A lightweight matrix library in Python.
Pymatrix is a lightweight matrix library built in Python. It supports a range of basic linear algebra operations.
from pymatrix import matrix m = matrix([ [1, 2], [3, 4] ]) a = m + m * 2 b = m * m c = m ** 3 d = m.det() e = m.inv()
Install directly from the Python package index using
$ pip install pymatrix
Pymatrix requires Python 3.4 or later. The package has no dependencies.
Pymatrix doubles as a simple command line matrix analysis utility. Installing via
pip automatically makes
pymatrix available on the command line:
Usage: pymatrix [OPTIONS] [FLAGS] Matrix analysis utility. Enter a matrix interactively at the terminal or pipe to stdin from a file, e.g. $ pymatrix < matrix.txt Elements are parsed as fractions (rational numbers) by default. An alternative parser can be specified using the --parser flag. Options: -p, --parser <str> One of 'int', 'float', 'complex', or 'fraction'. Flags: -h, --help Print this help text. -v, --version Print the version number.
Pymatrix exports a lightweight, general purpose matrix class,
Matrix. A matrix element can be any arbitrary object that supports the required arithmethic and comparison operators. All of Python's native numeric types — integers, floats, complex numbers, and rational numbers — are supported.
(Note that this library has been built for comfort, not for speed. If you have heavy-duty computational needs you should use a C-based alternative like NumPy instead.)
You can instantiate a matrix object directly, optionally specifying a fill value:
m = Matrix(rows, cols, fill=0)
You can instantiate a matrix object from a list of lists using the
from_list() static method:
m = Matrix.from_list([ [1, 2, 3], [4, 5, 6] ])
You can instantiate a matrix object from a string using the
from_string() static method:
string = ''' 1 2 3/7 4/7 5 6 ''' m = Matrix.from_string( string, rowsep=None, colsep=None, parser=fractions.Fraction )
Row separators default to newlines, column separators default to spaces. Leading and trailing whitespace is stripped from the string. Elements are parsed as fractions (rational numbers) by default.
You can instantiate an n x n identity matrix using the
identity() static method:
m = Matrix.identity(n)
matrix() function supports the syntax of all three static methods:
m = matrix([[1, 2, 3]]) m = matrix('1 2 3') m = matrix(3)
Matrix objects are iterable. Iteration proceeds left-to-right by column, then top-to-bottom by row; i.e. the top-left element will be returned first, the bottom-right element will be returned last.
The iterator returns a tuple containing the row number, the column number, and the element:
for row, col, element in matrix: ...
elements() method returns an iterator over just the matrix elements:
for element in matrix.elements(): ...
Matrices are indexed as two-dimensional arrays:
matrix[row][col] = element element = matrix[row][col]
Note that indices are zero-based in accordance with programming convention rather than one-based in typical math style, i.e. the matrix's top-left element is
matrix rather than
Matrix objects support the following methods:
Returns the adjoint matrix as a new object.
Returns the specified cofactor.
Returns the matrix of cofactors as a new object.
Returns an iterator over the specified column.
Iterator returning a column iterator for each column in the matrix.
Returns the specified column as a new column vector.
Returns a copy of the matrix.
Returns the cross/vector product of the matrix with
other as a new matrix. The cross product is only defined for pairs of 3-dimensional column vectors.
Returns a new matrix with the specified column deleted.
Returns a new matrix with the specified row deleted.
Returns the determinant of the matrix.
Vectors only. Returns the unit vector in the direction of the vector.
Returns the dot/scalar product of the matrix with
other. The dot product is only defined for pairs of vectors.
Returns an iterator over the matrix's elements.
None, two matrices are equal if they are the same size and their corresponding elements are equal, i.e.
e1 == e2.
delta is not
None, two matrices are equal if they are the same size and their corresponding elements agree to within
abs(e1 - e2) <= delta.
Returns the inverse matrix if it exists, otherwise raises
True if the matrix is invertible. Note that determining whether a matrix is invertible is as computationally expensive as actually calculating the inverse.
True if the matrix is square.
Vectors only. Returns the length of the vector.
Returns a new matrix formed by mapping
func to each element.
Returns the specified minor.
Returns the rank of the matrix.
Returns the row echelon form of the matrix.
Returns an iterator over the specified row.
.rowop_add(r1, m, r2)
In-place row operation. Adds
m times row
r2 to row
In-place row operation. Multiplies the specified row by the scalar
In-place row operation. Interchanges the two specified rows.
Iterator returning a row iterator for each row in the matrix.
Returns the specified row as a new row vector.
Returns the reduced row echelon form of the matrix.
Returns the transpose of the matrix as a new object.
pymatrix module exports the following functions:
u . v - the inner/scalar/dot product of the vectors
u x v - the vector/cross product of the 3D column vectors
Shortcut function for instantiating
Matrix objects; supports the syntax of the various static instantiation methods.
An invalid operation on a matrix object will raise a
This work has been placed in the public domain.


Took me a while to write about this, but I really love Project Euler. The page is a collection of math challenges, which require some programming (I saw just one which could have been computed by a closed formula without any help). The first ten are quite easy to solve and are more commonly known math problems. Prime numbers and combinatorics play a strong role. But then the difficulty rises quite quickly. Usually it takes me one to two hours to write a Python solution for one. If I would – like I should – write unit-tests for each single method and not for a few selected one, then I guess 50% more.
It’s great: each problem is a closed, separate problem, which requires some algorithmic thinking and – of course – some proper implementation. If you chose the wrong path time or space complexity will kill your ambitions quite quickly. But proper solutions are computed most of the time in less than a minute.
Most of the time I rely on basic python structures and common libraries. But I’ve also given NumPy, itertools, etc. a try. Speeds up the process quite a bit.
My next goal is to fix problem 47, because then I’ve handed in solutions for all of the first fifty problems.
The highest challenge (with also the highest difficulty level (for me) so far) was problem 668. Due to a really big (80 GiByte!) boolean array the computer had a hard time swapping memory. So it took almost 36 hours to finish. By the way: less than 900 people worldwide have solved this issue #tinyflakeofpride
Of course, several geniuses have dedicated pages to optimal solution strategies. Which is a nice idea. But I avoid them. Most of the times stepping back, thinking without a display about the problem and if the chosen approach was a good one, is more helpful. A solution by cheating is nothing which renders any reward.


An arithmetic circuit is a logic circuit that performs basic arithmetic operations like addition, subtraction, increment, decrement and transfer operations using a single combinational circuit. It uses multiplexers and full adders to do so. The selection bits, along with an additional input at 2 and 3 input positions of the multiplexer, determine the type of operation to be done on the input data. This is further clarified by the function table below. As usual, a 4-bit arithmetic circuit works with 4-bit data.
Function Table for Arithmetic Circuit:
Mano, M. (n.d), Register Transfer and Micro-operations: Arithmetic Circuit, Computer System Architecture (3rd Edition), pp. 106-108


One questions many “for sale by owner” sellers ask is “how can I determine if a potential buyer can afford to buy my house?” In the real estate industry this is referred to as “pre-qualifying” a buyer. You might think this is a complex process but in reality it is actually quite simple and only involves a little math. Before we get to the math there are a few terms you should understand. The first is PITI which is nothing more than an abbreviation for “principal, interest, taxes and insurance. This figure represents the MONTHLY cost of the mortgage payment of principal and interest plus the monthly cost of property taxes and homeowners insurance. The second term is “RATIO”. The ratio is a number that most banks use as an indicator of how much of a buyers monthly GROSS income they could afford to spend on PITI. Still with me? Most banks use a ratio of 28% without considering any other debts (credit cards, car payments etc.). This ratio is sometimes referred to as the “front end ratio”. When you take into consideration other monthly debt, a ratio of 36-40% is considered acceptable. This is referred to as the “back end ratio”.
Now for the formulas:
The front-end ratio is calculated simply by dividing PITI by the gross monthly income. Back end ratio is calculated by dividing PITI+DEBT by the gross monthly income.
Let see the formula in action:
Fred wants to buy your house. Fred earns $50,000.00 per year. We need to know Fred’s gross MONTHLY income so we divide $50,000.00 by 12 and we get $4,166.66. If we know that Fred can safely afford 28% of this figure we multiply $4,166.66 X .28 to get $1,166.66. That’s it! Now we know how much Fred can afford to pay per month for PITI.
At this point we have half of the information we need to determine whether or not Fred can buy our house. Next we need to know just how much the PITI payment is going to be for our house.
We need four pieces of information to determine PITI:
1) Sales Price (Our example is 100,000.00)
From the sales price we subtract the down payment to determine how much Fred needs to borrow. This result brings us to another term you might run across. Loan to Value Ratio or LTV. Eg: Sale price $100,000 and down payment of 5% = LTV ration of 95%. Said another way, the loan is 95% of the value of the property.
2) Mortgage amount (principal + interest).
The mortgage amount is generally the sales price less the down payment. There are three factors in determining how much the PI& interest) portion of the payment will be. You need to know 1) loan amount; 2) interest rate; 3) Term of the loan in years. With these three figures you can find a mortgage payment calculator just about anywhere on the internet to calculate the mortgage payment, but remember you still need to add in the monthly portion of annual property taxes and the monthly portion of hazard insurance (property insurance). For our example, with 5% down Fred would need to borrow $95,000.00. We will use an interest rate of 6% and a term of 30 years.
3) Annual taxes (Our example is $2,400.00)/12=$200.00 per month
Divide the annual taxes by 12 to come up with the monthly portion of the property taxes.
4) Annual hazard insurance (Our example is $600.00)/12=$50.00 per month
Divide the annual hazard insurance by 12 to come up with the monthly portion of the property insurance.
Now, let’s put it all together. A mortgage of $95,000 at 6% for 30 years would produce a monthly PI
Putting it all together
From our calculations above we know that our buyer Fred can afford PITI up to $1,166.66 per month. We know that the PITI needed to purchase our house is $819.57. With this information we now know that Fred DOES qualify to purchase our house!
Of course, there are other requirements to qualify for a loan including a good credit rating and a job with at least two years consecutive employment. More about that is our next issue.


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You will possess a good degree or PhD in Engineering, Physics or Mathematics. You will have exceptional skills in numerical analysis and mathematical modelling.
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GDP202 Algorithms and data structures
Game and simulation programming is heavily reliant on mathematical techniques to manipulate and display virtual environments and enforce the logic of game rules and mechanics.
This subject builds on the fundamental 2-dimensional and 3-dimensional mathematical concepts introduced in GDP 103 Fundamentals for Computer Graphics, taking an in-depth look at how such concepts can be implemented in code using the C++ programming language.
To fully understanding the formulae needed to manipulate the Vectors and Matrices used within all games, you will work through creating a basic math that can be redistributed and used within other applications. To ensure your implementation of the mathematical formulae are correct the maths library will be tested with a Unit Testing application.
You will also explore basic collision detection techniques and gain an understanding of binary operations.


In preparing my previous post on Net Energy Trends I wanted to include a back of the envelope calculation on the ERoEI of hydro electric power using the Three Gorges Dam as an example. But I got my decimals pretty muddled leading to an answer that was implausible. But I’ve now had a few days off to clear my head and I put a new battery in my calculator and so hopefully the calculation is now on the money.
Looking at just the labour and embedded energy of the concrete and steel and assuming a 45% capacity factor and 70 year life yields a partial ERoEI of 147. And so, despite substantial environmental harm and social disruption I must give dispatchable hydro electric power a big thumbs up. See the calculation below the fold.
The Three Gorges Dam on the Yangtze River in China is the largest hydroelectric scheme in The World. Operational since 2008 it has 22.5 GW installed capacity. The Itaipu Dam on the Parana River between Paraguay and Brazil produces a similar amount of electricity from 14 GW capacity and achieves this through a higher capacity factor.
Recent posts on ERoEI indicated that hydroelectric power had ERoEI >> 50 and I just wanted to check these claims. But before proceeding lets get the metric prefixes sorted since we have to manipulate some fairly large numbers:
mega = 10^6 = million
giga = 10^9 = billion
tera = 10^12 = trillion
peta = 10^15 = one thousand trillion
exa = 10^18 = one million trillion
Three Gorges Vital Statistics
Installed generating capacity = 22.5 GW
Capacity factor = 45% (0.45)
Concrete = 27.2 million m^3
Concrete = 65.2 million tonnes*
Steel = 463,000 tonnes
*1 m^3 concrete = 2.4 tonnes
1 TWh = 3600 TJ
1 toe = 42 GJ
The Energy Return
This is always the easier part of the ERoEI calculation but even here assumptions need to be made about capacity factor and lifespan. Wikipedia report 45% capacity factor which I presume is based on design criteria and performance to date. And I have assumed a 70 year lifespan. Lifespan could easily be much longer and this will simply add to the ERoEI.
0.45 * 22.5 GW * 24 hrs * 365.25 days * 70 years = 6213 TWh = 22.37 EJ
The Energy Invested
I am not going to attempt a detailed and complete analysis here but will try and make ball park estimates of energy consumed by labour and the main materials – concrete and steel.
60,000 workers laboured on the project that began in 1994  and was completed in 2003. Taking 1998 as the mid point China had a population of 1.242 billion and consumed 905 million tonnes oil equivalent (Mtoe) in energy that year . This yields a per capita consumption of 0.75 toe. The sum for the energy cost of labour therefore is:
60,000 workers * 0.75 toe per annum * 10 years = 450,000 toe = 18.9 PJ
There is a range of numbers for the energy content of materials. I am going to use:
Concrete = 1.9 GJ / tonne
Steel = 20 GJ / tonne
65.2 million tonnes concrete * 1.9 GJ / tonne = 123.9 PJ
463,000 tonnes steel * 20 GJ / tonne = 9.3 PJ
Total Energy Invested
labour 18.9 PJ + concrete 123.9 PJ + steel 9.3 PJ = 152.1 PJ
The partial ERoEI
Energy return = 22.37 EJ / energy invested 152.1 PJ = 147
Energy pay back time works out at an incredible 6 months.
(Energy produced in 1 year = 22.37 EJ / 70 = 319 PJ. Energy invested = 152.1 PJ. Hence energy pay back time = 152/319 = 0.48 years.)
I am quite satisfied with this answer. Some of the input numbers used may be wide of the mark and the energy inputs are far from complete. For example the diesel used on the construction site is not included along with many other energy inputs. But the answer is in the same ball park as calculated by other workers. Hydroelectric power is a tremendous source of dispatchable renewable energy. It does however come with high environmental and social costs. There’s no such thing as a free lunch in the energy world.
 Wikipedia: Three Gorges Dam
 Facts and Details: THREE GORGES DAM PROJECT
 Australian Government: Embodied Energy
 Wikipedia: Embodied Energy


There is a growing demand worldwide for a more informative and more appealing approach to teaching mathematics. Comparing Euclidean and spherical geometry leads to deeper understanding of concepts in both geometries.
The e-learning course Plane and Sphere: Comparative Geometry with the Lénárt Sphere gives insight into the basics of spherical geometry, and develops your skills to translate exercises in plane geometry to the sphere, and conversely. This competence and knowledge can successfully be applied in many topics in and out of mathematics, in geography, astronomy, or various fields of arts.
However, bold it may seem, comparing plane and sphere provides a viable route to hyperbolic geometry, one of the great mysteries of modern science for the layman, and at the same time one of the most important tools for the theory of relativity and other areas of modern physics.
Beyond mathematics and science, comparing different aspects about the same branch of mathematics leads to more empathic thinking in other areas of life, understanding and tolerance towards opinions different from your own, towards people with different cultural or social backgrounds.
For more info, please download our Training Agreement Form, and check out the pdf version of the Contents of the Course and some sample exercises. Don’t hesitate to contact us for further information.


What is the formula for blackjack
Calculating the House Edge for any Blackjack Game
How to get your child to love math – Age of Awareness – Medium 28 Jul 2016 ... I've found blackjack to be the single most amazing math education tool. ... millions of computer calculations show that a player should stand. Blackjack Betting Systems: Oscar's System Wins 99.98% of the Time A blackjack betting system first published in 1965 - Oscar's Blackjack Betting System - wins 4999 out of 5000 times.
One of those was a 10-to-1 payoff for a hand consisting of the ace of spades and a black jack (that is, the jack of spades or the jack of clubs). With the current rules, a blackjack hand doesn't even need to contain a jack. Rules . A blackjack game has a dealer and one or …
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The calculations are particularly simple if, as above, we choose a sample space in which ... The hand is called a “blackjack” if the two cards sum to exactly 21. +.
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The Basic Blackjack Strategy - SlideShare
Jun 2, 2017 ... The house edge in blackjack is easy to understand, but it's a multi-faceted subject. ... The formula for expected hourly loss looks like this:. How to Win at Blackjack — and Walk Out Of the Casino Alive - Medium Mar 20, 2017 ... During high school, I often drove my roommates to Native American casinos in the Midwest for fun. We often played Blackjack because it's easy ... The Kelly Criterion in Blackjack, Sports Betting ... - Computer Science Apr 20, 2005 ... The author initiated the practical application of the Kelly criterion by using it for card counting in blackjack. We will present some useful formulas ... The mathematics of blackjack: Probabilities Probability Theory Basics and Applications - Mathematics of Blackjack. ... The formula of probability for obtaining a certain favorable value is similar to that for ...
Blackjack Mathematics, Probability, Odds, Basic Strategy
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Tim Roberts maintains the website http://www.unsolvedproblems.org/ in which he presents unsolved problems from mathematics, mostly conjectures that yet lack a formal proof. While working on these problems is fun, it may be useful to know that some problems might be unsolvable, so they are not worth the effort trying to solve them.
By means of formal logic we can show that some problems are probably unsolvable. If we can reformulate a statement to be of the type "there does not exist any n for which ...", it is probably unprovable. Examples:
The Goldbach Conjecture states that every even number greater than 2 is the sum of two primes. A number is prime if it is divisible only by itself and 1. So, for example, 36 = 17+19.
This is equivalent to: For every integer n greater than 1, there is an integer k so that both n - k and n + k are prime numbers.
Employing the existential quantifier only, we can reformulate this to: There does not exist any integer n greater than 1 for which there does not exist an integer k so that both n - k and n + k are prime numbers. This can, if it is a false statement, easily be disproven, but it is probably impossible to prove.
Twin Primes Conjecture
The twin primes conjecture states that there are an infinite number of pairs of primes of the form 2n-1, 2n+1. That is, they differ by 2; for example, 41 and 43.
This is equivalent to: There does not exist any integer k which is larger than any pair of primes of the form 2n-1, 2n+1. "There does not exist any"... probably impossible to prove.
Take any positive integer: if the number is even, divide it by two; if the number is odd, triple it and add one (for example, if this operation is performed on 26, the result is 13; if it is performed on 5, the result is 16). Perform this operation repeatedly, beginning with any positive integer, and taking the result at each step as the input at the next.
For example, starting at 11, the sequence goes 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1.
The Collatz conjecture is: this process will eventually reach the number 1, regardless of which positive integer is chosen initially.
This is equivalent to: There does not exist any integer n for which the given algorithm does not result in the number 1. Probably impossible to prove!
However, Fermat’s Last Theorem is also a conjecture of the "there does not exist any n for which ..." type, which should render it unprovable, but it has been proven.
So I do not claim that the problems which seem to be impossible to prove are unprovable indeed, but probably they are.


|vid, 2007-11-20||Revision: 1.1|
"Big number" arithmetics requires special care on x86 architecture. You need to use some properties of arithmetic instructions, which are not immediately apparent.
I expect reader to understand binary representation of numbers, basics of binary arithmetics, and hexadecimal number notation.
Big numbers are numbers that consists of more bits than machine word contains. For example 1024-bit number is considered big number. Usually, size of big number is multiple of size of machine word, so we can say big number consists of multiple machine words.
Processor doesn't have instructions for direct manipulation with big number, but it provides instructions that can manipulate with machine words, which are part of big number.
I will provide examples for x86-32, where size of machine word is 32 bits. When I will refer to machine word, I mean 32-bit number, even though it is customary to refer to 32-bit number as double word or dword on x86.
Before continuing, download Intel Manual Volume 2 (2A and 2B), which contains instruction set reference. We will use it through the article.
As I stated previosly, big numbers usually consist of several machine words.
Ordering of machine words within big number is a problem similar to ordering bits within single machine words. There are two possibilities: either the most significant word comes first (analogous to big endian) or the least significant word comes first (analogous to little endian). The x86 architecture uses little endian for bit order within machine word, and we will use it for order of machine words in this examples too. There is no practical advantage in either way, it is only matter of agreement.
For example 64-bit number with value 1, would consists of dword with value 1 followed by dword with value 0.
dd 1 ;low order dword dd 0 ;high order dword
A 96-bit number containing (hexadecimal) value
dd 0xABCDEF00 ;low order dword dd 0x12345678 dd 0x01020304 ;high order dword
First operation we will demonstrate is addition. Look up
add instruction in manual.
We will start with adding value 1 to 96-bit
bignum (3 dwords). We simply add 1 to low
order (first) dword:
bignum dd 15 dd 0 dd 0 ... add dword [bignum], 1
There is a problem with this though. If low order number contains value 0xFFFFFFFF, then it will overflow to 0 after adding number. We must then add 1 to higher dword. We say that we carry 1 from lower dword to higher dword in case of overflow.
How to detect overflow? When
add causes overflow, it sets CF (carry flag).
This is one way:
add dword [bignum], 1 jnc done add dword [bignum+4], 1 done:
Still, same thing can happen during second addition. If first two dwords contained value 0xFFFFFFFF, then we must carry 1 to third dword:
add dword [bignum], 1 jnc done add dword [bignum+4], 1 jnc done add dword [bignum+8], 1 done:
add overflows, then entire operation on big number has overflown.
Depending on what we use bignum for, we can ignore or signal this
add dword [bignum], 1 jnc done add dword [bignum+4], 1 jnc done add dword [bignum+8], 1 jc overflow done:
There is also a "nicer" way. We have
adc instruction, which does same as
and if CF is set, then it adds extra 1 to destination. We use it like
add dword [bignum], 1 adc dword [bignum+4], 0 adc dword [bignum+8], 0
add does the addition, and sets CF is overflow occured. Following
does nothing if CF is 0 (no overflow during first operation), or adds 1 to
second dword if CF is 1. It also sets CF if overflow occurs, or clears it if no
overflow happened, just like
adc does same thing as first one.
We can use this way for adding any value, not just 1. No more than one bit ever
needs to be carried during addition (0xFFFFFFFF + 0xFFFFFFFF = 0x1FFFFFFFE).
Following is generic algorithm that adds
EAX to big number pointed by
add dword [edi], eax adc dword [edi+4], 0 adc dword [edi+8], 0
We can also add numbers bigger than 32 bits, by using
adc to add to higher dwords.
This example adds 0x12345678AABBCCDD to bignum:
add dword [edi], 0xAABBCCDD adc dword [edi+4], 0x1234567 adc dword [edi+8], 0
This way, we can add big numbers together. This example adds 128-bit (4 dword)
mov eax, dword [bignum1] add dword [bignum2], eax mov eax, dword [bignum1+4] adc dword [bignum2+4], eax mov eax, dword [bignum1+8] adc dword [bignum2+8], eax mov eax, dword [bignum1+12] adc dword [bignum2+12], eax jc overflow
Subtraction is analogous to addition, we just use
sbb instructions. In this case, we say that we
borrow 1 from lower dword to higher dword in case of
mov eax, dword [bignum1] sub dword [bignum2], eax mov eax, dword [bignum1+4] sbb dword [bignum2+4], eax mov eax, dword [bignum1+8] sbb dword [bignum2+8], eax mov eax, dword [bignum1+12] sbb dword [bignum2+12], eax jc underflow
Interesting problem is how to negate big number. We have
neg instruction, but
it doesn't work with big numbers so easily. That's why we will start with method
which we already know - subtraction. We will simply subtract big number from 0:
mov eax, 0 sub eax, dword [bignum] mov dword [bignum], eax mov eax, 0 sbb eax, dword [bignum+4] mov dword [bignum+4], eax mov eax, 0 sbb eax, dword [bignum+8] mov dword [bignum+8], eax
Negation can be also performed by inverting all bits (0->1, 1->0), and then add 1 to it. I won't explain why, it can be task for reader. You need to understand how are negative numbers represented in x86 architecture.
To invert all bits, we have
not instruction. Adding 1 to big number already was
described. So negating big number looks like this:
not dword [bignum] not dword [bignum+4] not dword [bignum+8] add dword [bignum], 1 adc dword [bignum+4], 0 adc dword [bignum+8], 0
After understanding this, as a bonus, we can explain how to use
instruction directly to negate big number. As we already know,
first inverts all bits, and then adds 1 to result. So we negate first (low order)
dword. If value of dword before negating is 0, after inverting bits it becomes
0xFFFFFFFF, and after adding 1 it is 0 again. But this is also only case when
addition needs to be carried to upper dword, and only case when
sets CF. In all other cases, CF is clear, and other dwords need to be just
bit-inverted. In practice, code to do this is not particulary nice:
neg dword [bignum] jnc not1 neg dword [bignum+4] jnc not2 neg dword [bignum+8] jmp done not1: not dword [bignum+4] not2: not dword [bignum+8] done:
Bitwise shifting is sometimes useful for big numbers (for example when they are used as floating point numbers).
First we will shift by 1 bit.
When we want to bitwise shift ordinary (not big) number, we use
shr instructions. When we use them to shift by 1, bit that is
shifted out of number is saved in CF. Problem is then, how to shift this bit into
In this case, we can use
They "rotate" number "through" CF. When they are used to rotate by 1, they shift
number, insert CF as new bit, and then save bit which comes out in CF.
Look these up in manual. This is how rotation looks then:
;shift left shl dword [bignum], 1 rcl dword [bignum+4], 1 rcl dword [bignum+8], 1 jc overflow ;shift right shr dword [bignum+8], 1 rcr dword [bignum+4], 1 rcr dword [bignum], 1 jc overflow ;often not needed
Shifting becomes interesting when we want to shift by more than 1 bit. In this
case, we need to carry more bits between dword operations. A 386 provided
useful instructions to do this,
shrd. They shift number like
sar, but insert bits from another operand instead of
using fixed value.
mov eax, [bignum+4] shrd [bignum], eax, 5 mov eax, [bignum+8] shrd [bignum+4], eax, 5 shr [bignum+8], 5
mov eax, [bignum+4] shld [bignum+8], eax, 5 mov eax, [bignum] shld [bignum+4], eax, 5 shl [bignum], 5
Testing for overflow is trickier in this case. We need to test if upper/lower N bits are all zero before shifting. For constant value (like 5), we can use mask:
test [bignum+8], 0x0000001F ;00000000 00000000 00000000 00011111 binary jnz overflow
test [bignum+8], 0xF8000000 ;11111000 00000000 00000000 00000000 binary jnz overflow
But with non-constant number of bits to shift, you would need to construct this mask.
Instead, you can use
xor eax, eax ;eax = 0 mov ebx, [bignum] shrd eax, ebx, 5 test eax, eax ;eax ?= 0 jnz overflow
xor eax, eax ;eax = 0 mov ebx, [bignum+8] shld eax, ebx, 5 test eax, eax ;eax ?= 0 jnz overflow
To multiply number, there is
mul instruction. We will
mul with one operand. Forms with 2
or 3 operands are not usable for big numbers.
mul multiplies 32-bit number in
EAX, and saves 64-bit result in
EDX:EAX. That means we have part that which is
"carried" to upper dword in
mov ebx, 10 ;EBX = multiplier mov eax, [bignum] mul ebx ;EDX:EAX = EAX*EBX mov [bignum], eax ;save result mov ecx, edx ;save carried part in ECX mov eax, [bignum+4] mul ebx add eax, ecx ;add carried part from previous multiplication mov [bignum+4], eax mov ecx, edx mov eax, [bignum+8] mul ebx add eax, ecx mov [bignum+8], eax cmp edx, 0 jne overflow
Multiplying with numbers which don't fit 32 bits (like multiplying two bignums) can't be done in any straightforward way.
Division is similar to multiplication. We will use one-operand form
div instruction. It takes 64-bit number in
EDX:EAX, stores result of division in
and remainder in
EDX. If result is bigger than 32-bits,
it throws exception, so we must make sure that this never happens.
We will start from "top" of number (high order dword). After every division, remainder in EDX is used as high 32bits of divident for subsequent division. Last vale of EDX is remainder from entire big number division.
mov ebx, 10 ;divisor mov edx, 0 mov eax, [bignum+8] ;EDX:EAX = number to divide div ebx mov [bignum+8], eax mov eax, [bignum+4] div ebx mov [bignum+4], eax mov eax, [bignum] div ebx mov [bignum], eax ;edx holds remainder from division
Again, dividing by values greater than 32 bits cannot be done "easy way".
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|2007-11-20||1.1||Partial rewrite and additions||vid|
|2007-11-06||1.0||First public version||vid|
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EE290o: Special Topics in Control (Resilient Networks): Spring 2014
Interconnected networks are becoming more and more important in society. Some examples of these networks include internet, transportation networks, power and utility networks, financial networks, sensor networks, multi-agent systems, social networks, etc.
Resilience of networks involves the topological structure, as well as dynamics of networks. The course will study structure (combinatorics, pretopology) and dynamics (deterministic and stochastic) on these networks. Scaling issues from microscopic to macroscopic behaviours, games on networks, the interplay between graph and dynamics (algebraic graph theory), performance measures for networks, queuing theory on networks, network calculus and scale-free complex networks phenomenon will be studied. Python programming language will be used with its graph library for working with sample example networks during the course.


Black Hills Corporation Quantitative Analyst II in Rapid City, South Dakota
SALARY RANGE: $65,800 - $85,570
Base salary is determined by the knowledge, skills and abilities of the applicant.
CLOSING DATE: This position will close on September 27, 2018.
LOCATION: Rapid City, SD
The Quantitative Analyst II will join a dynamic quantitative analytics team, playing a critical role in advancing the state of statistical forecasting, mathematical optimization, and supply chain modeling in the organization. This role will drive the development of a new suite of models, decision-support tools, and value-add services that drive decision-making, optimization, and competitive advantage across service functions and utility operations.
REPORTING RELATIONSHIP: Supply Chain Policy & Analysis Manager
ESSENTIAL JOB FUNCTIONS:
Participates as a key member of the company’s quantitative analysts’ team on company-wide projects.
Performs advanced quantitative analyses and supply chain model development to drive decision-making.
Build econometric, statistical, and mathematical models to solve complex forecasting and pricing/revenue/resource optimization problems.
Design and develop new technological applications and decision support tools, including programming models and web applications in R and Python and working with information technology teams to move models/applications from prototype to production.
Apply principles of data engineering, including working directly with information technology teams on data warehousing and database architecture projects to support the data needs of the Quantitative Analytics team.
Write efficient queries and extract, clean, process, and visualize large volumes of data to derive insights.
Validate, test, and control standards, including testing of assumptions, computational accuracy, and documentation of model weaknesses and risks.
Explain model design, risks, and outputs, and interface with executive leadership to translate complex analyses into action.
- Continuous pursuit of cutting-edge knowledge and skills in the fields of statistic, economics, operations research, computer science, and data science.
Finance, Accounting, and Regulatory Departments
Information Technology Departments
Utility Engineering, Operations, Gas Asset Optimization Departments
Continuous Improvement Team
Minimum 2 years of graduate-level academic or 3 years of professional experience in an Industrial Engineering, quantitative modeling, econometrics or data scientist role.
Minimum 2 years of experience and advanced proficiency in using statistical programming languages such as R and Python – SciPy and scikit-learn libraries.
Minimum 1 year of experience in database modeling and data warehousing principles with basic proficiency in SQL.
Highly proficient in mathematics: Calculus (differential, integral, stochastic), linear algebra and differential equations, probability and statistics
Familiarity with prototyping and developing applications in programming languages (Java/ C++/Python).
Familiarity with concepts in machine learning and simulation modeling.
Bachelor’s degree in Industrial Engineering, Operations Research, Computer Science, Applied Mathematics or related discipline required.
Master’s degree in Operations Research, Industrial Engineering, Econometrics, Computer Science, Applied Mathematics or related discipline preferred.
Statistical programming languages
Technology development lifecycle
Quantitative modeling design and validation
Statistics, mathematics, econometrics, and/or operations research
Interest in and basic knowledge of machine learning and big data analytics
Ability to thrive in a fast-paced undefined and ambiguous environment
Able to apply principles of the scientific method and empirical research
Exceptional work ethic
Entrepreneurial, creative, curious, and inquisitive
Exceptional math skills
Excellent problem solver
Ability to gain credibility of peers and executive leadership
- Past academic or work experience on issues affecting supply chain efficiencies and effectiveness.
- Applicant must be able to perform the essential job functions of the position with or without accommodation.
The information contained in this position description describes the general nature and level of work being performed in this job. This description is not intended to be an all-inclusive list of responsibilities, duties, and requirements for employees in this position. The incumbent is responsible for performing all duties in a safe and efficient manner in compliance with safe work procedures and safety regulations. This job description is not intended to constitute an offer or contract of employment. Job descriptions may and do change periodically. Where positions are covered by a collective bargaining unit agreement, the terms and conditions of the collective bargaining unit agreement will apply.
We are an EEO Employer


What a big term of learning our Year 3 and 4 Mathematicians have in front of them! They have begun the term by investigating the idea of equivalence in equations and that the equal symbol means that both sides of an equation need to balance and using operations such as addition, subtraction, multiplication and division to practice this skill. Students will also begin to investigate fractions and decimals, learning about equal parts of numbers. Students have begun to investigate measurements such as capacity, mass, perimeter and area. In the second half of the term, students will explore probability and chance by playing different games and thinking about the chances of winning.
You can support your child at home by playing card, dice and board games with them and talking about who wins and why they won.


If you think about which lottery tickets you should buy but which lucky numbers you should choose, this article is especially for you. One easy way to pick the lottery numbers that you find lucky for yourself. Besides, many people find this more interesting and fun than letting a computer pick your numbers quickly. But you wonder how to get those lucky numbers. What are the six lucky numbers to win the lottery? So if you do not have the numbers that resonate with you, we help you in this regard.
Table of Contents
What Are The Effective Ways For Finding Six Lucky Numbers To Win The Lottery
By following these ways, you will be able to find the six lucky numbers to win the lottery:
Prefer Traditional Lucky Numbers
People consider number seven as the lucky number in many places of the world. The poll conducted by mathematician Alex Bellos shows that seven is the most popular lucky number globally. The reason can be that there are seven days of a week, seven continents, Seven Wonders of the World, and seven seas.
But seven is not the lucky number only. Some other traditional lucky numbers around the world include three. The reason is that the good things come in threes mostly. Moreover, in Japan and China, people consider eight as their lucky number. On the contrary, the people in Germany consider four as their lucky number. Moreover, you can check the list of lucky and unlucky numbers from around the world that favor your luck.
The Disadvantage Of Choosing The Traditional Lucky Numbers
There is a demerit of using the traditional lucky number as your lottery number. The reason is that many people around the world will be using the same traditional lucky numbers. So if your traditional lucky numbers win, your chances of splitting the jackpot and winning a prize are high.
Creating Personal Meaningful Lucky Numbers
The famous way to fill out lottery tickets is by picking numbers that have personal and important meaning for you. For instance, you may create a lucky number from your birthday, the birthdays of your spouse, your wedding anniversary, or the birthdays of your kids and grandkids. When you make bets in form of couples, you find it lucky for yourself.
Furthermore, dates are not the numbers only that can have personal meaning for you. Rather, the number of childhood and the number of pets you have in your house can be lucky for you to win the lottery tickets.
The Disadvantage Of Choosing The Personally Created Lucky Numbers
When we talk about picking the lottery numbers, dates have the same problem as the traditional lucky numbers. Many people play with them. Second, dates are among the most famous lottery dates, so many people will consider the same lucky numbers. It will reduce the amount of winning cash if you win the lottery ticket.
Going With Your Intuitions
You should let your subconscious do the work for you sometimes. Try to find a quiet place to sit with some paper and pencil if you want to let your intuition pick your lucky numbers. Clear your mind, close your eyes, and take some deep breaths. Then think about any number in your mind. Write it on paper. So when you have enough numbers, check them out and see what you think about it. If you do not like any number, you can repeat the same exercise in this case.
Furthermore, if you want to be more random, write down the numbers on a piece of paper, close your eyes. Then let your pencil land on the number at random. Circle the number you have landed on and analyze if you find it lucky for you.
Using Numerology To pick Lucky Numbers
Numerology is a belief that numbers resonate in such a way that provides you spiritual qualities. So you can choose your lucky numbers by decoding those resonations. Besides, you can select the lucky days even to play the lottery. Also, there are several ways to use Numerology for picking up lucky numbers. It is one of the most effective ways to find out six lucky numbers to win the lottery.
One of the suitable ways is to create a table with the numbers from 1 to 9. Place one letter in one column so A = 1, B = 2, and so on. After the ninth letter, you will wrap around again so that K = 2, J = 1, and so on. Then plug in the letters having your name for getting one digit for each letter. After that, you can add those digits together to get a lucky number.
Moreover, you can do this for your first and last name, for the vowels of your name, or the consonants of your name. Additionally, you can select the names of your loved ones as well. Play around until you can find out the combination that best suits your luck.
Horoscopes Offer Lucky Numbers
If you do not want to play with the numerals yourself for picking up the lucky numbers, you can use the daily horoscope. Besides, many horoscopes include predictions of which days are going to be lucky for you. Hence, you can play the lottery on those days. Moreover, they also include a list of lucky numbers for the month, week, or day. You can find the lucky numbers from online horoscopes as well. Astro star and Lucky Number Horoscope are the best choices in this regard. Do not forget that fortune cookies include lucky numbers sometimes.
Using The Lucky Number Generators
You can use the lucky number generator to find the most suitable lucky number for you. It is the simplest way to choose the lucky number. Besides, lucky number generators use Numerology and randomness for selecting the right lucky number for you. Besides, you can use Lottery Pros and Ask the Oracle due to their improved services.
A lucky number generator is significantly different from letting the lottery picking numbers for you. It is all about what you feel is the most fun for you.
Some Warnings Regarding Lottery
It is fun to find and play lucky numbers. You will enjoy finding six lucky numbers to win the lottery. But keep one thing in your mind that all the lottery systems do not give you the opportunity to win a jackpot. Besides, every number has an equal chance of winning mathematically. Past performance does not affect your future performance. So these tips are just for the purpose of entertainment and fun. If you like to find out some more ways to feel lucky, try to explore the weird origins of your lucky superstitions.
Summing Up Six Lucky Numbers To Win The Lottery
If you want to win the lottery ticket, you should go with your lucky number. We have explained some lucky numbers to win the lottery in this article for your help. Besides, we have given you some effective ways to find your lucky number, including going with your intuitions, traditional lucky numbers, creating personally meaningful lucky numbers, Using Numerology, Using the horoscope, and lucky number generators. But we warn you that these tips are for entertainment purposes. Have fun with these effective ways and tips. We advise you never to gamble more money than you can afford to lose.


Hands on Manipulatives Simplify Prep Work and Enhance Learning In Collaborative Classrooms/ Individual Studies
Our pedagogical approach focuses on how students think, learn, and apply new knowledge in mathematics and empowers students to take ownership of their learning. This approach is consistent with the mathematical practice standards.
Math a magic kits contain activity base sheet, tactile manipulative and worksheets. Together these instructional materials provide formative assessments, relevant problem-centered activities to develop mathematical reasoning and sense making skills to personalize learning.
Implementing any new math curriculum is challenging and takes time. As you introduce and teach with the common core math standards using traditional teaching methodologies, the learning curve to being math-ready is big.
Math A Magic Kit accelerates the learning curve and prepares you to be up and running fast. We help k-12 teachers of all levels deepen their content knowledge
and train them to create effective standards-based, student-centered learning environments where all students achieve using Math A Magic Kits.
How It Works (Step By Step)
The class appropriate kit is given to each student at the beginning of the academic session. Each kits consists of a number of math experiments pertaining to the curriculum of the particular class.
The math teacher schedules the use of the kit as per his/ her curriculum and calls out to the students to get one of the kits on a particular date.
The students come with their kit and perform the math experiment under the supervision and guidance of their math teacher. This is repeated with other experiments in the kit throughout the year.


An elementary math curriculum for supplementary or home school should teach much more than the “how to” of simple arithmetic. A good math curriculum should have elementary math activities that build a solid foundation which is both deep and broad, conceptual and “how to”. Free online math tests for elementary, middle school, and high school students. All tests come with an instant feedback and an overall score that you can see on the computer screen. Timed tests are available, as well as printable math worksheets. EMBARC was originally created to support local teachers using Eureka Math, but we now serve 30,000 users each day across the nation. Our vision is: To build a collaborative community of Eureka Math users; To provide a common website to support all users of the Eureka Math curriculum; Click HERE to learn more about our community! Math Games offers online games and printable worksheets to make learning math fun. Kids from pre-K to 8th grade can practice math skills recommended by. Free Elementary Math Worksheets for Teachers, Parents, and Kids. Easily download and print our elementary math worksheets. Click on the free elementary math worksheet you would like to print or download. This will take you to the individual page of the worksheet. You will then have two choices.
Math Games. Do your students think math is a bore? Help them see this essential subject in a new way with these exciting math games! With adventures in every skill from counting to algebra, calculations to fractions, and much more, these interactive math games will have your students growing their knowledge while they play to win and beat their. Test your elementary math skills with this simple game! Three modes for just addition, addition & subtraction, OR addition, subtraction, multiplication, & division!
Elementary School Math blogs list ranked by popularity based on social metrics,. However, there is not a wealth of information about elementary math topics online. That is why I am here to help. The Mr.Elementary Math website is filled with resources that inspire, teach and support all educators. Free online math classes can help you master the basics without having to struggle through complicated textbooks or pay for a tutor. Check out this collection of the best free online math classes to learn how to solve just about any problem. 12/02/2018 · In this installment, we will present the best math apps for elementary school students. Quick Math Pack; Quick Math is a multi-app bundle, including individual apps focusing on mental arithmetic, times tables, fractions, and telling time. These apps are all timed, helping students to be quicker in solving math problems. Math Vs Zombies.
Coolmath Games is a brain-training site, for everyone, where logic & thinking & math meets fun & games. These games have no violence, no empty action, just a lot of challenges that will make you forget you're getting a mental workout! 09/12/2019 · Elementary Games. AddEmUp. A strategy game with a difference. Alpha Twist. Twist the letters back into shape by tapping on their joints and rotating any extended arms. Arrange Puzzle Game. Math Match Game. Test your memory AND your math skills, all in one game! Maze in 3D. Public online elementary schools must adhere to specific district and state academic standards to continue receiving funding and accreditation approval. This means specific content must be taught in math, social studies, science, and language arts courses. 29/01/2013 · The following five online math resources for grades K-5 offer everything from interactive activities to webcasts, printable worksheets, and more. Most of these sites also go far beyond elementary math, so make an effort to click around if you’re looking for.
Math Mayhem Play head-to-head with other students. Math Baseball They'll throw you a question. Math Mastery Online classes are available, but great free stuff including math tips and games. Minute Math Test yourself with a variety of quizzes. Web Math Minute More math quizzes to try.
24/04/2018 · Best Online Interactive Math Games for Elementary School. It’s important to spark an interest in math at a young age and build confidence in skills quickly. Fun interactive math games are a great way to do it. Puzzle Pics. How it works: Click and drag the. Gifted elementary students should be able to learn as fast as their abilities allow. CTY Online Programs's individually paced mathematics program, led by CTY instructors and tailored especially for gifted students, helps them do just that. Visit the links to the right to learn more about CTY Online Programs and distance education. Our online games reinforce important skills that are vital to elementary students and their educational process.was developed entirely by an elementary school teacher with the goal of reinforcing fundamental learning concepts in math, reading, spelling, language arts,.
Elementary Math Help. In this section, you will find explanations to many mathematical processes learned in elementary school, grades 1-8. The navigation on the left is set up to progress in a general order of how topics are learned; however, you students, parents, and tutors may find it more helpful to simply look for the topic you need. This is an annotated list of online math programs and curricula. Typically, the programs offer interactive math practice and/or animated/video lessons, track student progress, and include parent controls. Most of these are commercial programs, and the price varies according to the number of students and the subscription period. However, there. Math Tutoring Online: What is offered? Luckily for parents, there are countless sites out there that seek to assist the younger student in learning math online concepts. There are online games, graphics, and videos that all cater to the elementary school student, and they are free. Complete List of Online Math Resources. Whether you are confused by multiplication,. Elementary Mathematics is organized by grade level. Online Math Learning allows for kids to test different math skills in ways that will make them feel like they’re playing video games rather than being forced to learn.
Online elementary math classes give your child the opportunity to learn and practice all the necessary concepts taught in school, at home, in the comfort of their own home. Topics Covered in Elementary School Mathematics. Your child learns the basic building blocks of mathematics in elementary school.
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All three of DC Prep’s middle school campuses – Anacostia Middle Campus, Benning Middle Campus, and Edgewood Middle Campus – have been recognized by the DC Math Hub and EmpowerK12 this year as citywide math “Bright Spots” for achieving high math growth for students, according to the DC Math Report.
This is the first year a DC Math Report has been released by the DC Math Hub and EmpowerK12. DC Prep campuses have been awarded EmpowerK12’s Bold Performance recognition many times in past years. The DC Math Hub is a coalition at the DC Educational Research Collaborative whose research evaluates the most effective strategies for math instruction. EmpowerK12 is a nonprofit organization whose research highlights bright spots in education at the system, school, and classroom levels.
We are honored by this recognition and proud of our students, staff, and DC Prep community!


Case Studies - Ransom Everglades
Challenges and Goals cont...
Their first priority was to find a multi-dimensional tool for enhancing presentations in mathematics classes.
“We have always believed that technology should be an integral part of the study of mathematics,” said Duty. “As a result, we use a myriad of indispensable yet separate equipment and programs to support our teaching efforts.”
Today, teachers at Ransom Everglades regularly use the Texas Instruments graphing calculators in many of their courses and each student is required to own one. Additionally, the Geometer’s Sketchpad program is used to dynamically discover geometric relationships. The statistics courses use the Mini-tab program to analyze and graph statistical data. Finally, the calculus courses use Excel to discover and graph differential and integral relationships.
“The goal of the Mathematics Department of Ransom Everglades is to equip each student with the skills, knowledge and understanding of mathematics to succeed in all fields of study at the college level and beyond,” said Duty.
To accomplish the teaching of fundamental math concepts as well as the critical thinking skills necessary to use that knowledge wisely, teachers at Ransom Everglades incorporate a variety of methodologies into their daily instruction: class discussions, discovery and cooperative learning, technology and hand-on application projects.
And while it is important to note that each of the hardware and software tools currently being used at Ransom Everglades has been designed with a specific function in mind, Duty and others in the math department were looking for a new technology that would create a more interactive learning environment.


|9/15/2010 3:26:08 PM
|Description||Developed by Welles Wilder, the Swing Index tries to determine "real" price of a stock. The formula takes advantage of relations between current daily prices and prior day readings.
The Swing index ranges from -100 and 100.
Due to the erratic nature of this measure, typically, the Swing Index is utilized via the Accumulation Swing Index, which is the cumulative total of the daily Swing Index values.


Mathematical probability in blackjack
The probability of a blackjack in a single deck game is 4*16/combin(52,2) = 64/ So the probability of four in a row is (64/) 4 = / = 1 in However the actual probability is much less, because as the player gets each blackjack the ratio of aces to cards left in . May 14, · Probability Guide to Gambling: The Mathematics of Dice, Slots, Roulette, Baccarat, Blackjack, Poker, Lottery and Sport Bets [Catalin Barboianu] on UKRAINA-KREDIT.INFO *FREE* shipping on qualifying offers. Over the past two decades, gamblers have begun taking mathematics into account more seriously than ever before. While probability theory is the only rigorous theory modeling the uncertainty/5(8). Suppose that you are playing blackjack against the dealer. In a freshly shuffled deck (standard $52$ cards), what is the probability that neither of you are dealt a blackjack. Blackjack being $2$ c.
Blackjack Probability Odds
View Desktop Version. Doubling down. MaxWell MaxWell 2 2 bronze badges. A first explanation is the following: betting ten dollars each hand, you will in the long run lose an average of 1. In fact, when a lot of fives are used up, your odds will be much higher than if any of the other low cards were used up, even the six point cards.
Blackjack Math – Understanding the Math behind Advantage Play
Blackjack also known as twenty-one or sometimes pontoon is one of the most popular casino card games in the world. The name blackjack comes from the fact that when blackjack was first introduced in the U. One of those was a to-1 payoff for a hand consisting of the ace of spades and a black jack that is, the jack of spades or the jack of clubs. With the current rules, a blackjack hand doesn't even need to contain a jack.
A blackjack game has a dealer and one or more players. Each player plays against the dealer. All players are initially dealt two cards and the dealer is dealt one card face down and one face up these are called the hole card and up card respectively. Each player can then hit ask for an additional card until her total exceeds 21 this is called busting or she decides to stand stop taking cards for the rest of the hand.
Face cards count as 10 and an ace may be counted as 1 or After all of the players have finished, the dealer reveals the hole card and plays the hand with a fixed strategy: hit on 16 or less and stand on 17 or more. The player loses if she busts and wins if she does not bust and the dealer does observe that if both the player and the dealer bust, the player loses.
Otherwise, the player wins if her total is closer to 21 than the dealer's. If the player wins, she gets twice her bet; if she loses, she loses her money. If the dealer and player tie it is called a "push;" the player keeps her bet but does not earn any additional money. If the player's first two cards total 21, this is a blackjack and she wins 1.
Blackjack odds are percentage figures which represent your probability of losing or winning a hand. They can also represent the house edge or their profit margins as well. Usually probability odds don't mean much on the short term, but they clearly average out in the long term and this is why the casinos always win over the long term.
We decided to make a few tables and charts of the most common blackjack probability odds for various scenarios and situations found while playing blackjack. The most important odds percentage represents the dealer's edge in the game. This is the long term advantage that they have which will eventually take your money away. Blackjack is actually one of the most popular games in the casino and also has some of the lowest odds of all the casino games, except casino craps of course.
There is one feature that makes blackjack more desirable than any other casino game. There is actually a way to beat the house edge by increasing your odds. In fact, your probability odds in blackjack can be increase to the point where you would actually be making the profit in the long term, essentially turning the casino into a personal ATM. This practice is known as card counting and casinos don't like this because they know they will be losing money.
Before you start card counting, you should learn "blackjack basic strategy", which is the mathematically correct way to play every move in blackjack to get the best odds. This can lower the house edge to less than 1 percent. This is when you complement basic strategy with card counting to get the highest efficiencies. The first odds chart shows what kind of advantage the player has vs. The first column in the chart is what card the dealer has showing after the cards have been dealt.
The second column of the table shows the dealer's probability of going bust based on each card. The last column shows the advantage the player has and the probability of winning based on the basic strategy theory. Notice that the player advantage goes negative when the 10 cards and ace start showing up. This means the player is more likely to lose. This chart shows the probabilities of going bust after taking a hit.
Моя киска требовала разрядки, хотя бы с искусственным членом. What you want me to be for you today. Remember the brochures featuring a blond, middle-aged woman with AIDS. Попросту не отдавала себе отчета - так много внимания требовал работающий вибратор.


For example, there have been several assignments that would be more useful for an elementary or middle school age group and a subject far less abstract and exact as math. One example would be the storyboard/ visual learning tool that I blogged about here. In this particular assignment we were supposed to have at least two (apparently) hyperlinks. For a math class, I hesitate to have hyperlinks because if students are given permission to go off on the Internet, what is to stop them from merely looking up the answer to the math question rather than figure it out themselves? How would that be different than handing a student a calculator to teach them how to add, multiply, subtract, and divide?
This man starved himself to death because he was afraid of being poisoned!
A right triangle inscribed in a circle!
On a more positive note, this week I learned how to use Geometer's Sketchpad. This is one computer application that I will most definitely use when I get hired to teach. Even though I'm fairly well versed in the ins and outs of Geometry, I had a revelation, an epiphany, an Oprah A-HA! moment when I had a triangle inscribed in a circle so that the two of the vertices of the triangle were on the diameter of the circle and I moved the third vertex along the arc. By theorem, the angle of the vertex formed by the point on the arc is a 90° angle. Up until I wiggled that triangle around, I have to admit it was something I memorized, but was skeptical about. Using Geometer's Sketchpad it became a concrete knowledge for me. Imagine the possibilities of incorporating such software into my classroom! I think this would be far more useful than a storyboard. Even though they both are visual learning techniques. The difference is that a storyboard is geared towards stories, and Geometer's Sketchpad is geared towards math (and maybe science).


My fifth graders just finished their ordered pairs projects, and I am absolutely amazed by their creativity!
The assignment asked that kiddos create a picture that included a minimum of five shapes, used only straight lines, and was located in all four quadrants.
Students also had to create an organized table for each shape that included the quadrant number and ordered pair for each point. This paper would later be used as a directions page for another student to recreate their picture.
Take a look at their amazing work!
For board work the next day, each kiddo was given a blank four quadrant graph and another student’s direction page. It was so much fun to see how the images were redrawn. Some directions were spot on (all ordered pairs and quadrants were accurate) and the redrawn picture looked identical to the original. Others though, not so much!
I will definitely be doing this project again next year!


SCIENCE AND HUMANITIES
Mathematics courses embedded with MATLAB software has been introduced for the First and the Second-semester B.E & B.Tech programmes.
Symbolic Math toolbox with MATLAB software
Physics Laboratory – Approved Research Laboratory
|S.No||Name of the Equipments|
|8.||Micrometer slide comparator|
|9.||Four Probe setup|
|10.||Hall Effect setup|
|14||Optical isolation table|
Chemistry Laboratory – Name of the Major/Minor Equipments/Apparatus
|S.No||Name of the Equipments|
|1.||Digital pH meter|
|3.||Hot plate with thermostat|
|6.||Digital Conductivity meter 601 – EI|
|7.||Refrigerator 185 lit -GOE19B2|
|8.||Digital Flame Photometer Model 123|
|9.||Cyber scan bench top conductivity / TDS meter Model 510|
|10||Flash point apparatus|
|11||Fire point apparatus|
|12||Viscometer – Saybolt Viscometer|
|13||Cloud & Pour point apparatus|
|15||Hot air oven|
|16||Hotplate with stirrer|
|19||Double distillation unit|
|20||Stirrer (Magnetic and Mechanical)|
|26||Shimadzu digital weighing balance|
|28||Water testing electrodes|
|29||Computational facility – Gaussian software|
Language Laboratory – CALL HUB (Computer Assisted Language Learning)
The CALL Hub is equipped with 75 computers that are connected by LAN. It facilitates students’ learning experience by providing adequate exposure to language tutorials. The students are also exposed to web resources, self-study resources and online tutorials that imparts training learners belonging to all academic levels.
There are several programmed lessons and self-study language packages available in the CALL HUB to enhance the communicative competence of the technocrats.
The following is the list of language programmes that are used in our language lab.
- Self-study material for IELTS & TOEFL
- Programmed lessons on Spoken English
- Body Language – Nonverbal Communication
- Interview Etiquette
- Presentation skills and Group Discussions Business Communication
STUDY MATH AT KCT:
The Mathematics in Computer Algebra System (CAS), is a modern computing technology that provides great learning and teaching opportunities to both students as well as instructors. MATLAB is one of the most popular CAS programs that is widely used in mathematics classrooms especially at KCT. As more and more universities are adopting its use in education, it is necessary to study and analyze how the software could be used in teaching and learning of mathematics. MATLAB has been used in problem solving, computation, and visualization of mathematics through mathematical explorations etc. MATLAB is a technology that is used for developing mathematical thinking, concepts and skills, and a source of motivating students for learning mathematics. It is also a very useful tool in demonstrating connections in various underlying mathematical concepts in the teaching and learning processes.
One of the greatest benefits of computer technology is the accessibility of the mathematical concepts through visualization. MATLAB is one of the best known software which contains mathematical data visualization capabilities. MATLAB as a visualization tool has been used in the courses like linear algebra, calculus and differential equations etc. MATLAB is used as a visualization tool for applications of linear algebra course. MATLAB was used to teach undergraduate engineering mathematics students, Burton et al (2004).
The aim of introducing MATLAB in curriculum was to support students’ visual and graphical understanding of mathematics and their access to the numerical computation of the course.


F-1 nonimmigrant students who have U.S. degrees in certain programs in the fields of science, technology, engineering, or mathematics (STEM) are eligible to apply for a twenty-four-month extension of Optional Practical Training (OPT), in addition to the standard twelve months of OPT available to all F-1 nonimmigrant students.
As of January 21, 2022, the U.S. Department of Homeland Security (DHS) has added twenty-two fields of study to the list of programs that qualify for STEM OPT. The new fields of study include bioenergy, general forestry, forest resources production and management, human-centered technology design, cloud computing, anthrozoology, climate science, earth systems science, economics and computer science, environmental geosciences, geobiology, geography and environmental studies, mathematical economics, mathematics and atmospheric and oceanic science, general data science, general data analytics, business analytics, data visualization, financial analytics, other data analytics, industrial and organizational psychology, and social sciences, research methodology, and quantitative methods.
This expansion is the first move of several upcoming immigration policy changes announced by the Biden administration in an effort to attract and retain STEM talent within the United States. Ogletree Deakins’ Immigration Practice Group will continue to monitor developments with respect to these and other policy changes and will post updates on the Immigration blog. Important information for employers is also available via the firm’s webinar and podcast programs.


by J. Wagner and T.L. Stanton* (6/12)
- The Pearson square ration formulation procedure is designed for simple rations.
- In order for the square to work, follow specific directions for its use.
- Nutrient contents of ingredients and nutrient requirements must be expressed on the same basis (i.e., dry-matter or “as-fed”).
The Pearson square or box method of balancing rations is a simple procedure that has been used for many years. It is of greatest value when only two ingredients are to be mixed. In taking a close look at the square, several numbers are in and around the square. Probably one of the more important numbers is the number that appears in the middle of the square. This number represents the nutritional requirement of an animal for a specific nutrient. It may be crude protein or TDN, amino acids, minerals or vitamins.
In order to make the square work consistently, there are three very important considerations:
- The value in the middle of the square must be intermediate between the two values that are used on the left side of the square. For example, the 14 percent crude protein requirement has to be intermediate between the soybean meal that has 45 percent crude protein or the corn that has 10 percent crude protein. If barley is used that has 12 percent crude protein and corn that has 10 percent crude protein, the square calculation method will not work because the 14 percent is outside the range of the values on the left side of the square.
- Disregard any negative numbers that are generated on the right side of the square. Be concerned only with the numerical differences between the nutrient requirement and the ingredient nutrient values.
- Subtract the nutrient value from the nutritional requirement on the diagonal and arrive at a numerical value entitled parts. By summing those parts and dividing by the total, you can determine the percent of the ration that each ingredient should represent in order to provide a specific nutrient level. Always subtract on the diagonal within the square in order to determine parts. Always double check calculations to make sure that you did not have a mathematical error. It also is very important to work on a uniform basis. Use a 100-percent dry-matter basis for nutrient composition of ingredients and requirements and then convert to an as-fed basis after the formulation is calculated.
Corn represents (31.0 / 35.00) x 100 of the ration, or 88.57 percent. Soybean meal represents (4.0 / 35.00) x 100 of the ration, or 11.43 percent. Check of the calculation:
|88.57 lb corn x 10.0% CP||=||8.86|
|11.43 lb SBM x 45.0% CP||=||5.14|
|100.00 lb mixture contains||=||14.00 lb CP, or 14 percent.|
Using More Than Two Ingredients
It is possible to mix more than two ingredients using the Pearson square. For example, to prepare a 15 percent crude protein mixture that consists of a supplement of 60 percent soybean meal (45 percent crude protein) and 40 percent corn gluten meal (45 percent crude protein), and a grain mixture of 65 percent corn (9 percent crude protein) and 35 percent oats
(12 percent crude protein), take the following steps.
Since only two components can be used in the Pearson square method, the ingredients are combined first as follows:
|60% SBM x 45% crude protein||=||27.0|
|40% CGM x 45%||=||18.0|
|Protein in supplement mixture||45.0%|
|65% corn x 9.0%||=||5.85|
|35% oats x 12.0%||=||4.20|
|Protein in grain mix||10.05%|
|5.0 parts x 60%||=||3.0 parts SBM|
|5.0 parts x 40%||=||2.0 parts CGM|
|30.0 parts x 65%||=||19.5 parts corn|
|30.0 parts x 35%||=||10.5 parts oats|
|(3.0 / 35.0)||=||8.57% SBM|
|(2.0 / 35.0)||=||5.71% CGM|
|(19.5 / 35.0)||=||55.72% corn|
|(10.5 / 35.0)||=||30.00% oats|
|8.57 lb SBM at 45% CP||=||3.86 lb|
|5.71 lb CGM at 45% CP||=||2.57 lb|
|55.72 lb corn at 9% CP||=||5.01 lb|
|30.00 lb oats at 12% CP||=||3.60 lb|
|100.00 lb contains||15.04 lb or 15% CP|
Expressing Feed Composition
The crude-protein value of a feed or the percentage of any other component (e.g., calcium or phosphorus) can be expressed several ways. The two most common methods of expression are on an as-fed basis or dry-matter basis. Use the following procedure to calculate composition on a dry-matter basis.
Crude protein value on an as-fed basis divided by dry-matter content of the feed times 100 equals the crude-protein content on a dry-matter basis. If alfalfa hay is used as an example, the crude protein value is 17 percent on an as-fed basis. On a dry-matter basis, the crude protein value of the hay is calculated as follows: 17 / 0.91 (moisture content of 9 percent) times 100 equals 18.7 percent crude protein.
To determine the total digestible nutrient (TDN) content of the above alfalfa on a dry-matter basis, follow the same procedure: 50 percent (TDN value on an as-fed basis) divided by 0.91 (dry-matter content of the feed) times 100 equals 54.9 percent TDN on a dry-matter basis. Likewise, the crude-protein content or the TDN value also can be expressed on the basis of any given dry-matter level. For example, if you use a 90-percent dry-matter basis, use the following calculation. Given a TDN value of 76 percent and a dry-matter content of 86 percent (14 percent moisture), what would be the TDN value of this feed on a 90 percent dry-matter basis?
(76 x .90) / .86 = 79.5 percent TDN on a 90 percent dry-matter basis.
Ration Composition Calculations
If you know the dry-matter composition of a specific ration and want to determine what that composition will be on an as-fed basis for mixing, make the calculations shown in Table 1.
Conversely, if you know the “as-fed” composition of the ration and the dry matter of each ingredient, determine the ration dry-matter composition as shown in Table 2.
|Table 1: Converting from dry matter to as-fed.|
|Corn silage||70||35||70/.35 = 200||(200/233) x 100 =||84.84|
|Alfalfa||30||90||30/.90 = 33
|(33/233) x 100 =||14.16|
|Table 2: Converting from as-fed to dry matter.|
|Corn silage||65||35||65 x .35 = 22.75||(22.75/54.25) x 100 =||41.94|
|Alfalfa||35||90||35 x .90 = 31.50
|(31.50/54.25) x 100 =||58.06|
1 J. Wagner, Colorado State University professor, animal sciences and general manager, Southeastern Colorado Research Center; T. Stanton, former Extension feedlot specialist and professor, animal sciences. 9/93. Revised 6/12.
Colorado State University, U.S. Department of Agriculture and Colorado counties cooperating. Extension programs are available to all without discrimination. No endorsement of products mentioned is intended nor is criticism implied of products not mentioned.
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The American Mathematical Society (AMS) citation style guide used in mathematics. Specifically, Chapter 10 of the AMS Style Guide focuses on how to cite references.
There are three ways to cite references in-text. Select one and use in consistently in your paper.
1. Numbers within Brackets
Ex. Mathematicians help improve efficiency of data centers use Markov chains .
Note: With numerical citations, references should be numbered sequentially. If a reference is repeated, do not give it another number; rather, use the original reference number.
2. Name & Year
Ex. Mathematicians help improve efficiency of data centers use Markov chains [Smith2019].
Note: Use the author's last name and year of publication.
3. Alphanumeric Abbreviation
Ex. Mathematicians help improve efficiency of data centers use Markov chains [S19].
Note: You utilize the first letter of the last name, while also shortening the year.
If you use the Numbers within Brackets in-text citation style, use this format for your references:
[#] Author’s name as it appears. Title of book. Publisher, City of publication, Year of publication. Mathematical review number.
Online Journal Article
[#] Author’s name as it appears. Title of article. Shortened Journal Title. Volume Number (Year of publication), issue number, page range, DOI, mathematical review number.
If you use the Name & Year or Alphanumeric Abbreviation in-text citation style, instead of putting the reference number in brackets (ex. ), you will use whatever in-text citation style used in the paper and order the references alphabetically.
[DL99] J. Denef and F. Loeser, Germs of arcs on singular algebraic varieties and motivic integration, Invent. Math.
135 (1999), no. 1, 201–232, DOI 10.1007/s002220050284.MR1664700
Note: These are just some examples, please refer to the AMS Style Guide for more in-depth coverage of citations/references.


Learning to Lead in a Technical World
The Technology Student Association (TSA) is a national career and technical student organization dedicated to fostering personal growth, leadership, and opportunities in Science, Technology, Engineering, and Mathematics (STEM). Members of TSA apply and integrate these concepts through co-curricular activities, competitions, and related programs.
2017 COTSA State Conference Results
You can find the results for the 2017 Colorado TSA State Conference here:
Or…you can download the awards presentations as PDF documents:


Measuring square / rectangle yards
Step 1: Draw a diagram of the area. If you have the original house plans, that could help immensely.
Step 2: If your yard is not square or rectangular, section your yard on the sketch to make it easier to measure each area accurately.
Step 3: Using a tape measure, measure of each section and write them on your drawing.
Step 4: Calculate each area and total up. Always double check your measurements, adding 3 to 5% for miscalculations.
Measuring triangle shape yards
If you have a triangle shape yard, measure your length by width and divide the total amount by 2.
Measuring oval yards
If you have an oval shape yard, measure the width in a couple of places evenly along the length of your yard, as below. Add the measurements together then divide by the number of areas you measured to find the average width, then multiply by the length for the total amount of turf needed.
Measuring circular lawn area
Round yards are measured by measuring the radius then multiply the radius x radius x 3.14 (A = Pi x R²).


14th International Congress of Phonetic Sciences (ICPhS-14)
San Francisco, CA, USA
The work reported in the paper explores the possibility of formulating (parts of) a model for Danish intonation in mathematical terms. It is hypothesised that - if the prosodic phrasing is known - F0 of a stressed syllable can be described by a linear function with two independent variables, viz. its position in the sentence and in the prosodic phrase. Analysis of a material of read-aloud sentences shows the hypothesis to be tenable. Further analysis indicates that the mathematical model can be used for generating sentence and phrase intonation contours in a text-tospeech system.
Bibliographic reference. Petersen, Niels Reinholt (1999): "Modelling Danish sentence and phrase intonation", In ICPhS-14, 925-928.


Years 5 & 6 2023 - 2024
Our Year 5 & 6 Team
YEAR 6 - Please visit the above link regarding the upcoming visit the Robinwood
Mr Brooke-Mawson (5DBM), Mrs Morgan (5/6JM), and Miss England (6GE)
Educational Support Assistants
Mrs Lloyd, Miss Hulme, Mrs Holmes, Mrs Treherne, Miss Akhtar, Mrs Newman-Burke
Regular Weekly Timetable
PE: Monday (5DBM), Tuesday (5/6JM) and Wednesday (6GE)
Library days: Friday Class 5, Class 5/6 and Class 6 will all go to the library on Fridays
HOMEWORK: Our homework focuses on basic skills that support the foundations of learning: spellings, number facts/times tables and reading (listening to your children read).
TT ROCKSTARS: Your child can use these safely at home at any point under your supervision and monitoring. TT Rockstars is a carefully sequenced programme of daily times table practice. You can also check on their progress at any stage. Children have their own log ins to access TT Rockstars at home. Other maths apps may also be used, information will be shared by class teachers.
NUMBOTS: Your child can use Numbots safely at home at any point under your supervision and monitoring. Numbots is all about every child achieving the "triple win" of understanding, recall and fluency in mental addition and subtraction, so that they move from counting to calculating. Children have their own log in which is in their reading record.
MYMATHS: MyMaths is an interactive online teaching and homework subscription website for schools that builds pupil engagement and consolidates maths knowledge. Each week children will be set an online homework to complete. There are also a range of games for the children to play which link to what they have been learning in class.
1 MINUTE MATHS (WHITE ROSE MATHS HUB): 1-Minute Maths offers children engaging and easily accessible practice in basic number. There's no specific route or starting point. Having chosen a topic, each user answers a series of randomly generated questions (a different set of questions every time means they learn the concept, not a sequence of answers).
READING BOOKS: Reading books are handed out on Monday and are to be returned on Thursday. Please read as regularly as possible with your children.
As we have a mixed Year 5 / Year 6 class, as well as a Year 5 class and a Year 6 class, we have a 2 year rolling programme to ensure that all aspects of the curriculum are taught in a progressive manner. Children build upon prior learning, they do not simply repeat learning. Below is our 2 year curriculum overview for UKS2, showing areas of learning for each Foundation Subject. We are currently in Year B. We will move to Year A in September 2024.
To see the whole school curriculum overview, you can download the file at the bottom of the page.
Please find below the overview of learning in UKS2 for Autumn 2023
The I Can Help Information that was shared with parents in October 2023 can be found in the files below.
Files to Download
Years 5 & 6: News items
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