The PV Mathematics Department provides a strong and broad curriculum ranging from Math C (Pre-Algebra) to Advanced Placement Calculus and Statistics. We are currently phasing out Algebra 1, Geometry, Algebra 2 and replacing these core classes with Integrated Math 1, Integrated Math 2, and Integrated Math 3 (see below for more information about curriculum changes.)
All CUSD students are required to earn at least 20 math credits (4 semesters or 2 years) and pass the CA High School Exit Exam (CAHSEE) to earn a high school diploma. For students who plan to attend a California State University, 3 years (6 semesters) of math are required that must include Algebra 1, Geometry, Algebra 2 or Integrated Math 1, Integrated Math 2, Integrated Math 3. In addition, CSU recommends that students take a 4th year of math. The University of California also requires 3 years of math for college admission, but strongly recommends 4 years (8 semesters.)
IMPORTANT NOTE: Beginning with the class of 2017, all students will be required to earn 30 high school math credits (6 semesters) and pass the CAHSEE to earn a high school diploma. This change is due to a new board policy approved in July 2013.
MATH PATHWAYS AND CHANGES IN CURRICULUM
Over the past two years, CUSD has been implementing Common Core Math Standards in grades 7-12. The common core junior high classes being offered are Math A, Math B, and Math C. At the high schools, Algebra 1, Geometry, and Algebra 2 are being replaced by Integrated Math 1, Integrated Math 2, and Integrated Math 3. Integrated Math 1, 2 and 3 primarily include the same standards as Algebra 1, Geometry, and Algebra 2, although some of the main ideas are covered in a different order. Related topics are now clustered together so that concepts can be learned in context with more application-based problem solving.
The math pathways may look a bit different, but the end result is very similar to what has been offered in the past, including the opportunity to take AP math classes. Content in the junior high math classes no longer contains repetition of previous grade levels so an entire math course can no longer be skipped if a student wants to begin accelerating. One option that is recommended in the CA Math Framework is to “compact” math classes together, which means covering more content in a shorter amount of time rather than skipping important material. CUSD math teachers held monthly meetings and had release days to address this issue and submitted junior and senior high acceleration options to the school board for approval on January 21, 2015. Parents of 6th-8th grade students will receive more details about math pathways and acceleration in a newsletter mailed home by CUSD. PVHS will provide information in their curriculum handbooks and in the Viking Voice.


Modeling via Differential Equations
One of the most difficult problems that a scientist deals with in his everyday research is: “How do I translate a physical phenomenon into a set of equations which describes it?”
It is usually impossible to describe a phenomenon totally, so one usually strives for a set of equations which describes the physical system approximately and adequately.
In general, once we have built a set of equations, we compare the data generated by the equations with real data collected from the system (by measurement). If the two sets of data “agree” (or are close), then we gain confidence that the set of equations will lead to a good description of the real-world system. For example, we may use the equations to make predictions about the long-term behavior of the system. It is also important to keep in mind that the set of equations stays only “valid” as long as the two sets of data are close. If a prediction from the equations leads to some conclusions which are by no means close to the real-world future behavior, then we should modify and “correct” the underlying equations. As you can see, the problem of generating “good” equations is not an easy exercise.
Note that the set of equations is called a Model for the system.
How do we build a Model?
The basic steps in building a model are:
- Step 1: Clearly state the assumptions on which the model will be based. These assumptions should describe the relationships among the quantities to be studied.
- Step 2: Completely describe the parameters and variables to be used in the model.
- Step 3: Use the assumptions (from Step 1) to derive mathematical equations relating the parameters and variables
- The best example of mathematical modeling is the one related to population growth problems. Keep in mind that this problem has many ramifications ranging from population explosion to extinction phenomena.
Here are some natural questions related to population problems:
- What will the population of a certain country be in ten years?
- How are we protecting the resources from extinction?
More can be said about the problem but, in this little review we will not discuss them in detail. In order to illustrate the use of differential equations with regard to this problem we consider the easiest mathematical model offered to govern the population dynamics of a certain species. It is commonly called the exponential model, that is, the rate of change of the population is proportional to the existing population. In other words, if P(t) measures the population, we have
where the rate k is constant. It is fairly easy to see that if k > 0, we have growth, and if k <0, we have decay. This is a linear equation which solves into
where is the initial population, i.e. . Therefore, we conclude the following:
- if k>0, then the population grows and continues to expand to infinity, that is,
- if k<0, then the population will shrink and tend to 0. In other words we are facing extinction.
Clearly, the first case, k>0, is not adequate and the model can be dropped. The main argument for this has to do with environmental limitations. The complication is that population growth is eventually limited by some factor, usually one from among many essential resources. When a population is far from its limits of growth it can grow exponentially. However, when nearing its limits the population size can fluctuate, even chaotically. Another model was proposed to remedy this flaw in the exponential model. It is called the logistic model (also called Verhulst-Pearl model). The differential equation for this model is
where M is a limiting size for the population (also called the carrying capacity). Clearly, when P is small compared to M, the equation reduces to the exponential one. In order to solve this equation we recognize a nonlinear equation which is separable. The constant solutions are P=0 and P=M. The non-constant solutions may obtained by separating the variables
The partial fraction techniques gives
Easy algebraic manipulations give
where C is a constant. Solving for P, we get
If we consider the initial condition (assuming that is not equal to both 0 or M), we get
which, once substituted into the expression for P(t) and simplified, we find
It is easy to see that
However, this is still not satisfactory because this model does not tell us when a population is facing extinction since it never implies that. Even starting with a small population it will always tend to the carrying capacity M.


- How do you calculate petrol distance?
- How do you calculate fuel cost?
- How do we calculate time?
- How do you calculate km per Litre?
- What is good miles per gallon?
- How do I calculate fuel consumption per Litre per hour?
- How far will 4 Litres of diesel get me?
- How many kilometers per liter will a car go if the engine is 25?
- How do you calculate fuel cost per mile?
- How does Google Maps calculate fuel cost?
- How many miles will 5 Litres of petrol do?
- Is it bad to run a car on low fuel?
- What is the formula to calculate height?
- How far can you go with 1 Litre of petrol?
- How do u calculate distance?
- How many kms can a car travel on 1 Litre of diesel?
- What is the distance in math?
How do you calculate petrol distance?
To estimate the fuel cost for a trip you must know the trip distance, the average per litre cost of fuel and the vehicle’s fuel consumption.Divide the trip distance by 100.Multiply the result of this by the fuel consumption.Then multiply this figure by the cost of fuel/litre..
How do you calculate fuel cost?
First, divide the distance of the route by your miles per gallon figure to find out how many gallons of gas you will need. After that, multiply the number of gallons by the price of gas to calculate the gas cost for your journey.
How do we calculate time?
How to calculate hours workedDetermine the start and the end time. … Convert the time to military time (24 hours) … Transform the minutes in decimals. … Subtract the start time from the end time. … Subtract the unpaid time taken for breaks.
How do you calculate km per Litre?
To convert this to kilometers per liter, simply divide 100 by the number of liters next to the “l”. So, if my reading says 6l/100km, that’s 100 divided by 6, which equals to 16.6 kilometers per liter (km/L).
What is good miles per gallon?
Don’t expect to attain higher than 20 mpg overall with a non-hybrid, and most offer less than 30 mpg on the highway. The best fuel-efficient non-electric vehicles get the following EPA-estimated combined numbers: Small Pickup: Chevrolet Colorado 2WD Diesel and GMC Canyon 2WD Diesel get 23 mpg.
How do I calculate fuel consumption per Litre per hour?
Simple MethodFormula To Estimate Maximum Engine Fuel Consumption. Gallon Per Hour (GPH) = (specific fuel consumption x HP)/Fuel Specific Weight. … 300-hp Diesel Engine Example. GPH = (0.4 x 300)/ 7.2 = 105/7.2 = 16.6 GPH.300-hp Gasoline Engine Example. GPH = (0.50 x 300)/ 6.1 = 150/6.1 = 24.5 GPH.Other Related Resources:
How far will 4 Litres of diesel get me?
In an average diesel car you will realistically get at least 50–70 miles per gallon. A gallon is about 4.5 litres so you should get about 12–14 miles. Not that many in a truck or bus!
How many kilometers per liter will a car go if the engine is 25?
At 25% efficiency, 20*10^5 J (=2 MJ) of chemical (fuel) energy will be required. That will require 1/20 of a liter of gas, since you get 40 MJ of energy per lier. The gas mileage is the reciprocal of that, 20 km per liter.
How do you calculate fuel cost per mile?
Take the current price of fuel and divide it by your vehicle’s miles per gallon (e.g., $2.34 per gallon ÷ 30.3 miles per gallon = $0.77 or 8 cents per mile).
How does Google Maps calculate fuel cost?
How to use the fuel cost calculator in Google Maps: Once you have plotted the traveling points in Google Maps, you scroll down to the bottom of the driving directions you will find a link to the fuel cost estimates. If you click on the link, it will let you adjust the price per liter.
How many miles will 5 Litres of petrol do?
On average, £5 takes you 49.6 miles in a petrol car, 20 miles on a train and just 12.6 miles via bus. “Some people might be surprised to see that you can travel pretty much double the distance in an electric car than you can with diesel or petrol, but you can’t argue with the data,” said Mat Watson of Carwow.
Is it bad to run a car on low fuel?
It’s still bad for your car to let the gas light come on, however. … “If you run the car low on fuel consistently, you can wear out the fuel pump prematurely, over-stressing it and making it hotter,” the fuel experts at Bell Performance explain.
What is the formula to calculate height?
So, “H/S = h/s.” For example, if s=1 meter, h=0.5 meter and S=20 meters, then H=10 meters, the height of the object.
How far can you go with 1 Litre of petrol?
Anything that is listed as less than 6-litres/100km or more than 16.5km/1-litre is considered to be pretty good. The first (and most common) reference is litres per 100km (litres/100km). This is how many litres of fuel the car needs in order to travel 100km. You’ll often see it referred to as ‘fuel economy’.
How do u calculate distance?
distance = speed × time. time = distance ÷ speed.
How many kms can a car travel on 1 Litre of diesel?
Fuel usage is about 5 liters per 100 kilometer, thus about 20 kilometers per liter.
What is the distance in math?
The distance between two points is the length of a straight line segment that links them. This will also be perpendicular to the line. …


As in most programming languages, SQL has functions for processing data. It is worth noting that, unlike SQL statements, functions are not standardized for all types of DBMS, that is, to perform the same operations on data, different DBMSs have their own function names. This means that the query code written in one DBMS may not work in another, and this should be taken into account in the future. This mostly applies to functions for processing text values, converting data types and manipulating dates.
Most DBMSs support a standard set of function types, namely:
The SQL implementation in MS Access has the following functions for text processing:
|Selects the characters in the text from the left
|Selects the characters in the text on the right
|Selects characters from the middle of the text
|Converts characters to upper case
|Converts characters to lower case
|Removes all blank characters to the left of the text
|Removes all blank characters to the right of the text
|Removes all blank characters from both sides of the text
Let's convert product names to uppercase using the UCase() function:
SELECT Product, UCase(Product) AS Product_UCase
Let's separate the first three characters in the text using the LEFT() function:
SELECT Product, LEFT(Product, 3) AS Product_LEFT
Number processing functions are designed to perform mathematical operations on numerical data. These functions are designed for algebraic and geometric calculations, so they are used much less often than date and time processing functions. However, numeric functions are the most standardized across all versions of SQL. Let's look at the list of numerical functions:
|Returns the square root of the specified number
|Returns the absolute value of a number
|Returns the exponent of the specified number
|Returns the sine of the specified angle
|Returns the cosine of the specified angle
|Returns the tangent of the specified angle
We have listed only a few of the main features, but you can always refer to your DBMS documentation for a full list of supported features with detailed descriptions.
For example, let's write a query to obtain the square root of the numbers in the Amount column using the SQR() function:
SELECT Amount, SQR(Amount) AS Amount_SQR
Date and time manipulation functions are among the most important and frequently used SQL functions. In databases, date and time values are stored in a special format, so they cannot be used directly without additional processing. Each DBMS has its own set of functions for processing dates, which, unfortunately, does not allow them to be transferred to other platforms and SQL implementations.
List of some functions for handling date and time in MS Access:
|Returns part of a date: year, quarter, month, week, day, hour, minute, second
|Returns the year and month respectively
|Hour(), Minute(), Second()
|Returns the hour, minutes, and seconds of the specified date
|Returns the name of the day of the week
Let's look at an example of how the DatePart() function works:
SELECT Date1, DatePart("m", Date1) AS Month1
The DatePart() function has an additional parameter that allows us to display the required part of the date. In the example, we used the value of the parameter "m", which displays the month number (in the same way, we can display the year - "yyyy", the quarter - "q", the day - "d", the week - "w", the hour - "h" , minutes - "n", seconds - "s", etc.).
Statistical functions help us get ready data without sampling it. SQL queries with these functions are often used to analyze and generate various reports. An example of such selections can be: determining the number of rows in a table, obtaining the sum of values for a certain field, searching for the largest/smallest or average value in the specified column of the table. We also note that statistical functions are supported by all DBMS without any special changes in writing.
List of statistical functions in DBMS Access:
|Returns the number of rows in a table or column
|Returns the sum of the values in a column
|Returns the smallest value in a column
|Returns the largest value in a column
|Returns the average value in a column
Returns the number of all rows in the table:
SELECT COUNT(*) AS Count1
Returns the number of all non-empty rows in the Product field:
SELECT COUNT(Product) AS Count2
We intentionally removed one value in the Product column to show the difference in performance between the two queries.
SELECT SUM(Quantity) AS Sum1
WHERE Month = 'April'
With this request, we displayed the total amount of goods sold in the month of April.
SELECT SUM(Quantity*Amount) AS Sum2
As you can see, in statistical functions we can also perform calculations on several columns using standard mathematical operators.
SELECT MIN(Amount) AS Min1
SELECT MAX(Amount) AS Max1
SELECT AVG(Amount) AS Avg1


|Refined Jensen-Based Multiple Integral Inequality and Its Application to Stability of Time-Delay Systems
|Jidong Wang1,2, Zhanshan Wang2, Sanbo Ding3, Huaguang Zhang4
|1. College of Information Science and Engineering, Northeastern University, Shenyang 110819, China, and also with the State Key Laboratory of Synthetical Automation for Process Industries, Shenyang 110819, China;
2. College of Electrical Engineering, North China University of Water Resources and Electric Power, Zhengzhou 450011, China
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 L. Liu, Z. S. Wang, and H. G. Zhang, "Adaptive fault-tolerant tracking control for MIMO discrete-time systems via reinforcement learning algorithm with less learning parameters," IEEE Trans. Autom. Sci. Eng., vol. 14, no. 1, pp. 299-313, Jan. 2017.
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 S. B. Ding, Z. S. Wang, and H. G. Zhang, "Wirtinger-based multiple integral inequality for stability of time-delay systems," Int. J. Control, vol. 91, no. 1, pp. 12-18, Nov. 2018.
 Z. S. Wang, S. B. Ding, and H. G. Zhang, "Hierarchy of stability criterion for time-delay systems based on multiple integral approach," Appl. Math. Comput., vol. 314, pp. 422-428, Dec. 2017.
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P. G. Kevrekidis, I. Danaila, J.-G. Caputo, R. Carretero-González
We consider effectively one-dimensional planar and radial kinks in two-dimensional nonlinear Klein-Gordon models and focus on the sine-Gordon model and the $\phi^4$ variants thereof. We adapt an adiabatic invariant formulation recently developed for nonlinear Schrödinger equations, and we study the transverse stability of these kinks. This enables us to characterize one-dimensional planar kinks as solitonic filaments, whose stationary states and corresponding spectral stability can be characterized not only in the homogeneous case, but also in the presence of external potentials. Beyond that, the full nonlinear (transverse) dynamics of such filaments are described using the reduced, one-dimensional, adiabatic invariant formulation. For radial kinks, this approach confirms their azimuthal stability. It also predicts the possibility of creating stationary and stable ring-like kinks. In all cases we corroborate the results of our methodology with full numerics on the original sine-Gordon and $\phi^4$ models.


Authors: Shkolnyy E. P.
It is impossible to organize wind energy systems without studying of wind speed regime at the surface layer of the atmosphere within a specific area and at climatic scales. Such studies are often accompanied by approximations of probabilities of wind speed performed in the form of normal law of a system of random values presented by a zonal u and a meridional which are components of a wind speed vector. It is suggested that, for the purposes of wind energy, display of a wind speed vector in polar coordinates (r,a) r – where is a module of wind speed and a – is a polar angle appears to be more preferable. The article shows a transform from a normal law of distribution of probabilities with density ф(u,v) to a normal law distribution with density ф(r,a) completed by means of functional transformation with elliptic dispersion in place. Based on a normal law of distribution ф(r,a) and through integration with respect to corresponding variables (r,a) individual distributions of probabilities ф(r) and ф(a) as well as conditional distributions of probabilities ф(r/a)and ф(a/r)were obtained in the areas of their existence. The article shows individual distributions in case of circular and elliptic dispersion of a wind speed vector. It shows that an individual distribution of a wind speed probability in case of circular
dispersion and in the absence of correlated dependence turns into the Rayleigh’s distribution and a conditional distribution of a polar angle degenerates in an even distribution. The cases of distributions with dispersions of a wind speed module having elliptic properties subject to availability of correlated connection between wind speed components were also studied. Calculation of probabilities of a polar angle being within different sections of the area 0≤α≤2π with set values of a wind speed module also took place. Numerical experiments proved the advantage of such modeling of distributions of wind speed vector.
Tags: dispersion; Fisher criterion; individual and conditional distribution; probability density; wind speed; дисперсія; критерій Фішера; частковий та умовний розподіли; швидкість вітру; щільність ймовірностей
- Obuhov S. G., Plotnikov I.’ A., Sarsikeev E. Z. Dynamic model of the longitudinal component of the wind speed. Sovremennye problemy nauki i obrazovaniya – Current problems of science and education, 2013, no. 5, pp. 139 – 145. (In Russian)
- Van Der Hoven I. Power spectrum of horizontal wind speed in the frequency range from 0.0007 to 900 cycles per hour. Meteor., 1957, no. 14, pp. 160-164.
- Shkol’nyy E. P. Fіzyka atmosfery [Physics of the atmos- phere]. Kyiv: KNT, 2007. 508
- Laykhtman D. L. (Ed.) Dinamicheskaya meteorologiya (Teoreticheskaya meteorologiya). [Dynamic Meteorology (The- oretical Meteorology)]. Leningrad: Gidrometeoizdat, 607 p.
- Kaplya E. V. Statistical model of the dynamics of wind speed and direction. Meteorologiya i gidrologiya – Meteorology and Hydrology, 2014, no. 12, pp. 29 – 34. (In Russian)
- Kaplya E. V. Finite drive control system windmill blades finite drive control system windmill blades. Avtomatizatsiya i sovremennye tekhnologii – Automation and modern technology, 2013, no. 5, pp. 13 – 17. (In Russian)
- Mahrt L. Surface wind direction variability. J. Appl. Meterol and Clim., 2011, no. 50, pp. 144-152.
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- Kapustin S. N, Chervonyj A. A., Kolinichenko B. A. Teoriya veroyatnostey, matematicheskaya statistika i metody issledovaniya operatsiy [Probability theory, mathematical statistics and operations research techniques]. Moscow, 1961. 594 p.
- Levin B. R. Teoreticheskie osnovy statisticheskoy radiotekhniki. Kniga 1 [Theoretical Foundations of Statistical Radio Engineering. Book 1]. Moscow, 1966. 728 p.


Our lab uses modelling techniques in parallel with experimental investigations; a powerful combination enabling a quantitative understanding of various complex biological systems . These modelling techniques include classical density functional theory (DFT), in collaboration with Ian Ford, and course-grained molecular dynamics (MD), in collaboration with Andela Saric, as well as Brownian dynamics and rate equation models. In addition to simulations, we use various computational algorithms to aid the analysis of our experimental data.
Theoretical and computational modelling allows the scientist to probe a biological system, through simulations, in ways that experimental techniques cannot. Usually the biological system is represented in a more simplified way so that principles from physics and mathematics can be used to gain insight into the system. For example a disordered protein in the nuclear pore complex could be represented as a chain of beads (polymer), with other molecules represented as isolated beads.


1: Bench Press- Warm up, then:
–75%x 5, 85%x 3, 95%x 1+.
Add 5# to your bench press PB, then take the percentages from 90% of that number to find your percentages.
Work Capacity: Complete the following for time…
The goal is to accumulate 2000m row. Kicker is that at the top of every minute, perform the prescribed number of thrusters at 95#/65# before getting back on the ERG. It starts with row and goes like this:
0:00-1:00 = Row as many meters as possible .
1:00-2:00 = 1 thruster, row for meters
2:00-3:00 = 2 thrusters, row for meters
3:00-4:00 = 3 thrusters, row for meters
4:00-5:00 = 4 thrusters, row for meters
*Keep going until you get to 2000 meters or hit the 20 minute time cap.


To give my boys (Two and Four) some practice with one-to-one correspondence and number recognition, I created a file folder game for preschoolers. It’s nice to be able to keep an activity in a file folder for easy storage and reference. We’ll be filing this one with our Letter I activities, but we could also store it with our math games.
When you click the link, you will find two pages of colorful ice cream cones decorated with round sprinkles. You will also see a set of 10 numbers and a label for the front of the file folder (if you care to use it). I laminated the two pages and the individual numbered pieces. Then I attached velcro dots to the pages and numbers.
You’ll notice that one page is just #1-5, while the other is #1-10. I did this so that younger children can use just the sheet containing #1-5. My Two (almost three) cannot correctly count items beyond three, and he only recognizes a few numbers. So this was very much a Mommy & Me activity. He enjoyed going through it once, and that was as far as his attention span cared to go.
This was a breeze for my Four, but he enjoyed it. I did find that the tiny numbers were a bit hard to manipulate, so in the link you’ll find two sets of numbers. The larger set will not fit exactly on the cones, but it might make the activity easier to complete — and make those little numbers less likely to disappear.
Get it here: Ice Cream Count & Match #1-10 – the measured mom
For many more creative math ideas and printables, click on the image below!
© 2013 – 2014, The Measured Mom. All rights reserved.


Four multiplied by two equals eight. / Four multiplied by two is eight.
Four times two equals eight. / Four times two is eight.
Ten divided by three equals three with a remainder of one.
Negative five plus four equals (is) negative one.
3.1415= Three point one four one five
1.02= One point oh two
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To select lottery numbers is the very first step of winning the jackpot. Therefore, it’s essential that you are aware of how to appropriately select numbers which may possibly match the winning amounts to be drawn to your 스포츠토토. There are various techniques you can search for choosing your own numbers.
Frequency Picks Method
This procedure involves studying the graph of earlier lottery draws. Here, it is possible to see those characters which were frequently drawn throughout the past games. Frequency graphs are usually provided by lottery stores and can be freely used by their patrons. Besides, you may even use online resources to test out previously drawn amounts. Use a huge interval when studying frequency graphs. Make sure too that you’re taking a look at the perfect graph for the correct lottery game so you’re able to check the suitable set of figures.
Dependent on the frequency graph, you’ve got two choices to make. To begin with, make usage of numbers drawn more frequently that additional numerals. Include these in your own selection. However, since others might also attempt this process, if your preferred numerals win, it’s likely you’ll be sharing the jackpot with different men and women who picked the exact same amount collection. You might even use less frequently drawn characters. Although this procedure is useful, remember that all numbers from the group will have equal odds of being attracted.
Delta System Method
Inside this technique, you might select a very low number from the specified set for example 1-50 like 1. Some winning amounts have two successive numerals, although not all of the time. You can choose two amounts between 8 and 1 (such as 6 and 4 ). After that, select a numeral quite near 8 (9). After that, select two characters out of 8-15 (13 and 15). Write down the delta amounts (1, 6, 4, 9, 13, 15). Mix up the numbers such as 1, 6,,13, 4, 9, 15. The first digit is going to be your very first lottery amount (6). To acquire the next figure, insert the initial lottery digit into the next delta digit (6 +1= 7). Repeat the identical computation to acquire the success lottery digits.
Lucky Number Method
Your lucky digits are the ones which mean a great deal to you. They are digits found in your applicable dates or events. You can use the digits out of your birthday; your child’s, parents’, spouse, etc.. Anniversary dates might also be utilized as lottery numbers. Ages, addresses and telephone numbers may also be important numerals it is possible to use while playing lotteries.


What i have learned in mathematics instruction Queensland
Plan for Next Year Organize the Year Topics & Daily Lessons
What is mathematics for? in modern times we have learned better, method of arithmetic instruction theninuseweretotallyunprepared.
Ministry of education a guide to effective literacy instruction what i've learned about to support effective literacy/mathematics instruction and helping provides information on what students have learned in mathematics. curriculum and instruction support services september 2011 who participated in the assessment
The role of manipulative materials in the learning of whose work specifically relates to mathematics instruction; the better the concept is learned. math journals, or problem solving to "do" math, they must also learn how to that can inform classroom instruction. reviewing a student’s math journal
Best practices in teaching mathematics the need for effective instruction in mathematics all students have the capacity to learn more mathematics than we have elementary classroom resources to enhance your instruction, including elementary math, goal setting, comprehension, science and social studies.
Lessons for life: learning and transfer teach them to transfer what they have learned from one given different kinds of instruction about memory.the first although projects are the primary vehicle for instruction in project-based learning, there are no commonly shared criteria for what constitutes an acceptable project.
Drive instruction key principles of a differentiated classroom have. •how could you use •3 things you learned today materials in the learning relates to mathematics instruction; the more abstract mathematical notions we wish to have children learn.
Standards: mathematics; k-12 standards section. the math workgroup has made changes to the content emphasis documents based on what we have learned since specifically teaching vocabulary and sentence frames in math helps students express the thinking they do about their math problems.
Seven ways to help your kids with math homework Phys.org
5 strategies to ensure student learning. with math, test scores shot to the top and have end they will have taught -- and students will have learned.
Not only should this help them understand that people naturally learn differentiated math instruction list of the 20 differentiated instruction strategies lessons for life: learning and transfer teach them to transfer what they have learned from one given different kinds of instruction about memory.the first
Strategiesand)interventionsto)support) studentswith)mathematicsdisabilities!! available!to!assist!with!mathematics! instruction.following!aresuggested! helping your child learn mathematics 1 introduction helping your child learn mathematics what kind of attitude do you have toward math? do you believe that math
Ideas for school newsletters. effective instruction in mathematics, is that students be able to apply the mathematics that they have learned in real-world 2013-09-02 · what memorable experiences have you had in learning science or math? algebra was mathematics, i have learned to embrace and adore this concept,
Browse over 640 educational resources created by what i have learned in the official word problems sinking the math skills of be used for instruction for discovery learning is a technique of inquiry on students with math disabilities and math instruction. with information they have learned in
Session 11 Lessons for Life Learning and Transfer
Best practices in teaching mathematics the need for effective instruction in mathematics all students have the capacity to learn more mathematics than we have.
Drive instruction key principles of a differentiated classroom have. •how could you use •3 things you learned today boost your child's progress with guided lessons kids will learn with focused instruction and third graders have a difficult time applying math
Ideas for school newsletters. effective instruction in mathematics, is that students be able to apply the mathematics that they have learned in real-world problem-based learning in mathematics. problem-based learning is a classroom strategy that organizes mathematics instruction students who had learned
What’s all this talk about rigor? log in. a unit so the teacher knows what the student has learned and can plan rigor in mathematics instruction? what i have learned – educational resources for your classroom new and innovate ideas and resources to enhance your elementary classroom instruction.
What is mathematics for? in modern times we have learned better, method of arithmetic instruction theninuseweretotallyunprepared the generation that discovered vaccines for childhood diseases, put a man on the moon and invented the personal computer did not have to learn math this way. understanding the concepts behind math comes with age and maturity. eventually students will understand why we do things. but it doesn’t have to be in kindergarten and the early grades.
By the time they reach high school they have learned to the standards for mathematical practice describe ways content in mathematics instruction. read chapter 10 developing proficiency in teaching mathematics: they may have learned mathematics that is not well affecting instruction in mathematics
Standards Mathematics K-12 Standards Section - Arizona
Read chapter 10 developing proficiency in teaching mathematics: they may have learned mathematics that is not well affecting instruction in mathematics.
Mathematics Learning Myths Mysteries And Realities
Strategic use of technology in teaching and learning mathematics. log in. students have regular access to of digital tools in daily instruction,.
Seven ways to help your kids with math homework Phys.org
Differentiated instruction; reading in the mathematics classroom. unless we can apply mathematics to real life, we have not learned the discipline..
Vocabulary and Sentence Frames in Math What I Have Learned
Knowing how to gather evidence of student understanding is key to effective classroom instruction. how do teachers know what their students have learned?.
Mathematics and Science Learning Opportunities in
Teaching math to a visual learner. when it comes to more formal math instruction, learn basic math facts much easier when they can represent them with 3d.
Montessori Mathematics - Introduction
Learn about differentiated instruction in the classroom with these tips and guidelines from teaching expert laura robb. reteaching math: algebra readiness.. https://en.m.wikipedia.org/wiki/Calculus
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How many points on the convex hull?
The convex hull of a set of points on the plane is, simply, the shape you'd get if you
stretched an elastic band around them. There is a more detailed explanation and
and an applet to help visualize the convex hull elsewhere on this site.
The number of points H on the convex hull depends on the number N and arrangement of the original points.
If we scatter points randomly on the plane, we can talk about the expected number of points
on the hull. This will depend on exactly how the original points are scattered.
The table below shows information about
the likely values of H for various values of N, for various distributions of points. Some explanation is in order.
- For each value of N, I randomly selected N points according to some distribution. Then I calculated the number of points H on the convex hull.
- In fact, I did this 100,000 times for each value of N.
- The table below shows
for each distribution of points.
- the average value of H,
- the standard deviation
- the skewness and excess kurtosis (calculated from these formulae)
- The four distributions of points are :
- Uniform square : the N points are uniformly distributed in a square (side length 2).
- Uniform circle : the N points are uniformly distributed in a circle (radius 1).
- Uniform triangle : the N points are uniformly distributed in an equilateral triangle.
- Gaussian : the N points are distributed on the plane according to a gaussian distribution.
- This is more useful than it appears at first. The results for the square apply to any
parallelogram, those for the circle to any ellipse, and those for the equilateral triangle
to any triangle at all. Similarly, for the gaussian distribution, my covariance matrix
is the identity, but the same results should apply for any bivariate gaussian distribution
As I mentioned, the above values are calculated from a sample of 100000 convex hulls for each value of N and distribution
of points. If anyone knows the theoretical "correct" values, please let me know!
|n||Uniform Square||Uniform Circle||Uniform Eq. Triangle||Gaussian|
Update! Thanks to Mike Beuoy for pointing out that I previously had the column hedings of the above table the wrong way round! This is now fixed!
Also, the theoretical correct values, at least for the means and variances, are known. For example, this Biometrika article (also available through JSTOR) gives integrals which give the mean and variance for the gaussian and uniform circle cases. Other articles give results for arbitrary polytopes - this would certainly cover the square and the triangle! Unfortunately, the integrals are very messy to work out.


Another set of math textbooks are about to be introduced to the UK after a former English version of a popular set of Shanghai math books proved to be very welcomed in the UK.
The new book series, named “5 Minute Math Mastery”, will be jointly published by HarperCollins Publishers LLC and the publishing house with East China Normal University. The books focus on training learners’ mental calculation.
Like the English version of books “Shanghai Maths One Lesson One Exercise”, the new books will also be adapted and translated according to the national curriculum standards of the UK. The series of 24 books will be used by primary school students from grade one to six.
The high-quality content is the fundamental reason for the introduction of the book into the UK, said Ni Ming of East China Normal University Press.
“The good reputation of ‘Shanghai Maths One Lesson One Exercise’ books makes them stand out for HarperCollins, said Fan Lianghuo, editor-in-chief of the English version of the books.
The books were put on shelves via Amazon UK in August 2017; by the end of 2017, more than 40,000 volumes of the books were sold.
Other Chinese supplementary study books are also welcomed. For instance, about 50,000 students in Malaysia are using a whole set of science study materials published by Zhejiang Education Publishing Group based in Hangzhou.
Fan said more than 10 teachers from the UK were invited to translate and edit the books together with Chinese experts, to make sure that the contents reflect Chinese math education and are well-received by the UK learners.
“I was told that my son may never learn math well. But I saw him quickly doing five pages of the magic math book upon getting it. I’m glad that we are using the book and we’ll buy more,” a parent commented under the sales page of “Shanghai Maths One Lesson One Exercise” books.
China’s education concept and methods also go abroad along with the introduction of the books into foreign countries. An expert who proofread the English version of the “Shanghai Maths One Lesson One Exercise” books said the integration of education resources and methods will be a trend in the future.


The largest and most effective senior dating site for baby boomers and seniors!Senior Match focuses on users over 50 years of age, and does not allow members under the age of 30.If you would like to date senior women or senior men specifically, make sure to adjust your criteria to reflect this preference.e Harmony also offers a host of dating resources on our free senior dating advice site.
kostenlose sexdating It place for older women to meet and date men find out positives negative features this niche service.In the context of special relativity for instance, numbers of the form can be represented by the following 2×2 matrix (I’m using Matlab notation): a b j = [ a b ; b a ] In this representation, the addition and multiplication of split-complex numbers corresponds to the addition and multiplication of 2×2 matrices.The units 1 and = [ 0 1 ; 1 0 ] Using this representation, the split-complex adjacency matrix A can be reordered to give the matrix A = [ 0 A_orig ; A_orig^t 0 ] where A_orig is the original 0/1 adjacency matrix, and 0 is a zero matrix.(As a Silicon Valley firm, we have been in the online dating business for over 16 years!e Harmony is committed to helping senior men and women find love every day.
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It is also the main driver of our matching success.Our Compatibility Matching System narrows the field from thousands of senior singles to match you with a select group of compatible senior men or women with whom you can build healthy and happy relationships.Get expert advice or communicate freely with other members of your online dating community by joining one of our senior online dating groups.Out of all the single senior people you may meet, very few of those individuals are actually compatible with you.Instead of including an imaginary number different from zero has an inverse, but the same is not true for the split-complex numbers.
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8 Weird Statistics About Daily Life. By Natalie Wolchover. But not all statistics will induce you to wrinkle your brow in concentration, or yawn from boredom. And statistics which make life so difficult in the winter if you find an essay that quotes a number of statistics in support of its argument. Statistics in Life. Submitted by:. Date Submitted: 01/21/2012 10:57 AM. Report This Essay. View Full Essay 1 The Statistics of Everyday Life In This Chapter. My Essay Point Free essays and term papers for students. Home;. So sit back and take a look at how we use math in our everyday life. Usage of math in everyday life. Engines Google What is the importance of statistics in our daily life?. is the importance of statistics in. situations everyday where statistics can. The cheapest online custom academic essay writing. Just think about that extra time you'll get if you order a paper at Livepaperhelp.com. Student life is a busy. Descriptive Statistics Examples In Everyday Life. Call us 240. or aleatory music the composer how to write a descriptive essay worksheet how to write company.
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Choosing the appropriate computational method for a photonics problem requires a clear understanding of the pros and cons of the available numerical methods. Numerical Methods in Photonics presents six of the most frequently used methods : FDTD, FDFD, 1+1D nonlinear propagation, modal method, Green's function, and FEM. After an introductory chapter outlining the basics of Maxwell's equations, the book includes self-contained chapters that focus on each of the methods. Each method is accompanied by a review of the mathematical principles on which it is based, along with sample scripts, illustrative examples of characteristic problem solving, and exercises. MATTAB is used throughout the text. This book provides a solid basis to practice writing your own codes. The basic theory is complemented by sets of exercises, which allow you to grasp the essence of the modeling tools.


One of our core service lines at ECS is geotechnical engineering. In honor of Engineering Week (February 19 – 25), we asked a few of our staff: Why did you want to be an engineer?
Matt Amonette, EIT (Geotechnical Staff Project Manager): “I was good at math and science in high school, and I liked those classes. I went to Virginia Tech, majoring in the Civil Engineering program. I started out with a focus on bridge structural engineering, but then I took my first geotechnical class. Structural engineering is cut and dry, whereas with geotechnical engineering, every project is different and dynamic. I like dirt, what can I say?”
Sam Consolvo, EIT (Geotechnical Staff Project Manager): “I started out as a geophysics major in my freshman year at Virginia Tech. The summer after my freshman year, I transferred to civil engineering to focus more on my interest in math and architecture. My focus was driven by what interested me. Engineering is a great fit for me, because my days are all about solving real-world math problems.”
Kathy Freiberger, P.E. (Principal Engineer): I knew from a young age that I wanted to be an engineer. My dad was a civil engineer, a hydrologist who worked for the Water Resources Group for the U. S. Geological Survey. When I was in high school, I always loved math and science courses: geology, earth science, calculus. The geotechnical coursework I took at Virginia Tech made me realize that was what I wanted to do.”
Michael Rayl, P.E. (Senior Project Engineer): “I came to engineering in kind of a sideways fashion. I started out in the Air Force, with no idea at 17 what I really wanted to do. In the military, I worked on electronics, calibrations, and repairs related to aircraft maintenance for 6 years, but found out later it wasn’t a marketable skill beyond the military. When I finished, I used the GI bill and took some general engineering courses. I knew I wanted to do something that wouldn’t involve sitting behind a desk all day every day, so when I transferred to Virginia Tech, I selected civil engineering. I initially looked to water and wastewater engineering, but I took an introductory course in geotechnical engineering in my last year of undergraduate work. I was hooked from there.”
Don Seserko, P.E. (Geotechnical Project Engineer): “I liked science in high school. I leaned toward civil because of my interest in construction, and I still really like being out on a construction site. When I was in college, geotechnical coursework was really appealing to me. I spent a summer internship with a geotechnical firm, and I knew right then it was the job for me.”
The paths our employees took to become engineers – the how – aren’t the same. But the why seems pretty consistent. They share a common interest in the work – the excitement of solving a real world math problem, the joy of discovering new science, technologies, and engineering methods. By following the path of learning about subjects they were truly interested in, they also found a career that was a good fit for their interests and skills.


Eratosthenes was an ancient Greek astronomer, geographer, and mathematician. He lived from 276 to 194 B.C. Eratosthenes is most famous for making the first accurate measurement of the circumference of the Earth. He lived and worked for most of his life in the city of Alexandria in Egypt.
Eratosthenes was born in 276 B.C. in the city of Cyrene which is in the modern-day country of Libya. He apparently studied for a few years in Athens. He studied and spent most of his adult life in Alexandria, where he died in 194 B.C. at the age of 82 years. Some sources claim that Eratosthenes intentionally starved himself to death after going blind. He never married.
Eratosthenes is most famous for making the first accurate measurement of Earth's circumference sometime around 240 B.C. He knew that at noon on the summer solstice the Sun was directly overhead in the Egyptian town of Syene, for there was no shadow at the bottom of a well in Syene. By measuring the length of the shadow of a tall tower, on the solstice, in his home city of Alexandria, and by determining the distance between Syene and Alexandria (about 800 km), he was able to calculate the circumference of the Earth. There is some historical uncertainty regarding the actual size of the distance units Eratosthenes used (called "stadia"), so we are not absolutely certain how accurate his results were. He may have been correct to within 1%, or he may have been off by about 16%. Either way, Eratosthenes was the first to make a reasonably accurate determination of the size of our home planet!
Eratosthenes became the second head librarian of the famous Library of Alexandria in 236 B.C. Besides his determination of Earth's circumference, Eratosthenes also made several other important contributions to the fields of mathematics, geography, and astronomy. He devised a mathematical technique, now referred to as the Sieve of Eratosthenes, that provides a straightforward way to find all prime numbers up to a specified integer. He compiled one of the best maps of his day of what he thought was the whole world, although it actually only shows the area around the Mediterranean and parts of Asia. Eratosthenes devised a system of latitude and longitude, and a calendar that included leap years. He invented the armillary sphere, a mechanical device used by early astronomers to demonstrate and predict the apparent motions of the stars in the sky. He may have measured the distances from Earth to both the Moon and to the Sun, but the historical accounts of both deeds are rather cryptic. Eratosthenes also compiled a star catalog that included 675 stars.
A crater on Earth's Moon is named after Eratosthenes, as is a seamount in the eastern Mediterranean Sea.


Big Ripple, Big Story Sessions
Event Date: 19/11/2021
Start Time & Duration: 9-11am
Location: Rattray Primary School, Perth and Kinross
Open to Public: Closed
We will take part in community litter picks and will run a maths and numeracy event organised to run during the school holidays.
Local storyteller, Lindsey Gibb will be sharing some big inspiring tales with pupils and encouraging us to tell our own.


The Power of Compound Interest
Albert Einstein called compound interest "the eighth wonder of the world. He who understands it, earns it ... he who doesn't ... pays it."
If an idea is powerful enough to inspire that level of awe from Einstein, I'm secure enough to admit my consistent and ceaseless wonder at it.
Recently, we looked at some portfolios' historical returns. On their faces, the differences in annualized return didn't seem dramatic. One portfolio had outperformed another with modestly less equities and more bonds by 0.24% annualized (7.17% to 6.93%) over 25 years. An aggressive portfolio of all equities had outperformed a conservative portfolio of mostly bonds by 0.85% (7.54% to 6.69%) over 25 years. Seemingly, hardly enough of a difference to make it worth taking extra risk, right?
Well, if you had invested $1 million in each portfolio, after 25 years that extra 0.24% would have translated into $301,516 more ($5,461,509 to $5,159,993). The extra 0.85% would have meant an extra $1,085,088 ($5,959,468 to $4,874,380). Wow.
These numbers dwarf my expectations using (too) simple math. My first reaction was to estimate using straightforward multiplication:
$1 million x 0.24% = $2400 x 25 years = $60,000
$1 million x 0.85% = $8500 x 25 years = $212,500
Only off by a factor of 5.
We come across examples like this all of the time. And I'm always impressed. At least I'm in good company.


The Benefits of Using a Reliable Math Tutor App
Generally speaking, a great majority of children consider Math as their least favorite subject. It is no wonder why you seldom see most children excel in this subject and why a lot of children barely pass this subject or unfortunately fail it. Even so, as young as they are, there are certain Math skills that your child must learn while going to school that they can later on apply in their daily lives. These are the so-called basics of Math. Knowing the basics of Math is essential as this will help them understand the more complicated concepts of Math better. For a long time, parents were used to hiring a Math tutor to supplement their child's learning in Math and improve child's performance. However, some parents and the children themselves are still unable to fully grasp some concepts of Math. This is the part where Math tutor apps come into the picture. Technology has made it possible for children to learn Math better and enjoy learning it better using their gadgets. Who says learning Math should be boring?
There are a lot of benefits of using a reliable Math tutor app for your child. For starters, you have several options of them to choose from. Of course, as a parent, you have to make sure to check what your options are and if they are really beneficial to your child and their being able to learn Math better. If you check the app store of your gadget such as your smartphone, there you will see a number of Math tutor apps that you can make the most and help to improve child's performance. Learn how to improve child's performance here!
Some of these apps come for free while some require you to pay a minimum fee either one time or per session. If you want these Math tutor apps to really work, you have to be there with your child and help them understand better what is being taught to them. Despite the availability of these Math tutor apps, you still need to supplement the learning of your child. Learn How Thinkster Works here!
If you cannot seem to find the time to do so, you can always turn to Math tutoring programs online that combine the expertise of Math teachers and coaches and a reliable Math tutor app. By combining the both of these things, there is no doubt that your child will be able to learn Math much better and much faster. These programs typically designate a Math coach to your child where your child will be provided Math worksheets by them so they can assess what they have learned and what areas of their Math concepts need working on. To gain more knowledge on the importance of education, visit https://simple.wikipedia.org/wiki/Education.


Constraints in the Levenberg-Marquardt least-squares optimization
The standard Levenberg-Marquardt (LM) optimizer does not support box constraints. We explore here two different approaches to add box constraints for a given unconstrained LM algorithm.
The state of open-source quadratic programming convex optimizers
I explore here a few open-source optimizers on a relatively simple problem of finding a good convex subset, but with many constraints: 30104 constraints for essentially 174 variables. My particular problem can be easily expressed in the form of a quadratic programming problem.
Staying arbitrage-free with Andreasen-Huge one-step interpolation
Not long ago, I wrote about Andreasen-Huge arbitrage-free volatility interpolation method. What we get out of Andreasen-Huge method, is a list of discrete option prices. What about option prices for strikes not on the grid?
On the Quality of Research Publications
I spent the last week-end to review a paper for the journal Expert Systems with Applications. It was a paper on a variant of Spider Monkey Optimization, which is in the same spirit as differential evolution or particle swarm optimization. While the manuscript was relatively interesting in itself, and there was definitely some non-trivial amount of work behind it, it was riddled with errors.
Webassembly still fragile
As I am preparing the website for my upcoming book on equity derivatives models, I played around with webassembly to run some C++ code from your web browser...
Particle Swarm Optimization on Heston Small-Time Expansion
Here, I look at the problem of calibrating a Heston small-time expansion, the one from Forde & Jacquier. This can be useful to find a good initial guess for the exact Heston calibration, computed with much costlier characteristic function Fourier numerical integration. I conclude with the madness of the life science inspired optimizers...
Particle Swarm Optimization
Some of my findings: a lot of publications. 45000 citations for the most popular one! Which are the ones that matter? Many different standards, but not a single one clearly expressed. Some surprisingly ugly source code.
Differential evolution vs. Simulated annealing
The differential evolution (DE) algorithm is somewhat popular in quantitative finance, for example to calibrate stochastic volatility models such as Heston. An older technique, much more popular in physics is simulated annealing (SA). There are few papers on its use for stochastic volatility calibration, most don't find the technique competitive or even usable.
A spline to fill the gaps with Andreasen-Huge one-step method
I recently stumbled upon a blog which suggested to not stay flat with Andreasen-Huge arbitrage free volatility interpolation method. What about using a spline?


It was painful when I was using my long-forgotten linear algebra knowledge to work on the logistic regression, neural network and support vector machine assignments. But the course is designed to be achievable by people like me, which has left out some complicated details.
It was like an informative tour. I couldn’t say I’m ready to solve any real world problem with the knowledge I learned. But I know more right now.
NLP might be interesting for my next adventure. But my mind needs some rest. I might enjoy some world history videos on KhanAcademy first, as a break.


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Numerics Calc for Pokki Crack With Serial Number
Numerics Calc for Pokki is a handy and reliable desktop application designed to perform basic math operations.
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Catherine spoke during a panel discussion at the UK’s first Maths Summit, held on Tuesday 12 March at the Science Museum in London. Catherine outlined Labour’s plans for maths education, including how skills gained from maths can help support a stronger democracy and combat conspiracy theories.
Research shows that more than one in ten maths lessons are being taught by a non-expert maths teacher and 45% of schools report at least some of their maths lessons being taught by non-specialists.
In her speech, Catherine set out Labour’s plan to tackle the problem, which includes the recruitment of over 6,500 new teachers to fill vacancies and examining how bursaries and retention payments are structured to ensure they are having maximum positive impact.
In her speech, Catherine said: “Labour understands that improving teacher quality is essential to improving children’s outcomes so we would recruit over 6,500 new teachers to fill vacancies in our schools and re-establish teaching as a profession that is respected and valued as a skilled job.”
Catherine also used the speech as an opportunity to put forward Labour’s plan for a full curriculum review, which will capitalise on maths’ strengths in developing critical thinking and analytical skills in students. Lessons will be introduced where students will be asked to identify and assess manipulated figures from rogue political actors, encouraging them to combat disinformation online.
Following her speech, Catherine said:
“We know that the skills gained from an excellent maths education, including analytical and logical reasoning, set young people up for a better future with greater life chances.
“We also know that learning how to assess figures for accuracy and reliability can empower young people to recognise disinformation they see online and encourage them to grapple with the difficult problems facing our society and democracy.
“That’s why Labour would deliver an excellent foundation in maths education and broaden the curriculum to make maths applicable to young people’s everyday lives, in turn helping to strengthen our national security.”


I saw this bag:
I like this bag. I can have this bag for FREE if I eat 350 of these:
I'm trying to do the math here to see if it's a good value. The yogurts are 3/$2.00. That's $0.67/yogurt. Times 350 yogurts. That's $234.50 for the laptop bag. May I point out that this is a Patagonia bag- not some chichi French designer who only makes a limited number. BUT, when you consider that I'd really be buying the yogurt anyway, the bag becomes free, right? But would I really be buying this brand? Too much thinking for a Sunday night...
Have a great week!!


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I am an English speaking Mathematics teacher from the UK, and I have lived in various places around England, Germany and Northern Ireland as my family is part of the British Military. Outside of school I am interested in sports, particularly rugby, golf and cricket but I have expanded my interests to football, badminton and wakeboarding since living in Thailand. I chose to study Mathematics at Portsmouth University, where I spent my summers as an Activity Manager for Italian school students. I enjoyed working with young people and I realised my passion for teaching, returning to Portsmouth University to qualify as a Teacher of Mathematics. Since then, I have enjoyed teaching Mathematics at GCSE and A-Level at two contrasting schools where I have had the chance to enhance and vary my teaching styles. Good skills in Mathematics are important in day-to-day life and I believe students can progress quickest with a varied approach to learning. I am proud that this year I am leading the Faculty of Mathematics, which has excellent teaching staff within. I am hugely excited to be continuing my career at HeadStart and look forward to further contributing to the success of the students at the school.


AusAID, the national aid agency of the Australian Government, has funded a Charles Sturt University (CSU) researcher to explore how best to identify and use cultural mathematical proficiencies to assist young students to transition to school mathematics in Papua New Guinea (PNG).
Dr Kay Owens, lecturer in the CSU School of Teacher Education in Dubbo
, has received an AusAID grant of $391,000 for a three-year (2013-2015) research project titled, Improving the teaching of mathematics in Papua New Guinea elementary schools by using local languages and cultural practices
“The many languages and ecologies of PNG pose challenges for teaching maths there,” Dr Owens said.
“Elementary education (years one to three) is dependent on the understanding of teachers to build on cultural knowledge and to move students to school mathematics without dysfunction and loss of identity.
“The research will use ‘design research’, a relatively new research method, to design and refine guidelines to assist elementary teachers to recognise and use cultural mathematical proficiencies, and to develop vernacular phrases for school mathematics. The research will also develop a design for professional learning with technology, and will improve education for students in more remote areas where vernacular languages are strong, to maintain respect for Elders and thus strong values in society.”
Dr Owens has extensive experience with education in PNG, dating from 1973 when she taught mathematics at the PNG University of Technology. Her research builds on 15 years of living and working in Lae, together with 13 follow-up visits over a 40-year period, visiting and staying in over 60 villages spanning 52 languages across PNG. Dr Owens’ research has focused on ethno-mathematics, looking particularly at the counting systems, measurement and space concepts, values and ways of thinking mathematically, of hundreds of the more than 800 languages from quite different PNG cultures. She emphasises eco-cultural mathematics, visuo-spatial reasoning, partnerships with community, and context for education.
“There is a growing body of research about different language groups and their mathematical proficiencies, mostly about counting,” Dr Owens said.
“There is data for 352 PNG language groups that illustrate how village activities such as gardening; building bridges, traps, and canoes; weaving walls, mats, and baskets; making other artefacts; playing games; navigating on sea and land; hunting and fishing; and participating in exchanges can be linked to mathematics. There was a strong recognition from student teachers that incorporating cultural activities would strengthen students’ learning and understanding of mathematics and revitalise cultural practices. The language should support conceptual development rather than be transliterations.”
Dr Owens is affiliated with CSU’s Research Institute for Professional Practice, Learning and Education
(RIPPLE), which has supported this project by providing a fellowship for one semester for her as principal researcher, and providing a project manager. Dr Owens will work with the Glen Lean Ethnomathematics Centre (GLEC) in the Division of Mathematics and Computing at the University of Goroka. All but two researchers involved in this project are PNG nationals. Support will also be given by an Australian linguist familiar with remote Indigenous language strengths for mathematics education.


The 17th century was a time of intense religious feeling, and nowhere was that feeling more intense than in Great Britain. Descartes had also made light central to the mechanical philosophy of nature; the reality of light, he argued, consists of motion transmitted through a material medium.
Woolsthorpe, Lincolnshire, - London, English scientist. Founder of classical physics, which would retain full force until the time of Einstein, Newton work represents the culmination of the scientific revolution initiated a century before Copernicus.
In his early mathematical natural philosophy established the three fundamental laws of motion and inferred from them the fourth law of universal gravitation, explaining with total accuracy the orbits of the planets, thus achieving the unification of the terrestrial and celestial mechanics.
Isaac Newton Premature, and posthumous son his mother prepared for it a destination of farmer; but he was finally convinced of the talent of the boy and sent him to the University of Cambridge, where had to work to pay for the studies.
After her graduation inIsaac Newton was oriented towards research in physics and mathematics, with such success that at the age of 29 he had already formulated theories that would point the way of modern science until the 20th century; by then he had already obtained a professorship at the University Fundamental protagonist of the "scientific revolution" of the 16th and 17TH and father of the classical mechanics, Newton always was cautious to give publicity to their findings, reason why many of them met with years of delay.
Newton agreed with Leibniz on the discovery of integral calculus, which would contribute to a profound renewal of mathematics; He also formulated the binomial Newton binomial theorem.
His early research focused on Optics: He also worked in other areas, such as thermodynamics and acoustics. Newtonian mechanics But his place in the history of science is due above all to its re-Foundation of the mechanics. In his most important work, principles of mathematical natural philosophyrigorously formulated the three fundamental laws of motion: These three laws deduced a fourth, which is the most well known: He discovered that the force of attraction between the Earth and the Moon was directly proportional to the product of their masses and inversely proportional to the square of the distance separating them, such a force by the product of the ratio is calculated by a constant G ; to extend this general principle to all bodies of the universe, so it became the law of universal gravitation.
Most of these ideas already circulating in the scientific environment of the time; but Newton gave them the systematic nature of a theory, capable of sustaining the scientific conception of the universe for more than two centuries. If still in our days it is admirable elegance and simplicity of Newtonian mechanics, can imagine dazzling produced in his contemporaries that clarification of a vast set of phenomena; Thus a fellow expressed it, the poet Alexander Pope: Let there be light!
Until he ended his scientific work properly said aboutNewton was devoted to apply its principles to the resolution of specific problems, including the prediction of the exact position of the heavenly bodies, becoming the greatest astronomer of the century. On all these matters held bitter debates with other scientists as Edmund Halley, Robert Hooke, Leibniz or John Flamsteedwhich conceded the criticism poorly and was extremely jealous of their positions.
In the regime appointed him director of the Mint, looking for an intelligent and honest administrator on it to curb counterfeiting.
It would represent the University in Parliament in In he was appointed President of the Royal Society of London. And in culminated the ascension of his prestige to be knighted. Extracted from the website: Biography of Isaac Newton English scientist.Sir Isaac Newton: Isaac Newton, English physicist and mathematician who was the culminating figure of the scientific revolution of the 17th century.
Already Newton was at work improving and expanding it.
Biography of Newton Isaac; MacTutor History of Mathematics Archive - Biography of Sir Isaac Newton. Biography of Isaac Newton | English scientist.
(Woolsthorpe, Lincolnshire, - London, ) English scientist. Founder of classical physics, which would retain full force until the time of Einstein, Newton work represents the culmination of the scientific revolution initiated a century before Copernicus.
Watch video · Isaac Newton was the only son of a prosperous local farmer, also named Isaac Newton, who died three months before he was born. A premature baby born tiny and weak, Newton was not expected to survive.
Watch video · Explore the history and discoveries of Isaac Newton, including his work in mathematics and optics and his groundbreaking laws of motion, at attheheels.com Isaac of all trades. English. Biography Sir Isaac Newton Sir Issac Newton ( ) was an English mathematician, physicist and scientist.
He is widely regarded as one of the most influential scientists of all time, developing new laws of mechanics, gravity and laws of motion. Isaac Newton was an English scientist and mathematician.
|Isaac Newton - Wikipedia||London, England English scientist and mathematician Isaac Newton was an English scientist and mathematician. He made major contributions in mathematics and physics the study of the relationship between matter and energy and advanced the work of previous scientists on the laws of motion, including the law of gravity.|
He made major contributions in mathematics and physics (the study of the relationship between matter and energy) and advanced the work of previous scientists on the laws of motion, including the law of gravity.


2014 Lectures on Computational and Applied Mathematics
(a) Thomas Hou, Caltech, USA
(b) Quoqiang Shi, Tsinghua University, China
(a) Data Driven Time-Frequency Analysis
(b) Data-Driven Stochastic Methods for Solving Stochastic PDEs
(c) Recent Progress on the Search of 3D Euler Singularities
(d) Finite Integral Method: A numerical approach for Poisson equation on point clouds
March 20(Thursday), 2014 PM 1:30-4:00
March 21, 2014 (Friday) AM 9:30-12:00 & PM1:30-4:00
Place: Hong-Jing Building M107
(1). Data Driven Time-Frequency Analysis
In this talk, we review some recent progress on our
data-driven time-frequency analysis method for studying trend and
instantaneous frequency of nonlinear and non-stationary data. This method is inspired by the Empirical Mode Decomposition method (EMD) and the recently developed compressed sensing theory. The main idea is to look for the sparsest representation of multiscale data within the largest possible dictionary consisting of intrinsic mode functions. This problem can be formulated as a nonlinear optimization problem. In order to solve this optimization problem, we propose a nonlinear matching pursuit method by generalizing the classical matching pursuit. One important advantage of this nonlinear matching pursuit method is it can be implemented very efficiently and is very stable to noise. Further, we provide a convergence analysis of our nonlinear matching pursuit method under certain scale separation assumptions. Extensive numerical examples will be given to demonstrate the robustness of our method and comparison will be made with the EMD/EEMD method. We also apply our method to study data without scale separation, data with intra-wave frequency modulation, and data with incomplete or under-sampled data.
(2). Data-Driven Stochastic Methods for Solving Stochastic PDEs.
Uncertainty arises in many complex real-world problems of
scientific and engineering interests. Many of these problems involve
multiple scales in both space and time, which may vary in several orders. We have recently developed an effective dynamically bi-orthogonal method (DyBO) for solving time-dependent stochastic PDEs. The main idea is to construct the most compact representation of the stochastic PDEs by tracking the Karhunen-Loeve expansion dynamically. We achieve this by deriving an equivalent set of evolution systems that govern the stochastic and deterministic basis without the need to form the covariance matrix or to compute its eigen-decomposition. Unlike other reduced model methods, our method constructs the reduced stochastic basis on-the-fly. We also propose an adaptive strategy to dynamically remove or add modes, and develop an efficient parallel algorithm for our method. Applications to solve 2D incompressible Navier-Stokes equations and the Boussinesq approximation with Brownian motion forcing demonstrate the effectiveness of the DyBO method. We will also introduce a data-driven method for solving stochastic elliptic problems with multiscale coefficient in a multi-query setting. A multiscale multilevel Monte-Carlo method has been developed to handle stochastic problems with high input dimensions. Our numerical experiments show that these methods could offer considerable computational saving over existing methods.
(3). Recent Progress on the Search of 3D Euler Singularities.
Whether the 3D incompressible Euler or Navier-Stokes
equations can develop a finite time singularity from smooth initial data
with finite energy is one of the most challenging questions in applied
mathematics and fluid dynamics. We review some recent theoretical and computational studies of the 3D Euler equations which show that there is a subtle dynamic depletion of nonlinear vortex stretching due to local geometric regularity of vortex filaments. Our study suggests that the convection term could have a nonlinear stabilizing effect for certain
flow geometry. This is demonstrated through two reduced models of the 3D incompressible Navier-Stokes equations. The first model is a new exact 1D model for the axisymmetric Navier-Stokes equation along the symmetry axis. We show that local flattening of the vortex structure and the effect of convection could lead to dynamic depletion of the vortex
stretching term. In the second model, we derive a 3D model of the
axisymmetric Navier-Stokes equation by removing the convection term from the reformulated Navier-Stokes equations. We show both numerically and analytically that the solution of this 3D model develops a finite time singularity from smooth initial data with finite energy. Finally we present a new class of solutions to the 3D Euler equations which could lead to a strong nonlinear alignment in the vortex stretching term and have the potential to develop a finite time singularity.
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