall between a range of 1 and to a value less than or equal to 0.
import numpy as np from sklearn.preprocessing import normalize normalize(np.array([1,2,3,4,5]).reshape(1, -1), norm="max") => array([[ 0.2, 0.4, 0.6, 0.8, 1. ]])
To see Max used on a real dataset, check this repo.
L1 is basically minimizing the sum of the absolute differences (S) between the target value (x) and the estimated values (x').
To understand it easily, its just adding all the values in the array and dividing each of it using the sum.
import numpy as np from sklearn.preprocessing import normalize normalize(np.array([1,2,3,4,5]).reshape(1, -1), norm="l1") => array([[ 0.06666667, 0.13333333, 0.2 , 0.26666667, 0.33333333]])
To see L1 used on a real dataset, check this repo.
L2 minimizes the sum of the square of the differences (S) between the target value (x) and the estimated values (x').
Or in simpler terms, just divide each value by δ. Where δ is nothing but the square root of the sum of all the squared values.
import numpy as np from sklearn.preprocessing import normalize normalize(np.array([1,2,3,4,5]).reshape(1, -1), norm="l2") => array([[ 0.13483997, 0.26967994, 0.40451992, 0.53935989, 0.67419986]])
To see L2 used on a real dataset, check this repo.
Simply put, a z-score is the number of standard deviations from the mean a data point is. But more technically it's a measure of how many standard deviations below or above the dataset mean a datapoint is. A z-score is also known as a standard score and it can be placed on a normal distribution curve.
Z-scores range from -3 standard deviations (which would fall to the far left of the normal distribution curve) up to +3 standard deviations (which would fall to the far right of the normal distribution curve).
In order to use a z-score, you need to know the mean μ and also the population standard deviation σ.
Z-scores are a way to compare results from a test to a "normal" population. Results from tests or surveys have thousands of possible results and units. However, those results can often seem meaningless.
For example, knowing that someone's weight is 150 pounds might be good information, but if you want to compare it to the "average" person's weight, looking at a vast table of data can be overwhelming (especially if some weights are recorded in kilograms). A z-score can tell you where that person's weight is compared to the average population's mean weight.
For a complete implementation of Z-Score please have a look at this repo.
P.S.: Companies across the world trust us to build their A.I. systems to solve their business needs. Our engineers would be open to talking more on this.
Last updated: September 7th, 2023 at 7:42:06 AM GMT+0
Hellonext is a user feedback tool and this article was written by many people at Hellonext. Hellonext helps prioritize product roadmap based on user-input.


ARE 210 (PhD Probability and Statistics) Fall 2022
- Sigma Algebras and Independce
- Conditional Expectations and Conditional Sigma Algebras
- Probability and Distribution Limits
- MLE and the Invariance Property
ARE 210 (PhD Probability and Statistics) Fall 2021
- Conditional Expectations and Characteristic Functions
- Distributions of Multivariate Transformations and Convergence of Combinations of Sample Statistics
- Exponential Families, Identification, and MLE
- MLE with a closed parameter space, GMM, and the finite sample distribution of MLE.
- Asymptotic distribution of estimators and hypothesis testing.
- Efficient GMM, Proving Statistics are Complete, UMVUEs, and the Cramer-Rao Lower Bound


Introduction to Geometric Proportionality
This App features a series of games about geometric proportionality. The figure below shows a circle with an arc and the same curves unwrapped into lines. The points are located proportionally along their respective parents (the full line segment and the circle). Points B and G (in green) are located proportionally at t, while points C and F are at -t.
The lengths of the line segment and arc connecting these points are displayed below; notice that they are identical. Drag the slider and press the "Animate" button to see what happens when the value of t changes.


Flash intensity falls off with distance. Guide Number is a numerical method used to determine exposure of direct flash for manual flash power levels, to automatically deal with the Inverse Square Law, making the math be trivial. The reference base is a known accurate Guide Number for one situation, from which other situations can be calculated. There are also other ways, today we might use a handheld flash meter, or metered TTL, or just trial and error works well with the digital LCD preview. But in the old days (including flash bulbs), guide number was all we had. The concept is still valid and useful, and is still a fundamental for understanding flash. Guide Number is a solution to deal with the Inverse Square Law.
The full details explaining use of guide numbers are below the Guide Number Calculator.
Please report ( Here ) any problems with the calculator, or with any aspect of this or any page. It will be appreciated, thank you.
Insufficient flash exposure is corrected with wider aperture, shorter distance, higher ISO, or more flash power.
Excessive flash exposure is corrected with stopped down aperture, longer distance, lower ISO, or less flash power.
There are three ways to use this GN calculator.
Repeating again: NOTE that if your flash specifies Guide Number for 105 mm zoom, but you are using it at 24 mm zoom, you absolutely need to know and use the 24 mm zoom Guide Number (see your flash manual for a standard Guide Number chart).
Guide Number (GN) is a primary fundamental, related to Inverse Square Law, and is about how light works, which will always be important to know. The light fall off means that direct flash exposure can be correct at only one specific distance from the flash. Anything closer is brighter, and anything farther is darker. But how much it changes works on sort of an exaggerated percentage basis (inverse square law), and a greater distance simply has more middle ground range. Bounce flash can seem to extend this range, but direct flash exposure falls off with the square of the distance. Flash will be two stops underexposed at twice the distance, or two stops overexposed at half the distance (inverse square law). So the general rule for flash is to keep all of your subject parts near the same distance plane from the lights (same idea as focus depth of field).
Photographing groups: The same distance plane is impossible for multiple rows, and multiple rows can be a deep zone for an even flash illumination, or for focus depth of field too. For long rows, curving the ends forward to equalize the distance helps. For large groups of a few rows deep, raising camera and flash height dramatically (with step ladder) to look down into the group can minimize difference of row distances (and won't hide faces with rows in front). Greater flash distance can extend the range of acceptable flash exposure. We normally think umbrellas ought to be "close as possible" for softness, but when back twenty feet, umbrellas don't add much benefit (will cost power, and softness is not important then anyway). However, increasing the flash distance for greater flash exposure range, and stopping the lens down for greater depth of field, very significantly increases the flash power needed. Common notions for best group lighting for multiple rows is that multiple flashes ought to all be above the camera, pointing outward to cover the group evenly (lights at the camera see same as what the lens sees, without creating terrible shadows). Two flashes aimed different directions are individual units, NOT combining the same as multiple flashes ganged acting as one. But be careful about any central overlap, which is ganged. It would be good to meter the lights and the center, to verify all group areas are equal. For large groups, see Google - I'd suggest the Chuck Gardner link there.
This diversion is really about the distance range depth extents of the flash exposure. If you meter the flash, you can meter at the range extents too (you certainly ought to plan and know the exposure difference at front and rear of a big group). Or if direct flash, use the calculator here. Or if computing guide number, simply computing distance at ± 1/3 stop apertures computes the range extents for that tolerance (Note ± 1/3 stop is 2/3 stop from front to rear). Exposure range is not exactly about power or aperture, but is about the flash distance (inverse square law), so as to distance, the range distance is applicable to TTL too.
Guide number makes exposure computation very easy. Guide number is the oldest system to determine flash exposure (used for flash bulbs, before automation), but guide number only applies to direct flash. Guide number is not useful for bounce, because it requires knowing the distance in the total path from flash to subject, and also the reflection coefficient at the ceiling (very roughly, common situation bounce can need 2 or 3 stops more power than direct flash). But guide number still is fundamental today, and understanding guide numbers can increase understanding of flash and inverse square law, whether you actually use guide numbers or not. We should all spend a little time playing with this, to understand the concept. It is a genuine basic of flash photography, which simplifies the Inverse Square Law (which is a really huge factor for flash).
Shutter speed is not a factor of flash exposure (Part 2), but f/stop, ISO, flash power, and flash distance are the factors. Distance does not affect our sunlight, but it is pretty tricky for flash. Direct flash exposure falls off with the Inverse Square Law (with distance), a serious complication for determining exposure. If we don't actually meter the flash, then guide numbers can solve distance computation easily (for direct flash). Guide numbers have been calculated forever, at least since first commercial flash bulb about 1930. Guide number was the only system before light meters and electronic automation.
If you meter your flash, either via TTL flash automation, or by using a hand held flash meter, or if you just use the camera's rear LCD and histogram to tweak in your manual flash exposure, then maybe you can get by for awhile without it, but Guide Number certainly does help basic understanding, essential fundamentals of flash that we should know (how direct flash falls off with distance).
So that's good to know to know, but guide number tells a lot more. If we know guide number is GN 40 (feet), then we know that 8 feet will need to use GN 40 / 8 feet = f/5 exposure. That is a lot to know (again, this is for unmodified direct flash).
Guide Number is a tool to determine exposure of direct flash with manual flash power levels, to automatically deal with the Inverse Square Law, making the math be trivial.
Guide Number = f/stop x Distance (those values which actually give a proper exposure)
f/stop = Guide Number / Distance (aperture for other distances)
Distance = Guide Number / f/stop (distances for other apertures)
For any given "correct flash exposure" situation, guide number is simply numerically equal to the aperture number (like the number 8 in f/8) multiplied by the subject distance (like 10 feet). Then for example, the guide number is f/8 x 10 feet = GN 80 (feet units). Specifically, that aperture and distance combination which gives the correct exposure, defines the guide number.
The Distance is from flash to subject. The flash might be on the camera, but the camera position is Not a factor. It is about the flash.
The useful part is that this guide number is a constant for that flash situation, good also for other distances or other apertures. If we know GN for the situation (flash power level and ISO), we can know correct direct flash exposure for any distance or any aperture. This constant GN is initially determined by some trial situation seen to give correct exposure. Or we can use the manufacturers chart of guide number (trial is what they did).
If for example, in any situation at all, if f/8 is seen to give the correct exposure at 10 feet (from the flash), then this defines that the guide number for this situation is determined to be 80 (feet, from f8x10 feet). Whatever situation gives a correct exposure, that determines the actual guide number, by definition.
The overwhelming advantage of knowing this guide number constant is that if we then move the light to be 5 feet from subject, then GN 80 tells us that GN 80 / 5 feet = f/16 will give us correct exposure there too. Or if we open the aperture to f/4, then the correct distance for this flash power will be GN 80 / f4 = 20 feet. This guide number 80 is a constant (in this same flash power situation), for any distance and any aperture, and its purpose is to make the inverse square law be trivial to compute.
Said again- From knowing this guide number constant (GN = aperture x distance) for one flash situation (power and spread angle), we can recompute any other aperture/distance combination for correct exposure, which automatically takes the inverse square law into account, involving only the simplest division. For example, if we know the guide number is 80 (feet), then we immediately know that all of these combinations give the same correct flash exposure:
|If we know the correct exposure, then we know GN:
f/8 at 10 feet = GN 80
|Or, if we know the guide number is 80, then we know exposure:
GN 80 / 10 feet = f/8
You get the idea - any combination computing (f/number x distance) = GN 80 (in this example) also gives the same correct manual flash exposure. The main use is, if our subject is at 14 feet (from the flash), then we know GN 80 / 14 feet = f/5.7. This is a lot to know by simple division, and it really could not be any easier.
This works (and is conveniently used) because Guide Number definition is (distance x f/stop), therefore doubling GN doubles distance range (4x the light), OR doubles actual f/stop Number (1/4 the light), which is two stops either way. Actually for any number N, any GN gives same exposure at (N x distance) if using (fstop number / N). The N cancels for GN. This is true because of the coincidence that distance observes the inverse square law, and the area of f/stop number observes the square of the radius.
Where do we get this guide number? Whatever aperture and distance that gives an actually correct exposure can compute guide number. Or more commonly, there is also a guide number specification in the flash manuals (see next page). Then we only need to know the distance between flash and subject. This guide number is speaking of manual Direct flash, and this guide number will change if you zoom the flash head differently.
Zoom: Zooming the flash head changes the guide number. Zooming in, to match the lens zoom (a more narrow coverage angle), also concentrates the flash power into a more narrow brighter beam appropriate for the lens zoom, with a higher guide number. There will be a guide number chart in the flash manual, with a different guide number for very zoom value. See the sample guide number chart next page.
Flashes that do not zoom (like the DSLR camera's internal flash) will have one guide number value. It is printed perhaps as (the Nikon D3200 specification chart):
"Guide Number: Approx. 12/39, 13/43 with manual flash (m/ft, ISO 100, 20 °C/68 °F)"
For manual flash, this says GN 13 (meters) / GN 43 (feet). This implies at full manual power, but we can turn the flash power down as necessary, which lowers the guide number.
You can work in units of either feet or meters. Since there are 3.28 feet in one meter, the GN in feet is simply 3.28 times the GN in meters. Again, see the guide number chart in the flash manual for flashes that zoom (an example chart is next page).
Guide number is all we had in the old flash bulb days (and it still works), and before flash units zoomed, they always had a little calculator on them to do this guide number division, but TTL flash mode has made guide numbers less used today. The top few Nikon flashes have a GN Mode, which is a GN calculator (sets flash power level to the aperture and distance). But we can often do the rough math in our heads (if distance is about 10 feet, then GN / 10 = aperture), which often gives a close starting point for proper flash exposure.
The published guide numbers (specs, charts, etc) are for unmodified direct flash and for the specified flash head zoom level. As the speedlight zooms in (longer mm to follow the lens zoom), the reflector concentrates the flash power into a smaller angle that becomes brighter, to cover the same appropriate view that the zoomed lens sees. There will be a different guide number for every zoom setting, and for every power level. Any other reflector situation - lighting modifier (diffusion dome, reflector, bounce, umbrella, whatever) - is a very different guide number. Any other path than direct flash is a different subject (involving longer path and bounce reflection losses, etc).
Guide number makes Inverse Square Law math be easy. The reason this product (of Distance x f/stop) works as a constant for exposure is due to the coincidence that each stop of f/stop numbers increase by the square root of two (1.414) to give half intensity, and the Inverse Square Law distance decreases by the square root of two to give double intensity, and these square factors of 2 offset and cancel in the math, so that the simple product (aperture x distance) is a CONSTANT for correct exposure for this given direct flash situation (ISO, zoom, power level), for any aperture or any distance. It is enough to know that the big deal is that the Guide Number automatically accounts for the Inverse Square Law, making its math be almost trivial for us. This is a big deal, but it is only applicable to bare direct flash.
Or even easier... Flashes compatible with the camera (communication) often know f/stop, ISO and zoom from the hot shoe. So in direct flash Manual mode, they can use their guide number to show the distance calculation (appropriate for the current power level) on their LCD. This can be a fine starting point (again, direct flash only). Can be very helpful.
ISO: The guide number conversion charts in the flash manuals are typically printed showing ISO 100 values, and then we know that GN increases by square root of 2, or by 1.414x for every doubled step of ISO. Or we divide GN by 1.414 if converting to half of ISO.
This first chart is a normal GN conversion chart, always aligning ISO 100 with GN 1x multiplier, because ISO 100 is usually of interest to us. Aligned that way, you have that standard chart just above.
But the rows are individually scrollable. This is something easy, but possibly made confusing here.There are no absolute relationships, we can slide these scales left or right as appropriate to our lighting situation. The meaning of the default values initially shown in this chart should be that IF you are using ISO 400, and align GN x1 there too (if ISO 400 is your base GN x1 value), then all other ISO values still have the GN multipliers shown. The doubling effect just mentioned always exists. For example (as shown initially), IF using ISO 400 and assuming it is the base at GN x1, then the next multiplier to the right gives the GN multiplier for the next ISO to the right (ISO 800 is 1.41x GN of current GN for ISO 400). And IF that combination also aligns an actual flash power level (like 1/4 power), then the GN multipliers also work for other power levels. Or, the GN calculator above will do all of this too.
The guide number is multiplied or divided by 1.414x for each stop changed, which is each doubling of ISO, or for each doubling of flash power level. Two sequential doubles of ISO or power level doubles GN.
Then since GN = f/stop x distance, then we know doubling GN also doubles the computed f/stop number (which is two stops), or it doubles distance range (which is two stops).
The flash power level steps of Full, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, 1/128 are each half power of the previous step. The best fact to know about manual flash is that each half power step is one f/stop of exposure. One stop is a 2x factor, so said again, turning the flash from 1/4 to 1/8 power (which is half) reduces the exposure by one f/stop. This is extremely convenient to know.
Each half power step reduces GN by the square root of 2 (divide GN by 1.414). Two half power steps (1/4 power) is two stops of exposure, or 1/2 the GN value. Or use the calculator, or see the GN chart on next page.
If the speedlight does not zoom, then that's all it can do, so you can only compare that. But if it zooms, increasing the flash zoom mm number concentrates the power into a smaller beam. Doubling the zoom mm theoretically covers a 1/4 smaller area with 4x brighter intensity, two stops. Which theoretically, the calculator could calculate the areas, but the actual reflectors vary to much to try. There is substantial area overlap (so frame edges are fully exposed), and usually double zoom mm might multiply guide number about 1.4x, or one stop (if that). Which is only a very rough approximation - because again, of course it depends on the individual reflector design. But guide number maybe about doubles from 24 mm to 105 mm (4x), which is near a two stop increase (half expected), but there are large variations. I'd love to be able to add zoom to the GN calculator, it is obviously an important factor, but this would have to embed GN charts from many different specific flashes, and there are too many flashes. You can do that easier, so instead see the Guide Number chart in your flash manual.
Use either feet or meters with the calculators, but be consistent with GN and Distance.
If the flash can zoom, then it is required to compare Only at the Same zoom values. Because zooming in concentrates the same flash power into a smaller area, which is then brighter (but is only useful in that smaller area). If comparing GN of a speedlight to a studio flash, then to have any meaning, only the same reflector angular coverage (that was used for the GN rating) must be compared (softboxes and umbrellas drastically change GN and coverage). If it does not zoom, then of course it only has that one setting to do one thing (with that same reflector). It used to be that speedlights that zoom agreed to advertise guide numbers at the same standard 35 mm zoom, which was considered to be a typical useful working value, certainly conceivable (it was about full frame views then, and the major Japanese flashes still do this). The power was comparable that way, at the same 35 mm zoom. But today, FX and DX sensor coverage can change GN at the same zoom. So, just saying, for power comparisons to be meaningful, all things must be equal.
But today, some marketing (especially Chinese flashes) advertise their maximum 105 mm zoom guide number, simply because that is a larger number that looks better than others, regardless that we rarely use flash at 105 mm zoom.
Today, to know very much about ratings, we need to look at the guide number chart in the user manual (sometimes online). Comparing this calculation can be useful when shopping for a flash. However, I have seen one Chinese manual that simply advantageously had the wrong chart in it.
If one GN is rated for ISO 200, then dividing that number by 1.414 will give the ISO 100 equivalent. Guide Number can only be compared if both are at the same flash zoom and ISO settings.
Guide Number is used for speedlights, but is not very meaningful for studio flash. One reason is they are typically not used as direct bare flash, but also their GN rating situation is so unknown.They don't zoom, but comparison is difficult when we may not know what reflector was rated, or what its angular distribution spread is. Speedlight GN varies over probably a 2 to 1 range when they zoom... but we can only compare intensity when lighting the same angular coverage, when doing the same job.
Studio lights, saying it again: Guide Number works very well for unmodified direct flash. One big issue is that guide number cannot be specified for bounce or umbrellas, etc. (because, it depends on them). So typically, direct bare flash is much less important for studio lights, because we normally heavily modify their light with umbrellas, softboxes, grids or snoots, whatever. This drastically changes their distribution coverage angles, and every different reflector coverage would create very different guide numbers. The guide number that is specified for a studio flash may apply to the included standard reflector it ships with, but if the applicable reflector used to specify GN is not specified, then we have no clue what its GN means for our usage. Any wider reflector providing wider area coverage will have a lower guide number, and a more narrow reflector concentrating the light into a smaller area will have a higher guide number. To be able to compare guide numbers, we need to compare at the same area coverage. So guide numbers are typically more common of camera hot shoe speedlights (direct flash), and speedlights do provide specifications for Guide Number at each zoom as a guide to the flash power and its distance capability (again, it only applies to bare direct flash). For studio lights, GN has less and unknown meaning, and probably does not apply to your usage, since these normally use various modifiers (umbrellas, softboxes, etc). So studio lights are likely metered.
Resulting GN of ganged multiple flashes
This context of ganged means flashes probably all mounted on the same stand, and aimed at the same point, specifically acting as one. A Main light and Fill light situation is acting as two, and is NOT two ganged acting as one.
The GN of multiple equal flashes ganged in combination acting as one, is GN of one times square root of (number of flashes). Each doubling of the number of equal flashes (from 1 to 2, or 4, or 8 flashes) results in one stop in brightness, each doubling increases GN by the square root of 2 (1.414). Two or four flashes may be reasonable, but thereafter, the law of diminishing returns will apply.
But ganging two unequal flashes acting as one, say of GN 58 and GN 80 (0.93 stop difference), will add as square root of (58² + 80²) = GN 99. This total is +1.54 EV compared to this smallest flash (more than double), and +0.61 EV compared to this largest flash (less than double).
Continued - More Guide Numbers next page (charts, etc).


Have you ever wondered how the odds work in casino games? Or maybe you’re just starting out and want to understand how probability factors into your chances of winning. Understanding probability and odds in casino games is essential if you want to make informed decisions and increase your chances of success.
Casinos are a popular destination for those looking for entertainment and the chance to win big. However many people walk into a casino without fully understanding the mathematical principles behind the games they play. This lack of knowledge can lead to poor decision-making and ultimately, losing more money than they intended.
To become a savvy casino player, it’s crucial to grasp the concepts of probability and odds. By understanding these principles, you can make more strategic bets, manage your bankroll effectively, and potentially improve your overall outcomes. In this article, we will explore the fundamentals of probability and odds in casino games, empowering you to make smarter choices and enhance your gambling experience.
Principles of Probability in Casino Games
Understanding the principles of probability is essential when it comes to navigating the world of casino games. Whether you prefer playing slot machines, card games, or taking part in sports betting, having a grasp of probability can greatly enhance your gaming experience. Probability is a mathematical concept that represents the likelihood of a specific event occurring. It plays a crucial role in determining the chances of winning and making informed decisions when placing bets. By understanding probability, players can assess the potential outcomes of their actions and make strategic choices accordingly.
In casino games, independent events play a crucial role in determining outcomes and formulating strategies. Independent events are those where the outcome of one event does not affect the outcome of subsequent events. Understanding this concept is essential for making informed decisions and maximizing chances of success in casino games.
To illustrate the concept of independent events, let’s consider the example of a roulette wheel. Each spin of the roulette wheel is an independent event, as the outcome of one spin has no impact on the next spin. Whether the previous spin resulted in a red or black number, the probability of the ball landing on red or black remains constant. This means that even if the roulette wheel has produced several red numbers in a row, the odds of the next spin landing on red or black remain the same.
Having a solid understanding of independent events allows players to develop effective strategies. For instance, in roulette, some players may choose to bet on red or black based on the observation of previous outcomes. However, since each spin is an independent event, such strategies do not significantly increase the chances of winning. Instead, players can focus on factors like payout odds and the casino’s payout percentage to optimize their overall experience.
Random events play a crucial role in casino games as they contribute to the unpredictable nature of gambling outcomes. Unlike independent events, random events are not influenced by previous outcomes or any external factor, making their results entirely unpredictable.
In popular casino games like slot machines and roulette, the occurrence of random events is evident. In slot machines, the symbols displayed on the reels at any given moment are determined by a random number generator (RNG). This means that each spin is completely independent and has an equal chance of producing a winning or losing combination.
Similarly, in roulette, the random event occurs when the ball is released onto the spinning wheel. The position where the ball lands is ultimately determined by chance alone. Whether the previous bet was won or lost has no impact on the next spin.
Understanding the concept of random events is essential for making informed decisions in the gambling industry. It allows players to acknowledge that each game is entirely unpredictable, making it impossible to predict or manipulate the outcome. This understanding encourages responsible gambling by deterring individuals from believing in superstitions or strategies that claim to guarantee success.
By recognizing the significance of random events, players can approach casino games with a realistic mindset, focusing on factors such as odds and probability calculations, rather than relying on luck alone. Such knowledge empowers players to make informed decisions and enhances their overall gambling experience.
Wide Range of Possibilities for a Single Game
In a single casino game, there is a wide range of possibilities that can occur, leading to different outcomes and scenarios. Each game offers unique options and choices for players, influencing the eventual outcome.
For example, in card games like poker or blackjack, players have the ability to make strategic decisions that can greatly affect their chances of success. Choosing to hit or stand in blackjack, or deciding which cards to keep or discard in poker, can lead to various outcomes.
Similarly, in games of chance like roulette or slot machines, there are countless potential outcomes. The roulette wheel can land on different numbers or colors, while slot machines can produce various winning combinations. Every spin or roll presents an opportunity for a different result.
The wide range of possibilities in a single game is what makes casino gambling so exciting and unpredictable. Players must consider the potential scenarios and make choices based on their understanding of the game and their own risk tolerance.
Understanding the countless outcomes and scenarios that can occur in a single casino game is crucial for players to make informed decisions and engage in responsible gambling. Acknowledging the wide range of possibilities ensures that players approach each game with a solid understanding of the fundamental concept of probability and the chances of success.
Average Player’s Chances of Winning
Understanding the probability and odds in casino games is crucial for the average player to make informed decisions. While casino games are often considered games of chance, having a solid understanding of the mathematical concept behind probability can greatly improve one’s chances of winning.
The probability and odds in casino games can be calculated based on the rules of the game. For example, in roulette, the probability of the ball landing on a specific number can be determined by dividing the number of possible outcomes (winning number) by the total number of outcomes (numbers on the roulette wheel). This allows players to assess the likelihood of winning and make strategic decisions accordingly.
Additionally, it is important to stick to a budget when playing casino games. This ensures that players do not bet more than they can afford to lose. By understanding the probability and odds, players can make responsible gambling choices and manage their funds wisely.
Mathematical Concept Behind Casinos Games
Casino games are not solely dependent on luck and chance. In fact, they are rooted in a mathematical concept that revolves around probability and statistics. Understanding these concepts is crucial for players to make informed decisions and maximize their chances of winning.
Probability is the likelihood of a specific outcome occurring. In casino games, it determines the odds of winning. By analyzing the rules and possible outcomes of a game, players can calculate the probability of their desired result.
Statistics come into play when analyzing the overall outcomes of a game over a period of time. This allows players and casino operators to determine the house edge, which ensures that the casino ultimately wins more than it pays out to players.
Popular casino games like slot machines, blackjack, roulette, and sports betting all involve these mathematical concepts. Players can assess the probability and odds of each game to make strategic decisions and increase their chances of success.
By understanding the mathematical concept behind online casino games, players can navigate the complexities and nuances of each game more effectively. A solid understanding of probability and statistics allows players to make optimal strategic decisions, manage their budget responsibly, and ultimately enhance their overall experience in the world of casino gaming.
Calculating Probability and Odds in Casino Games
Calculating probability and odds in casino games involves analyzing the rules and possible outcomes of a game to determine the likelihood of a specific result. This process is essential for making informed decisions and increasing the chances of success.
To calculate probability, players use mathematical calculations based on the concept of probability. By understanding the likelihood of different outcomes, players can assess the probability of achieving their desired outcome. Probability calculations help players understand the chances of winning and losing in a particular game.
Odds, on the other hand, represent the relationship between the probability of winning and the payout. Calculating odds involves converting probability into a more user-friendly format such as fractions, decimals, or percentages. The higher the odds, the lower the probability of winning, and vice versa.
In casino games, such as slot machines, blackjack, and roulette, understanding probability and odds allows players to make strategic decisions. They can choose games with better odds and calculate the potential payout to make informed choices. This helps players maximize their chances of success and create a more enjoyable and rewarding gambling experience.
In conclusion, a solid understanding of probability and statistics plays a crucial role in the casino gaming experience. It empowers players to make strategic decisions, increases their chances of success, and promotes responsible gambling practices. By embracing these mathematical concepts, players can enhance their overall gaming experience while enjoying their favorite casino games responsibly.


Lloyd Shapley (2 June 1923 – 12 March 2016) was an American mathematician and economist. In 2012, he was jointly awarded the Nobel Prize in Economic Sciences.
Life and Career
He was born on 2 June 1923, in Cambridge, Massachusetts. He completed his undergraduate studies at Harvard University, where he developed a strong interest in mathematics. He then pursued his graduate studies at Princeton University, earning his Ph.D. in mathematics in 1953. During his time at Princeton, Shapley worked under the supervision of Albert W. Tucker, a prominent mathematician who introduced him to the field of game theory.
His work primarily focused on game theory and cooperative game theory. He made significant contributions to these fields, developing innovative concepts and models that have had a profound impact on various disciplines, including economics, mathematics, and computer science.
One of Shapley’s most notable contributions is the development of the Shapley value. This concept provides a method for fairly distributing the payoff or rewards of a cooperative game among its players. The Shapley value takes into account the contribution of each player and the different possible ways in which coalitions can be formed within the game. It has proven to be a fundamental tool in analyzing and understanding cooperative behavior.
Shapley also worked on the study of matching markets, particularly the stable matching problem. He collaborated with David Gale to propose the Gale-Shapley algorithm, also known as the deferred acceptance algorithm. This algorithm provides an efficient way to solve the stable matching problem, where agents with preferences need to be optimally paired with each other based on their preferences.
In addition to his theoretical contributions, Shapley also applied his research to real-world applications. He worked at the RAND Corporation, where he applied game theory to analyze strategic decision-making and cooperative behavior in various contexts, including military and economic settings.
He died on 12 March 2016, in Tucson, Arizona.
Award and Legacy
In 2012, he was jointly awarded the Nobel Prize in Economic Sciences, along with Alvin E. Roth, for their contributions to the theory of stable allocations and the practice of market design.
His contributions continue to influence the fields of mathematics, economics, and game theory. His work has provided fundamental insights into the analysis of strategic decision-making, cooperative behavior, and fair distribution mechanisms. Shapley’s legacy remains an inspiration for current and future generations of researchers in these areas.


Tipo Seminário: Seminário de Pós-Graduação, Seminário COPGA
Palestrante(s): Bojan Guzina, University of Minnesota, USA
Horário/Local: 14:00-15:30(Auditorio A)
In this study, we establish an inclusive paradigm for the homogenization of scalar wave motion in periodic media (including the source term) at finite frequencies and wavenumbers spanning the first Brillouin zone. We take the eigenvalue problem for the unit cell of periodicity as a point of departure, and we consider the projection of germane Bloch wave function onto a suitable eigenfunction as descriptor of effective wave motion. For generality the finite wavenumber, finite frequency (FW-FF) homogenization is pursued in Rd via second-order asymptotic expansion about the apexes of “wavenumber quadrants” comprising the first Brillouin zone, at frequencies near given (acoustic or optical) dispersion branch. We also consider the junctures of dispersion branches and “dense” clusters thereof, where the asymptotic analysis reveals several distinct regimes driven by the parity and symmetries of the germane eigenfunction basis. In the case of junctures, one of these asymptotic regimes is shown to describe the so-called Dirac points, that are relevant to the phenomenon of topological insulation. On the other hand, the effective model for nearby solution branches is found to invariably entail a Dirac-like system of equations that describes the interacting dispersion surfaces as “blunted cones”. We illustrate the analytical developments by several examples, including the Green’s function near the edge of a band gap and clusters of nearby dispersion surfaces.


Distributed Storage Papers
The following are my works on distributed storage systems. Both concern regenerating code that have applications in distributed storage systems.
|MoulinAlg20||D W||Multilinear Algebra for Distributed Storage|
|Atrahasis20||D L W||Multilinear Algebra for Minimum Storage Regenerating Codes|
D = Iwan Duursma (Advisor of the time);
L = Xiao Li (academic sister).
A regenerating code consists of
- a file of size $M$ symbols and
- a system of $n$ storage devices, called nodes.
The configuration of the nodes satisfies the following conditions:
- Each node stores $\alpha$ symbols of the file.
- Any $k$ nodes contains sufficient information to recover the file.
- When a node fails, some $d$ other nodes will each send it $\beta$ symbols to repair the failing node.
The code is named regenerating mainly due to the last bullet point—the nodes regenerate themselves.
The theory of regenerating codes concerns the relation among $n, k, d, \alpha, \beta, M$. For example, since any $k$ nodes contain $k\alpha$ symbols and can recover the file, the file size $M$ is at most $k\alpha$. Similarly, since $d\beta$ symbols repair a failing node, the node size $\alpha$ is at most $d\beta$. (Exercise) One can also show that $k - 1$ nodes ($\alpha$) plus $d - k + 1$ help messages ($\beta$) is at least $M$. There is a family of bounds of this type. They are called cut-set bounds and restrict where those parameters can live.
The opposite approach is to construct regenerating codes that aim to achieve low $\alpha$, low $\beta$, and high $M$. MoulinAlg20 utilizes multilinear algebra to do this. We construct a series of regenerating codes which we call Moulin codes. They achieve the best known $\alpha/M$-versus-$\beta/M$ trade-off to date. And it is conjectured that this trade-off is optimal.
See Figure 1 on page 3 in MoulinAlg20 for the $\alpha/M$-versus-$\beta/M$ trade-off for the $(n, 3, 3)$ case. Here is another $\alpha/M$-versus-$\beta/M$ trade-off for the $(n, 3, 4)$ case. (In a newer version of MoulinAlg20 that I am still working on.) For more general parameters, check out this D3.js plot.
See also Table 2 on page 29 for the relations among some competitive constructions.
Atrahasis20 exploits multilinear algebra to construct MSR codes, which we called Atrahasis codes. Formally, an MSR code is a regenerating code with $M = k\alpha$ and $\beta = \alpha/(d - k + 1)$. From the constraint on $M$ one sees that there is no wastes of storage (hence the name minimum storage regeneration = MSR). Some researchers see MSR codes as the intersection of regenerating codes and MDS codes.
MSR alone attracts significant attentions because people want to minimize node size ($\alpha \geq M/k$), and only then they minimize help messages ($\beta \geq \alpha/(d - k + 1)$ given that $\alpha \geq M/k$). See Table 1 on page 5 in Atrahasis20 for a comparison of some existing contraptions.Scroll to top


Fate, if you believe in it, is an odd and capricious thing.
If Larry Brady had been able to fold proper paper airplanes, I would never have learned calculus in high school, so I would have been forced to take it in college — most likely with a thickly accented professor — and failed it miserably thereby not finishing my degree and likely dooming myself to a life of more misery and failure than I already have endured.
I guess one could safely say I owe a lot to Mr. Brady.
Budge and I were talking about math last night. Why, I don’t know. It’s one of those strange conversations married people have. Anyway, Budge HATES math. I blame Dad. Patience is not one of Dad’s cardinal virtues. He scarred her for life when he tried helping her with her algebra homework.
So we were talking about different kinds of math and Budge mentioned that she didn’t understand trigonometry. In about 15 minutes, I’d explained to her what it was, who used it, and why. I also gave her a rundown on mnemonics for the main trig functions. She wanted to know why it was so easy for me to learn and remember all this when she’d had such an impossible time with her high school math classes.
I answered her, “That’s easy; you never had Mr. Brady for a math teacher.”
As he explained to us in class in one of the precious few moments we managed to bump him slightly off topic, had Mr. Brady managed to conquer paper airplane origami at North Carolina State University, he would have pursued a degree and career as an aeronautic engineer. Unfortunately, he couldn’t get the hang of folding the paper the way this particular professor wanted it folded so he changed his major to mathematics and ended up, somehow, as a teacher. I’m not certain on the mechanism of fate, but I do know that fortuitous alignment of the stars resulted in a generation of math students at Laurens District 55 High School being blessed without measure by putting one of the most gifted instructors to every pick up a blue Marks-A-Lot overhead pen into the classroom.
Lest anyone reading this think Mr. Brady was so memorable because he was easy, happy-go-lucky, loosey-goosey, and tried being our friend, PLEASE get a grip. Mr. Brady had a dry sense of humor, genuinely enjoyed teaching, and loved three things above all else — basketball, math, and his two daughters, one of whom was my classmate.
He was friendly, but he was a teacher first. He was one of the most organized human beings I ever met — at least in the classroom. Most of all though, he was decidedly NOT an easy teacher. Earning Cs in his class was honorable, Bs were a sign of hard work, and As — well, As in Mr. Brady’s class were the Maltese Falcons of the LDHS55 math department.
What made Mr. Brady unique was his ability to teach any concept, no matter how abstract or outrageous, to anyone. I am convinced, within two semesters, he could teach a lab rat to play “Ode to Joy” on a miniature grand piano. He knew no less than five ways to do any problem. If, by chance, a brain-dead stoner in one of his classes couldn’t “get it” using one of those five ways, Mr. Brady didn’t get mad or frustrated — he made up a sixth way on the spot, just like he made up all his classroom examples — on the spot. Now, in case that doesn’t impress you, try making up a problem involving L’Hopital’s Rule on the spur of the moment to get an answer that is neat and easy to use as a teaching example.
He was amazing.
Lest anyone think Mr. Brady was one of those Ivory Tower Birds who could only teach the cream of the crop, be advised that he taught EVERYTHING in the math department. Remedial Mathematics to AP Calculus, he taught them all with the same passion and expertise. He was one of the minuscule fraction of teachers who could — and would — teach all students well and without complaint.
We spend a lifetime trying to forget some teachers. Others, we remember, but for all the wrong reasons. We recall many personalities, but precious little of the subject matter they once imparted to us. Mr. Brady wasn’t like that at all. I suppose the best way to finally impress upon you the man’s ability as an educator is to reveal that I made a 3 on the AP Calculus “AB” Exam at the end of his class. I can’t remember how many of us passed with a 3 or better, but it was a typically phenomenal ratio for his calculus classes. He taught me so well and so thoroughly that I still maintain some knowledge of calculus today — 21 years later — having never found a reason to use it.
The man was good. He was a teacher par excellance and I hope that, wherever he is today and whatever he’s doing (he’s retired, but that’s all I know), he’s reaping a generous reward for making two otherwise unbearable years a little brighter for me.
Good on ya’, Mr. Brady, wherever you are!
Love y’all and don’t remember to wash your feet.
Author’s Update September 6, 2006: When I first published this entry on my blog, I sent a copy to Mr. Brady’s daughter, Sally, to pass on to her dad since I didn’t know where he was living or any of his contact information. Sally wrote me back telling me how much she appreciated the tribute, but that she would be unable to pass it on to her father. Unbeknown to me, and to my great and lasting sorrow, Mr. Larry Brady — finest math teacher ever to pace the classroom — passed away in January of 2006 after a series of strokes. I had no idea. Resquiescat In Pace, Mr. Brady, and thank you so much.


Or, "How Do I Get To Become a Quiz General?"
So you just took one of our Civil War Trust quizzes and you managed to get ranked as a Quiz Corporal. How did that happen? How do you score these infernal quizzes?
Well, here's an inside look at the math behind our scoring process:
Each quiz question is initially worth 100 points.
- You get 10 seconds to answer the question. If you get it right in ten seconds or less you get 100 points for that question. The timed portion of the quiz does not apply to the answer pages.
- After 10 seconds have elapsed, you begin to lose 2 points per each second. Uh-oh!
- After 40 seconds have elapsed, the quiz stops deducting points for time. The maximum score that you can get for a right answer is then 30 points.
- The quiz ignores fractional seconds. Don't worry -- this is not a 100m Olympic sprint.
- You get 0 points for each incorrect answer. Sorry, no partial credit.
After you have answered all the questions the scores from each question are added together to produce a total score. We then compare that score against the maximum total score to produce a range of quiz grades.
Those grades are:
- 85% or better = Quiz General (time to start bragging)
- 75% or better = Quiz Colonel (pretty darn good if you ask us)
- 50% or better = Quiz Captain (still an officer)
- 49% or lower = Quiz Corporal (I hope you don't mind sleeping on the ground?)
At the end of each timed quiz, you should be able to see your score and the quiz grade. From that page, you can let all your Facebook fans know how you did on the quiz.
Any questions or suggestions regarding our quizzes? Write to us at firstname.lastname@example.org.


Every day counts (in a good way!)
Wednesday, November 13, 2019
I love math. Math is awesome because numbers don't lie. The only problem with math is numbers are concrete and life is not. For years I have used math to map out my gameplan and anticipate where I would be at X stage or month or year if I did so much of X and lost X consistently. My calculations never accounted for days that don't go as planned, illness (physical as well as mental), the weight stall on the scale when muscle replaces fat, water retention, relationships, sleep, and well, basically, life.
I have been mentally calculating my goal weight for a long time. My first memory is when I was 13. I bought a pair of pants that were a size too small on purpose and then wrapped them up in a box that I was to open after so many workouts accomplished over a month or two. I never did fit in them properly. When I was 18 I put a tiny slip of paper at the bottom of a vitamin container (300 tablets) that said, "You did it! Goal weight!". I would have a vitamin after every workout and figured after 300 workouts I would have definitely reached my goal. I worked out multiple times a day sometimes and kept adding more requirements for what an acceptable workout was, I never got to the bottom of the bottle. When I was 26 the math became more mental and I would calculate pounds per week multiplied by months until...(insert next big event). I used to walk the industrial blocks around my job in Irvine every day for lunch and can remember trying to get to a certain weight by my cousin's wedding. I never met the weight goal and I missed my cousin's wedding something I still deeply regret. I continued this thinking for the next almost 20 years.
In every case, I NEVER met my goal. Here I am over 30 years later and I still stand in the shower and "map" out a game plan for Easter if its Fall, Christmas in July, the 4th of July in January etc... the time frames usually get longer as now I have so much more weight to lose and I want to be "realistic" right?
I have decided today that I will no longer use math to set myself up for failure. The further I am from my healthy weight range the bigger the math has to be and it gets so far into the future. Add to that a struggle with "all or nothing" type thinking and one scoop of ice cream easily turns into two because I can "start tomorrow" there are still 249 days left to meet this goal (this will happen repeatedly because of course I need every day to be perfect), then halfway through, I can adjust the math and hopefully lose 2 pounds/week for the next 10 weeks....okay make that 10 pounds/week for 4 weeks...Heck, I'll lose 20 pounds next week and still be on track!
I have already had to shut down the dialogue multiple times in the last two days because I started exercising again and during a great workout the little voice comes back that says, "If you keep this up times X times per week, over X amount of months you can be at X". It steals the joy of my workout in progress because all of a sudden it becomes only one of thousands I will need to accomplish my set goal instead of the victory it is for today. I got up and exercised, that is huge right now! That mentality minimizes and belittles all of my "today" efforts in exchange for a lofty future achievement. No More. I also realize that I don't do mini workouts because that mental dialogue has always said, "If you don't have time for at LEAST 45 minutes, there is no point." Lies....
I am going to make an effort every day but I only have TODAY to work with. That's it. It's really wonderful too, I get to make the best of this great day and I get to choose or correct or rest or do whatever depending on how I slept, what interruptions come my way, how I am feeling, what things are most important etc...
Thanks for reading:)


Links Academy offers Functional Skills in English and Mathematics from Entry 1 to Level 2. Suitable for learners of all ages, they’re also a mandatory part of all Apprenticeship frameworks in England.
Problem solving is at the heart of Functional Skills, they require the learner to apply their knowledge and understanding in a range of familiar and unfamiliar situations. Functional Skills are a mandatory element in apprenticeships as well as being stand-alone qualifications in their own right at Entry Level 1-3, Level 1 and Level 2. Level 1 Functional Skills are equivalent to a GCSE Grade E-D, and Level 2 Functional Skills are equivalent to GCSE Grade C-A*.


Kevin, Alana and Uncle Norm..
Take one healthy measure of math, blend in two cousins and their wacky Uncle Norm. Next mix in some mayhem, music, a lot of laughs, and a big serving of learning. It’s a formula that amounts to plenty of mathe-magical fun with The Prime Radicals! This new live action series for kids aged 6-8 is compelling and entertaining – never didactic – and uses humourous, hands-on, real-world scenarios to make numbers cool for kids, based on the math curriculum for young learners. Stay tuned for The Prime Radicals season 2 in the fall of 2013!
More exciting episodes ...
The multi award-winning Canadian television series that has hooked children aall across Ontario is back for a second season. The Prime Radicals Season 2 officially launches on TVOKids on Thursday, September 5, 2013 at 6:30 p.m. in Ontario—and online across Canada at www.tvokids.com. Produced by Ottawa’s GAPC Entertainment, the series takes the mystery out of math and puts the fun back into learning for kids aged 6 to 8.
52 x 15 min.


A differentiated approach to adaptive learning – keep your students learning and engaged this summer!
Front Row offers a suite of tools across Math, ELA and Social Studies to help your students grow. • Math – 34,000+ questions aligned to K-8 standards • ELA – 400+ ELA articles, each available in multiple reading levels • Social Studies – Ready-to-go lessons • Data reports – Over 15 reports to track student growth • Benchmark assessments
Lessons are common core aligned. Students begin by taking a pretest within a domain then move to practice sets, lessons, and assessments. Front Row will always be free for teachers. Set up your account today.


Tom Torlakson is impressed with River Islands Technology Academy. So impressed that the man who oversees 10,000 public schools and the education of 6 million students as California’s State Superintendent of Public Instruction made his second visit in three years to the Lathrop charter school. The infusion of cutting edge technology to advance science, technology, engineering, and math education first lured Torlakson to visit in 2013.
Last spring, California held a statewide Assessment of School Performance and Progress testing for grades 3 -8 to ascertain students’ progress “in a more rigorous education regimen associated with the Common Core standards that were adopted in 2010”.
Performance was measured by the percentage of students who exceeded state standards, met state standards, nearly met state standards and did not meet state standards in English and mathematics.