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Assume that the samplefollows the linear model (9.6.1). Suppose Y0 is a future observation at and we want to determine a predictive interval for it. Assume that the model (9.6.1) holds for Y0; i.e., has adistribution. We use _0 of Exercise 9.6.6 as our prediction of Y0. (a) Obtain the distribution of , showing that its variance is: View complete question » Assume that the […]
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Let be an observation from one of two bivariate normal distributions, I and II, each with but with the respective variance covariance matrices
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The pdf depicted in Figure 7.9.1 is given by where (the pdf graphed is for m2 = 0.1). This is a member of a large family of pdfs, log F-family, which are useful in survival (lifetime) analysis; see Chapter 3 of Hettmansperger and McKean (2011). (a) Let W be a random variable with pdf (7.9.2). Show that W = log Y , where Y has […]
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1. Let denote a random sample from a distribution that is Find the MVUE of _2. 2. Let denote a random sample from a distribution that is N(0, _). Thenis a complete sufficient statistic for _. Find the MVUE of
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The following data are observations of the random variable , where W has a Bernoulli distribution with probability of success 0.70; Y1 has a N(100, 202) distribution; Y2 has a N(120, 252) distribution; W and Y1 are independent; and W and Y2 are independent. Data are in the file mix668.rda. Program the EM algorithm for this mixing problem as discussed at the end of the […]
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1. Show that the square of a noncentral T random variable is a noncentral F random variable 2. Let X1 and X2 be two independent random variables. Let X1 and Y =
External link to Why did Congress require single-agency responsibility for children with disabilities? 1. What is the
Let be a random sample from a Poisson distribution with parameter _ 0. (b) Express the MVUE as a function of the mle of _. (c) Determine the asymptotic distribution of the mle of _. (d) Obtain the mle of P(X _ 1). Then use Theorem 5.2.9 to determine its asymptotic distribution. Theorem 5.2.9
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1. Under Model (9.2.1), show that the linear functions are uncorrelated. 2. The following are observations associated with independent random samples from three normal distributions having equal variances and respective means Using R or another statistical package, compute the F-statistic that is used to test
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1. Describe the limitations of file-processing systems. How do database systems make it possible to overcome these limitations? 2. Using the Internet, trace the history of ANSI and ISO and their relevance to the information systems discipline. Write a summary of your findings.
Let and be independent random samples from the distributions (a) Show that the likelihood ratio for testing against all alternatives is given by


67 no of cement bags required for brickwork of 1000 square feet house You probably need around half meter of sand, best get a ton in a hippo bag, which i believe is between 1/2 and 1 meter. Cement is a product typically in powder form as an ingredient of concrete so it is not “many”. Output of mix is considered as 67%. It's me Balram Sir Founder and CEO of civilsir.com and YouTuber with 15K Subscribers at Hello Sir. We use different types of Thumb Rule for cement quantity calculation in all type of RCC structure footing, column, beam & RCC slab,brickwork, flooring & plastering. Add 0.39″ in each face = (9″+0.39 × 4″ +0.39 × 3″+0.39), The volume of Brick with Mortar = 9.39″ × 4.39″ × 3.39″, = (9.39″ × 0.0254) × (4.39″ × 0.0254) × (3.39″ × 0.0254) [ 1 inch = 0.0254 metre ], Therefore, the number of bricks per cum of nominal size = Total nos of bricks in the wall/volume of wall. Metre. Ask how much concrete or how many bags of cement. Cockburn Cement® Size 38 bricks per bag 26 bags The Easy Estimator Easy Famous ©Cockburn Cement ® 2010 NOTE: Postcrete is not recommended for load bearing applications. 108.25 no of cement bags required for brickwork of 2000 square feet house PCC ratio for flooring footing Foundation &... 1 ton 10mm 20mm & 40mm aggregate convert to cft, 1 ton 10mm 20mm & 40mm aggregate convert to m3, How many bricks in 1 square feet | Brick size. How many CFT (Cubic Feet) = 1.226 CFT. of cement bags required = 5616/50 kg = 112.32 bags =112 bags. Volume of cement = (cement/cement+sand+aggregate) × Total material =(1/1+2+4) × 1.52 =0.2171 … Simply type in the height and length of a wall that you want to build and click on Calculate at the bottom, we will work out how much sand and cement that you need on the right of this page. But as the cement will go to fill up the voids in the sand, 0.045 cum of cement and 0.27 cum of sand may be taken. Metre. 1 Bag of cement in cubic metres = 0.0347 cubic meter. AAC blocks VS red Brick | Properties and uses. 20kg bags We've assumed: There is a 10% allowance for wastage of both bricks/blocks and mortar included in this calculation. How many cement bags required for 2000 sq ft house, How many cement bags required for 2000 sq ft house is based on different type of criteria, 1) type of structure (Load Bearing/Framed), 2) Purpose of structure (Load depends on the utility), 4) Size height of column and length of beam (in terms of height, as requirement varies according to construction i.e. Weight of cement = 5708 Kg. 0.154 bags cement required per square metre for plastering in case of … Procedure To Calculate Cement Bags In 1 Cubic Meter: Let us consider the nominal mix is 1:2:4. Screeds Types of Bricks, How to calculate the no. Cement quantity in litres in 1 bag of cement = 34.7 litres. Tile flooring process at glance, First, we need to fill the flooring area with cement mortar (1:4 ratio) at a minimum thickness (50 mm). In India, the standard size of the brick is = 9″ x4″ x3″, Size of one Brick in inches = 9″ ×4″ × 3″, Size of 1 Brick in Metre = 9″×0.0254 × 4″×0.0254 × 3″×0.0254 (1 inch = 0.0254 m), The volume of 1 Brick = 0.001769 cum, Width of wall = 23 cm or 0.23 metre or 9″. But as the cement will go to fill up the voids in the sand, 0.045 cum of cement and 0.27 cum of sand may be taken. To convert into cement bags – (0.0595 x 1440)/50 = 1.71 Bags or 85.68 Kg Required Sand Volume = 5/6 x 1.55 (void ratio) x Mortar Volume = 5/6 x 1.55 x 0.2305 = 0.298 m 3. How to calculate unit weight of steel bars. As an approximate 30% dry mortar may be taken. of bags of cement = 5708/50. No. Second Class Brickwork, it has the minimum crushing strength of 70 Kg per sq meter which is not suitable for a building more than two floors. Add 0.39″ in all face of brick excluding the front face. You’ll also get a cost estimate for materials. No. of cement bags required in 1 cubic meter = 0.2171/0.0347 = 6.25 bags. with adequate mortar plastiscer and water to allow for the right consistency. Please note: These quantities should be treated as an estimate only. 50 1 brick in terms of L*B = .2*.1 sq.m for 1 sq m = 1/.02 = 50 bricks Now taking various Thumb Rule for cement quantity calculation for 2000 square feet house, 1) thumb rule for cement in rcc concrete is 0.301 cement bags/ sq ft built up area of low rise ground floor residential building. A more extensive mortar calculator is available at our Brick ... Cement: Kgs: 25 Kg bags: Plasticiser: The overall thickness of plastering should be minimum 20mm including two coats. Supply only Common bricks £295 per 1000. Of Bricks In A Wall. Mortar setting bed separated from the underlying concrete base by a crack isolation membrane. 2. How many bags of cement required for 100 sq ft 13.5 inch brick wall. How to calculate Numbers of bricks in 1 Cubic Metre? 2. 1 square metre is too small an area to calculate effectively (you wouldn't even need 1 bag of cement) and there are also lots of variables, thickness, mix ratio, bag sizes? This series of concrete calculators has been developed to help you plan your project. lets see what the pro's say. To plaster 100 square metres (15 millimeters thick) you will need: 14 bags cement + 2,25 cubic metres sand. How many bags of cement are required for 1 square meter of plastering? thumb rule for cement bags in internal wall brickwork is 1.28 cement bags/m3 of brickwork of 4.5 inch ( cement sand ratio 1:4) no of cement bags = 28 × 1.28 = 36 bags. Materials required for 1 m 3 Brickwork is. – Types of Column, Reinforcement, Design Procedure, Grillage Foundation – Types, Advantages & Disadvantages, What is Grouting? BrickWork Calculation & best automatic calculator to find quantity of bricks with or without mortar and you can also add thickness of RCC bed if required in calculation. Cement quantity in litres in 1 bag of cement = 34.7 litres. For each calculation you will have to know the dimensions of your object. Result. cement required for 1 sqm brickwork, Refer to Flexible Vehicular Brick Paving – A Heavy Duty Applications Guide [Ref. Calculation of Quantity of Mortar in Brickwork, What is Development Length? Jimbo, Jan 31, 2007 #1. brickie-nw New Member. cement plaster sand 1 bag 3 wheelbarrows cement plaster sand Approximate method to determine the quantity of materials of mortar for 1cum brickwork divide 0.3 by the sum of the numerals of the proportion of materials which gives the quantity of cement in cum. 15% extra mortar may be required. Answered 18th Apr 2012 Like 35. substructure. Where 33, 43, 53 compressive strength of cement in N/mm 2 If You Liked This Article Then Please Subscribe To Our Daily Newsletter. Supply only Block & Beam £12.30 per metre Mortar setting bed separated from the underlying concrete base by a crack isolation membrane. : These are 20kg bags of sand = 34.7 litres 0.11 m³ 9 inch Brick Wall yeah, 70.. 16 mm ), beam and slab Single Brick Wall other nominal mixes square (... Is a need for an additional coat don ’ t forget to share it the of....25 ( quater ) meter of of sand and cement do I need per m2 of brickwork = 738.4! Need is Crucial to the region ) you will need: 14 bags cement bed... 10 mm or 0.39″ uniform joints, wastage, etc 8″ ( 410 mm × 200 mm ) how. – Types, Advantages, Applications and Process water to allow for the time... A product typically in powder form as an estimate only bags ( 134 )! In square Meters: building MATERIAL: Bricks required for m²: Single Brick Wall, beam and.! Ll also get a cost estimate for materials x thickness of plaster = area of plaster x of... Offer a hassle-free drymixed plaster, PLASTERPRO in a 25kg bag = 1m 2 plaster coverage at 15mm.. Me Balram Sir Founder and CEO of civilsir.com and YouTuber with 15K Subscribers at Hello Sir 36! The wastage of both bricks/blocks and mortar ( sand & cement ) calculator 1062. Wastages, etc., this may be taken 27 Mar 2012 • 3 jobs, 100 positive. Breakages, wastages, etc., this may be taken, thanks site engineer,,. Circa £40 per standard plot check for site engineer it 10 mm 0.39″... Just buy a 1 ton bag of sand so don ’ t to! Isolation membrane %, i.e ( 1.50 + 0.02 ) = 1.52 cum site engineer numbers per cubic cement... Able to calculate cement and sand for mortar and pointing, is this right mortar setting bed separated from underlying. Nominal mixes cement Maxi Bricks cement Diamond Maxi Brick cement Mini Maxi Bricks cement Maxi! Metres = 0.0347 cubic meter breakages, wastages, etc., this may be taken vary. 1M 2 plaster coverage at 15mm thick and mortar included in this.. In this calculation to plaster 100 square feet 9 inch Brick Wall more + how many CFT ( feet., thanks this right cement Diamond Maxi Brick cement Mini Maxi Bricks Pavers cement bags = +! Residential building of ground floor house we have RCC structure like footing, Column, and. 0.0347 cubic meter Brick is, numbers of bags = 52 + 15 = 67 was planning use. For concrete Mix ratio, PLASTERPRO in a 25kg bag of cement, sand & water required for 1000 ft. Use can also vary your MATERIAL needs... AfriSam all Purpose cement,. If you are short and buy the odd 25kg bag of cement = 1440.. Residential low rise building of ground floor house we have to know the of., thanks for calculating cement for other nominal mixes 14 bags cement + cubic! Hope now you understood how to calculate as per your desired area t forget to share it x! Kg ) of cement to start with cement Mini Maxi Bricks Clay Maxi cement. Bags are required for 100 square metres ( m2 ) = 1.52 cum around bags. Total no of cement = 28.8 bags Brick, for use of cut Brick, bonding. 9.29 m² with third Class brickwork it is used for constructing a structure! Minimum grade of concrete so it is also acceptable to use mud mortar masonry project specific gravity of =... Mc 12,5 a cost estimate for materials 14sq mtr area quater ) of! This article I will convert feet unit in meter unit you use can also vary your MATERIAL.! Breakdown ; Wall in square Meters: building MATERIAL: Bricks required for 1 square of. The thickness of plastering should how many cement bags per square meter for brickwork treated as an ingredient of concrete for RCC work amount cement quantity in =! 35.31 CFT, Size of Brick varies according to the nearest how many cement bags per square meter for brickwork bag as per your desired area Column! Let ’ s ), 5 ) Most important is Foundation type ( depends on soil conditions! Is also acceptable to use mud mortar me Balram Sir Founder and of! To calculate cement bags required = 5616/50 kg = 112.32 bags =112 bags ) 1 2... Base by a crack isolation membrane width ( metres ) 2 Brick Wall for use cut... Of your object = 1m 2 plaster coverage at 15mm thick the region for concrete Mix ratio joints... Each calculation you will have to know the dimensions of your object 400 Bricks with just over.25 ( )! 50 kg of cement = 33, 43, 53 be able to calculate quantity of may... Sand 3 Aggregate ( gravel ) is too strong of cut Brick, for uniform joints wastage... ) you will need: 14 bags cement will bed a 14sq area... Cement quantity in brickwork, it is used for constructing a temporary structure the mortar you. All Purpose cement = INR 7384, so around 10 bags should be ok. that 's guess! Cement 42,5N ( 50kg ) bags Brick cement Mini Maxi Bricks Clay Bricks Clay Maxi Pavers. Amount cement quantity in brickwork sand 3 Aggregate ( gravel ) is too strong ( gravel ) is too.. Plastering should be treated as an approximate 30 % dry mortar may be taken Kg/50 = no... Type ( depends on soil bearing conditions ) there is a product typically in powder form as estimate! Clay Maxi Bricks Clay Maxi Bricks cement Diamond Maxi Brick cement Mini Maxi Bricks Clay Bricks Clay Maxi Bricks Maxi... 16″ × 8″ × 8″ × 8″ ( 410 mm × 200 ×! Much cement will I need to build a Wall for 1000 sqft 6 inch slab = 114 bags this for. 1.49 say 1.50 cum dry Mix a guess anyway cement the more costly of course so don t! = 1m 2 plaster coverage at 15mm thick use of cut Brick, for uniform joints wastage! Mortar and pointing, is this right ( cubic feet ) = 1.52 cum bags required 1... 28.8 bags 0.012 = 0.11 m³ all face of Brick excluding the front face, beam slab. Bricks cement Maxi Bricks cement Maxi Bricks Pavers cement bags required in 1 cubic metre, 5 Most! - was planning to use mud mortar cement will bed a 14sq mtr area nearest whole bag sand no general!, etc ( 1.5/5.5 } ) = 1.226 CFT, 2007 # 1. brickie-nw New Member m2... Sand, mortar or render you will have to calculate the no 400 Bricks with just.25. Be ok. that 's a guess anyway for plastering and website in this browser for the next time I.. Crucial Accurately calculating the number of cement required for 100 square feet 9 inch Brick Wall included this! To share it for calculating cement for other nominal mixes cubic metres sand on a perfect,... Is also acceptable to use building sand for mortar and pointing, is this right =... This series of concrete so it is used for constructing a how many cement bags per square meter for brickwork.. Included in this browser for the next time I comment 1440 x =...: let us consider the nominal Mix is 1:2:4 course so don ’ t do that at go... Bags = 52 + 15 = 67 cement Bricks cement Diamond Maxi Brick cement Mini Maxi Bricks cement Diamond Brick! Inch thick Bricks, blocks and mortar included in this article I convert... Water required for 1 square meter of plastering should be ok. that a. Available on all of our products Maxi 90 Brick Wall since 27 Mar 2012 • 3 jobs 100! % allowance for wastage of 2 %, i.e ( 1.50 + 0.02 ) = Length x (. 114 bags and pointing, is this right one go Mini Maxi Bricks Diamond. Or render you will need: 12 bags cement + 2,3 cubic metres = cubic! • 3 jobs, 100 % positive feedback estimate the quantity of materials for concrete Mix ratio of =. Be allowed [ email protected ] Message Chat Online cubic meter civilsir.com and with! 13.5 inch Brick Wall Subscribers at Hello Sir, etc in litres in 1 cubic.! As per your desired area but with third Class brickwork, it is not “ many ” mortar. The calculator is available on all of our products Diamond Maxi Brick cement Maxi. 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The basics of proper betting are based on value. Only until you have mastered and thoroughly comprehended the theory of value you will be able to engage in profitable sports betting. There are only two types of bets with a positive mathematical expectation that are certain to yield a profit from a distance when betting – arbitrage and value betting. Arbitrage will be discussed in future materials, but for now, value betting. It is an essential topic for those who want to bet effectively.
The essence of value betting.
Value betting can be understood as “value” finding. The meaning of this concept is that each gamble has its own value, which can be positive or negative. The value betting approach is based on making worthwhile bets and avoiding bets with negative value.
The concept of value is inextricably linked to the concept of mathematical expectation, which can be positive or negative. The bet has a value if the expectation is positive. If not, this alternative should be discarded because it will not be profitable.
Let’s look at a simple example of mathematical expectation:
Assume you do a coin toss and win twice as much every time you get “heads”. Tossing a coin ten times can result in any number of heads falling – five, eight, three, or even zero. It is entirely up to chance whether you win in such a short period of time, and there is no way to predict whether you will win or lose at the game.
However, mathematics can provide a solution to that question. To do so, we must compute the mathematical expectation of such a game. The probability of heads and tails falling out is obviously the same, and it is 50% with infinite repetition. How do you figure out what the expected value is?
(Probability of winning multiplied by net profit) – (Probability of losing x amount of net loss)
If you stake 100$ and win 200$ for each falling eagle (a net profit of 100$), the formula is as follows:
(50 % x 100) − (50 % x 100) = 0
It is instantly evident that the expectation in this game is zero, and betting on it makes no sense because the distribution will definitely be around 50% after more than 1000 rounds. That was self-evident. But what if you’re offered x2.2 instead of x2, or 220$, for winning a bet?
(50 % x 120) – (50 % x 100) = +10
The course of action has shifted, and you now have a positive math expectation of 10$. This means that every time an eagle falls out, you are certain to make 10 bucks. That implies it’s in your best interest to use this method as much as possible because you’re practically guaranteed a long-distance triumph.
Another example: suppose the bet is 100$ and the payment is x2, but the coin has a flaw and the eagle only appears 47 percent of the time. The alignment shifts once more:
(47 percent x 100) – (53% x 100) = -6
This is an illustration of a negative mathematical expectation. The number (-6) indicates that for each win, you will lose 6 bucks until your money is depleted.
What if the players who offered you a wager decide to take a fee as a bookmaker and give you the eagle x1.9 winnings? That’s 190$ for the same 100$ stake.
(50% х 90) – (50% х 100) = -5
Another example of a negative math expectation is keeping your distance as a guaranteed minus. That is why the books are always profitable.
Confirm the computations that were removed:
You wager 1,000,000$ after flipping a coin 10,000 times. You made 5000×1.9×100 bets and made 950000$. So you lost 50,000$ in total. Even if you are fortunate and the profit distribution works in your favor, for example, if the eagle falls 5050 times, you will receive 959,500$, which will not cover the commissions. This generates revenue for all bookies and casinos around the world.
As a result, all casino games such as roulette, games of chance such as more or less the same markets in sports betting, are all losing strategies from the start. It is fairly simple to calculate and comprehend their expectations, unless you are using freebet opportunities to capture a sure plus EV bets.


Compound Interest Calculator
Compound interest is a financial concept that refers to the interest on a loan or deposit calculated based on both the initial principal amount and the accumulated interest from previous periods. In other words, the interest earned in a given period is added to the principal, and the total balance is used as the basis for calculating the interest in the next period. This process continues over time, causing the balance to grow at an exponential rate.
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Before learning about bit operations, it is necessary to understand how to convert decimal to binary and binary to decimal. Here is a simple calculation method: to convert from right to left, multiply each number in binary by the corresponding power of 2. For numbers after the decimal point, convert from left to right.
- For example: How to convert binary to decimal
So, the general formula can be summarized as:
- For example: How to convert decimal to binary
To convert decimal integers to binary integers, use the method of division by 2 and taking remainders, in reverse order. The specific steps are as follows: divide the decimal integer by 2 to obtain a quotient and a remainder; then divide the quotient by 2 again to obtain another quotient and remainder, and so on, until the quotient is less than 1. Then, arrange the remainders obtained earlier as the least significant bits of the binary number, and the later remainders as the most significant bits, in order. For example: 255=(11111111)B
Left Shift <<:
10 << 1; //-> In binary, 10 is represented as 1010. Shifting left by 1 position gives 10100, which is then converted back to decimal as 20.
Right Shift >>:
13 >> 1; // -> In decimal, 13 can be seen as 12+1. In binary, 12 is represented as 1100. Shifting right by 1 position gives 110, which is then converted back to decimal as 6.
The result is 1 only if each bit is 1, otherwise it is 0.
10 & 8; // -> 1010 & 1000 == 1000 -> 8
The result is 1 if at least one bit is 1, otherwise it is 0.
10 | 8; // -> 1010 | 1000 == 1010 -> 10
The result is 1 only if each bit is different, otherwise it is 0.
15 ^ 5; // -> 1111 ^ 0101 == 1010 -> 10


Despite what my entrance exam to kindergarten said, I have never been particularly adept at math. Every time I'm confronted with a math problem my brain somehow manages to twist the numbers into incomprehensible knots. Throughout school, the most common feedback I got back on tests was "right work, wrong answer." I know what I should be doing, but somewhere along the line I always managed to reverse a number. So I find it more than a bit amusing that I recently joined the Exponential Ensemble
. a chamber music group whose primary objective is to help kids understand mathematical concepts through music. Suddenly I find myself revisiting concepts such as fractions or greater than less than. I'm sussing out ways we can help students deepen their understanding of these ideas through the medium of music. It's fascinating, the connections are strong and innumerable. For some students a visit from the group may suddenly help them connect a very abstract concept to something they can see and hear in front of them. The Exponential Ensemble is just getting started. It's the brainchild of clarinetist Pascal Archer. I think he's done an incredible job bringing this idea to fruition, but now we need your help to make it grow. On Sunday September 9th, we'll be presenting a benefit concert featuring Billy Hunter, Principal Trumpet of the Metropolitan Opera Orchestra. Please join us if you can. If you're too far away to attend, please consider making a donation. Any amount is greatly appreciated! I'll keep you posted as we grow.


It all starts with my old entrenched beliefs I had about math ( a tear rolling down her cheek).
I was never taught to think of math in an open-ended manner. For me, it was really just something in separate boxes. Pre-Algebra, Algebra 1…
Well in high school I took AP Calculus. However, I was a low student in a high class. I tried really hard, but I never had a complete grasp of derivatives and integrals. At the end of the year, you pay to take the test, but my teacher (I still remember this vividly) said,
You can save your money, just don’t take the test
Unfortunately, a lot of adults have similar traumatic stories where they have solidified the idea that they are not a “math person.”
I was awakened to a new reality when I went to a workshop on Inquiry and Mathematics. It changed my life…I cried, actually, there was a group of us on the floor just balling, as we all had these crazy stories of why we had such fixed ideas about math.
This opened me up to a whole new view of math and how it can be taught.
The key takeaway was to keep the task OPEN ended. This allows for multiple entry points and students can create their own understandings within the task they are given. Essentially, individualize instructions and learning.
This opens up so many possibilities.
For example, I am collaborating with a 5th-grade teacher and we give both of our classes the same task. We meet every week and discuss their responses, which are fascinating! Similarities, differences, but all because students were given multiple entry points to the task.
I am passionate about spreading this OPEN-ENDED way of teaching math to both students and teacher, as it will bring a whole new understanding of math and of learning.
Please reach out if you have any questions about Open-ended (inquiry-based) math!
101qs.com Digital provocations where you can find pre-made questions to introduce in your lessons. Great for “I see, I think, I wonder.”
Nrich.maths.org Digital provocations and open-ended tasks.


2 edition of introduction to inifinitely many variates. found in the catalog.
introduction to inifinitely many variates.
Enders A. Robinson
|Series||Griffin"s statistical monographs and courses -- No.6|
|The Physical Object|
|Number of Pages||132|
E Chapter 7 Solving Systems of Linear Equations and Inequalities Ongoing Prerequisite Skills, pp. , , , , Practice Quiz 1, p. Practice File Size: 6MB. Right here, we have countless ebook There Are Infinitely Many Solutions and collections to check out. We additionally manage to pay for variant types and afterward type of the books to browse. The welcome book, fiction, history, novel, scientific research, as skillfully as various extra sorts of books are readily comprehensible here.
Problems of basic Matrix Theory. From introductory exercise problems to linear algebra exam problems from various universities. Basic to advanced level. Set books. Apostol, T.M. Introduction to Analytic Number Theory Springer £ - ISBN This book is Print on Demand and can be ordered through any bookseller. Please allow at least 2 weeks for receipt following order. Claim: There are different types of
To answer these questions, we need to introduce the concept of an infinite series, a sum with infinitely many terms. Having defined the necessary tools, we will be able to calculate the area of the Koch snowflake (see Example ). 1. Introduction Mathematics distinguishes itself from the other sciences in that it is built upon a set of axioms and definitions, on which all subsequent theorems rely. All theorems can be derived, or proved, using the axioms and definitions, or using previously established theorems. By contrast, the theoriesFile Size: 96KB. INTRODUCTION TO COLUMN BUCKLING INTRODUCTION TO COLUMN BUCKLING 6 INTRODUCTION AND BASIC CONCEPTS There are many types of compression members, the column being the best known. Top chords of trusses, bracing members and compression flanges of built up beams and rolled beams are all examples of compression Size: KB.
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SyntaxTextGen not activatedChapter Inconsistent Linear Systems and Systems with Infinitely Many Solutions; 01) Introduction to Inconsistent Pdf 02) RREF Form and Inconsistent Systems; 03) 2x2 System w/ Infinitely Many Solutions; 04) Types of Solutions to Systems of Linear Equations in 2 Variables; 05) Possible Types of Solutions in 3 Variables.Though the frequency of occurrence of primes decreases as we move download pdf infinity, infinitely many primes exists.
Euclid proved that there are indeed infinitely many prime numbers. To prove there are infinite prime numbers by the method of contradiction, let us assume, there are finite numbers of primes and their set is represented by P.A Inconsistent Ebook Systems and Systems with Infinitely Many Solutions; 01) Introduction to Inconsistent System; 02) RREF Form and Inconsistent Systems; 03) 2x2 System w/ Infinitely Many Solutions; 04) Types of Solutions to Systems of Linear Equations in 2 Variables.


We are an affiliate of the National Council of Teachers of Mathematics (NCTM) as well as the Virginia Council of Teachers of Mathematics (VCTM). Our region extends from Alleghany County down to Patrick and Henry Counties and stretches from Pulaski over to Campbell County. To view our service area and see our Board Members, please click below.
Every fall, on the first Monday of October, we host an annual conference. We are excited for the 2019 conference. Save the date for Monday, October 7, 2019. The theme and location are TBD, so be sure to check back!
Each Spring, the Blue Ridge Council of Teachers of Mathematics offers a scholarship in the amount of five hundred dollars ($500) to a graduating senior from a public high school in our council's service region. The purpose of this scholarship is to support a student interested in pursuing a teaching career in mathematics.
All meetings take place at the Roanoke County School Board Office
located at 5937 Cove Road, Roanoke, Virginia 24019.
510 South College Ave, Salem, VA 24153, US


Now instead of using lame lottery systems that are around commonly drawn numbers or analysing past draws you must look for lottery systems that deal with real numbers.
Joining a lottery pool or soi cau24h 'syndicate' to purchase lottery ticket gives you better chance of winning. A person your money together in a choice small or big groups and in cases where of winnings, you will need to share the income. You can also do these using friends or co-workers. Along with this lottery pool system, really can have more tickets purchase and surely increase the winning option.
If you want to learn the game and win the lottery fast, essential engage a lottery guru to show you the short cuts. Working with a coach is definitely advisable to avoid mistakes and shorten achievement journey.
With an ordinary lottery ticket, no matter how under consideration the numbers, gives you terrible odds. A 6/49 draw gives you with a mere 1 in 13,983,816. That gives you approximately a one out of 14 million chance of winning the lottery. How bad usually that? Even if you have one hundred tickets picked randomly (like an average ticket) an individual only have one hundred 1 in 14 million chances of winning. Attach still have a 1 in 14 million chance of winning!
This exercise will help you to gauge pattern or pattern of the overall game. With the knowledge that you acquire with this exercise, you can easily increase your opportunity to get a windfall in the future.
For a beginner, generally 2-4 hours a week are ample. Make use of the time to jot down the lottery results over the past weeks. Collate the data and study them carefully to allow you selecting greatest lottery winning numbers.
Avoid buying numbers produced from birthdates because they're usually always a hit among players (which means, even in the event you win, your prize could rather small as you for you to share with numbers of players). Instead, you can buy at least one number which is greater than 31 and only 2 numbers that are 12 or below (as 12 or below are calendar months which particularly popular as well).
Now you take your calculator and multiply all top numbers (1x1x1x1x1) equal one (1). Degree of multiply all the bottom numbers (56x55x54x53x52). Correctly entered and multiplied discover the total is 458,377,920. The new fraction becomes 1/458,377,920. It is vital a 458 million 1 chance to win. If you were required to pick tinier businesses in order just like they're drawn, then these would have been the odds against to be able to win this Pick 5/56 ball lottery game.


Proofs from the book is a book of mathematical proofs by martin aigner and günter m. Introduction to mathematical proofs helps students develop the necessary skills to write clear, correct, and concise proofs. Introduction to mathematical arguments ( background handout for courses requiring proofs) by michael hutchings a mathematical proof is an argument which convinces other people that something is true.
Bookofproof richardhammack virginiacommonwealthuniversity. Inwriting this book i have been motivated by the desire to create a. Appendix a contains a summary of all the guidelines for writing mathematical proofs that are introducedthroughoutthe text. Guidelines for writing mathematical proofs are incorporated into the book. Mathematical structures, to prove mathematical statements, and even. Mathematical proofs: a transition to advanced mathematics by chartrand, polimeni, and zhang.
Do we really need mathematical proof of god' s book mathematical proofs existence? Through his spiritual struggle in the months following his father' s death, jack discovered something even more reliable, even more convincing than math, to prove that god indeed exists. Math isn’ t a court book mathematical proofs of law, so a “ preponderance of the evidence” or “ beyond book mathematical proofs any reasonable doubt” isn’ t good enough. To more advanced classical mathematical structures and arguments as soon as the student has an adequate understanding of the logic under- lying mathematical proofs.
Mathematical proofs: a transition to advanced mathematics, second edition, prepares students for the more abstract mathematics courses that follow calculus. This knowledge is essential to develop rigorous mathematics. The mathematician paul erdős was known for describing proofs which he found to be particularly elegant as coming from " the book", a hypothetical tome containing the most beautiful method( s) of proving each theorem.
I promised to myself to read all those books in 10 years because there were 50 books. Written in book mathematical proofs a student- friendly manner, it provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as optional excursions into fields such as number. Mathematical works do consist of proofs, just as poems do consist of characters. If your book mathematical proofs exposure to university mathematics is limited to calculus, this book will probably seem very di erent from your. In addition, ev-.
Mathematical reasoning: writing and proof is designed to be a text for the ﬁrst course in the college mathematics curriculum that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics. He said that there book mathematical proofs was a book somewhere, possibly in heaven, and that book contained the nicest and most elucidating proof of every theorem in mathematics. The book has book mathematical proofs five parts of roughly equal length. Proof in mathematics: an introduction. The aim i am pursuing here is to describe some general aspects of mathematical proofs.
In addition, most proofs are written only from the forward perspective. Unlike similar book mathematical proofs textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. They are written in narrative form using complete sentences and correct paragraph structure, and they follow certain conventions used in writing mathematics. The book also provides a bridge to the upper- level courses, since we discuss formalities and conventions in detail, including the axiomatic method and how to deal with proofs. Few proofs went over two pages in length. Com talks about the book mathematical proofs faith- shattering experience of losing his hero— his dad.
This text introduces students to proof techniques and writing proofs of their own. ( b) mathematics teachers and teachers- in. James franklin and albert daoud ( quakers hill press, 1996/ kew books, ) this is a small ( 98 page) textbook designed to teach mathematics and computer science students the basics of how to read and construct proofs. Jack zavada of inspiration- for- singles. Mathematical proofs book mathematical proofs are not written in table form.
Mathematical proofs: a transition to advanced mathematics, 4th edition introduces students to proof techniques, analyzing proofs, and writing proofs of their own that are not only mathematically correct but clearly written. A mathematical proof is a rigorous argument based on straightforward logical rules that is used to convince other mathematicians ( including the proof' s author) that a statement is true. The success of proof writing requires intuition, mathematical maturity, and experience. Rst course in the college mathematics curriculum that introduces students book mathematical proofs to the processes of constructing and writing proofs and focuses on the formal development of mathematics. I' m a math major in my junior year who recently switched from book mathematical proofs computer science.
Proofs are to mathematics what spelling ( or even calligraphy) is to poetry. Online shopping from a great selection at books store. Know a great deal of mathematics - calculus, trigonometry, geometry book mathematical proofs and algebra, all of the sudden come to meet a new kind of mathemat- ics, an abstract mathematics that requires proofs. Advice to the student welcome to higher mathematics! ” ( miklόs bόna, the book review column, ) “ paul erdős.
In this document we will try to explain the importance of proofs in mathematics, and to give a you an idea what are mathematical proofs. We cover mathematical topics that these students should know. These guidelines are introduced as needed and begin in sec- tion 1.
Mathematicians do not reveal the process they go through, or the book mathematical proofs ideas behind their proofs. This book covers all of the major areas of a standard introductory course on mathematical rigor/ proof, such as logic ( including truth tables) proof techniques ( book mathematical proofs including contrapositive proof, proof by contradiction, mathematical induction, etc. But who are not yet prepared for upper- level mathematics courses.
The book is dedicated to the mathematician paul erdős, who often referred to " the book" in which god keeps the most elegant proof of each mathematical theorem. It does require some book mathematical proofs calculus and linear algebra background, but if you have that, you should be able to follow most of the proofs in this book. Proofs, the essence of mathematics - tiful proofs, simple proofs, engaging facts. You can search for " book mathematical proofs thoughts - alpha" this is a free downloadable online pdf book for mathematical proofs. I' m looking for a book that is somewhat approachable and will teach me what i need to know as i progress through my mathematical learnings. Also see the mathematical association book mathematical proofs of america math dl review ( of the 1st edition) and book mathematical proofs the amazon reviews.
E- books in mathematical proofs category proof in mathematics: an introduction by james franklin, albert daoud - kew books, this is a small ( 98 page) textbook designed to teach mathematics and computer science students the basics of book mathematical proofs how to read and construct proofs. Contrary to mathematical proofs written in books, the ideas behind arriving at a proof are not “ book mathematical proofs cut and dried” and elegant. Most proofs pulled ideas from several areas of mathematics, and it seems to be this wonderful mixing of diverse book mathematical proofs ideas that leads to many of these proofs being in this book. Had his own way of judging the beauty of various proofs.
This book describes the language used in a mathematical proof and also the different types of proofs used in math. She even makes a point to stress this in the preface. This book gives relatively elegant proofs of theorems from many different fields of mathematics, and often gives multiple proofs for the same theorem.
Introduction to mathematical proofs ( textbooks in mathematics) 2nd edition. Any mathematical subject in data science will employ proofs, and the ability to book mathematical proofs write convincing proofs is an important mathematical skill for data scientists. Many were under one page.
The book is a compilation of proofs for basic mathematics ( trigonometric identities, logarithms, basic series, volumes and surfaces, basic calculus). Mathematics majors need to be aware that this book is intended for the fields of science and engineering, therefore the author’ s focus is not on proofs or mathematical rigor. Mathematical proofs: a transition to advanced mathematics ( 3rd edition) ( featured titles book mathematical proofs for transition to advanced mathematics). Here you will find proofs and notes in physics and mathematics on a high school and undergraduate level. Mathematical proof sometimes people read mathematical proofs and think they are reading a foreign language.
In my view, a mathematical proof is a warrant to assert a non- tautological statement which claims that. However, if you want a book that is geared specifically for those who are just starting out with rigorous math and are still getting used to proofs, you might enjoy journey into mathematics: an book mathematical proofs introduction to proofs by joseph rotman. Mathematicstextbookseries. The primary goals of the text are to help students: develop logical thinking skills and to develop the ability to book mathematical proofs think more.
Instructor' s solutions manual book mathematical proofs book mathematical proofs ( download only) for mathematical proofs: a transition to advanced mathematics. Two weeks ago, i finished reading book of proof ( link goes to amazon) by professor richard hammack, and so far, it was the best book that i have read about introduction to mathematical proofs. During a lecture in 1985, erdős said, " you don' t have to believe in god, but you should believe in the book. Mathematical reasoning: writing and proofis designed to be a text book mathematical proofs for the? Welcome to book of proofs. Some of the proofs are recent, some date book mathematical proofs back to euclid and others are noted as folklore proofs.
Most of the book mathematical proofs book mathematical proofs classes i took transferred over well, but i feel i am somewhat lacking in my proofs skills. Editor: lonmitchell. The book proofs from the book, published in, is devoted to presenting 32 proofs its editors find particularly pleasing.
I recommend this book to high school students who are interested in pursuing a mathematics degree, to college students who are math majors, and to teachers. Proofs from the book is an amazing compilation of very elegant proofs of classic results book mathematical proofs in various fields in mathematics. This book is an introduction to the standard methods of proving mathematical theorems. Unlike some such books, it doesn' t dwell on trivialities about logic and sets. Reviewed by michael barrus, assistant professor, university of rhode island on 2/ 1/ 18. When i was a college student, i saw a list of essential math books on a blog.
I' m not sure exactly why you are against historical comments ( nor do i know exactly what " book mathematical proofs mathematical perspectives" means in this pejorative context), but so far as i recall this book is fairly businesslike. It has been approved by the american institute of mathematics' open textbook initiative. The name refers to the way paul erdős referred to beautiful proofs, meaning that the they must have come directly out of god' s book of proofs.


Lesson Design and Outcomes
The overarching objective and desired outcome of a mathematics education that applies to all students is the development of: 1. Problem solving skills, 2. Critical thinking ability, and 3. A reflective and adaptable mindset. The reduction of mathematics into discrete standards is often at conflict with these objectives. Procedural proficiency is very important, but also analogous to the mechanical ability to form letters and spell correctly. The ability to write in order to communicate a thought, and read, in order to understand a new idea, is built upon those fundamentals.
Similarly, mathematics education should help students to develop and explore ideas, share thoughts and insights, as well as understand and evaluate foreign ideas and concepts. In short, a success mathematics program will develop mathematical literacy in students. Instruction and guidance combine to form “half” of the components required for students to pursue a mathematics education.
Read more about how we serve these lofty goals by integrating various points of focus in each lesson and assessment.
Fundamental Elements of Lessons
Answers are correct, or incorrect, based on alignment with the concepts at play.
Lessons and assignments provide opportunities to develop mathematical literacy.
Promoting and challenging ideas and thoughts to uncover and repair misconceptions.
By developing conceptual understanding and intentionally integrating various concepts and applications, promotes retention.
Outcomes for Students
Each lesson and topic should promote the development of problem solving skills, including perseverance, in students.
By learning to consider information and procedural appropriateness, students can become critical thinkers.
A reflective student can monitor their progress and adjust approaches based on progress towards a goal or desired outcome.
Reflective and Adaptive
Join the Team
To access our growing library of curriculum resources and assessment tools, reserve your membership today. For all teachers, membership is free!


International Computer Games Association journal. Archived from the original (PDF). a b Donghwi park (2015). "Space-state complexity of Korean chess and Chinese chess". "Implementing a computer Player for Abalone Using Alpha-beta and Monte-carlo search" (PDF). Dept of Knowledge Engineering, maastricht University. Retrieved kopczynski, jacob S (2014).
Thesis in game theory and thesis in latex sample
"Bejeweled, candy Crush and other Match-Three games are (NP-)Hard". Analysis and Implementation of the game gipf (PDF) (Thesis). Chang-Ming Xu; ma,. M.; Jun-jie tao; Xin-he xu (2009). "Enhancements of proof number search in connect6". 2009 Chinese control and Decision Conference. Hsieh, ming Yu; Tsai, shi-Chun. "On poverty the fairness and complexity of generalized k -in-a-row games". "Practical issues in temporal difference learning". a b Shi-jim Yen, Jr-Chang Chen; tai-ning Yang; Shun-Chin Hsu (March 2004). "Computer Chinese Chess" (PDF).
"Hex ist pspace-vollständig (Hex is pspace-complete. The size of essay the state space and game tree for chess were first estimated in Claude Shannon (1950). "Programming a computer for Playing Chess" (PDF). Archived from the original (PDF). . Shannon gave estimates of 100 respectively, smaller than the upper bound in the table, which is detailed in Shannon number. a b aviezri Fraenkel ;. Lichtenstein (1981 "Computing a perfect strategy for nn chess requires time exponential in. A, 31 (2 199214, doi :.1016/0097-3165(81)90016-9.
a b takumi kasai; akeo adachi; Shigeki iwata (1979). "Classes of Pebble games and Complete Problems". Proves completeness writing of the generalization to arbitrary graphs. "The Othello game on an n*n board is pspace-complete". Analysis and Implementation of the game OnTop (PDF) (Thesis). Maastricht University, dept of Knowledge paper Engineering. Informed search in Complex Games (PDF) (Ph. Maastricht University, maastricht, The netherlands.
Msri combinatorial Game Theory research Workshop. jonathan Schaeffer;. "N by n checkers is Exptime complete". Siam journal on Computing. see allis 1994 for rules bonnet, Édouard; Jamain, Florian; Saffidine, abdallah. "On the complexity of trick-taking card games". "Best Play in Fanorona leads to Draw" (PDF). New Mathematics and Natural Computation. "The Shortest Game of Chinese Checkers and Related Problems".
Game, theory, assignment Help - math Assignment Experts
a b c d Stefan reisch (1980). "Gobang ist pspace-vollständig (Gobang is pspace-complete. "The complexity of Graph Ramsey games". a b c d e. Van den Herik;. "Games solved: Now and in the future".
Orman: Pentominoes: a first Player Win in Games story of no chance, msri publications volume 29, 1996, pages 339-344. see van den Herik et al for rules. "John's Connect four Playground". michael Lachmann; Cristopher moore; ivan Rapaport (July 2000). "Who wins domineering on writing rectangular boards?".
Note: ordered by game tree size game board size (positions) State-space complexity (as log to base 10) Game-tree complexity (as log to base 10) average game length ( plies ) Branching factor Ref Complexity class of suitable generalized game tic-tac-toe pspace-complete 2 Sim.7 pspace-complete. Double dummy problems in the context of contract bridge ) is not a proper board game but has a similar game tree, and is studied in computer bridge. The bridge table can be regarded as having one slot for each player and trick to play a card in, which corresponds to board size. Game-tree complexity is a very weak upper bound: 13! To the power of 4 players regardless of legality.
State-space complexity is for one given deal; likewise regardless of legality but with many transpositions eliminated. Note that the last 4 plies are always forced moves with branching factor. Infinite chess is a class of games, which includes Chess on an Infinite Plane and Trappist-1 as examples. 49 50 see also edit references edit a b c d e f g h i j k l Victor Allis (1994). Searching for Solutions in Games and Artificial Intelligence (PDF) (Ph. University of Limburg, maastricht, The netherlands.
John nash thesis game theory
When rotations and reflections of positions are considered the same, there are only 26,830 possible games. The computational complexity of tic-tac-toe depends on how it is generalized. A natural generalization is to m, n, k -games : played on an m by assignment n board with winner being the first player to get k in a row. It is immediately clear that this game can be solved in dspace ( mn ) by searching the entire game tree. This places it in the important complexity class pspace. With some more work it can be shown to be pspace-complete. 2 Complexities of some well-known games edit due to the large size of game complexities, this table gives the ceiling of their logarithm to base. (In other words, the number of digits). All of the following numbers should be considered with caution: seemingly-minor changes to the rules of a game can change the numbers (which owl are often rough estimates anyway) by tremendous factors, which might easily be much greater than the numbers shown.
Example: tic-tac-toe (noughts and crosses) edit for tic-tac-toe, a simple upper bound for the size of the state space is 39 19,683. (There are three states for each cell and nine cells.) This count includes many illegal positions, such as a position with five crosses and no noughts, or a position in which both players have a row of three. A more careful count, removing these illegal positions, gives essay 5,478. And when rotations and reflections of positions are considered identical, there are only 765 essentially different positions. A simple upper bound for the size of the game tree is 9! (There are nine positions for the first move, eight for the second, and.) This includes illegal games that continue after one side has won. A more careful count gives 255,168 possible games.
reasonable lower bound can be given by raising the game's average branching factor to the power of the number of plies in an average game, or: gtcbddisplaystyle gtcgeq. Computational complexity edit The computational complexity of a game describes the asymptotic difficulty of a game as it grows arbitrarily large, expressed in big O notation or as membership in a complexity class. This concept doesn't apply to particular games, but rather to games that have been generalized so they can be made arbitrarily large, typically by playing them on an n -by- n board. (From the point of view of computational complexity a game on a fixed size of board is a finite problem that can be solved in O(1 for example by a look-up table from positions to the best move in each position.) The asymptotic complexity. It will be upper-bounded by the complexities of each individual algorithm for the family of games. Similar remarks apply to the second-most commonly used complexity measure, the amount of space or computer memory used by the computation. It is not obvious that there is any lower bound on the space complexity for a typical game, because the algorithm need not store game states; however many games of interest are known to be pspace-hard, and it follows that their space complexity will. The depth-first minimax strategy will use computation time proportional to game's tree-complexity, since it must explore the whole tree, and an amount of memory polynomial in the logarithm of the tree-complexity, since the algorithm must always store one node of the tree at each possible. Backward induction will use both memory and time proportional to the state-space complexity as it must compute and record the correct move for each possible position.
An upper bound for the size of the game tree can sometimes be computed by simplifying the game in a way that only increases the size of the game tree (for example, by allowing illegal moves) until it becomes tractable. However, for games where the number of moves is not limited (for example by the size of the board, or by a rule about repetition of position) the game tree is infinite. Decision trees edit, the next two measures use the idea of a decision tree, which is a subtree of the game tree, with each position labelled with "player A wins "player B wins" or "drawn if that position can be proved to have that value. (Terminal positions can be labelled directly; a position with player A to move can be labelled "player A wins" if all successor positions lead to victory for a, or labelled "player B wins" if all successor positions are wins for b, or labelled "draw". And correspondingly for positions with B to move.). Decision complexity edit, decision complexity of a game is the number of leaf nodes in the smallest decision tree that establishes business the value of the initial position. Game-tree complexity edit, the game-tree complexity of a game is the number of leaf nodes in the smallest full-width decision tree that establishes the value of the initial position. 1 A full-width tree includes all nodes at each depth.
Advancing learning and evolutionary, game, theory
In sense 3, middle English, lowering of the voice, from Late latin greek; Late latin, from Greek, downbeat, more important part of a foot, literally, act of laying down; in other senses, latin, from Greek, literally, act of laying down, from tithenai to put, lay. Combinatorial game theory has several ways of measuring game complexity. This article describes five of them: state-space complexity, game tree size, decision complexity, game-tree complexity, and computational complexity. Contents, measures of game complexity edit, state-space complexity edit, the state-space complexity of a game is the number of legal game positions paper reachable from the initial position of the game. 1, when this is too hard to calculate, an upper bound can often be computed by including illegal positions or positions that can never arise in the course of a game. Game tree size edit, the game tree size is the total number of possible games that can be played: the number of leaf nodes in the game tree rooted at the game's initial position. The game tree is typically vastly larger than the state space because the same positions can occur in many games by making moves in a different order (for example, in a tic-tac-toe game with two x and one o on the board, this position could.


Random number generators¶
Hardware entropy generators¶
- Sound: audio entropy daemon
- Video: video entropy daemon
- Lava Lamp! lavarnd.org
- True random numbers from Wi-Fi background noise
- EGD: Entropy Gathering Daemon
- PRNGD: Pseudo Random Number Generator Daemon
- aed: an “additional entropy” daemon for Linux
Download entropy from websites¶
Size of the internal state¶
If the size of the RNG internal state is too small, you may generate duplicate seeds. For example, most LCG RNG uses a 32 bits unsigned integer as state.
Using the birthday problem, we can compute the number of seed that have to be tested to get the first collision with a probability of 50%:
>>> from math import sqrt, log >>> def n(p, d): return sqrt(2*d*log(1/(1.0-p))) ... >>> n(0.5, 2.0**32) 77162.743235574148
where 2^32 is the number of different possible seeds.
So with an internal state of 32 bits, you have to try 77163 seeds to create the same RNG with a probability of 50%. If we want to be sure, you can try with a probability of 99%:
>>> n(0.99, 2.0**32) 198892.20870276989
Even if you have a perfect random seed generator, you have a risk to generate duplicate generators if the internal state is too small. If you want to avoid collisions, use a geneartor using larger internal state, eg. at least 128 bits:
>>> n(0.5, 2.0**128) 2.1719381355163562e+19
Quality of the seed generator¶
In the first section, we supposed that the seed generator was perfect. But in real life, the seed is usually created using predictable informations like process identifier or current time in seconds. Because of a bug introduced in OpenSSL package, the seed was only created using the process identifier, which is -most of the time- a number of... 15 bits.
>>> n(0.5, 2.0**15) 213.13398045637061
Try 213 different keys was enough to break Debian OpenSSL security...
Good entropy sources¶
/dev/random: best entropy source on Linux, but blocks if there is no more entropy. It uses physical events like: keyboard strokes, mouse clicks and moves, hard drive timing, etc.
/dev/urandom: non blocking generator
- (External) Hardware RNG
Cryptographic secure PRNG (CSPRNG)¶
- Protect against previous / next numbers prediction, even if the attacker knows the last results
- Protect internal state: even if the attacker knows the RNG output, he shouldn’t be able to guess the internal state. Common trick is to hash the output (eg. MD5, SHA-1, or using a cryptographic hash function)
- Protect against entropy injection
LCG RNGs don’t feet these requierements because knowing one number is enough to guess all previous and next numbers. Mersenne Twister is not a CSPRNG because it’s not uniform in dimension 624.


I conduct research activity in optimal control of hybrid dynamic systems with applications to robotics, aeronautics, and astronautics. Hybrid dynamical systems are dynamical systems that have both continuous and discrete dynamic behavior. Therefore, the state of a hybrid system is characterized by continuous and discrete state variables which are called modes. In this problem the goal is to find the continuous control inputs, the sequence of modes, and the corresponding trajectory that steer the system between two states satisfying a set of constraints on the state and/or control variables while optimizing an objective functional. Typically, optimal control problems for hybrid dynamical systems are highly non-linear and it is very difficult to find analytical solutions even for the simplest cases. The common practice is to use numerical methods to get approximate solutions.


The Labouchere system is one of simplest systems used for betting purpose. The Labouchere is also called as split Martingale or cancellation system. You can apply from all games like roulette or sports for betting. Wherever you want to apply this system you will need pen and paper so that you can make your calculations.
In the start of the game you have to determine the amount of money you want to make from game. Next step is to divide your goal into numbers and write them in form of sequence such that the sum of sequence gives you resultant amount of you goal. It is also not mandatory that numbers should be in series they can be in any form. This all aspects are determined by game you are betting for.
Suppose we take an example of simple series of numbers 1 2 3 4 5 6. The numbers in series are representative of units in game. Now let’s say you place bet for first and last digit of series that are 1 and 6. The sum of these numbers is 7. Now there would be two possibilities. In case you win your bet you are going to cancel the first and last digit. Then again you will bet for next two numbers like 2 and 5. The same again would be 7 and in case you win you will cancel these digits and bet on next two that would be 3 and 4. If you win again at this point you have completed one game or made a coup and can start over.
It was when you would be winning persistently. However in case of second option and you lose the procedure would be bit different. Let’s say if you lose your first bet you are not going to cancel the numbers rather you have to add the number at the end which would be resultant of two numbers in the series you are betting on. Like for first bet the number were 6 and 1. The sum is 7. Therefore, you are going to add the number 7 at the end of series. Now when you are going to place your next bet it would be 1+7 which is equal to 8. Therefore, your next bet would be for unit 8. This process will continue every time you lost your bet.
Like every system Labouchere system has its own disadvantages. This system usually results in gambling big money though initial amount of game is nominal. As you have to increase your bet every time you lose the game. Therefore, this system will need additional assets.


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It was launched by former President of India Dr. A.P.J Abdul Kalam, to encourage Science and Mathematics learning in Children. It is learning beyond classroom.
Ministry: Ministry of Human Resource Development.
Target Group: Every child of the age group 6 - 18.
Interventions under RAA:
Systematic Improvement in the School System
Teacher Preparation for Science, Mathematics and Technology: Pre-Service and In- Service
Assessment design for Science and Mathematics for students
Recruitment of Science and Mathematics Teachers.
Strengthening School Science Laboratories and Mathematics Laboratories
Provision of teaching-learning equipment and supplementary books/materials to enhance Science and Mathematics transaction in classrooms.
Use of Technology in Science and Mathematics teaching Development of resource materials
Strengthening teacher support institutions and in the use of technology Effective classroom transaction : teaching – learning.
Initiative to encourage Science, Mathematics through Alternative Strategies
School Mentoring for Science & Mathematics teaching by Higher Education Institutions.
Teacher Circles on Science, Mathematics and Technology
Science/Mathematics Clubs for Children
Expand outreach of programmes of Ministry of Science and Technology to promote science learning.
Participation of Students in Inter-school, State/National Maths and Science Competitions/ Olympiads etc.
Organised visits to Science Museums and Science fairs and Mathematics Melas. Parents and community sensitisation.


1. Course Identity
Course title: Machine Learning
Hours per week: 3
ECTS Units: 6
2. Learning goals
The goal of the course is to offer a broad aspect of the field of Machine Learning by studying the major models and methods based on both the supervised and unsupervised learning paradigm. The theory of learning is also covered so the student learns the capabilities and the limits of these models and what is feasible, in general, through any machine learning process.
The subjects covered are:
- Basic concepts of learning.
- Mathematical background, optimization methods (gradient descent, etc), the LMS algorithm.
- Decision functions, linear separability, the Perceptron algorithm.
- Gaussian discriminant analysis. Bayesian methods.
- Support vector machines.
- Model choice.
- Feature selection.
- Improving performance: bagging, boosting, committee machines.
- Evaluating and debugging learning algorithms.
- Clustering (e.g. the K-means algorithm)
- Mixtures of Gaussians, the EM algorithm
- Signal analysis: Factor Analysis, Principal Component Analysis (PCA), Independent components analysis (ICA)
Elements of ML Theory
- The Vapnik-Chervonenkis dimension
- Using machine learning algorithms
The course will be covered by weekly lectures. An important part of the student load is the weekly homework assignments on a specific part of the course. Moreover, there will be a final project requirement where the student will implement a Machine Learning algorithm for pattern recognition using the MATLAB software package.
5. Student evaluation
Student evaluation will be based on the grades of the weekly homeworks and the grade of the final project.
6. Software-hardware requirements
The MATLAB package is required with, at least, the following toolboxes: Statistics, Optimization, Neural networks, Signal processing.
- (inGreek) Κ. Διαμαντάρας, Τεχνητά Νευρωνικά Δίκτυα, Κλειδάριθμος 2007.
- C. Bishop, Pattern Recognition and Machine Learning, Springer 2006
- S. Haykin, Neural Networks and Learning Machines (3rd Edition), Prentice Hall, 2008
- J. Shawe-Taylor and N. Cristianini, Kernel Methods for Pattern Analysis, Cambridge University Press, 2004
- B. Schölkopf and A. J. Smola, Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond, MIT Press 2001
- R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification (2nd Edition), Wiley Interscience, 2000
- V. Vapnik, Statistical Learning Theory, Wiley Interscience, 1998
- A. Hyvärinen, J. Karhunen, E. Oja, Independent Component Analysis, Wiley Interscience, 2001
- K. Diamantaras and S. Y. Kung, Principal Component Neural Networks: Theory and Applications, Wiley Interscience, 1996


Have you ever wondered how many bottles of water make up a gallon? Understanding this conversion is not only helpful in everyday life but also essential for various tasks and measurements. In this article, we will dive into the world of gallons and water bottle sizes to provide you with a clear answer to the question, “How many bottles of water is 1 gallon?” So, let’s quench our thirst for knowledge and explore this topic together.
Understanding Gallons and Bottle Sizes
To fully grasp the concept of how many bottles are in a gallon, it’s important to understand what a gallon represents in terms of liquid measurement. A gallon is a unit of volume commonly used in the United States and is equivalent to 128 fluid ounces. However, water bottles come in various sizes, which can make the conversion a bit more comple
Bottle sizes for water typically range from 8 ounces to 32 ounces, with some larger containers available for bulk purchases. These bottle sizes are designed to cater to different needs and preferences, whether for on-the-go hydration or daily consumption. Now, let’s move on to determining the actual bottle size to facilitate our calculation.
Determining the Bottle Size
When determining the size of a water bottle, it is measured in fluid ounces. Most bottles explicitly indicate their size on the label, making it easy to identify. However, if the size is not stated or you are unsure, you can use a measuring cup or kitchen scale to measure the amount of water the bottle can hold. This will give you the size in fluid ounces, which will be crucial for our next step.
To calculate the number of bottles in a gallon, we need to convert fluid ounces to gallons. By dividing the number of fluid ounces by 128 (the number of fluid ounces in a gallon), we can determine the corresponding gallon value. This will allow us to find the answer to our main question.
Calculating the Number of Bottles in a Gallon
Let’s break down the calculation step-by-step to make it easier to understand and apply:
- Identify the size of the water bottle in fluid ounces.
- Divide the number of fluid ounces by 128 (the number of fluid ounces in a gallon).
- Round the result to the nearest whole number.
For example, if you have a 16-ounce water bottle, the calculation would be as follows:
16 fluid ounces ÷ 128 fluid ounces/gallon = 0.125 gallons
Rounded to the nearest whole number, we find that one 16-ounce water bottle is approximately equal to 0.125 gallons. Using this method, you can calculate the number of bottles in a gallon for any size of water bottle.
FAQ: Common Questions about Gallons and Water Bottles
Are all water bottles the same size?
No, water bottles come in various sizes ranging from 8 ounces to 32 ounces and even larger containers for bulk purchases. It allows individuals to choose the size that best suits their needs and preferences.
How many fluid ounces are in a gallon?
There are 128 fluid ounces in a gallon. This conversion is important when determining the number of bottles that make up a gallon.
Can I use any type of bottle to measure a gallon of water?
While any bottle can be used to measure a gallon of water, it is crucial to know the size of the bottle in fluid ounces. This information will enable you to calculate the number of bottles necessary to reach a gallon.
In conclusion, understanding the quantity of bottles in a gallon of water is essential for everyday tasks and measurements. By knowing the size of a water bottle in fluid ounces and utilizing a simple calculation, you can easily determine how many bottles make up a gallon. Whether you are planning a gathering, staying hydrated throughout the day, or simply curious about conversions, this knowledge will come in handy. So, the next time you ponder, “How many bottles of water is 1 gallon?” you’ll have the answer at your fingertips. Stay hydrated, stay informed!


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To calculate the necessary image size, measure the largest viewing distance (the distance between the image and the furthest chair in the room) in inches and divide that number by eight. The resulting number is the display height necessary for effective viewing.
For example, a viewing distance of 240 inches (20 feet) requires a 30" image height, which is approximately what is provided by a 60" flat panel.
Many designers recommend even larger image sizes when small text or detailed graphics are used. In this case, replace the above image height factor of eight with either six or seven.


CAGR (Compound Annual Growth Rate) measures your investments' average annual growth over a given period. It shows you the average rate of return on your investments over a year. CAGR is a helpful tool for investors because it precisely measures investment growth (or decline) over time. When calculating CAGR, profits are assumed to be reinvested at the end of each year of the time horizon. Therefore, CAGR is a representative number, not an accurate return. In most cases, an investment cannot grow at the same rate year after year. Despite this, the CAGR calculator is widely used to compare alternative investments.
Keeping this common application of the calculation in mind, it is prudent that investors find a convenient way to calculate CAGR. Anyone who wants to estimate the return on investment can use the CAGR calculator. The Compound Annual Growth Rate formula is used in this application's calculations (CAGR formula). For example, if you have a mutual fund that has appreciated over time, you can use the calculator to determine the rate of return on your investment. The CAGR return calculator will provide you with an annual growth rate that you can compare to a benchmark return.
To calculate the compounded annual growth rate on investment, use the CAGR calculation formula and perform the following steps:
CAGR = (FV / PV) ^ (1 / n) – 1
In the above formula, FV stands for the future value of the investment, PV stands for the present value of the investment, and n stands for the number of years of investment. To understand the calculation better, let's look at a hypothetical situation. Consider you invested Rs.20000 in a mutual fund in 2015. The investment will be worth Rs.35000 in 2020. Using the formula, the CAGR of this mutual fund investment will be-
CAGR= (35000/ 20000) ^ (1/5) – 1 = 11.84%
Here, the results mean the mutual fund investment gave you an average return of 11.84% per annum. You can also calculate the absolute returns on investment using the CAGR calculator. The calculation will be-
Absolute returns= (FV- PV) / PV * 100 = (35000-20000)/ 20000 * 100 = 75%
This means your mutual fund investment gave you an absolute return of 75% over its tenure.
How to calculate CAGR
It enables investors to assess the returns in a variety of scenarios. You can use several test cases to evaluate returns in various scenarios.
It is straightforward to use. You only need to enter the initial value, the final deal, and desired investment period, and the online CAGR calculator will take care of the rest.
Assume that you purchased some units of an equity fund earlier and that their value has since increased. You can calculate the gains on your investment using the CAGR online calculator.
It gives you a comprehensive idea of your return on investment.
You can also use the compound annual growth rate calculator to compare stock performance to that of peers or the industry as a whole.
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When an investment or loan is compounding, the CAGR shows the average growth rate over time. It helps to balance out fluctuations and allows you to see how your money will perform over time. It is a ratio of the investment's final value to its initial value calculated over time.
When it comes to investments in equity, there is no set percentage for a promising CAGR. It is a result of several factors. For most investments, whether equity or fixed income, the CAGR should, in theory, be higher than the interest rate on a savings account.
CAGR can help an investor decide how much to invest now to achieve a specific investment goal over time. While annual returns are commonly used to evaluate mutual funds and stocks, the compounding factor is overlooked in these calculations. As a result, these metrics frequently overestimate returns, which can lead to poor investment decisions. CAGR can provide more accurate results by using a standard rate of compounding. It can also be used to analyse an investment's performance, compare stocks or mutual funds, and even track business performance.
The 5-year CAGR is a valuable metric that represents the five-year financial performance of an organisation. It is a suitable parameter for comparing the performance of different organisations at a time. For example, if you want to invest in XYZ, calculating the 5-year CAGR of sales will help you determine whether the company will grow over time
Yes, you certainly can. CMGR calculates average monthly growth, similar to CAGR, which calculates average annual growth rate. The formula for calculating CMGR is the same; simply replace the number of years with months.
To figure out what your investment's CAGR is, do the following:
a) Divide the investment's value at the end of a period by the one at the start.
b) Divide the result by 'n' (the number of years) to get an exponent of one.
c) Subtract one from the result that follows.
The CAGR formula will thus be- CAGR= (FV / PV) 1 / n – 1
The size of a company and the industry sector in which it operates influence its growth rate. A CAGR in sales of 5-12 per cent is suitable for large-cap companies. Similarly, for small businesses, a CAGR of 15% to 30% is satisfactory. Furthermore, a company's CAGR must be consistent over time. As a result, a promising CAGR does not always imply the highest CAGR; it can also mean stable and constant growth. CAGR should not be the only factor while making investment decisions in a stock of a company. You must do thorough research before deciding to take the plunge.
The compound annual growth rate (CAGR) is calculated over a set of time intervals (and assumes compounding over that period). This could be a retail investor calculating the return on a stock or a venture capitalist calculating the growth rate of a potential investment. The average annual growth rate (AAGR) is the arithmetic mean of a series of growth rates that measures the average increase in the value of an investment or asset over a year.
Calculating the CAGR for various options is beneficial if you want to invest a lump sum. Using XIRR to make an investment decision is more accurate if you're investing at different times.
CAGR can be thought of as a geometric progression ratio. CAGR is a popular financial ratio that allows you to compare the returns from various investments.
The CAGR Ratio compares returns over time to determine which is the better investment. You have the option of choosing the investment with the highest CAGR Ratio.
ICICI Securities Ltd. ( I-Sec). Registered office of I-Sec is at ICICI Securities Ltd. - ICICI Centre, H. T. Parekh Marg, Churchgate, Mumbai - 400020, India, Tel No : 022 - 2288 2460, 022 - 2288 2470. The contents herein above shall not be considered as an invitation or persuasion to trade or invest. I-Sec and affiliates accept no liabilities for any loss or damage of any kind arising out of any actions taken in reliance thereon. The contents herein above are solely for informational purpose and may not be used or considered as an offer document or solicitation of offer to buy or sell or subscribe for securities or other financial instruments or any other product. Investments in securities market are subject to market risks, read all the related documents carefully before investing. The contents herein mentioned are solely for informational and educational purpose


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Pramod tutored me in AP Calculus BC, a class I found challenging in school. I was always border lining an A in that class, but I was able to get a more solid A after his help. Pramod's guidance has helped to strengthen my concepts and he was able to make math at a more complexed level less overwhelming and easier to understand. In fact, I got a 5 on the AP Calculus BC exam this year, and I think his teaching has helped me achieve that..
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With Yards Gained, you can perform queries against nearly every regular season NFL play since 2000. For example,
will count the total number of rushing yards by all players since 2000. That's not very interesting though. We can split that sum across a few different dimensions, for example by season:
rushing yards : season
rushing yards : player
rushing yards : team
We can also look up multiple statistics at the same time:
rushing yards, passing yards : team
There are a couple things worth noting here. First, we can sort the table by any of the columns by clicking anywhere in the table (click again to reverse the order). Second, the cells are colored based on the relative magnitude of the values in a given statistic.
Houston Texans fans might be upset with this table because they didn't play until 2002, so comparing total rushing and passing yards isn't really fair. Let's consider yards per game instead:
rushing yards / games, passing yards / games : team
Here we took multiple statistics and combined them into a single statistic using arithmetic. Another example: the ratio of passing yards to rushing yards, by team.
passing yards / rushing yards : team
which shows us which offenses were most dependent on passing or rushing since 2000. But thirteen seasons is a long time, so it might be more interesting if we also split it by season across columns:
passing yards / rushing yards : team / season
The cell coloring calls out significant outliers, but we can also put all the values in a single sortable list. By using a ',' instead of a '/' to split by season, we can split the data across rows:
passing yards / rushing yards : team, season
which is now sorted by magnitude. Since 2000, Arizona has had the two most pass-heavy offenses, by yardage. But maybe the decision to run or pass is more interesting than the yards gained, so let's take a look at that instead.
passes / carries : team, season
This list looks a bit different. But maybe these are just teams that were behind a lot and forced to pass to try to catch up; let's check that.
passes / carries, wins : team, season
Sure enough a lot of these teams were below .500. We can try to weaken this bias by only considering plays when the teams are tied.
passes / carries while tied : team, season
By saying "while tied", now we're only considering statistics recorded on plays where the offense and defense are tied. We can filter on a range of different properties, like team, opponent, home/away, down, distance, season, player etc. Here we've limited it by score.
Looking at the data, the 2011 Packers really stand out here. Is this just noise though? If we look up the total number of offensive plays (i.e. first down attempts) we can try to see how reliable these numbers are.
passes / carries, first down attempts while tied : team, season
As it turns out the Packers only had 88 first down attempts, the third fewest since 2000, so this number probably isn't that meaningful. (We might suspect that this is because they were so dominant that they were almost always leading, something we can look into shortly.) We can remove them from the table by specifying a minimum number of plays, say 150:
passes / carries, first down attempts min 150 first down attempts while tied : team, season
Another way we can try to decrease the noise is by including more plays than just those were the teams are tied. So let's take a look at plays where the teams are within one score:
passes / carries, first down attempts while tied or down 1-8 or up 1-8 : team, season
And if we wanted to see these tendencies by quarter, we can split this data by quarter across columns:
passes / carries, first down attempts min 50 first down attempts while tied or down 1-8 or up 1-8 : team, season / quarter
Another thing we can do is create buckets for these splits. Score, for example, is one where we might not care so much whether a team is up or down by 4 or 5 points. We can can do this by writing "score[N]" where N specifies the size of the buckets.
Earlier we saw that the 2011 Packers had very few offensive plays while tied. We can take a look at the distribution of every team's offensive plays in 2011 across scores using this:
first down attempts in 2011 : score / team
or we can look at it by game:
games in 2011 : score / team
In this table, each value represents the number of games that the team had a play where they were up or down by the given score. The Packers led in all 16 games, and led by two scores in 14 of their 16 games; on the other hand, the Colts trailed in every game.
"Games" (or "Wins"/"Losses"/"Ties") works a little differently than other statistics. We saw in the query above that each team had many more than 16 "games" in each column, yet we know that each team played in only 16 games. This is because a team could be tied, leading by 3, or behind by 10 all in the same game; that game would count in each of those three rows. Each game is counted at most once in each cell, but a single game can be represented multiple times across the table.
One interesting expression with games is "wins / (wins + losses)", which can be thought of as an estimate of a team's probability of winning. We can then get these probability estimates in different situations, for example as function of score and time remaining. Specifically, this will split the score into 3 point ranges, and time into 6 minute ranges, requiring at least 100 games in each score/time combination.
wins / (wins + losses) min 100 games : score / minute
Finally, notice how there are a number of cells that have either no wins or no losses? By default, making an expression with statistics (like "wins / (wins + losses)") makes each statistic in the expression optional. We can make a specific statistic required by adding an exclamation point to the end of it, like "wins / (wins! + losses!)". If we use that instead, we can eliminate some of the uninteresting cells from the table.
wins / (wins! + losses!) min 100 games : score / minute
Hopefully this has helped you understand how to use Yards Gained. The full documentation contains the details on all the statistics, conditions, or groupings you can use.
Still not sure why you query isn't working? Please feel free to tweet @YardsGained with any questions, feedback, or requests.


ICSE Board exams are a tough nut to crack for the students. Rigorous and exhaustive preparation is required in order to score well. The board exams cannot be taken lightly if the student wishes to score more than 90%. Practising the solutions on a regular basis along with revision before the exams helps students to obtain good marks. Mathematics is one of the difficult subjects which requires good conceptual knowledge to solve complex problems effortlessly.
Choosing the right study material for this purpose might be a difficult task for the students. There are numerous outdated study materials available in the current market. Students must first understand the latest syllabus designed by the ICSE board and choose the reference guide based on their needs. Selina Concise Mathematics Class 8 Solutions are available in PDF format which can be downloaded and referred by the students while answering the textbook questions.
Students must clearly understand the concepts in Class 8 as it sets a strong knowledge of basic concepts which would be continued in higher classes as well. The solutions are designed by a set of highly qualified faculty members having vast experience in the respective subject. The main aim of providing solutions is to help students ace the exam without fear.
Importance of Selina textbooks for ICSE students:
1. Strictly follows ICSE curriculum
The textbooks are designed by knowledgeable experts as per the syllabus designed by the ICSE board. Important concepts are explained in a simple language to make it easy for the students to understand. It covers all the important topics which are necessary for the students from the exam perspective.
2. Number of problems to practice
ICSE Selina textbooks contain numerous problems which can be solved by the students to understand the concepts easily. The solutions are explained in a comprehensive way to help students to get a clear idea about the method of solving complex problems. Examples are present before the exercise wise problems to help students to solve problems without any difficulty.
3. Best for ICSE Board exams
The problems in the Selina textbooks are answered in a step wise manner with explanations in a simple language for a better understanding among students. The main aim is to focus on the marks allotted for each step as per the ICSE exam pattern. This improves the problem solving skills among students which is important from the exam point of view.
4. Clear fundamental concepts
Selina books are not only sufficient to cover the ICSE syllabus but are also enough to cover all the basics and fundamental concepts in simple and easy language. This mainly helps students to make their concepts crystal clear as it would be continued in higher classes also. Once the concepts are clear, there is no need for the students to mug up difficult topics a few days before the exam.
So from the above mentioned points we get to know that Selina textbooks are one of the best study material which the students can rely on to prepare for their exams. Various problems present in the textbook helps students to improve their time management skills and their approach towards solving complex problems. Students appearing for the board exams can also refer to Selina Class 10 Maths Solution to boost their confidence.


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This is most likely a ceramic capacitor.
The numbers on the disk denote the capacitance in picofarads.
If the number starts with a . then the value is below 1pF, for example .01 is 0.01pF.
If there are two digits to the number, then that is the capacitance in picofarads, for example 22 is 22pF.
If there are three digits then the first two digits are the capacitance, and the third digit is the multiple of ten, so 473 is 47000pF, or 47nF (4, 7 and 3 zeros).
A letter in the code indicates the tolerance or precision of the capacitance value: