Here you can download the Mathematics app in Khmer and English Language for your kid to let them learning math along playing.
If your kid likes to play a smartphone game, you should download the Mathematics app in the Khmer and English Language for your kid. And also, there are lots of useful features in the Khmer Mathematic app that it could allow your kid learning math along playing the mobile phone.
The Mathematic app support both Khmer and the English language that could help your children to improve the knowledge and skill about math. With the mathematic app, your kid could learn reading the number, counting, comparing, Add, and Subtract. Moreover, your kid could do the math exercises available in the app to improve their mathematical skill. And also, you can check a lot of useful Android app in Khmer here.
Download the app
Currently, the Mathematic app in the Khmer Language is only available for Android devices. To download and install the app on your phone or tablet, please follow the download link below. And also, you can search in the Google Play Store with the word “Math for Kids Khmer and English.”
The app features
There six sections in the app that could allow your kid to learn and practice the math skill. Here are options in the app that your kid could learn:
- Read: in this section, your kid can learn to read the number from “Zero” to “Nine.” And also, Your kid can learn to read the numbers by repeat after the app showing and spelling to each number 0 to 9.
- Count: In this tab, the app will display the numbers or the animals. And also, your kid can choose the correct amount of the animals that show on the screen.
- Compare: Your kid can learn to compare two numbers.
- Add: Your kid can learn the mathematic add function.
- Subtract: Your kid can learn the mathematical subtract function.
Moreover, in all sections in the app, it has the exercises that could help your kid to improve a lot of the math skill. Also, Let’s download the Mathematics app in Khmer for your kids now.


Also graphs the function and the trapezoids. Now download this program onto your Calculator, and head on to Calculus and see how helpful it is! It estimates areas under curves using this method. Unfortunately, this function only returns the derivative of a single point. For example, suppose you have graphed sin x. It also draws the rectangular or trapezoidal regions under the graph. When the derivative is positive, the line is green.
Also included is the definite integral over the region. Note the function expression in the upper left corner. . That can be a big help to you in checking your work. Power Rule, Product Rule, Quotient Rule, Chain Rule, Definition of a Derivative, Slope of the Tangent Line, Slope of the Secant Line, Average Rate of Change, Mean Value Theorem, and Rules for Horizontal and Vertical Asymptotes.
It will find Area Between Curves, Volume of Circular Revolution Around a Vertical Line and Around a Horizontal Line, Centroid, Arc Length, Surface Area of Revolution, Definite Integral of a function from A to B, Riemann Sums Area Approximations - Left, Right, Midpoint, Trapezoid, and Simpson's Rules , Nth Derivative based on power rule Nth Antiderivative based on power rule , and Root Approximation Methods Newton, Bisection, and Secant Methods. Here I have chosen —2 to 5 for the y range. This version fixes an issue with Y0 variable from the previous version. Accumulation functions take lots of computation, and that makes them graph very slowly. So I need to know if I'm doing my homework right or else I'm screwed on test day if I've been doing it wrong. This program does all the work for you; the only thing you'll need to do, is to write the answer down on the sheet of paper.
The calculator displays the derivative at the bottom of the screen. Just make sure you have multiple choices given! Enter the desired x value, such as 6. This page shows you two ways to compute a definite integral with numeric limits, and how to plot an accumulation function. It will give you area between curves, volume of circular revolution of between two curves, 1k 04-02-18 Calculus Formulas It shows basic formulas for Calculus. The realtime progress meter shows how far the program has progressed for time-consuming high accuracy calculations, and the standard interface makes it easy to navigate. Change in function value per small change in x. When it is zero, the line is black.
Just enter the 2 by 2 matrix and the program will find the two Eigen Values, define the equilibrium point, and give you the solutions. The program keeps doing that for x2, x3, x4, and x5. Of course, the derivative of a function is also a function because it is typically different at different points along the original function. There may be a wait before it is displayed. Correctly works with negitive Z Scores. The program does the Newton's method and shows you all the values you need.
The program finds the values of X1 and f X1 and returns them to you. This is a program, which calculate the probability under the normal curve. The viewing window for those screen shots is —2π to 2π in the x direction and —2 to 2 in the y direction. Just like the slope of a line is rise over run, or change in y divided by change in x, the derivative of a function is calculated by looking at the change in y divided by the change in x, except looking at only a very small slice of a function at a time. Then you get an estimate with Simpson's method for 100 intervals.
It will do so much for you and it will really help you in Calculus. Accumulation Functions An accumulation function is a definite integral where the lower limit of integration is still a constant but the upper limit is a variable. All that you have to provide is a function or two and two bounds. This program provides a variety of tools for slope fields: you can enter a differential equation, render the resultant field, edit the window settings, find the slope value at a specific x,y point, and trace an antiderivative over the field to verify that it is correct. Contains Euler's Method, Riemann sums using left, mid, right, trap, and Simpson methods, and Slopefield for graphing differential equations.
You can also specify a specific x value to calculate the exact value of the derivative at a single point. It will save you lots of time and work that you will have to struggle with for about 30 minutes when this program does it in about 5 minutes. You enter a function and your first guess, X0. Instead of calculating a specific value, the calculator displays a general expression for the derivative. At this selection, the command fnInt will appear on the command screen.
Have you ever wanted to perform a quick antiderivation? This image shows the derivative at various points as the slope of a tangent line. Mathematical Background The derivative of a function is its slope at a particular point. Here I have chosen —2 to 5 for the y range. It also allows you to use the same function multiple times. In the future I will make a program that also shows all steps. Example: Suppose you must find the definite integral. Set Xmin to the lower limit of integration, and set Ymin and Ymaxto whatever values make sense in the problem.


The Pareto principle is the result of the work of the 19th Century economist, Vilfredo Pareto. He realized that wealth in Italy was distributed unevenly, and mathematically proved his concept.
Today, the Pareto principle is more commonly known as the 80-20 rule. Simply put, 80 percent of problems are the result of 20 percent of the causes. The power of the Pareto principle is immense. It conserves resources by letting you focus on a small number of issues to eliminate a disproportionally large number of problems.
Of note, the numbers 80 and 20 are not set in stone. It often turns out to be 70-35 or 90-12. Also note that since the percentages are of two different things (causes and effects) they do not have to add up to 100.
The most common way of displaying the Pareto principle is on the Pareto chart.


Abbie (6), not wanting to be outdone by Stephen's expression of brilliance in regards to math facts, told me that she knew what iced coffee was: coffee over ice. Great Abs, but once again, let's aim a little higher! Having only just completed Kindergarten, school is lots of fun for her and sitting with Mommy to work through her math book is something she wants to do. Here's a shot of her working on place value.
Tuesday, July 3, 2007
I used to think I was a fun Mom, but perhaps not so much these days. Just when my kids were expecting a break from school work, I decided to add a little lesson each day to keep their brains working. Stephen (9) has assured me that his brain is working fine and to prove it, he told me that 2 x 2 = 4. Well, let's aim a little higher than that! Here's a shot of him looking ever so joyful, at work on his "Summer Bridge Activities" book - which is really code for "boring school work" book.


Genius Maker contains 34 educational software programs covering Mathematics, Physics, and Chemistry for high school students. It includes Graph plotter, Analytical geometry, Matrix algebra, Equation solver, Triangle solver, Unit converter, Refraction of rays, Lens and mirrors, Color theory, Transverse waves, Radioactive decay, Periodic table, Inorganic compounds, functional groups and Gas Laws.
Version 3.0 includes Inorganic compounds and Functional groups modules.
What's new in this version:
Version 3.02 includes improved interface and performance.


Pi Day. A day to celebrate that transcendental number, π. A day to eat circular desserts, and reflect on the nature of the most famous constant in mathematics.
No matter what field of science, technology, engineering, or mathematics you may be in, π probably plays a prominent part. Yet certain tau infidels dispute this.
I Like Pi!
π, sometimes called pi, is possibly the most famous mathematical constant of all. It’s defined as the ratio of the circumference of a circle to its diameter:
This number shows up all sorts of places, yet the heathen Tauists believe that the true circle constant should be the ratio of the circumference of a circle to its radius:
How Great Tau Art?
Advocates of τ make a few points, the first typically being the definition of a radian. The radian is a unit of angular measure, defined such that an angle of 1 radian is measured by a circular arc whose length is equal to the radius of the circle.
Based on that definition, there are 2π radians in a complete circle. A Tauist would point out that it looks more natural for there to just be τ radians in a complete circle. In fact, they suggest that τ is not a near-lookalike of π, but actually stands for “turning”.
It’s understandable that these Tauists prefer that τ radians = 360°. This is a common affliction among physicists as well, who create systems of measure that set various physical properties equal to 1. Simple multiplication can be quite an annoyance, after all.
Tau is Already Taken
Incidentally, τ already has multiple meanings in physics and engineering, including torque (τ), sheer stress (τ), and the tau (τ) lepton. It has various other meanings elsewhere. Think this doesn’t matter?
Here’s a little imaginary tale.
It involves the imaginary number,
Despite being imaginary, this number appears quite often in STEM fields. Yes, even in engineering, which usually concerns itself with “real” values.
Except in electrical engineering.
You see, the symbol was already in use in electrical engineering by the time that complex analysis worked its way into the field. It denotes a time-varying current, as opposed to which denotes a constant current. (This nomenclature is consistent elsewhere as well: is time-varying voltage, whereas is DC.)
So what did we do? We called the imaginary number instead of .
It looks funny, and it gives us “imaginary number “, but it lets us keep our time-varying current . If a symbol is already in common use in a field, the field will not change its meaning.
Far as the Pi Can See
Although τ shows up in a few mathematical equations, π shows up in numerous places in statistics and in engineering, including many places where replacement with τ would introduce an unnatural factor of .
404 Pun Not Found
Kidding aside, I have nothing against tau. It’s sometimes useful to look at things from a new perspective.
In Carl Sagan’s Contact, the SETI researchers search for alien radio signals at a frequency of . If the aliens had been Tauists, Dr. Arroway would have missed their radio signal.
(On the other hand, the fact that Dr. Arroway later finds interesting structure in the digits of π suggests that God Himself prefers π to τ.)
Why did I bring up Carl Sagan? Maybe my mind is just on billions and billions of pies. Mmmm… pie.
So I’ll close with one of the most famous equations in mathematics: Euler’s Identity. It’s been called the most beautiful equation in mathematics, because it relates five important mathematical constants: e, i, π, 1, and 0.
Marvel in its magnificent mathematical beauty. Happy Pi Day!


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1 numbered red die (with curved edges)
1 dotted blue die (with curved edges)
Material: safe, non-toxic and odorless EVA foam (formaldehyde-free, phthalate-free, PAHs-free)
Made in Taiwan; ST - Safety Toy
[Suitable for ages 3 - 4]
Object: To learn how to start easy counting at a tender age. The curved edges and soft materials also make it safer, and easier to grasp and roll. Parents can spend more quality time with their children and help them learn to count as well.
Toss the numbered die and call out the number. Teach the child to recognize numbers.
Toss the dotted die and count how many dots. Call out the number of dots seen.
Roll the numbered and dotted dice together and add the number of dots rolled out to the number rolled out, and vice-versa. Call out the answer.
4. Touch Test
Roll the two dice together and ask the child to touch the die for the number or the dots you call out. For example, if a ‘2’ on the numbered die is rolled out and ‘4 dots’ on the dotted die are rolled out and 4 is being called out, the child will have to touch the dotted die. This will help the child to recognize the numbers as well as count the dots fast.
5. Match Test
Roll the dotted die. Count the dots rolled out. Take the numbered die and ask the child to touch the number that matches the dots, and vice-versa.
6. Bigger or smaller
Roll the two dice together and ask the child to touch whichever die has the bigger number. Then the same process can be repeated for the smaller number.
7. Jump forward or backward
Roll the two dice together. Jump forward the number of steps, according to the number rolled out on the numbered die (The steps according to the dots or the number of the dice that face up) and jump backward the number of steps, according to the number of dots rolled out on the dotted die. The game can be alternated by jumping backward the number of steps, according to the number rolled out on the numbered die and jumping forward the number of steps, according to the number of dots rolled on the dotted die.
8. Even and odd numbers
Make a starting and finishing point. Have 2 players to start the game together. Ask the children to move only one small step at a time. Roll one of the dice. If the number or the number of dots is an even number, move 2 steps forward. If the number or the number of dots is an odd number, move 1 step backward. The person to reach the finishing point first is the winner.
Copyright © ElephantCube


Search Printable Triangle Worksheets For students who are just beginning to understand the differences between shapes and acquire vocabulary related to 2D objects, a triangles worksheet will help them understand how to recognize and manipulate the common three-sided object. With this worksheet generator, you can make free worksheets for calculating the area of triangles, parallelograms, other quadrilaterals, and polygons (pentagons/hexagons) in the coordinate grid. The worksheets can be made in PDF or html formats. The problems give the coordinates of the vertices of the shapes and ask to calculate the area.Browse Printable Area of a Triangle Worksheets. Award winning educational materials designed to help kids succeed. Start for free now!Area of a triangle: sine formula Geometry Math Worksheets. November 17, 2022 by ppt. Free questions on “Area Of A Triangle: Sine Formula” will help you improve your math understanding. You can also find thousands of math skills. Geometry students can use these worksheets to improve their math skills. Cookie.1.All congruent triangles are equal in area but the triangles equal in area need not be. congruent. (True/False) 2.Any side of the parallelogram can be chosen as base of the parallelogram. (True/False) 3.The distance around a circular region is known as area of that circle. (True/False)How to find out the area of a triangle. In order to find the area of a triangle, start by multiplying the base of the triangle by its height. Once you have this, divide by 2 which will give you the area. You divide by 2 because a parallelogram can be divided into 2 triangles. This Area of a Triangle Worksheet allows children to practise this ...Here, the area is the region occupied by the triangle. As already discussed before in types of triangles, we would find the area of equilateral triangles, isosceles triangles, and scalene triangles. Area of Triangles worksheets teaches the different types of triangles, computation of the area and perimeter, unde concepts of median & centroid, and pythagorean theorem.
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Area Of A Triangle Showing top 8 worksheets in the category - Area Of A Triangle. Some of the worksheets displayed are Area of triangles, Area of a triangle, Area of a triangle, Sj area rectangles triangles, Triangle areas by trig, Perimeter and area, 6 area of triangles and quadrilaterals, Find the area and perimeter of triangles.Area of a Triangle #2. Worksheet. Acute Triangles: Find the Missing Height. Worksheet. Obtuse Triangles: Find the Missing Base. Worksheet. Acute Triangles: Find the Missing Base. Worksheet. Geometry Detective: Area of a Triangle #3.Grade 5 Geometry Worksheets: Area Of Triangles | K5 Learning www.k5learning.com. grade area worksheets triangles geometry math worksheet triangle finding printable k5 learning pdf right perimeter k5learning similar. Area Of A Triangle Worksheet #1 - Color Version - Tim's Printables www.timvandevall.com. Worksheet - Area Of A Triangle studylib.netTriangle Worksheets Free and Printable. These Triangle Worksheets cover perimeter, area, and the Pythagorean Theorem. All come with corresponding answer pages. Teachers, parents, …Grade 6 Geometry Worksheets - Free & Printable | Geometry Worksheets www.pinterest.com. area worksheets triangles geometry parallelograms trapezoids grade math worksheet triangle 6th printable quadrilaterals sixth k5learning areas maths 5th pdf. Grade 6 Math Worksheets Perimeter And Area Of Triangles - Google Search www.pinterest.comBrowse Printable 4th Grade Area of a Rectangle Worksheets. Award winning educational materials designed to help kids succeed. ... Start for free now! Learning Library. ... Entire Library Printable Worksheets Games Guided Lessons Lesson Plans Hands-on Activities Interactive Stories Online Exercises Printable Workbooks Science Projects Song VideosWorksheets. 13 Images about Worksheets : Area of triangle worksheet | Teaching Resources, area of a triangle worksheets 7th grade | Click on the sample worksheet and also Circumference and Area of a Circle Worksheet | Math Monks. Worksheets www.missbsresources.com. worksheets area triangle geometry differentiated maths resourcesArea Of A Triangle Free Printable Worksheets – Learning How To Read british-learning.com. worksheet area worksheets maths printable triangles key triangle trigonometry ks3 answer math answers pdf geometry trig cazoom introduction learning homeschool. 10 Best Images Of Worksheets Area Of Kite - Rhombus And Kite Area Worksheet, Kites Worksheets ...Feel free to download and enjoy these free worksheets on functions and relations .Each one has model problems worked out step by step, practice problems, as well as challenge questions at …A triangle’s area equals half the area of a rectangle. Thus, the area of a triangle is deduced from the formula A = ½ BH, where A represents the area, B represents the base, and H represents the triangle’s height. When parents and teachers teach children the concept of the area of a triangle, it can be difficult for children to understand ...Get free questions on “Constructing the circumscribed or inscribed circle of a triangular” to improve your math understanding and learn thousands more math skills. Geometry students can find perfect worksheets in math.Geometry Area of right triangles Area of right triangles Geometry worksheets: find the area of right triangles Students find the areas of each right triangle. The measurements of all three sides of each triangle are given. These worksheets are printable pdf files. Worksheet #1 Worksheet #2 Worksheet #3 Worksheet #4 Worksheet #5 Worksheet #6 5 MoreFind Page 10 Of 83 Properties Matching Property For Sale In Lurgan Area From Stewart Estate Agents property .attribute.hasSmoking property .attribute.hasPets property .attribute.requiresReference Allows pets Allows smoking property .attribute.broadband Off street parking Garage Long Term Let Holiday Let Summer Only Let Divisible into lots.Study guide 2020–23; MATP121 Linear Algebra and Geometry 1; MATP121 Linear Algebra and Geometry 1 (7 cr) Open the course unit brochure on Sisu.Study level: Basic studies.Grading scale: 0-5.Browse Printable 7th Grade Area of a Triangle Worksheets. Award winning educational materials designed to help kids succeed. ... Start for free now! Learning Library. ... Entire Library Printable Worksheets Games Guided Lessons Lesson Plans Hands-on Activities Interactive Stories Online Exercises Printable Workbooks Science Projects Song VideosGet free questions on “Area Of Sectors” to improve your math understanding and learn thousands more math skills. Geometry students will find the perfect math worksheets. Categories Geometry , Math Post navigation Area of a Triangle 1 Tim's Printables from www.timvandevall.com. Find the missing side using the area. 17 pics about area of a triangle worksheet | teaching resources : These sheets help students recognize the formula for the area of a rectangle, triangle, octagon, and more. This handout, which presents right triangles and other triangles as geometric shapes for calculating area, makes great material for 5th grade and 6th grade. The base length (b) and altitude (h) are depicted on the figure. Substitute them in the formula A = bh/2 and obtain the area. Area of Triangles | Integers – Worksheet #2This Area and Perimeter Worksheet will produce nine problems for solving the area and perimeter of different types of triangles. This worksheet is a great ...Browse Printable 6th Grade Area of a Triangle Worksheets. Award winning educational materials designed to help kids succeed. Start for free now!, CvC, FVwtG, QRsG, OSRuQ, iDoWT, pCeaJI, DIsRJA, lzhEJW, waerdM, RwBvO, uesxO, dlPCN, kse, aFWu, zOJKn, ggKI, oxXxg, hcZJC, mKLO, xGkAvE, dhUh, kjz, CRV, SXS, xMsI ...For this, our Iceberg Triangle Area Differentiated Worksheets may be to your liking. These worksheets present a series of triangles made to look like icebergs floating in freezing water, and students must use the provided measurements to determine the area of each triangle. These worksheets are also differentiated, with higher ability versions ...Area Of Triangles Worksheet Pdf. Area Of A Triangle Worksheets. 9+ Geometry Worksheet Examples For Students. Area Of A Triangle Equals Base Times Height Divided By 3. Area Of …


I was so fascinated by the pictorial representation of mathematical sequences and patterns embedded in plants, flowers, trees and even in the spiral shapes of our galaxies that I felt compelled to reblog ‘plantsandbeyond’s’ post. It is my hope that you enjoy it as much as I do.
The Fibonacci sequence appears in the smallest, to the largest objects in nature. It is a way for information to flow in a very efficient manner.
The actual Fibonacci sequence is this series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. Simply put, the next number in the sequence is formed by adding up the previous 2 numbers. (0 + 1 = 1, 1 + 1 = 2, 2 + 1 = 3, and so on.)
The Fibonacci sequence is named after Leonardo of Pisa, who was known as Fibonacci. Though Fibonacci first introduced the sequence to the western world in 1202, it had been noted by Indian mathematicians as early as the sixth century.
The Fibonacci defines how the density of branches increases up a tree trunk, the arrangement of leaves on a stem, and how a pine cone’s scales are arranged. Yet you will…
View original post 305 more words


What is mathematics
Mathematics – a science that initially emerged as one of several directions of your search for truth (in Greek philosophy) within the field of spatial relations (surveying – geometry) and calculations (arithmetic), for sensible human demands essay writer service to count, calculate, measure, study the shapes and motion of physical bodies. Later it developed into a rather complicated and multifaceted science of abstract quantitative and qualitative relations, types and structures. There is certainly no frequently accepted definition of mathematics. Initially, it was used to calculate, measure, and to study the shapes and motions of physical objects by way of deductive reasoning and abstraction. Mathematicians formulate new conclusions and try to establish their validity based on well-chosen axioms and definitions.
Mathematics arose from time immemorial in the sensible requirements of man, its content material and nature have changed over time. In the initial objective representation of a optimistic integer, from the representation of a line segment because the shortest distance in between two points. Mathematics has come a lengthy way prior to it became an abstract science with well-formed fundamental concepts and specific study strategies. New specifications of practice, expand the scope of the ideas of mathematics, fill the old concepts with new which means. The concepts of mathematics are abstracted from the qualitative features precise to every single offered range of phenomena and objects. This reality is quite essential within the application of mathematics. Yes, the quantity 2 does not have any certain substantive which means. It might refer to two books, and to two machines, and to two concepts. It applies nicely to these and several other objects. https://www.sdsu.edu/ Similarly, the geometric properties of a sphere do not modify based on no matter whether it’s produced of steel, copper or glass. Obviously, abstraction from the properties from the object impoverishes our understanding of this object and its characteristic material functions. In the similar time, it is actually this abstraction that offers mathematical concepts generalization, generating it probable to apply mathematics to various all-natural phenomena. This means that precisely the same laws of mathematics, the identical mathematical apparatus could be really successfully applied to biological, technical, economic and other processes.
There are many diverse sorts of sampling procedures in statistics. These strategies are named based on how the sample was obtained. In what follows, we are going to look at systematic sampling and understand more regarding the ordered procedure used to get this sort of sample.
No matter how cautious you are, there is certainly usually a measurement error. The error just isn’t aspect -It is an error in regards to the measurement approach. In science, a measurement error is named an experimental error or an observational error. There are actually two most important classes of observation errors: random error and systematic error. Random error varies unpredictably from ewriters pro one particular dimension to another, whilst systematic error has the same value or proportions for each and every measurement. In the event you take several measurements, the values ??are grouped about the true worth. Hence, an accidental error mostly impacts accuracy. Ordinarily, a random error affects the last considerable digit of your measurement.


1 edition of Waves and stability in continuous media, Taormina, October 1987 found in the catalog.
Waves and stability in continuous media, Taormina, October 1987
|Statement||edited by A. Donato, S. Giambò.|
|Series||Seminars and conferences|
|Contributions||Donato, A., Giambò, S., Meeting on Waves and Stability in Continuous Media (4th : 1987 : Taormina, Italy)|
|LC Classifications||QA927 .W39 1988|
|The Physical Object|
|Pagination||xi, 355 p. :|
|Number of Pages||355|
|LC Control Number||90198914|
Andrea Donato's 22 research works with citations and reads, including: Waves and Stability in Continuous Media: Proceedings of the 10th Conference on WASCOM Thermal convection and stability of other flows in porous media are covered and a chapter is devoted to the problem of stability of flow in a fluid overlying a porous layer. Nonlinear wave motion in porous media is analysed, and waves in an elastic body with voids are investigated. Acoustic waves in porous media are also analysed in some : Springer-Verlag New York.
Numerical Prediction of Damage Ship Stability in Waves. Instituto Superior Tecnico, Lisbon. IST. Portugal. Maritime Research Institute Netherlands. MARIN. The Netherlands. Ship Stability Research Centre, Universities of SSRC. United Kingdom. Glasgow and Strathclyde. National Technical University of Athens, Ship NTUA-SDL. Greece. Design. Get this from a library! Waves in Continuous Media. [Sergey Gavrilyuk; N I Makarenko; S V Sukhinin] -- Starting with the basic notions and facts of the mathematical theory of waves illustrated by numerous examples, exercises, and methods of solving typical problems Chapters 1 & 2 show e.g. how to.
Waves and Imaging through Complex Media Softcover reprint of the original 1st ed. Edition by P. Sebbah (Author) out of 5 stars 1 rating. ISBN ISBN Why is ISBN important? ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book. 1/5(1). - October 31th, ). Ph.D. Student (with an Italian government scholarship) at Mathematics Department, Uni-versity of Bologna, (November 1st, - October 31th, ). Fellowships Teaching Assistantship at Engineering faculty, University of Brescia (November 1st, - October 31th, ). Scientific habilitation.
Central Government supply estimates 2002-03 for the year ending 31 March 2003.
Parties and Politcal Change in Bolivia
More than booty
Instructors manual to accompany Psychology
Unearthing Chinas past
The Canada lancet
pros and the ex-cons
Proceedings of the ACM Sigmetrics Conference on Measurement & Modeling of Computer Systems, 1982 (Performance Evaluation Review)
Word of mouth.
Speaking in tongues and its significance for the Church
entity-relationship approach to logical data base design
Agricultural export assistance and high-value product exports
Delaware Department of Correction
Get this from a library. Waves and stability in continuous media, Taormina, October [A Donato; S Giambò;]. Waves and Stability in Continuous Media. First organized inthe WASCOM conference to bring together researchers and scientists from all over the world to discuss problems, promote collaborations and shape future directions for research in the field of stability and wave propagation in continuous media.
This book contains recent contributions in the field of waves propagation and stability in continuous media. The volume is the sixth in a series published by World Scientific since Sample Chapter(s) Chapter 1: Analysis of an Electric Network Containing Multi-Dimensional Semiconductor Devices (1, KB) Contents.
Waves and Stability in Continuous Media Roberto Monaco First organized inthe WASCOM conference was designed to bring together researchers and scientists from all over the world to discuss problems, promote collaborations and shape future directions for research in the field of stability and wave propagation in continuous media.
Shock Waves for Squares Discrete Boltzmann Models with Speeds 1, √2, 2, 2√2, 4, and Zero Existence, Uniqueness and Stability of Regular Steady Motions of a Second Grade Fluid A Moving Boundary Problem in Dynamics of Gases with Viscosity. The book contains recent contributions in the field of waves propagation and stability Taormina continuous media.
In particular, the contributions consider discontinuity and shock waves, stability in fluid dynamics, small parameter problems, kinetic theories towards continuum models, non-equilibrium thermodynamics, and numerical applications. Starting with the basic notions and facts of the mathematical theory of waves illustrated by numerous examples, exercises, and methods of solving typical problems Chapters 1 & 2 show e.g.
how to recognize the hyperbolicity property, find characteristics, Riemann invariants and conservation laws for quasilinear systems of equations, construct and analyze solutions with weak or strong.
System Upgrade on Tue, May 19th, at 2am (ET) During this period, E-commerce and registration of new users may not be available for up to 12 hours. Media –, ), a series of efficient numerical schemes are developed for the one dimensional scalar wave equation within various types of media.
Stability and accuracy are analyzed and. Interaction of hydrodynamic waves with plane shock waves under the linear approximation is studied.
Two classical problems, namely, wave transformation and a rippling instability on a shock wave. “This book is a graduate level text based upon a lecture course on waves in continuous media with particular emphasis on fluid media.
It is aimed at students of applied mathematics, mechanics and geophysics. Waves in a stratified fluid and stability of such waves are also discussed. It will be completely retired in October This page will automatically redirect to the new ADS interface at that point. SAO/NASA ADS Physics Abstract Service Find Similar Abstracts (with default settings below) Table of Contents WAVES AND STABILITY IN CONTINUOUS MEDIA.
Proceedings of the 15th Conference on WASCOM Waves are oscillations that move in space and time and are able to transport energy from one point to another. Quantum mechanical wavefunctions are discussed in Chap.
In this chapter we simulate classical waves which are, for instance, important in acoustics and electrodynamics. This book contains recent contributions in the field of waves propagation and stability in continuous media.
The volume is the sixth in a series published by World Scientific since  Some results on the subject have been presented in form of communication in A. Strumia:Covariant Euler-Lagrange equations as systems of conservation laws with constrained field variables, in theIV Meeting Waves and Stability in Continuous Media, Taorminain by: 1.
This book contains about 20 invited papers and 40 contributed papers in the research areas of theoretical continuum mechanics, kinetic theory and numerical applications of continuum mechanics.
«Back to Waves and Stability In Continuous Media--Proceedings of the 12th Conference On Wascom Find in a Library Find Waves and Stability In. This volume is the fifth in a series of proceedings which started in The contributions include the latest results on the theory of wave propagation, extended thermodynamics, and the stability of the solutions to partial differential equations.
No existing book covers the beautiful ensemble of methods created in topology starting from approximatelythat is, from Serre's celebrated “Singular homologies of fibre spaces.”This is the translation of the Russian edition published in with one entry (Milnor's lectures on the h.
sense: pure loss of stability, parametric roll, broaching, dead ship condition (resonant roll in beam seas)], i.e., wave steepness, non- linearity, frequency contents of the spectrum, statistical distribution of wave and crest height and spatial behaviour of the waves and non-linear wave kinematics.
Develop better understanding of uncer. This book contains about 20 invited papers and 40 contributed papers in the research areas of theoretical continuum mechanics, kinetic theory and numerical applications of continuum mechanics.
Waves and Stability In Continuous Media--Proceedings of the 12th Conference On Wascom Find out more about OverDrive accounts. Save Not today. Add tags for "Waves and stability in continuous media: proceedings of the Vth International Meeting, Sorrento, Italy, October ".
Be the first. Similar Items.Oscillations and Waves by IIT Kharagpur. The book is targeted at the first year undergraduate science and engineering students. Starting with oscillations in general, the book moves to interference and diffraction phenomena of waves and concludes with elementary applications of Schr¨odinger’s wave equation in quantum mechanics.A Bibliography of Publications of Riccardo Fazio Riccardo Fazio University of Messina Mathematics Sant’Agata, Messina Italy Tel: +39 (0) 90


Last time, I mentioned a question:
Taleb and others have mentioned that the bell curve (or Gaussian) does not deal with outliers well; it gives them a very small probability, and the parameter estimates end up being highly dependent on them.
Yet, one of the justifications of the Gaussian is that it's the max-entropy curve for a given mean and standard deviation.
Entropy is supposed to be a measure of the uncertainty associated with a distribution; so, shouldn't we expect that the max-entropy distribution would give as high a probability to outliers as possible?
There are several answers.
First: a basic problem is that phrase "a given mean and standard deviation". In particular, to choose a standard deviation is to choose an acceptable range for outliers (in some sense). If we have uncertainty about the standard deviation, it turns out the resulting curve has a polynomial decay rather than an exponential one! (This means distant outliers are far more probable.) Essentially, estimating deviations from data (using maximum-likelihood) makes us extremely overconfident that the data will fall in the range we've experienced before. A little Bayesian uncertainty (which still estimates from data, but admits a range of possibilities) turns out to be much less problematic in this respect.
This is definitely helpful, but doesn't solve the riddle: it still feels strange, that the max-entropy distribution would have such a sharp (super-eponential!) decay rate. Why is that?
My derivation will be somewhat heuristic, but I felt that I understood "why" much better by working it out this way than by following other proofs I found (which tend to start with the normal and show that no other distribution has greater entropy, rather than starting with desired features and deriving the normal). [Also, sorry for the poor math notation...]
First, let's pretend we have a discrete distribution over n points, xn. The result will apply no matter how many points we have, which means it applies in the limit of a continuous distribution. Continuous entropy is not the limit of discrete entropy, so I won't actually be maximising discrete entropy here; I'll maximise the discrete version of the continuous entropy formula:
f(x) maximising sum_i: f(xi)log(f(xi))
Next, we constrain the distribution to sum to a constant, have a constant mean, and have constant variance (which also makes the standard deviation constant):
sumi[f(xi)] = C1
sumi[xif(xi)] = C2
sumi[xi2f(xi)] = C3
To solve the constrained optimisation problem, we make lagrange multipliers for the constraints:
Partial derivatives in the f(xi):
1 - log(f(xi))
Setting this equal to zero and solving for f(xi):
That's exactly the form of the Gaussian: a constant to the power of a 2nd-degree polynomial!
So, we can see where everything comes from: the exponential comes from our definition of entropy, and the function within the exponent comes from the Lagrange multipliers. The Gaussian is quadratic precisely because we chose a quadratic loss function! We can get basically any form we want by choosing a different loss function. If we use the kurtosis rather than the variance, we will get a fourth degree polynomial rather than a second degree one. If we choose an exponential function, we can get a doubly exponential probability distribution. And so on. There should be some limitations, but more or less, we can get any probability distribution we want, and claim that it is justified as the maximum-entropy distribution (fixing some measure of spread). We can even get rid of the exponential by putting a logarithm around our loss function.
Last time, I mentioned robust statistics, which attempts to make statistical techniques less sensitive to outliers. Rather than using the mean, robust statistics recommends using the median: whereas a sufficiently large outlier can shift the mean by an arbitrary amount, a single outlier has the same limited effect on the median no matter how extreme its value.
I also mentioned that it seems more intuitive to use the absolute deviation, rather than the squared deviation.
If we fix the absolute deviation and ask for the maximum-entropy function, we get something like e-|x| as our distribution. This is an ugly little function, but the maximum-likelihood estimate of the center of the distribution is precisely the median! e-|x| justifies the strategy of robust statistics, reducing sensitivity to outliers by making extreme outliers more probable. (The reason is: the max-likelihood estimate will be the point which minimizes the sum of the loss functions centred at each data point. The derivative at x is equal to the number of data points below x minus the number above x. Therefore the derivative is only zero when these two are equal. This is the minimum loss.)
What matters, of course, is not what nice theoretical properties a distribution may have, but how well it matches the true situation. Still, I find it very interesting that we can construct a distribution which justifies taking the median rather than the mean... and I think it's important to show how arbitrary the status of the bell curve as the maximum entropy distribution is.
Just to be clear: the Bayesian solution is not usually to think too much about what distributions might have the best properties. This is important, but when in doubt, we can simply take a mixture distribution over as large a class of hypotheses as we practically can. Bayesian updates give us nice convergence to the best option, while also avoiding overconfidence (for example, the asymptotic probability of outliers will be on the order of the most outlier-favouring distribution present).
Still, a complex machine learning algorithm may still need a simple one as a sub-algorithm to perform simple tasks; a genetic programming approximation of Bayes may need simpler statistical tools to make an estimation of distribution algorithm work. More generally, when humans build models, they tend to compose known distributions such as Gaussians to make them work. In such cases, it's interesting to ask whether classical or robust statistics is more appropriate.


Create a histogram from double values in a raster.
FastMapHistogram only works with integer values, which is good for performance
but means that, in order to use FastMapHistogram with double values, each value
must be multiplied by a power of ten to preserve significant fractional digits.
For example, if you want to save one significant digit (2.1 from 2.123), set
sigificantDigits to 1, and the histogram will save 2.1 as "21".
Important: Be sure that the maximum value in the rater multiplied by
10 ^ significantDigits does not overflow Int.MaxValue (2,147,483,647).


Winning in bingo is largely a matter of chance, and the odds may not always be in your favor.
To truly comprehend why you might not be winning at bingo, it’s essential to fully understand how the game works, the different variations of the game, and the mathematical principles that underpin it. This section will elucidate these key components of bingo.
How Bingo Works
Bingo is a relatively straightforward game to play, but there are several key elements involved.
- Bingo Cards: At the start of the game, each player is given a bingo card. A typical bingo card consists of a 5×5 grid of numbers.
- Drawing Numbers: The game organizer or a computer will randomly draw numbers one at a time.
- Marking Numbers: As each number is called out, players will check their bingo cards and mark off the corresponding number if it appears on their card.
- Winning: The objective of the game is to be the first player to complete a specific pattern of marked numbers on their bingo card. This pattern can vary from game to game. Common patterns include a straight line (horizontal, vertical, or diagonal), four corners, or even the entire card. The first player to complete the pattern and call out ‘Bingo!’ is the winner.
Types of Bingo Games
There are several different variations of bingo played around the world. Here are a few of the most popular ones:
- 75-Ball Bingo: This is the most common version of bingo played in North America. The bingo card consists of a 5×5 grid of numbers, with the columns labeled B, I, N, G, O.
- 90-Ball Bingo: This is the most popular version of bingo in the UK and Australia. The bingo card consists of a 3×9 grid of numbers.
- 80-Ball Bingo: This is a relatively new variation of bingo that is often played online. The bingo card consists of a 4×4 grid of numbers, and each column is a different color.
- 30-Ball Bingo: Also known as ‘speed bingo’, this is a fast-paced version of the game played with only 30 numbers. The bingo card consists of a 3×3 grid of numbers.
The Mathematics Behind Bingo
Understanding the mathematics behind bingo can help you better appreciate the game and why winning can sometimes seem so elusive. The key mathematical principles involved in bingo are probability and combinations.
- Probability: This refers to the likelihood of a specific event occurring. For example, the probability of any given number being drawn next in a game of 75-ball bingo is 1/75. As the game progresses and more numbers are drawn, the probability of each remaining number being drawn next increases.
- Combinations: This refers to the different ways a group of objects can be arranged or selected. In bingo, this can relate to the different combinations of numbers that can form the winning pattern on your bingo card. For example, in a simple one-line game of 75-ball bingo, there are 5! (5 factorial) or 120 different combinations of numbers that could form a winning line.
Understanding these mathematical principles can help you better appreciate the odds of winning at bingo and why it can sometimes seem so challenging to win. For a more detailed explanation of these principles and how they apply to bingo, you may want to consult a probability textbook or a mathematics resource online.
Common Misconceptions about Winning Bingo
While bingo is a game of chance, many players hold certain misconceptions about how the game works and strategies to win. This section aims to debunk some of the most common misconceptions about winning bingo.
The Gambler’s Fallacy
The Gambler’s Fallacy is a common misconception not just in bingo, but in many games of chance. It is the belief that past events can influence future events. For example, if a player has been on a losing streak, they might believe that they are ‘due’ for a win and may start to bet more aggressively. Similarly, in bingo, a player might think that because a certain number hasn’t been called for a while, it is more likely to be called next. However, the reality is that each bingo draw is an independent event, and the odds of any particular number being drawn remain constant throughout the game. Understanding the Gambler’s Fallacy is crucial for maintaining a rational approach to playing bingo and other games of chance.
Myths About Bingo Strategies
There are several myths and misconceptions about strategies to win at bingo. Here are a few of the most common ones:
- Buying More Cards Increases Your Chances of Winning: While it is true that buying more cards will give you more chances to win, it doesn’t necessarily guarantee a win. Each card has an equal chance of winning, and buying more cards only increases the absolute number of winning combinations you have, not the probability of any one card winning.
- Certain Numbers Are Called More Frequently: Some players believe that certain numbers are called more frequently than others and try to select cards with those numbers. However, in a fair game of bingo, each number has an equal chance of being drawn. Any perceived patterns in the numbers called are purely coincidental.
- Playing at Off-Peak Times Increases Your Chances of Winning: Some players believe that playing at off-peak times, when there are fewer players, increases their chances of winning. While it is true that playing with fewer opponents may increase your chances of winning, it also often means smaller prize amounts.
- Sitting Closer to the Caller Increases Your Chances of Winning: This is a superstition that some players hold, but in reality, where you sit has no bearing on your chances of winning.
Remember, bingo is a game of chance, and while there are strategies you can employ to manage your money and enjoy the game more, there is no way to influence the outcome of the game. It is important to approach the game with a healthy attitude and an understanding of the odds.
The Role of Probability in Bingo
Understanding probability is crucial for anyone who plays games of chance, including bingo. This section will cover the basics of probability, how it applies to bingo, and how you can calculate your odds of winning.
Basics of Probability
Probability is a branch of mathematics that deals with the likelihood or chance of different outcomes. It is usually expressed as a fraction or a decimal between 0 and 1. A probability of 0 means the event is impossible, while a probability of 1 means the event is certain. For example, the probability of rolling a 3 on a six-sided dice is 1/6 or approximately 0.1667.
The probability of an event happening is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, in a standard deck of 52 cards, the probability of drawing an Ace is 4/52 or 1/13 because there are 4 Aces in a deck of 52 cards.
For a more detailed understanding of probability, you may refer to this Wikipedia page on Probability.
Applying Probability to Bingo
In bingo, probability plays a crucial role in determining your odds of winning. For example, in a game of 75-ball bingo, at the start of the game, the probability of any given number being drawn is 1/75. As the game progresses and more numbers are drawn, the probability of each remaining number being drawn increases. For example, after 10 numbers have been drawn, the probability of any specific remaining number being drawn next is 1/65.
Calculating Your Odds of Winning
To calculate your odds of winning at bingo, you need to consider several factors:
- Number of Cards: The more cards you are playing, the more chances you have to win. However, this also means you need to divide your attention between more cards, which can be challenging.
- Number of Players: The more players there are, the lower your chances of winning because you are competing against more cards.
- Pattern: Some patterns are easier to complete than others. For example, a single-line pattern is easier to complete than a full-card pattern.
- Numbers Called: As the game progresses and more numbers are called, your odds of winning change.
Calculating the exact odds of winning at bingo can be quite complex because it involves calculating the probability of multiple events happening simultaneously. However, understanding the basics of probability and how it applies to bingo can help you make more informed decisions about how many cards to play, which games to participate in, and how to manage your money. For a more detailed explanation of how to calculate your odds of winning at bingo, you may want to consult a mathematics textbook or a probability and statistics resource online.
Strategies for Playing Bingo
While bingo is predominantly a game of chance, there are still some strategies you can employ to increase your chances of winning or at least to make your money last longer and enhance your enjoyment of the game. Here are some strategies to consider:
Choosing Your Bingo Cards
Here are some tips for choosing your bingo cards:
- Spread of Numbers: Try to select cards with a good spread of numbers.
- Avoid Duplicates: Try to select cards with as few duplicate numbers as possible.
- Consider the Pattern: If you know the pattern you need to complete to win, consider selecting cards that already have some of the numbers in the pattern marked off.
Remember, while these tips can help you select cards with a higher probability of winning, there is no way to guarantee a win as bingo is a game of chance.
Patterns to Watch Out For
In many bingo games, the objective is to complete a specific pattern on your bingo card. Being aware of the patterns you need to complete can help you focus your attention and increase your chances of spotting a win. Here are some common bingo patterns to be aware of:
- Single Line: This is the most basic pattern and involves completing a single horizontal, vertical, or diagonal line on your bingo card.
- Double Line: This involves completing two lines on your bingo card. The lines can be horizontal, vertical, or diagonal.
- Four Corners: This involves marking off the four corner numbers on your bingo card.
- Full Card: This involves marking off every number on your bingo card.
Different games may have different patterns, so it’s essential to be aware of the pattern you need to complete to win.
Money Management Strategies
Managing your money wisely is crucial for enjoying a game of bingo and ensuring that you don’t spend more than you can afford to lose. Here are some money management strategies to consider:
- Set a Budget: Decide beforehand how much money you are willing to spend on bingo and stick to it.
- Limit Your Cards: Playing with more cards increases your chances of winning but also increases the cost. Decide beforehand how many cards you are comfortable playing with and stick to it.
- Consider the Cost: Some bingo games have higher ticket prices than others. Consider the cost of the tickets and the size of the prizes when deciding which games to play.
It’s important to play responsibly and not spend more than you can afford. For more information on responsible gambling, you can visit this Wikipedia page on Responsible Gambling.
Psychological Aspects of Playing Bingo
Playing bingo, like any other game of chance, involves not only understanding the game mechanics and employing strategies but also managing one’s psychological state. The emotional and psychological aspects of playing bingo can significantly impact one’s experience and even their chances of winning. This section will delve into the psychological aspects of playing bingo, including the impact of losing, dealing with frustration, and maintaining a positive mindset.
The Impact of Losing
Losing is an inevitable part of playing games of chance like bingo. However, how one deals with losing can significantly impact their overall experience and their approach to future games. It’s common to feel disappointed or frustrated after a loss, especially if you were close to winning. However, it’s important to remember that bingo is a game of chance, and losing does not reflect on your skills or abilities.
It can be helpful to set realistic expectations before playing and to remind yourself that losing is a part of the game. It’s also important to manage your money wisely and not to spend more than you can afford to lose.
For more information on dealing with losses in gambling, you can visit this Wikipedia page on Problem Gambling.
Dealing with Frustration
It’s natural to feel frustrated in such situations, but it’s important to manage this frustration constructively.
Here are some tips for dealing with frustration while playing bingo:
- Take Deep Breaths: Taking slow, deep breaths can help to calm your nervous system and reduce feelings of frustration.
- Take a Break: If you find yourself feeling overly frustrated, it may be helpful to take a short break from playing. Get up, stretch, and clear your mind before returning to the game.
- Practice Mindfulness: Mindfulness involves staying present and fully engaging in the present moment.
Remember, it’s okay to feel frustrated, but it’s important to manage that frustration in a healthy way.
Maintaining a Positive Mindset
Maintaining a positive mindset is crucial for enjoying the game of bingo and for managing the inevitable ups and downs that come with playing. Here are some tips for maintaining a positive mindset while playing bingo:
- Stay Positive: Try to focus on the positive aspects of the game, even if you are not winning. For example, focus on the fun of playing, the excitement of the game, and the social interactions.
- Set Realistic Expectations: Setting realistic expectations before playing can help to reduce disappointment and frustration if you don’t win.
- Practice Gratitude: Focusing on the things you are grateful for can help to shift your perspective and maintain a positive mindset.
Remember, maintaining a positive mindset is not only important for enjoying the game of bingo but also for maintaining good mental health and wellbeing. For more information on maintaining a positive mindset, you can visit this Wikipedia page on Positive Psychology.


A Beautiful Mind is a biographical book by author Sylvia Nasar. The content of the book is about John Forbes Nash, Jr., a prodigy and legend at the age of 30, who lights up the world of mathematics by solving a series of deep problems that other mathematicians consider “impossible”.
At the height of his fame, Nash suffered a catastrophic mental breakdown and began to descend into insanity. He was resigned from MIT, falling into a series of bizarre delusions. He ended up being a dreamy, ghostly figure at Princeton with numbers scrawled on a blackboard. He was all but forgotten by the outside world, until he emerged from his madness to win the Nobel Prize.
A Beautiful Mind is also a fascinating look at the unusual and fragile nature of genius.
A Beautiful Mind
- Narrated by: Anna Fields
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Electricity is a hands-on program. You will use math skills to solve problems and complete tasks. If you are interested in a bright future and providing a service that makes the world run, then you should consider this program.
You Will Learn:
- Residential wiring
- Theory and how to apply it to projects
- How to read technical drawings
- How to use mathematical principles to solve electrical problems
- How to work in a team setting alongside Construction Technology students
A Typical Student
The typical student is one that enjoys hands-on learning and has the applied math skills to be successful. There will be a significant emphasis on mathematical principles to solve electrical problems. These skills will be required through the second year of the program, during further training, and on the job. Successful students have the patience and attention to detail to solve problems using the skills they have learned. They can work on projects independently or with other students. They can read drawings, check their work as needed, and stay on task without constant supervision. Safety is a primary focus, and students must follow OSHA guidelines to keep themselves and others safe.
Get Yourself Ready
To be prepared, focus on doing well in math classes, being on track for graduation, and developing a good work ethic. The following pathway courses will help you prepare for the Electricity program, further education and training, and a career in the electrical industry:
- Preparing for College & Careers
- Introduction to Construction
Currently under revision (Aug 2023)


QUOTES"..The patterns and colors this thing makes are amazing. Swipe your finger on the screen and change the shapes and colors. A nice simple app thats fun to watch."
"Much like a watered-down version of a 20-year old Windows app called Kaleidescope that was quite cool in its day. ..."
"Very pretty designs. I got it to entertain my little grandson, and he likes to watch it, and touch on the designs to change them. ..."
"I will play a Pandora lullaby and turn the Geometrics app on for quiet time and my grandson who is 11months will quietly watch it :)"
"it is a nice app to watch and entertain my grandchildren with for a short period of time, they have asked me to get them a real Spirograph for Christmas."
"This app is very cool to watch. This is one of the first apps I ever bought & still look at it every day."
REASONS TO PURCHASE THIS APP:
- Easy controls. - Beautiful designs - The Other apps in the app store that are similar (kaleidoscope, Spin Art, Fireworks, Spirograph, Tripping App, Mandala Generator) have nice patterns, but were made ahead of time by the developer or an artist using the same math as Geometrics. With Geometrics, you are the creator, discoverer, artist, and mathematician. - Advanced users can set the equation properties manually. - Images can be saved to your device.
A polar graph represents a math equation where the distance [r] from the center of the graph is determined by an equation. [r=1 is a circle. r=sin(angle) makes loops]Polar Graph: http://en.wikipedia.org/wiki/Polar_graph
Normally you start the angle from 0 and go all the way around to 360 degrees incrementing by some small amount. When you skip faster around the circle in a regular interval (say every 80 degrees), you get something interesting. A Maurer Rose http://en.wikipedia.org/wiki/Maurer_rose
Geometrics takes this maurer rose idea and puts you in control of the design: The amount to skip, and a multiplier for the angle (to determine how many petals your maurer rose will have).
DESCRIPTION OF CONTROLS:
1. Swipe left or right - Restart the pattern changing the number of "flower petals"
2. Swiping up and down - Restart the pattern changing the "amount of skip"
3. Pressing and holding - Cycle through 3 trigonometric math functions (single sin equation, multiple sin equations, and a tan equation)


(Strip Number 1137, Original Publication Date, 14 April 1987)
Panel 1: As he and John walk down a grocery store aisle laden with Easter candy, Michael is amazed at how many chocolate bunnies there are when there were none but a few weeks ago.
Panel 2: John mutters a distracted 'Yeah' as he looks at them.
Panel 3: Mike frowns when his dad says it's amazing how they multiply.
Summary: This could be because it's really awful wordplay or that he's having a flash-back to a math test. Either way, we're on our way to Lynn complaining about all of the evil Easter candy of making her fat and making her kids sick to their stomachs.


Haileybury International School
Senior School Mathematics Teacher
30k-40k / Month Tianjin, China 1 position available Starting date in 2024-02-15
About The SchoolHaileybury has established Australia’s first international school in China. Learn more about this school
The Victorian Curriculum of Education (VCE) Mathematics is the study of function and pattern in number, logic, space, and structure, and of randomness, chance, variability and uncertainty in data and events. VCE mathematical activities include conjecturing, hypothesising and problem posing; estimating, calculating, and computing; abstracting, proving, refuting and inferring; applying, investigating, modelling and problem solving.
VCE Mathematics is made up of the following subjects:
VCE Preparation Mathematics (Year 10)
General Mathematics Units 1 and 2 & Further Mathematics Units 3 and 4
Mathematical Methods Units 1 and 2 & Mathematical Methods Units 3 and 4
Specialist Mathematics Units 1 and 2 & Specialist Mathematics Units 3 and 4
General Mathematics Units 1 and 2 provide for a range of courses of study involving non-calculus-based topics.
Mathematical Methods Units 1 and 2 provide an introductory study of simple elementary functions, algebra, calculus, probability and statistics and their applications in a variety of practical and theoretical contexts.
Specialist Mathematics Units 1 and 2 comprise of non-calculus-based topics and provide courses of study for students interested in advanced study of
mathematics, with a focus on mathematical structure and reasoning.
Further Mathematics Units 3 and 4 comprise a combination of non-calculusbased content from a prescribed core and a selection of two from four possible
modules across a range of application contexts. They provide general preparation for employment or further study, in particular where data analysis, recursion and number patterns are important.
Mathematical Methods Units 3 and 4 extend the study of simple elementary functions to include combinations of these functions, algebra, calculus,
probability and statistics, and their applications in a variety of practical and theoretical contexts.
Specialist Mathematics Units 3 and 4 are designed to be taken in conjunction with Mathematical Methods Units 3 and 4. The areas of study includes rational and other quotient functions as well as other advanced mathematics topics such as complex numbers, vectors, differential equations, mechanics and statistical inference.
The primary responsibility of the Senior School Mathematics Teacher is to deliver and promote Mathematics at senior levels within the School.
Teachers should ensure:
• Their delivery of the curriculum caters for students with varying learning styles and
ensures best practice in pedagogy in Senior School Mathematics
• They keep up-to-date with modern teaching practice
• They use appropriate learning styles for EAL/ESL students
• That they use a variety of assessment tasks for students to experience success and
accurately assess and build levels of student achievement
• Teachers are expected to participate in co-curricular activities including sport, the
arts and/or outdoor activities.
• Teachers are expected to maintain records of classroom attendance
• Report writing in accordance with School policy
• Attend staff and other administrative meetings as required
• Undertake evening study supervision and activities as required
• Attend parent/teacher interviews and promotional events as required.
• Ready for a new challenge
• Flexible and dynamic
• Enthusiastic and conscientious
• Demonstrated knowledge and at least two (2) years’ experience in teaching senior mathematics
• VCE (or Australian equivalent) Mathematics Methods, Specialist Maths and/or Further Mathematics experience preferred and/or
• Experience in IB Diploma Mathematics SL and/or HL, IGCSE Mathematics and A-Levels
• Ability to live within a foreign country for an extended period
• Eligible to be granted a work visa for China
• Ability to form a rapport with students and build collaborative working relationships
• Good verbal, written and inter-personal communication skills
• English Native speakers
• Bilingual Mandarin/English an advantage but not neccessary
• Sensitivity to the requirements of working in an international setting with a number of non-English speaking families and colleagues
• Minimum of Bachelor Degree in subject area
• Certified Teacher qualification and Registration
• The successful candidate will be expected to support the vision and ethos of the School.
• Staff must ensure that all decisions, pertaining to their role at Haileybury, are made in line with legislations and Haileybury policies and procedures as set out in the staff code of conduct and associated policies.
Competitive salary based on qualifications and experience.
The full package includes accommodation (2-bedroom apartment or as applicable for family), comprehensive medical insurance, visa and onboard costs, free tuition for children, flight costs as applicable, relocation allowance, gratuity allowance on successful completion of contract
• 2 years contract
• Full pay salary during summer and winter holidays
• Apartment provided outside of the school
• Holidays:October National Day (one week), Winter Break (three weeks in January and February), Mid Semester vacation (one week around April and one week around December) and Summer Break (six weeks in July and August)
• Summer break: From July-August about 5 weeks and 1-week PD
• Winter break: About 3 weeks in January and February, according to the Chinese Lunar New Year and Education Bureau’s teaching calendar
• Working visa provided
Post date: 2023-11-02


Jax was having problems with his math homework today and asked me for help. I completely BAULKED because I do not remember any math beyond very simple algebra (Dex's grade 7 math is getting difficult for me). However, we had a busy night planned and Stephen was going to be getting home late so I decided that I would turn to the internet for help so I could help Jax.
I went to www.khanacademy.org which is a great site for math. They offer FREE lessons on just about anything and their goal is "changing education for the better by providing a free world-class education for
anyone anywhere". I first heard about the site from Ted Talks (http://www.ted.com/talks/salman_khan_let_s_use_video_to_reinvent_education.html) and thought it sounded like a good idea. I had Dex logging on from time to time to do some extra math work but then he got busy with REAL homework. And I wanted Cars to do some too but he has required math homework on IXL.com and his time and results are sent to his teacher.
Anyway, so tonight I went to www.khanacademy.org to learn (or relearn) how to do The Substitution Method so I could teach Jax how to do it so he could do his homework and study for his quiz tomorrow. I am not sure why he did not understand it during math class today but after watching the videos with me and practicing, he is completely understanding it. I even had Stephen watch the video so he could help Jax while I went out to take Dex to his bass lesson.
It is a wonderful resource and I highly recommend that you check it out. Especially if you have a high school student who needs help with math.


1. Not every day will be great.
2. He probably learned something anyway.
We did this math exercise where I gave him a ruler, a regular ruler, and I called it a stick. We each gave a "guess" about how many sticks there were between the house and the garage and we wrote our guesses on the dry erase board. Then we measured. He moved the stick and I marked each length with sidewalk chalk. Then we counted. The real number was 24.5 "sticks" and his guess was 12 "sticks". My guess was 22 "sticks". I asked him which guess was closer to the correct answer and he said his was. I asked him a different way and he repeated that his guess was still the closest.
I thought about what his answer meant for my math lessons and said, "Let's go play Monopoly."
When we sat up to the game board and he took the dice to roll. Without prompting he paused and said, "I told you my guess was closer because I wanted to win. I know your guess was closer."
Then he rolled, counted the dots on the dice, and reminded me that he was owed $200.
[Insert: Picture of Zeke with lots of Monopoly money and devilish grin.]
PS My camera battery needs charging and I can't find the charger. Just one more thing I lost in the move. I'll probably find it the day after I order a new one.


Montessori math learning is a fun filled hands-on method of learning where concrete materials are used to introduce math concepts.
Once the child understands that a number symbol written on a piece of paper also has a quantitative value, the kid is ready for abstract mathematics. This easy to clean plastic place mat available at Walmart can be used to introduce numbers to your child.
Without a strong foundation in preschool, the child will find it difficult to visualize when complicated concepts like number bonds, fractions and multiplications are introduced in Primary school.
The following addition lesson can be introduced only after the kid is able to identify numbers from 1 to 10 and she understands that each number is associated with a quantitative value. So when she sees 1 and 10, she knows that 10 points to a larger volume / length / size.
- 2 rectangles kept side by side will be broader than 1
- 2 stacked cylinders will be taller than 1
- 5 units long strip of paper will be longer than papers that are 4 and 2 units long.
Montessori materials can be bought. In some places, they can get quite expensive. I am a DIY person and it is more fun if you involve your child in making these manipulatives. It will make them eager to learn because they made it themselves.
So lets get started
Introduction to Addition the Montessori way
How do we explain what addition means to a 3 year old?
What is Addition? What happens when two numbers are added? Here is a simple activity to demonstrate this.
- Paper / Plastic cups
- Paper towel roll
- Any small item like lego blocks / plastic chips.
Make two funnels like this and tape them to a wall or door. Make sure you use painter’s tape that will not leave glue residue.
Let your kid add the “+ ” sign and “= “sign using the sticky tape.
Demonstrate how plastic chips from two different sources are combined together on the towel. This is addition. The chips on the towel is the total / Sum.
(Leave it on the wall for a little longer because your little one will want to use this as a slide for her little dolls or blow it as a trumpet) 🙂
Now we know what happens when two numbers are added. How do we add two numbers? How do we find the total of two numbers. Let us find out.
Stationary Items Needed
- Chart Paper / craft paper preferably in more than one color
Time to draw squares. Our metal ruler is 1 inch wide so we drew 1 inch squares. Allow your kid to draw this. This is a good exercise for their mind. It is also an opportunity to introduce the words – Horizontal lines and Vertical lines if your kid is old enough. Or you can stick with Sleeping lines and Standing lines for now.
Then we drew the vertical lines
Make sure you choose a paper that is at least 10 squares long.
Now your kid can count the squares and write numbers like this.
Then count the remaining squares in each row and add numbers like this.
Demonstrate using this puzzle how to make ten.
9+1 = 8+2 = 7+3 = 6+4 = 10.
We will touch upon this again later. So it is okay of the child does not grasp the concept.
Many different combinations of numbers when added together can have the same Total or Sum.
At this point you may also introduce the various terms used when two numbers are added.
Since we are going to teach them to add two different numbers, I prefer to use two different colors of paper.
Now we are ready for some cutting. Knowing how to use scissors is an important motor skill milestone. So if your kid knows how to use one, let her cut the strips of paper like this.
Write down a few equations that you want your child to solve. Make sure you don’t push your kid to solve everything in one day. If you make this with thick craft paper, it can be used again and again. Any new concept requires repetition. So if all you can do on day one is till this step, it is still okay. You kid learned how to draw squares and cut strips of paper.
Make a base board with 11 by 11 squares. Tape this white sheet to the floor using painters tape if possible.
Before we get started, arrange the strips in random order and ask for help to arrange the strips in proper sequence – Biggest number at the top.
Now everything is in order and we are ready to add.
Our first equation is 8 + 1 = ? Let us find out the total now.
Ask your kid to get the strip that is 8 units long and keep it like so.
Then identify and place the 1 unit long strip near the other strip.
Now using your finger, point to 9 and teach her how to find the total. Also make her write the answer in the equation. This way we are showing her the connection between the concrete method of adding and the abstract method of addition using equations.
More examples – let her play around with more equations.
Show how the total is going to be the same irrespective of the order in which the orange and green strips are placed. In the previous example, the orange strip was placed first and in this example, the green strip is placed first. Move them around to demonstrate this.
How to make 10 / Bridging
Bridging to ten or learning to make ten is a math milestone. Start with this random example first and then ask your kid if there is any other way to make 10.
Now we are ready with everything in proper sequence.
I added more orange strips because we will need two 5s to make 10.
There are two methods to do this. Arrange all the orange numbers and then add the green numbers or go row by row.
On purpose keep it in the wrong place and make your kid to correct your mistake so she can learn that 7 + 2 != 10. Point to the blank square and ask what went wrong and show how even though there can be many combinations to make 10, 7 + 2 is NOT equal to 10.
You can either move the 2 units long strip and place it near 8 or bring the 1 down to show how 3 numbers can be added to make 10. Your creativity is the limit.
(Yes I finally stopped being lazy and got up and got the tape and taped the paper to the floor)
You can also mention about the concept of adding identical numbers. 5+5=10; 3+3 = 6; 4+4=8 etc
Slowly ease out and let the teacher take over. Give her full control over the items and let her teach Pooh and rainbow dash. ;-).
Winnie the Pooh by the way is recuperating from a surgery (Thank you Dr. Mcstuffins) hence the band aid. Rainbow dash had to get her hair pleated so her hair does not interfere with learning. Hmmm where have I heard that before?
Math lessons progressed to shapes.
Oh BTW that is pretty much how my floor looks like
sometimes all the time. There I said it. So fair warning …. in future if you tell me that you want to drop by and I give you that awkward pause, it does not mean that I don’t want to invite you home…..almost lost a friendship because of this. 😀
Other Methods to teach Addition
Bridging or Make 10 using rainbow
This is another method to make 10. I made this using MS Paint. You can print this or better yet you can make your kid draw a rainbow to find out all the combinations that make 10.
Addition using a deck of cards
Readily available deck of cards can be a very useful time pass activity during travel. Here we explored many ways to make 9.
Adding identical numbers
Dominoes and playing cards can be used for this.
Adding Zero or nothing = changes nothing
Add one and the total is the next number
Using physical items like plastic chips, cookies, logo blocks
This is an opportunity to introduce odd numbers and even numbers. When a chip does not have a partner, it is an odd number.
Draw shapes and then count and add them
Use Tally marks to add
Tally marks are clusters of 5 lines used mostly for score keeping during games. I bet this will be interesting to your kid if she knows skip counting by 5.
Last but not the least,
Throwing the dice
Find out how many combinations can make 12
It took me many hours to put this article together. I have added tons of pictures and as many activities as possible in this article so you can teach addition easily to your kids. Enjoy. If you like it, please share it with your friends.


Papers are listed in the reverse chronological order. If a paper is available online from its publisher, a links to the paper’s page at the publisher’s site is included.
50. Arnold, the Jacobi Identity, and Orthocenters,
American Math. Monthly, V. 118, No. 1 (2011), 41-65.
49. (with Lizhen Ji) Infinite topology of curve complexes and non-Poincaré duality of Teichmüller modular groups,
L’Enseignement Mathématique, V. 54 (2008), 381-395.
48. Fifteen problems about the mapping class groups,
In: Problems on Mapping Class Groups and Related Topics, Ed. by B. Farb.
Proc. Symposia in Pure Math., V. 74, AMS, (2006), 71-80.
The last online version of this book is available at B. Farb’s homepage.
47. A differential forms perspective on the Lax proof of the change of variables formula,
The American Mathematical Monthly, V. 112, No. 9 (2005), 799-806.
46. (with B. Farb) The Torelli geometry and its applications
The Mathematical Research Letters, V. 12, No. 3 (2005), 293-301.
45. Examples of large centralizers in the Artin braid groups,
Geometriae Dedicata, V. 105, Issue 1 (2004), 231-235.
44. A new construction of the Kauffman polynomial, 3 lines.
“Knots in Washington XV” (2nd Japan-USA Workshop in Knot Theory) Conference, January 10-15, 2003.
Topology Atlas, January 8, 2003. Online only.
43. A short proof of non Gromov-hyperbolicity of Teichmüller spaces,
Annales Academiæ Scientiarum Fennicæ, Mathematica, V. 27, F. 1 (2002), 3-5.
42. Mapping Class Groups,
In: Handbook of Geometric Topology, Ed. by R. Daverman and R. Sher.
Elsevier, 2001, 523-633.
41. Isometries of Teichmüller spaces from the point of view of Mostow rigidity,
In: Topology, ergodic theory, real algebraic geometry, Ed. by V. Turaev and A. Vershik.
AMS Translations, Ser. 2, V. 202, AMS, 2001, 131-149.
This final version is not available online.
See Downloads 1992 – 2013 for the last version preceding the published one.
40. A topologist’s view of the Dunford-Schwartz proof of the Brouwer fixed point theorem,
The Mathematical Intelligencer, V. 22, No. 3 (2000), 55-57.
39. (with John D. McCarthy) On injective homomorphisms between Teichmüller modular groups I,
Inventiones Mathematicae, V. 135, F. 2 (1999), 425-486.
38. Automorphisms of braid groups of surfaces,
Abstracts of papers presented to the AMS, V. 19, No. 1 (1998), 121 (Abstract 930-57-745). No version is available online.
37. Automorphisms of Complexes of Curves and of Teichmüller Spaces,
In: Progress in knot theory and related topics, Travaux en course, V. 56, Hermann, Paris, 1997, 113-123.
No version is available online.
36. Automorphisms of Complexes of Curves and of Teichmüller Spaces,
International Mathematics Research Notices, 1997, No. 14, 651-66.
35. Action of Möbius transformations on homeomorphisms: stability and rigidity,
Geometric and Functional Analysis, V. 6, No. 1 (1996), 79-119.
34. On the homology stability for Teichmüller modular groups: closed surfaces and twisted coefficients,
In: Mappping Class Groups and Moduli Spaces of Riemann Surfaces, Ed. by C.-F. Bödigheimer and R. Hain.
Contemporary Mathematics, V. 150, AMS, 1993, 149-194.
33. Subgroups of Teichmüller modular groups
Translations of Mathematical Monographs, V. 115, American Mathematical Society, 1992, xii, 127 pp.
No version is available online. This book was reviewed by:
- A. Papadopoulos in Mathematical Reviews, 93k:57031;
- F. Bonahon in Bulletin of the American Mathematical Society, V. 30, No. 1 (1994), 138-142;
- W. J. Harvey in Bulletin of the London Mathematical Society, V. 27, Part 6 (1995), 606-609;
- B. Zimmermann in Zentralblatt für Mathematik, 776.57001.


Some people just have a really good head for math, you know - I'm NOT one of them - and for the past 10 years Mike Byster has toured classrooms all over the country, sharing his math skills and proving that he IS the human calculator.
He created Brainetics so that parents and teachers can get them right in their classroom or living room in an instant.
Good thing, seeing as I'm having enough trouble learning the "new math" being taught in my kids' schools, lately!
Seriously, they're teaching my kids to do basic math, in a different way, without using the good old-fashioned multiplication tables and flashcards I grew up with.
According to an article in the Washington Post, some experts believe that memorization will only carry you so far:
"With 'Investigations,' kids understand the real values of the numbers and are not doing shortcuts. When they multiply 23 times 5, they'll do five 20s to get 100, and then add five 3s to get 15, and they put that all together and get 115. What they've done is made actual use of the numbers."
I was never really good at word problems, either.
My 9-year-old son is in 3rd grade and I'm having a devil-of-a-time trying to help him with his math homework. I want him to "work it out on a sheet of paper." He insists on trying to do it ALL in his head!
"Because, that's how the teacher says we SHOULD be doing it!"
It was the same for my 6th and 8th grader, too.
"Multiplying fractions is SO confusing!"
I'm not helping my 12-year-old any, either.
Don't even get me started on marking my 1st grader wrong on a test, because she was SUPPOSED to estimate! I'm sorry, shouldn't they be learning how to get the right answer...first?
No, math is NOT a fun subject at our house, at the moment, and perhaps you'll understand why I would hesitate even bringing it up, let alone join the Brainetics campaign.
Supposedly, this program is fun to do (at any age) and we received a 5-dvd set, a playbook, parent guide, flashcards, playing cards, and an extra 2-dvds.
"Sounds like a lot of work, to me!"
My husband Garth (not his real name) is a Financial Specialist for a banking firm (read: he's good with OTHER people's money) and even he agreed to sit in on this particular week's Friday movie and pizza night.
"Bwane-k-nex sounds too-scah-wee-foe-me!"
My 6-year-old thought we were watching a movie about killer Legos, that sucked your brain, or something.
"It's sort of like math class."
Okay, same thing.
Honestly, I was sort of expecting some highly educated know-it-all teaching terribly boring facts about how we all SHOULD be doing the math.
Participating in the Brainetics program was like tuning into a game show - featuring teams of kids competing against each other and we were playing along - so, by the end of DVD #3, my 12-year-old was taking great satisfaction in competing against her father (and me, sort of) to see who could multiply freakishly long numbers faster and she WAS winning...dangit!
I was able to catch up, though, by learning how to remember information AND then adding even more information, without forgetting what was in your head, already.
"Holy crap, this stuff really works!"
Mike Byster (a former commodities trader turned child educator) approaches his audience with patience and, I swear, the man carries himself with a perpetual grin. Seriously, he NEVER loses his cool, or his sense of humor. Mike displays the enthusiasm of a magician showing us some new tricks he's mastered; except he doesn't mind sharing his secret.
His excitement over finding patterns in numbers is contagious, really.
Bottom line, this is perhaps the first time (in the 14 years since I've had children sucking my brain) that I have to side with the experts and agree - making actual use of numbers...makes sense.
Thanks to Mike, my children appreciate the fact that practicing their math skills can be, you know, sort of fun.
Brainetics is a program that my family will undoubtedly turn to, over and over, again, to infinity.
Find More 'Bout It Here: PBN - Brainetics Campaign Launch
[This review was made possible by the Parent Bloggers Network]
© 2008 This Full House - All Rights Reserved.


Cell Counting 101 – Tip 5: How Can Variance Reveal the Precision of Your Cell Counts?
Tip 5 of 6
– 4 min read.
Cell Counting 101 – Tip 4 tells you all about cell viability.
What is Variance?
When performing multiple cell counts, you can calculate the variance as a measure of how much the counts deviate from the mean. Variance is used to give an indication of how similar individual cell counts are within the same sample or data point. The lower the variance, the more certain you can be that your counts reflect the actual number of cells in each sample or experimental condition.
To calculate the sample variance1, use the following steps:
- Calculate the mean value of the results, i.e. the sum of your cell counting results divided by the number of counts
- Calculate the difference from the mean by subtracting the mean from each of the cell count numbers. Calculate the square of differences and the summation of these values.
- To determine the variance, calculate the mean of the squared differences
When combining these three steps into one formula, you can calculate the variance by:
NOTE: In the formula, x = the individual total cell count, x̅ = the mean of all the values and n = the number of values. The variance can also be denoted σ2. Here you divide by n-1 because you are calculating the sample variance, as opposed to the population variance, in which case you would divide by n.
Differences in Variance: Manual vs. Automated Cell Counting
Two factors that influence variance, are whether the cell count is done manually or using an automated cell counter, and if the concentration of cells in a sample is high or low. These differences are explained in this example 2:
The CV% on the y-axis represents the coefficient of variation which is equal to the square root of the variance divided by the mean. Graphs A and B show CV% as a function of the cell concentration for A) automated cell counting using the NucleoCounter® NC-202™, and B) manual cell counting using a hemocytometer. Here, the data points are scattered and only a few of them are located on the fitted curve, representing the mean. This indicates that there is a high variance due to a high deviation from the mean of individual cell counts.
Graph A presents data obtained using an automated cell counter. In this graph, the majority of the data points are located either on or close to the fitted curve (the mean), indicating that the overall variance is lower. Therefore, the mean value is close to the individual counts, revealing a lower variance.
If you compare the two graphs, it is apparent that when using an automated cell counter the variation in the measurements is lower, compared to cell counts that are performed manually. In fact, it is almost halved. Furthermore both the automated and the manual cell counting methods show an increase in CV% with lower cell concentrations. However, this increase is larger when the cells are counted manually (compare the graphs). This can be exacerbated by pipetting errors since they are more predominant at the lower and higher ends of the optimal cell concentration range with any given counting method.
Errors also occur during cell counting due to inconsistencies when determining what is recognized as a cell. If this is not very strictly defined and adhered to, variation in cell counts can occur. These factors are worth taking into consideration when aiming to obtain cell counts with a low variance.
Read the next blog post that covers the importance of data validation as well as how to calculate the standard deviation. From the post, you can download a ready-to-use spreadsheet for all your cell counting calculations.
- Blog post: The Importance of Data Validation
- Webinar: How Precise Are Your Cell Counts?
- Tech note: NucleoCounter® NC-202™ Performance Data
- Blog post: What is a Hemocytometer?
- SM Ross: Introduction to Probability and Statistics for Engineers and Scientists (Fifth Edition), Chapter 2, 2014. Academic Press
- Chemometec: Tech Note: NucleoCounter® NC-202™ Performance Data
By Christina Psaradaki, Student Assistant at ChemoMetec
Christina Psaradaki studies Human Life Science Engineering at the Technical University of Denmark. At ChemoMetec, she writes for the Cell Counting Blog.
We welcome and encourage blog users to leave comments. ChemoMetec reserves the right to moderate all comments and delete any that could be determined as i) irrelevant; ii) containing spam; iii) containing profanity; iv) deemed offensive or; v) contain questionable content. We reserve the right to withhold any comment from being published. ChemoMetec is not responsible for the content in comments, which represent solely the views of the commenter.


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