After that, we choose the one with the maximum profit for the entire subproblem. Key Differences Between Greedy Method and Dynamic Programming. Dynamic Programming; A greedy algorithm is one that at a given point in time, makes a local optimization. All rights reserved. Less … If you want the detailed differences and the algorithms that fit into these school of thoughts, please read CLRS. For example, if we write a simple recursive solution for Fibonacci Numbers, we get exponential time complexity and if we optimize it by storing solutions of subproblems, time complexity reduces to linear. Dynamic Programming is generally slower. 3. However, in order for the greedy solution to be optimal, the problem must also exhibit what they call the "greedy-choice property"; i.e., a globally optimal solution can be arrived at by making locally optimal (greedy) choices. Der Begriff wurde in den 1940er Jahren von dem amerikanischen Mathematiker Richard Bellman eingeführt, der diese Methode auf dem Gebiet der Regelungstheorie anwandte. Finally, the answer to the ith state is the maximum between these two choices. Also, each step depends on the next states, which we already calculated using the same approach. When it comes to dynamic programming, the 0/1 knapsack and the longest increasing subsequence problems are usually good places to start. It aims to optimise by making the best choice at that moment. Next, we iterate over the activities in descending order. It aims to optimise by making the best choice at that moment. So the problems where choosing locally optimal also leads to a global solution are best fit for Greedy. The idea is to simply store the results of subproblems, so that we do not have to re-compute them when needed later. Dynamische Programmierung ist eine Methode zum algorithmischen Lösen eines Optimierungsproblems durch Aufteilung in Teilprobleme und systematische Speicherung von Zwischenresultaten. In general, if we can solve the problem using a greedy approach, it’s usually the best choice to go with. Go ahead and login, it'll take only a minute. Dynamic Programming is based on Divide and Conquer, except we memoise the results. Dynamic Programming is used to obtain the optimal solution. Take this question as an example. In Dynamic Programming, we choose at each step, but the choice may depend on the solution to sub-problems. Dynamic Programming & Divide and Conquer are similar. The greedy approach is suitable for problems where local optimality leads to an optimal global solution. Suppose there are n objects from i=1, 2, …n. For example, the 0/1 knapsack problem can’t be solved with a greedy approach. Then Si is a pair (p,w) where p=f(yi) and w=yj. The total time complexity of the above algorithm is , where is the total number of activities. Where the Knapsack can carry the fraction xi of an object I such that 0<=xi<=1 and 1<=i<=n. Consider the … :). This algorithm has time complexity, because of the getNext function complexity. "Memoization" is the technique whereby solutions to subproblems are used to solve other subproblems more quickly. Greedy method follows a top-down approach. Dynamic programming is less efficient and can be unnecessarily costly than greedy algorithm. Dynamic programming approach extends divide and conquer approach with two techniques (memoization and tabulation) that both have a purpose of storing and re-using sub-problems solutions that may drastically improve performance. This approach is called top-down dynamic programming. The local optimal strategy is to choose the item that has maximum value vs weight ratio. 1. Privacy. When facing a problem, we can consider multiple approaches to solve it. Greedy Algorithm. Wherever we see a recursive solution that has repeated calls for same inputs, we can optimize it using Dynamic Programming. Taking look at the table, we see the main differences and similarities between greedy approach vs dynamic programming. Below are some major differences between Greedy method and Dynamic programming: Attention reader! In this tutorial, we explained the main ideas behind the greedy approach and dynamic programming, with an example of each approach. In cases where the recursive approach doesn’t make many calls to the same states, using dynamic programming might not be a good idea. And then we can obtain the set of feasible solutions. A greedy method follows the problem solving heuristic of making the locally optimal choice at each stage. Don’t stop learning now. Tags: Algorithmcompetitive Programmingdymanic programinggreedy approach, Difference between greedy Algorithm and Dynamic programming, Creating a Classifier using Image-J(FIJI) for 3D Volume Data Preparation from stack of Images, Spring Batch tutorials with SpringBoot -Part 1. More efficient as compared to a greedy approach. Taking look at the table, we see the main differences and similarities between greedy approach vs dynamic programming. The final answer will be stored in . Step3: The formulae that used while solving 0/1 Knapsack is, Let, fi(yj) be the value of optimal solution.


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ss is two digits, ranging from 00 to 59, that represent the second.n* is zero to three digits, ranging from 0 to 999, that represent the fractional seconds.Following his time at Louisiana State University, O'Neal was drafted by the Orlando Magic with the first overall pick in the 1992 NBA draft.He quickly became one of the best centers in the league, winning Rookie of the Year in 1992–93 and leading his team to the 1995 NBA Finals.After a season-and-a-half with the Suns, O'Neal was traded to the Cleveland Cavaliers in the 2009–10 season.
YYYY is four digits from 1753 through 9999 that represent a year.DD is two digits from 01 to 31, depending on the month, that represent a day of the specified [m]m/dd/[yy]yy [m]m-dd-[yy]yy [m][yy]yy myd mm/[yy]yy/dd mm-[yy]yy/dd [m]m.[yy]dmy dd/[m]m/[yy]yy dd-[m]m-[yy]yy dd.[m]m.[yy]yy dym dd/[yy]yy/[m]m dd-[yy]yy-[m]m dd.[yy]yy.[m]m ymd [yy]yy/[m]m/dd [yy]yy-[m]m-dd [yy]yy-[m]m-dd[m]m, dd, and [yy]yy represents month, day, and year in a string with slash marks (/), hyphens (-), or periods (.) as separators. A two-digit year that is less than or equal to the last two digits of the cutoff year is in the same century as the cutoff year.A two-digit year that is greater than the last two digits of the cutoff year is in the century that comes before the cutoff year.hh is two digits, ranging from 00 to 23, that represent the hour.mm is two digits, ranging from 00 to 59, that represent the minute.


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Baccarat, first played in French casinos, is a classic card game included in Hoyle's products.Baccarat is often thought of as a skill-less game involving almost all luck and no skill.
Eight 52-card packs are shuffled together and delt by the dealer from a box called "a shoe which releases once card at a time, face down, onto the playing table. Object of the Game
The players try to form a combination as close to nine as possible using two or three cards. Face cards and 10s count as zero, Aces count as one and other cards have a value equal to their card.When calculating a total, 10s are ignored. Using this logic, a hand totalling 11, is equal to a count of one. Naturals
Naturals is the term used when a player has a count of 8 or 9 in the first two cards. If the circumstance arises such taht the bank is the only participent to have a natural, all players that bet on the bank's hand, win. If a player(not the bank) has a Natural, all players that bet on that hand win. A natural 9 always beats a natural 8 and if two of the same naturals appear, all bets are withdrawn. 바카라사이트


1. For Windows or Linux - Press Ctrl+D
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3. For iPhone (Safari) - Touch and hold, then tap Add Bookmark
4. For Google Chrome - Press 3 dots on top right, then press the star sign
Enter your derivative problem in the input field.
Press Enter on the keyboard or on the arrow to the right of the input field.
In the pop-up window, select “Find the Derivative of the Integral”. You can also use the search.
In mathematics, Leibniz's rule for differentiation under the sign of the integral, named after Gottfried Leibniz, tells us that if we have an integral of the form.


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The student will:
- learn the topics necessary for successful first-year university studies - theorems, rules and formulas expressing the basic relationships of elementary mathematics, basic concepts of the beginnings of mathematical analysis, etc.;
- master the methods of solving and studying the main types of equations and inequalities;
- be able to formulate the studied theorems and rules in Russian, use mathematical terminology and symbols; to formulate definitions (or give descriptions) of the basic concepts of the studied sections of elementary mathematics, vector algebra and mathematical analysis, explain in Russian and write down solutions using mathematical terms and symbols.


Released Test Questions Math 2 Introduction - Grade 2 Mathematics The following released test questions are taken from the Grade 2 Mathematics Standards Test. 2nd grade math games for free. These quizzes offer a chance at teacher-assisted self-practice. explain my thinking clearly when I write so a reader can understand my math thinking; Tap/click the following links to print math tests from Unit 1: 1. 3. Your child will have fun learning 2nd grade math with mostly dynamically created problems. Your child will have fun learning 2nd grade math with mostly dynamically created problems. Enjoyable Learning of Grades 1 and 2. Preview this quiz on Quizizz. Math Interactive Online Quizzes for Second Grade. The Common Core State Standards for Math expect students in 2nd grade to be laying the groundwork for more complicated math tasks.
Addition, subtraction, place value, and logic games that boost second grade math skills. 2nd grade math games for free. Preschool Reception Grade 1 Grade 2 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade 10 Grade 11 Grade 12. It is a good place for teachers and parents to home school their kids effortlessly. But with Math Games’ wide selection of curriculum-based games, learning and perfecting these skills doesn’t have to be a chore – instead, it’s an exciting game! 1st grade math tests for kids. General math quiz questions are given for the students to increase their knowledge. Note: A score of 16 or more on this second grade math test is a good indication that most skills taught in second grade were mastered Want a solution to this test…
Word names for numbers - fourth grade math test Addition up to 20,000 - fourth grade math test Prime and composite numbers - fourth grade math test Even and odd, Fourth grade test - fourth grade math test Addition word problems up to 20,000 - fourth grade math test Addition of 3 or more numbers up to 30,000 - fourth grade math test Estimation of sums by rounding off data - fourth grade math test
In set XVII let’s complete 10 easy multiple choice questions on general math quizzes. Played 100 times. Mathematics.
***** Learning Made Easy ***** Math Kid Grade 2 is a great educational tools for school-age children. 1st grade math tests for kids to practice grade 1 skills. Second grade math quizzes online – This page is a collection of online math tests which children can use while in school or at home to review various math skills studied in 2 nd grade. Features: * App Mode: Practice/Test. Not sure where to start? 2nd grade math tests for kids to practice grade 2 topics.Quizzes are on - Addition, subtraction, division, multiplication, sets, data and graphs, comparisons, numbers, place … These quizzes are free and always online and can be used to study both on PC and mobile devices. Grade 2 (DEPED) MATH 2nd PERIODICAL TEST | College Graduate vs Grade 2 Exam - Duration: 21:01.
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Elementary math online addition quiz. ... Can you pass Math Quiz for grade 5 of Percentage Application - Duration: 4:43. 100 times. * Ability to edit student's profile. Edit.
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Women of Mathematics and Beyond
Monday, 11 June 2018 | 1.15 p.m.
Institute of Physics
THEP room, 5th floor, room 05-427
>>> Press release: "More role models in the natural sciences" (11.06.2018) <<<
The exhibition ‘Women of Mathematics and beyond’ staged by the Faculty of Physics, Mathematics and Computer Science and the PRISMA Cluster of Excellence at JGU was officially opened on Monday, 11th June. It profiles 22 female researchers working in the fields of mathematics and physics, and is designed to encourage young female science students to pursue an academic career to make up for the underrepresentation of women in their subjects.


Mon: 1pm-7pm, Tue-Thu: 10am-7pm, Fri: 12pm-6pm, Sat: 10am-6pm, Sun: Closed
It was great as usual. My daughter can't wait to go back next week. 'Math hasn't been more fun!', she says!
The children are given prompts and left to their own. There's no help or tips given whatsoever. When my daughter went up to them to show her writing, they just gave a sticker and said goodbye. Waste of time.
My daughter enjoyed it and can't wait to go back next week. The math was done in a fun way involving tricks and games.
Children worked in a non stressful environment, explored fun ways to tackle math through games and group activities. My daughter enjoyed it.
Kids liked it...it was also interactive!
Great for kids and adults. Loved it
Fun for kids
My child liked.
1243 San Tomas Aquino Rd. San José, CA 95117Enlarge Map


You have already seen one example of a function call:
The name of the function is type, and it displays the type of a value or variable. The value or variable, which is called the argument of the function, has to be enclosed in parentheses. It is common to say that a function "takes" an argument and "returns" a result. The result is called the return value.
Instead of printing the return value, we could assign it to a variable:
>>> betty = type("32")
>>> print betty
As another example, the id function takes a value or a variable and returns an integer that acts as a unique identifier for the value:
>>> betty = 3
Every value has an id, which is a unique number related to where it is stored in the memory of the computer. The id of a variable is the id of the value to which it refers.
Python provides a collection of built-in functions that convert values from one type to another. The int function takes any value and converts it to an integer, if possible, or complains otherwise:
ValueError: invalid literal for int(): Hello
int can also convert floating-point values to integers, but remember that it truncates the fractional part:
The float function converts integers and strings to floating-point numbers:
Finally, the str function converts to type string:
It may seem odd that Python distinguishes the integer value 1 from the floating-point value 1.0. They may represent the same number, but they belong to different types. The reason is that they are represented differently inside the computer.
Now that we can convert between types, we have another way to deal with integer division. Returning to the example from the previous chapter, suppose we want to calculate the fraction of an hour that has elapsed. The most obvious expression, minute / 60, does integer arithmetic, so the result is always 0, even at 59 minutes past the hour.
One solution is to convert minute to floating-point and do floating-point division:
>>> minute = 59
>>> float(minute) / 60.0
Alternatively, we can take advantage of the rules for automatic type conversion, which is called type coercion. For the mathematical operators, if either operand is a float, the other is automatically converted to a float:
>>> minute = 59
>>> minute / 60.0
By making the denominator a float, we force Python to do floating-point division.
In mathematics, you have probably seen functions like sin and log, and you have learned to evaluate expressions like sin(pi/2) and log(1/x). First, you evaluate the expression in parentheses (the argument). For example, pi/2 is approximately 1.571, and 1/x is 0.1 (if x happens to be 10.0).
Then, you evaluate the function itself, either by looking it up in a table or by performing various computations. The sin of 1.571 is 1, and the log of 0.1 is -1 (assuming that log indicates the logarithm base 10).
This process can be applied repeatedly to evaluate more complicated expressions like log(1/sin(pi/2)). First, you evaluate the argument of the innermost function, then evaluate the function, and so on.
Python has a math module that provides most of the familiar mathematical functions. A module is a file that contains a collection of related functions grouped together.
Before we can use the functions from a module, we have to import them:
>>> import math
To call one of the functions, we have to specify the name of the module and the name of the function, separated by a dot, also known as a period. This format is called dot notation.
>>> decibel = math.log10 (17.0)
>>> angle = 1.5
>>> height = math.sin(angle)
The first statement sets decibel to the logarithm of 17, base 10. There is also a function called log that takes logarithm base e.
The third statement finds the sine of the value of the variable angle. sin and the other trigonometric functions (cos, tan, etc.) take arguments in radians. To convert from degrees to radians, divide by 360 and multiply by 2*pi. For example, to find the sine of 45 degrees, first calculate the angle in radians and then take the sine:
>>> degrees = 45
>>> angle = degrees * 2 * math.pi / 360.0
The constant pi is also part of the math module. If you know your geometry, you can verify the result by comparing it to the square root of two divided by two:
>>> math.sqrt(2) / 2.0
Just as with mathematical functions, Python functions can be composed, meaning that you use one expression as part of another. For example, you can use any expression as an argument to a function:
>>> x = math.cos(angle + math.pi/2)
This statement takes the value of pi, divides it by 2, and adds the result to the value of angle. The sum is then passed as an argument to the cos function.
You can also take the result of one function and pass it as an argument to another:
>>> x = math.exp(math.log(10.0))
This statement finds the log base e of 10 and then raises e to that power. The result gets assigned to x.
So far, we have only been using the functions that come with Python, but it is also possible to add new functions. Creating new functions to solve your particular problems is one of the most useful things about a general-purpose programming language.
In the context of programming, a function is a named sequence of statements that performs a desired operation. This operation is specified in a function definition. The functions we have been using so far have been defined for us, and these definitions have been hidden. This is a good thing, because it allows us to use the functions without worrying about the details of their definitions.
The syntax for a function definition is:
def NAME( LIST OF PARAMETERS ):
You can make up any names you want for the functions you create, except that you can't use a name that is a Python keyword. The list of parameters specifies what information, if any, you have to provide in order to use the new function.
There can be any number of statements inside the function, but they have to be indented from the left margin. In the examples in this book, we will use an indentation of two spaces.
The first couple of functions we are going to write have no parameters, so the syntax looks like this:
This function is named newLine. The empty parentheses indicate that it has no parameters. It contains only a single statement, which outputs a newline character. (That's what happens when you use a print command without any arguments.)
The syntax for calling the new function is the same as the syntax for built-in functions:
print "First Line."
print "Second Line."
The output of this program is:
Notice the extra space between the two lines. What if we wanted more space between the lines? We could call the same function repeatedly:
print "First Line."
print "Second Line."
Or we could write a new function named threeLines that prints three new lines:
print "First Line."
print "Second Line."
This function contains three statements, all of which are indented by two spaces. Since the next statement is not indented, Python knows that it is not part of the function.
You should notice a few things about this program:
So far, it may not be clear why it is worth the trouble to create all of these new functions. Actually, there are a lot of reasons, but this example demonstrates two:
As an exercise, write a function called nineLines that uses threeLines to print nine blank lines. How would you print twenty-seven new lines?
Pulling together the code fragments from Section 3.6, the whole program looks like this:
print "First Line."
print "Second Line."
This program contains two function definitions: newLine and threeLines. Function definitions get executed just like other statements, but the effect is to create the new function. The statements inside the function do not get executed until the function is called, and the function definition generates no output.
As you might expect, you have to create a function before you can execute it. In other words, the function definition has to be executed before the first time it is called.
As an exercise, move the last three lines of this program to the top, so the function calls appear before the definitions. Run the program and see what error message you get.
As another exercise, start with the working version of the program and move the definition of newLine after the definition of threeLines. What happens when you run this program?
In order to ensure that a function is defined before its first use, you have to know the order in which statements are executed, which is called the flow of execution.
Execution always begins at the first statement of the program. Statements are executed one at a time, in order from top to bottom.
Function definitions do not alter the flow of execution of the program, but remember that statements inside the function are not executed until the function is called. Although it is not common, you can define one function inside another. In this case, the inner definition isn't executed until the outer function is called.
Function calls are like a detour in the flow of execution. Instead of going to the next statement, the flow jumps to the first line of the called function, executes all the statements there, and then comes back to pick up where it left off.
That sounds simple enough, until you remember that one function can call another. While in the middle of one function, the program might have to execute the statements in another function. But while executing that new function, the program might have to execute yet another function!
Fortunately, Python is adept at keeping track of where it is, so each time a function completes, the program picks up where it left off in the function that called it. When it gets to the end of the program, it terminates.
What's the moral of this sordid tale? When you read a program, don't read from top to bottom. Instead, follow the flow of execution.
Some of the built-in functions you have used require arguments, the values that control how the function does its job. For example, if you want to find the sine of a number, you have to indicate what the number is. Thus, sin takes a numeric value as an argument.
Some functions take more than one argument. For example, pow takes two arguments, the base and the exponent. Inside the function, the values that are passed get assigned to variables called parameters.
Here is an example of a user-defined function that takes a parameter:
print bruce, bruce
This function takes a single argument and assigns it to a parameter named bruce. The value of the parameter (at this point we have no idea what it will be) is printed twice, followed by a newline. The name bruce was chosen to suggest that the name you give a parameter is up to you, but in general, you want to choose something more illustrative than bruce.
The function printTwice works for any type that can be printed:
In the first function call, the argument is a string. In the second, it's an integer. In the third, it's a float.
The same rules of composition that apply to built-in functions also apply to user-defined functions, so we can use any kind of expression as an argument for printTwice:
As usual, the expression is evaluated before the function is run, so printTwice returns SpamSpamSpamSpam SpamSpamSpamSpam instead of 'Spam'*4 'Spam'*4.
As an exercise, write a call to printTwice that does return 'Spam'*4 'Spam'*4. Hint: strings can be enclosed in either single or double quotes, and the type of quote not used to enclose the string can be used inside it as part of the string.
We can also use a variable as an argument:
>>> michael = 'Eric, the half a bee.'
Eric, the half a bee. Eric, the half a bee.
Notice something very important here. The name of the variable we pass as an argument (michael) has nothing to do with the name of the parameter (bruce). It doesn't matter what the value was called back home (in the caller); here in printTwice, we call everybody bruce.
When you create a local variable inside a function, it only exists inside the function, and you cannot use it outside. For example:
def catTwice(part1, part2):
cat = part1 + part2
This function takes two arguments, concatenates them, and then prints the result twice. We can call the function with two strings:
>>> chant1 = "Pie Jesu domine, "
>>> chant2 = "Dona eis requiem."
>>> catTwice(chant1, chant2)
Pie Jesu domine, Dona eis requiem. Pie Jesu domine, Dona eis requiem.
When catTwice terminates, the variable cat is destroyed. If we try to print it, we get an error:
>>> print cat
Parameters are also local. For example, outside the function printTwice, there is no such thing as bruce. If you try to use it, Python will complain.
To keep track of which variables can be used where, it is sometimes useful to draw a stack diagram. Like state diagrams, stack diagrams show the value of each variable, but they also show the function to which each variable belongs.
Each function is represented by a frame. A frame is a box with the name of a function beside it and the parameters and variables of the function inside it. The stack diagram for the previous example looks like this:
The order of the stack shows the flow of execution. printTwice was called by catTwice, and catTwice was called by __main__, which is a special name for the topmost function. When you create a variable outside of any function, it belongs to __main__.
Each parameter refers to the same value as its corresponding argument. So, part1 has the same value as chant1, part2 has the same value as chant2, and bruce has the same value as cat.
If an error occurs during a function call, Python prints the name of the function, and the name of the function that called it, and the name of the function that called that, all the way back to __main__.
For example, if we try to access cat from within printTwice, we get a NameError:
Traceback (innermost last):
File "test.py", line 13, in __main__
File "test.py", line 5, in catTwice
File "test.py", line 9, in printTwice
This list of functions is called a traceback. It tells you what program file the error occurred in, and what line, and what functions were executing at the time. It also shows the line of code that caused the error.
Notice the similarity between the traceback and the stack diagram. It's not a coincidence.
You might have noticed by now that some of the functions we are using, such as the math functions, yield results. Other functions, like newLine, perform an action but don't return a value. That raises some questions:
The answer to the third question is yes, and we'll do it in Chapter 5.
As an exercise, answer the other two questions by trying them out. When you have a question about what is legal or illegal in Python, a good way to find out is to ask the interpreter.


MATH KID is an excellent app that provides students with visual representations to help them practice mathematical skills like addition, subtraction, multiplication, and division.
MATH FRIENDZY is a great app for practicing a wide range of mathematical skills.
With MYSCRIPT CALCULATOR, students can write math problems in their own handwriting and it will compute the problem for them.
MATH ACADEMY is a great way for students to practice mathematical skills like addition, subtraction, multiplication, and division at an elementary level.
TABTOR MATH is an outstanding app that is Common Core aligned and provides students with individualized instruction that meets their individual needs. Students' moves are recorded as they show their work so that the teacher can see where exactly students are making mistakes. Each problem is also accompanied with an instructional video explaining the process to solving the problem.
This is a free app, but doesn't work without the Tabtor program which is not free. The program can be purchased at www.tabtor.com
KIDS MATH COUNT NUMBER GAME is an amazing app for students learning numbers, counting, and number patterns.
NUMBER MATH APP allows students to practice mathematical skills that deal with number sense. Students can practice skills from patterns to rounding to greater than and less than on different levels.


Globally slots are the most popular casino games. At all gaming houses, you will find slot games. However, few players understand how the machines work. Most slot players have wrong concepts of how the slot machines operate. Slot games are thrilling but generate a lot of profit for casinos. However, with an understanding of how they work, you can change the house advantage to be yours. Go through this post to learn about how the slots work and perhaps, in the end, you may be interested in trying them.
Random Number Generators
Presently slot machines use a computer for the generation of random numbers, which in turn determine the results of your game. In the past slots used mechanical random numbers generation. Mark you, results are random, and you can’t tell a cycle base of the games. Therefore, even pros can’t predict the outcomes making the game fair to both the house and players.
Weighting Determines How Stops are Picked
Where the weight lies is where the slot machine will regularly stop. For example, a device with ten symbols and has one special symbol that comes once in one hundred spins, the odds of getting that symbol thrice is one out of a million spins. Other symbols may have higher chances of coming back, and this motivates players to continue spinning the reels
Par Sheet Controls the Odds
All modern machines for slot games are programmed with par sheets that specify weighting of stops on a reel. The stops may be on symbols or even on black spaces. Par sheets also make odds and house edges of the machines. Players may not actually understand what edge of the house and payback percentages are. However, understanding the term payback percentage is essential as it means the mathematical probabilities of the amount of machines payback.


In the vast seas of mathematics, navigating the waters of problem-solving requires not only skills but a guiding compass to steer through challenges. This article, “Mathematics Navigator: Charting a Course for Problem-Solving Excellence,” serves as a comprehensive guide for individuals seeking to master the art of mathematical problem-solving. Whether you are tackling basic arithmetic or navigating the complexities of advanced calculus, the strategies outlined here will empower you to chart a course through mathematical challenges with confidence, precision, and the precision of a seasoned navigator.
The Navigator’s Philosophy: A Strategic Approach to Problem-Solving:
Becoming a mathematics navigator involves adopting a philosophy of problem-solving as a journey. It’s not just about reaching a destination (the solution) but about navigating the intricate paths and discovering the beauty of mathematical landscapes. A navigator understands that the process is as crucial as the outcome.
Mapping the Mathematical Landscape: Recognizing Diverse Territories:
Mathematics presents a diverse landscape of challenges, each territory demanding a unique set of skills and strategies. Recognizing the diversity of these territories is essential for effective navigation. A skilled navigator understands that mapping the mathematical landscape is crucial for charting a course tailored to the specific nature of each problem.
Decoding Complexity: Navigational Tools for Uncharted Waters:
Complex mathematical problems often resemble uncharted waters. Navigating through complexity involves using a set of navigational tools to break down problems into manageable components, understand their relationships, and systematically unveil solutions. A mathematics navigator sees each complex problem as an opportunity to employ navigational expertise.
Visualization: Navigational Charts for Insightful Journeys:
Visualization is the navigator’s chart, providing a visual representation of the mathematical terrain. Creating mental images, sketching diagrams, and using visual aids enhance the understanding of mathematical concepts. Visualization not only accelerates the learning process but also provides an intuitive approach to navigating through mathematical challenges.
Building a Navigational Toolkit: Strategies for Every Challenge:
Navigating mathematical challenges requires a versatile toolkit of problem-solving strategies. From systematic trial and error to employing advanced techniques like differentiation, building a diverse set of tools ensures adaptability to various challenges. A mathematics navigator selects the right navigational tool for each leg of the mathematical journey.
Simplicity as the Navigator’s North Star:
Simplicity becomes the North Star for a mathematics navigator. Striving for solutions that are not only correct but also elegantly simple demonstrates a mastery that transcends mere computation. A navigator avoids unnecessary complexities, choosing paths that lead to clear and concise solutions.
Pattern Recognition: Navigational Beacons in the Mathematical Sea:
Pattern recognition serves as navigational beacons in the mathematical sea. Training oneself to identify recurring sequences, relationships, and hidden structures within problems expedites the problem-solving process. Navigating through mathematical challenges becomes smoother as navigational beacons guide the way.
Persistence: The Wind in the Navigator’s Sails:
Persistence is the wind that propels the navigator’s sails through mathematical challenges. Viewing problems as opportunities for growth and learning, a navigator persists in the face of difficulties. Each mathematical challenge becomes a voyage, and persistence is the driving force that propels the navigator toward excellence.
Effective Time Management: Navigating with Precision:
Effective time management is the navigator’s precision instrument. Allocating time judiciously based on the complexity of each problem ensures efficiency without sacrificing accuracy. Navigating with precision becomes a strategic advantage, allowing the mathematics navigator to chart a course through mathematical challenges with accuracy and efficiency.
Reflective Practice: Learning from Each Leg of the Journey:
Reflective practice is the navigator’s logbook, documenting insights gained from each leg of the mathematical journey. After solving a problem, taking the time to reflect on the approach, identifying strengths, and considering alternative strategies fosters continuous learning and improvement. The navigator learns and grows with each mathematical voyage.
Collaboration: Navigating the Seas with Fellow Explorers:
Collaboration becomes the fleet of ships navigating the mathematical seas. Engaging in collaborative problem-solving sessions, sharing insights with peers, and learning from diverse perspectives enrich the navigational experience. Collaboration not only broadens the navigator’s perspective but also fosters a sense of community within the mathematical realm.
Celebrating Navigational Triumphs: Hoisting the Victory Flag:
Every solved mathematical problem is a navigational triumph for the mathematics navigator. Acknowledging and celebrating these triumphs, no matter how small, reinforces a positive mindset and fuels motivation for the next mathematical journey. Celebrating triumphs becomes a ritual, affirming the navigator’s skill and perseverance.
“Mathematics Navigator: Charting a Course for Problem-Solving Excellence” encapsulates the essence of mastering the art of mathematical problem-solving. By adopting a navigator’s philosophy, recognizing the diverse mathematical landscape, and deploying a versatile set of navigational tools, individuals can navigate mathematical challenges with confidence and precision. Remember, the journey of a mathematics navigator is not just about finding solutions; it’s about the joy of exploration, the satisfaction of charting a course through complexity, and the fulfillment of mastering the artistry within the realm of mathematics. As you embark on your journey as a mathematics navigator, let this guide be your compass, helping you navigate the mathematical seas with the confidence, precision, and excellence of a true problem-solving maestro.


Adaptive Regression by Mixing (ARM) was introduced in:
Yuhong Yang: Adaptive Regression by Mixing. Journal of American Statistical Association, 96:454, 574-588, 2001.
ARM fuses the predictions of a set of models according to an estimation of their accuracy. The fused model obtained with ARM is a linear combination of the predictions of the original models. This way, it is possible to fuse predictions obtained with different models and algorithms. For instance, one could combine the predictions of a Neural Network with the predictions of CART etc.
For futher details, please check the overview of the ARM algorithm.
Data must be provided in csv format where:
All you need to provide is the path to your prediction matrix in csv format and the number of iterations:
$ java -jar armfusion.jar -csv path_to_preds -iters num_iters
At the end of the run, the fused model is printed. Below, we show a fused model obtained by fusing 5 models:
0.7 * y0 + 0.0 * y1 + 0.1 * y2 + 0.2 * y3 + 0.0 * y4
In the example, the first model y0 is assigned a weight of 0.7. Models y2 and y3 receive the weights 0.1 and 0.2 respectively while the remaining y1 and y4 have zero weights.
This implementation of ARM has been used in the following publications:
I Arnaldo, K Veeramachaneni, UM O'Reilly: Flash: A GP-GPU Ensemble Learning System for Handling Large Datasets. Genetic Programming. Lecture Notes in Computer Science Volume 8599, 2014, pp 13-24.
Veeramachaneni, K; Arnaldo, I; Derby, O; O’Reilly, UM: FlexGP: Cloud-Based Ensemble Learning with Genetic Programming for Large Regression Problems. Journal of Grid Computing. November, 2014.


Quick biography :
1944 : Ecole Polytechnique, graduated in 1947 1948 : M. S. in Aeronautics from the California Institute of Technology 1952 : Ph.D. in Mathematical Sciences from the University of Paris 1949-1957 : CNRS. 1955-57 : professor of mathematics in Geneva 1957-58 : professor at the École Polytechnique. 1958 : IBM 1987 : professor of mathematics at Yale University. IBM Fellow Emeritus, (Physical Sciences) at the IBM T. J. Watson Research Center, Professor of the Practice of Mathematics at Harvard. 1995 : Professeur de l'Académie des Sciences de l'École Polytechnique. Distinctions : "Barnard Medal for Meritorious Service to Science" (1985) Franklin Medal for Signal and Eminent Service in Science (1986) Alexander von Humboldt Prize (1988) Charles Proteus Steinmetz Medal (1988) "Science for Art" Prize (1988) Harvey Prize for Science and Technology (1989) Nevada Medal the Wolf Prize in Physics the Honda Prize (1994)
If you want to know more about Mandelbrot, check out the following pages!
Diese Artikel gehören zu: Mandelbrot Project


The PCP Calculator allows you to compare the costs of financing your car through a PCP loan and provides transparency of the real costs of PCP finance including monthly repayment schedules, costs and depreciation figures so you can make an informed choice when buying a new or used car with PCP finance. Using the PCP Calculator Using the PCP Calculator will give you access to working out the amount that your monthly car loan repayments will amount to when you have taken out a PCP car loan. The calculator will also display an illustration showing you the exact amounts you should expect to be repaying each month.
Use the PCP calculator to work out how much your month car loan repayments will be when taling a Personal Contract Purchase (PCP) car loan. The PCP car loan calculator will also provide an illustration of how much you could expect to repay each month based on different repayment periods. PCP Personal Contract Purchase Calculator Use our PCP (Personal Contract Purchase) calculator to get a full breakdown of your PCP deal. We will calculate your payments, total costs, total interest charged and provide a schedule of payments detailing each month of the contract.
APR is the "price" of a loan quoted in terms of an interest rate. Once you know how much it costs to borrow, you can compare loans and credit cards by comparing the APR. For example: In it's simplest form if you borrow £100 at 10% APR. Over the course of one year, you will pay £10 in interest because £10 is 10% of £100.
The Advanced APR Calculator finds the effective annual percentage rate (APR) for a loan (fixed mortgage, car loan, etc.), allowing you to specify interest compounding and payment frequencies. Input loan amount, interest rate, number of payments and financing fees to find the APR for the loan. You can also create a custom amortization schedule.
General APR Calculator Real APR: 6.335% View Amortization Table 74% 25% 1% Principal Interest Fees Mortgage APR Calculator Use the calculator below for mortgage loans in the United States. Real APR: 4.608% 55% 45% 0% Principal Interest Fees Related Interest Calculator | Loan Calculator | Mortgage Calculator
By multiplying the periodic APR by the payment frequency, we receive the annual percentage for the APR: APR = APR_i × q = 0.50933 × 12 = 6.232 %. Estimate Effective APR. However, the above figure isn't the actual cost of your credit, as we have so far omitted the effect of compounding interest.
This basic APR Calculator finds the effective annual percentage rate (APR) for a loan such as a mortgage, car loan, or any fixed rate loan. The APR is the stated interest rate of the loan averaged over 12 months. Input your loan amount, interest rate, loan term, and financing fees to find the APR for the loan.
At a Representative APR of 9.9% and an annual interest rate of 9.48% (fixed) you would pay 47 monthly payments of £233.86 with one optional balloon payment of £4,155.00 which includes the £1 option to purchase fee. The total amount payable (including your deposit) would be £15,396.42.
To find out what your monthly repayments could be: Enter the price of the car you'd like to buy. Enter the amount you'll pay as a deposit. How long you want to borrow for. The calculator also shows what your Annual Percentage Rate, or 'APR' could be.
The APR is how much it will cost for your total borrowed amount as a percentage. Sign in to get a personalised quote Important information: This calculator is for illustration purposes only. Your actual repayments could be lower or higher depending on your personal circumstances.
The calculator will do the sums for you. The car loan payment calculator will give you an approximate guide to what someone with a particular credit rating will get. However, when you apply for a loan, this will be based entirely on your particular circumstances, personal credit rating and the criteria of the loan provider - so your.
The calculator will show you comparison costs for personal contract purchase plans and hire purchase - based on an assumed APR - so you can see which might suit you better. Car loan option If you're buying from a private seller instead of a dealership, some car-finance options may not be available to you. But you could consider a personal loan.
Get a car finance quote. Representative example: Borrowing £6,500 over 60 months with a representative APR of 19.9%, an annual interest rate of 19.9% (fixed) and a deposit of £0. The amount payable would be £166.07 per month, with a total cost of credit of £3,464.37 and a total amount repayable of £9,964.37. This is representative of.
PCP (Personal Contract Purchase) PCP is perfect for drivers who: Want lower monthly payments; Might want to change their car at the end of their agreement; And can estimate their annual mileage. At the end of the agreement you have a few options: Hand the car back Pay an optional final payment and keep the car
Our car finance calculator gives figures for PCP, hire purchase and balanced payment agreements on prestige and performance cars. Just input a registration or car details and get figures in under 60 seconds. For refinance, private sales or a business purchase please contact us directly for a tailored quotation via Live Chat, email or phone. 1.
What you do at the end: To keep your car at the end of a PCP, you'll need to make a final large 'balloon' payment - or you can simply hand back the keys and walk away. Use our car finance calculator to see how much your new car will cost. Source: Motiv Finance. Representative 7.9% APR.
Our car finance calculator allows you to choose from any of these options to see what your repayment plan would look like. Regardless of the type of finance you choose, you will need to select how much you want to borrow, select the term of the loan and the APR. If you are taking out a PCP or HP agreement, you will need to enter your deposit.
Apr Pcp Calculator - The pictures related to be able to Apr Pcp Calculator in the following paragraphs, hopefully they will can be useful and will increase your knowledge. Appreciate you for making the effort to be able to visit our website and even read our articles. Cya ~.
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We can distinguish many game strategies based on progression and many mathematicians have searched for effective ways to win at roulette. Although not a single strategy guarantees success, the most popular strategy for a long time is the martingale strategy, which is based on the classic progression. This strategy consists of increasing the stake after each loss and returning the amount to the original value after each win.
In roulette, as well as in live roulette, players often opt for simple bets, e.g. Colours. Some are also waiting for a number of lucky wins to increase their stake, e.g. three black in a row, three odd numbers in a row, etc.
However, it is very risky to play online roulette using the martingale strategy, especially at roulette tables with strict betting limits. You will eventually get to a point where you cannot raise your bets anymore. Additionally, the rate at which the stakes are increasing can be very fast, so you need to carefully manage your money. You can try this strategy in the free demo roulette version to see how risky it is.
Another strategy that you can consider is based on the Fibonacci sequence. It is also a progressive system, but in this case the bet increases more slowly; the amount you bet is equal to the sum of the previous two.
Many players strive to find an effective way to win at this game.


An Introduction to Game Theory
Order ID 53003233773 Type Essay Writer Level Masters Style APA Sources/References 4 Perfect Number of Pages to Order 5-10 Pages
Dominant Strategies Teaching Example 1. In this 2-by-2 game Rose has 2 pure strategies: Top or Bottom. Colin can choose Left or Right. Can an economist predict which of the 4 outcomes will occur? Rose, Colin Left Right Top 1, 2 0, 1 Bottom 2, 1 1, 0 When is it okay to lie? 2. Getting Caught. Anita, Barbara and Carly share a townhouse. On Tuesday the girls promised each other to stop eating those oversized muffins from Tim Hortons. Yet, Wednesday morning Anita and Barbara catch each other in the line-up at Tim Hortons. Both girls have broken their promise. Should they tell Carly? UA UB Confess Lie Confess -10, -10 -5, -20 Lie -20, -5 -15, -15 Prisoners Dilemma 3. You and Him are taken into police custody and put in separate interrogation rooms. You can either Deny the crime or Deal (plea bargain). He has the same options. The payoffs give the number of years you will spend in jail (less is better). Can we predict the outcome? What if this was a Repeated Game? YearsYOU, YearsHIM Deny Deal Deny 1, 1 6, 0 Deal 0, 6 3, 3 Credible Threat 4. Big Pig, Little Pig (Bergstrom) Two pigs are in a Skinner Box. There are 5 kilograms of tasty pig food in a trough. If one of the pigs crosses the room and pushes the button an additional 5 kilograms of food will drop into the trough. Each pig has 2 pure strategies: Push or Wait. One of the pigs called Big Pig is faster at running across the room and is faster at eating. Little Pig is at a disadvantage. Is there a Dominant Strategy equilibrium? Could Little Pig issue a Credible Threat that would result in an equilibrium? FoodBP, FoodLP Wait Push Wait 3, 2 10, 0 Push 7, 3 9, 1 Group Projects 5. Two students are forced to by their professor to work on a group project. Their grade, G depends on how much effort each student puts into the project G = e1 + e2. Each student can either Work Hard e = 5 or Slack Off e = 1. Working has costs C1 = 2e1 and C2 = 2e2. Rewards in the payoff matrix should be computed as R1 = (e1 + e2) 2e1 and R2 = (e1 + e2) 2e2. Complete the table. Is there a Dominant Strategies equilibrium? Discuss Repeated Games in this context. Discuss Reputation in this context. R1, R2 e2 = 5 e2 = 1 e1 = 5 e1 = 1 Nash Equilibrium Teaching Example 6. Is there a Dominant Strategies Equilibrium is this game? Discuss the Nash Equilibrium (Stability) RYOU, RHIM Left Right Top 2, 1 0, 0 Bottom 0, 0 1, 2 Battle of the Sexes 7. A loving couple must decide what to watch on the living room television. There is another TV in the basement. The payoffs in the table below are often called a Game of Complements. Explain. Is there a Dominant Strategies Equilibrium? Identify Nash Equilibria. Discuss the First Mover Advantage UHIM, UHER Kenny vs Spenny Gilmore Girls Kenny vs Spenny 50, 30 20, 20 Gilmore Girls 20, 20 30, 50 Saying I Love You 8. First Mover Advantage Is there a Dominant Strategy when it comes to saying, I love you? Explain why there is no First Mover Advantage in this game. UHE, USHE I Love You Talk about Economics I Love You 15, 15 -10, 0 Talk about Economics 0, -10 5, 5 Chicken 9. Two high-school boys take their fathers cars to opposite ends of a parking lot and speed towards a head-on collision. Any boy who turns is labelled the Chicken and will undergo peer torment for the next week. Going straight is regarded as heroic. Is there a Dominant Strategy? Why is this often called a Game of Substitutes. Identify Nash Equilibria. Comment. Do we care that there are two Nash? Is there a First Mover Advantage? Discuss Reputation. UYOU, UHIM Turn Straight Turn 0, 0 5, 10 Straight 10, 5 -5, -5 Games of Substitutes 10. Avoiding your Ex (Another Game of Substitutes a.k.a Dis-coordination) RYOU, RYOUR EX Montanas Kelseys Montanas -200, -200 200, 200 Kelseys 200, 200 -200, -200 Mixed Strategies Equilibrium Teaching Example 11. Player One, who chooses Rows calculates the variable p = Probability (Top) in an attempt to keep Player Two indifferent between a pure strategy of Left and a pure strategy of Right. Player Two calculates the variable q = Probability (Left) in an effort to keep his opponent indifferent between Top and Bottom. We arrive at a Stalemate. Since both players are indifferent, there is an equilibrium. The probability of top is equal to p = __________ The probability of Left is equal to q = __________ Assume independence. What is the most likely outcome in this game? RYOU, RHIM P(Left) = q P(Right) = 1 q P(Top) = p 1, 3 2, 1 P(Bottom) = 1 p 2, 1 1, 2 Baseball is Boring! 12. A speedy runner has just reached First Base and Second Base is unoccupied. The runner has pure strategies to Steal second base or Wait. The pitcher has pure strategies to Pitch (Throw to Home) or Pickoff (Throw to First). If the runner attempts to Steal while the pitcher implements a Pickoff, the runner gets a very low reward and the pitcher is happy. If the runner attempts to Steal while the pitcher throws home, the runner is happy, and the pitcher is unhappy. Calculate the mixed strategies equilibrium. Assume independence. What is the most likely outcome? Explain why baseball is boring to watch. RPITCHER, RRUNNER Steal q Wait 1?q Pitch: p 0, 4 2, 0 Pickoff: 1?p 3, 0 0, 1 Asymmetric Payoffs 13. Adam and Bruce are looking for dates. The only available women are Carly and Diane. If both boys ask the same girl she will turn them both down (substitutes). Payoffs in this game are asymmetric. Discuss. Calculate the mixed strategies equilibrium. Interpret the probabilities calculated in Part b. UADAM, UBRUCE Bruce asks Carly Bruce asks Diane Adam asks Carly 0, 0 1, 1 Adam asks Diane 9, 1 0, 0 Rock, Paper, Scissors 14. Player A (Rows) calculates p1 = Probability (Rock) and p2 = Probability (Paper) and obviously p3 = 1 p1 p2 in an effort to leave her opponent indifferent between pure strategies. Player B (Columns) calculates q1 = Probability (Rock) and q2 = Probability (Paper) in an effort to leave his opponent indifferent between Rock, Paper and Scissors. Discuss the resulting equilibrium. What would be the Mixed Strategy when Sheldon and Leonard play Rock, Paper, Scissors, Lizard, Spock? $YOU, $HIM Rock Paper Scissors Rock 0, 0 1, 1 1, 1 Paper 1, 1 0, 0 1, 1 Scissors 1, 1 1, 1 0, 0 Closing Comments 15. Discuss why All Dominant Strategy Equilibria must also be Nash Equilibria. Mixed Strategy Equilibria do not exist in a game where there is a Dominant Strategies Equilibrium. Old Test Questions 16. Adam and Andrea Adams have been married for two years. Bob and Bernice Loblaws have been married for three. Every Tuesday night Adam and Bob go bowling. One Tuesday night Andrea accidentally runs into Bernice at some questionable Mississauga bar. Trouble is that Andrea is wrapped around some guy named Thor and Bernice is flirting with Fabio. Each lady faces two possible Pure Strategies. She can either Talk and tell her spouse about his friends wife or Lie; saying nothing. Her payoff depends rather critically on the strategy followed by the other woman. Payoffs below are in terms of utility. Based on the matrix above identify the equilibrium outcome. Briefly discuss whether it would be worthwhile for the two women to form a Pact prior to returning home. If so, how would that Pact work? R1, R2 Player Two Talk Lie Player One Talk -5, -5 5, -20 Lie -20, 5 0, 0 17. A market is supplied by two firms. Each firms revenue R depends on whether they advertise or not. Each firms revenue also depends on whether their competitor advertises. Payoffs in revenue are shown in the matrix below. Advertising costs $2. Profits are revenues minus advertising costs. Assuming that firms act to maximize profits, what is the equilibrium outcome of this game? Would it be worthwhile for these two firms to form a Pact? If so, what would be the terms of this agreement? R1, R2 Player 2 Ad No Ad Player 1 Ad 3, 3 5, 0 No Ad 0, 5 2, 2 18. Cathy and Karen have exclusive rights to provide babysitting services in their neighborhood. Each babysitter can either charge $5 or $10 per hour. Their weekly revenues depend critically on what price the other sitter charges. A payoff matrix shows their potential revenues. Briefly discuss the equilibrium outcome of this game. Re-write and solve this payoff matrix as a tree-diagram. Discuss whether it would be worthwhile for the girls to form a pact in this situation. R1, R2 Karen 5 10 Cathy 5 200, 200 400, 100 10 100, 400 250, 250 19. The payoff matrix to a game is provided below. Payoffs depend on the unknown parameters of ?, ?, ? and ?. (a) Solve for the Mixed Strategy Equilibrium in terms of these unknown parameters. Solve for restrictions which must be placed on the values of these parameters which ensure that [Top | Right] is a Dominant Strategy Equilibrium. Solve for restrictions which must be placed on the values of these parameters to
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Four County High School Math Field Day
Two cars leave from the same place at the same time, traveling in opposite directions. The rate of the faster car exceeds that of the slower car by 16 miles per hour. After 2 hours, the cars are 180 miles apart. Find the rate of the slower car.
On March 13, 2018, students from Boone, Clay, Kanawha and Putnam counties will answer questions like this (and harder ones) as they compete at the University of Charleston in the RESA III Regional Math Field Day competition. There will be 112 students competing in this event.
Each county sends three students per grade (grades 4-9) and a high school team of 10 students, representing grades 10-12, to compete. The 4th-9th grade students compete for individual awards and 10th-12th grade students compete for both individual awards and team awards. Individual awards are given for the top three places in each grade 4th-9th and the top 10 places in the high school (10th-12th) division. A team award is given to the county high school (10th-12th) team with the highest score on team events. Individual winners go on to compete at the State Math Field Day competition.
For more information about the event, please contact Jennifer Grimsley Hoffman, Program Director – Mathematics, University of Charleston, 304-357-4887 or email@example.com.
The answer to the problem, by the way, is 37 mph.


Image via WikipediaCable Green was featured in the Chronicle of Higher Education in an article called "State of Washington to Offer Online Materials as Texts" by Martha Ann Overland. I loved the article because it promotes all of the things I am so excited about in education right now: free, openly licensed textbooks, open education resources, and the creation of communities that are creating freely accessible learning materials. It is a well-written and balanced article that discusses the promise and possibilities of OER as well as the problems
I was surprised to see that they were having problems finding math resources: "During a recent meeting of mathematics professors and librarians who are designing the courseware for Washington's algebra, precalculus, and statistics courses, it was clear that no one was completely satisfied with what could be found online."
I work at College of the Redwoods where the Math department has created a couple of textbooks and I received an email from David Nelson who is the project manager for the Florida Distance Learning Consortium to let me know about the free pre-algebra textbooks at the Stitz-Zeager website (this looks like an excellent collection).
There is also a free webinar happening on Thurs. Jan. 13th on a free online math textbook at The Stitz-Zeager Open Access Precalculus Project.
There are links to College of the Redwoods open math textbooks in this post here:


We were all very excited to invite our parents into the classroom this morning to have a go at some maths activities together. Our main focus was pattern and trying to create more complex patterns which had more than 2 shapes. The activities included decorating biscuits, using nature to make patterns, printing using fruit and making patterns using peg boards. We also wanted to show out parents how well we are doing with learning our number bonds to 10 so some activities allowed us to explore that with them. Otters were so happy that their parents were able to spend the morning in the class with them.


Course: Elementary Math – Grade 5
Grade Level: Advanced 4 – 5 (struggling 6th graders may apply)
Day/Time: Monday 9:00 – 10:15am
Instructor: Cathy Youngblood
Cost: $48 per month + $20 application fee
Books: Saxon Math Homeschool 6/5, Student textbook (3rd Ed.), ISBN# 1591413184. Saxon Math Homeschool 6/5, Tests and Worksheets (3rd Ed.), ISBN# 1591413222; Saxon Math Homeschool 6/5, Solutions Manual (3rd Ed.), ISBN# 1591413265. You can purchase all three as a kit at CBD.
Description: We will cover the concepts students need to master as they prepare for Middle School Math. Various concepts include: order of operations, geometry and measurement, integers, divisibility concepts, ratios, statistics and probability, prime and composite numbers, patterns and sequences, decimals and percentages, powers and roots. Students will specifically learn about making a multiplication table, adding/subtracting fractions with a common denominator, multiplying by multiples of 10 and 100, perimeter, simple probability, decimal parts of a meter, reciprocals, volume, square roots, graphing points on a coordinate plane, and more. In addition to classroom teaching, other resources will be used to enhance the class and help students to better understand the course material when they are working on their own. Homework will be assigned for each day of the week, and tests will be given periodically to solidify the student’s understanding of the material. If your child is advanced in math as a 5th grader, and will be heading into 6th grade math, please look into Middle School Math #1 class.
Course: Middle School Math # 1
Grade Level: Advanced 5 – 6 (struggling 7th graders may register)
Day/Time: Wednesday 9:00 – 10:30am
Instructor: Ellie Ingle
Cost: $58 per month + $30 application fee
Books: Prentice Hall Mathematics: Course 1 (2003/2004 ed.), ISBN# 0130631361; Prentice Hall Math Course 1 Study Guide and Practice Workbook (2004 – paperback), ISBN# 0131254553. Order used online or call 1-800-848-9500.
Description: This is an introduction to what students will face as they enter middle school math. We create a path for students to develop an in-depth understanding of key mathematical concepts needed to succeed in higher level math classes. This foundational class introduces the concepts needed for Middle School Math #2 (7th grade math) and some early Pre-Algebra. We will cover whole numbers, rational numbers, decimals, number theory, fractions, ratios, proportions, percentages, data/graphs, geometry concepts, and integers in preparation for one-and two-step equations and inequalities. In addition to classroom teaching, some on-line teaching resources (videos & examples) will be used to enhance the class and help students when they are working on their own to better understand the course material. Homework will be assigned to enhance classroom lessons and given for each day of the week, while tests will be given at the end of each chapter. If your child is advanced in math as a 6th grader, please look into Middle School Math #2 class.


Something I’ve been thinking about lately is the cost of commuting. If your daily commute takes 20 minutes (round trip), as mine does, how much time are you really spending per-month, and per-year behind the wheel?
Let’s do the math.
There are 251 working days in 2013, and assuming 10 days of vacation per year it’s safe to assume the average person will commute 241 days out of the year.
Therefore, we come down to total time behind the wheel in 1 year: 80.33 hrs. DANG! So, yeah, for a short commute like that, the average person spends two-work-weeks behind the wheel. Tragic.
You could be spending more than 160 hours, or a months worth of work-time behind the wheel every year if you have a 20 minute one-way drive.


Marc Levoy has been one of the key leaders behind Google’s recent advances in computational photography, including portrait mode & HDR+. He’s also a professor emeritus at Stanford, and in this lecture series, he offers a very thorough, technical education in digital photography—for free.
The only knowledge I assume is enough facility and comfort with mathematics that you’re not afraid to see the depth-of-field formula in all its glory, and an integral sign here or there won’t send you running for the hills. Some topics will require concepts from elementary probability and statistics (like mean and variance), but I define these concepts in lecture. I also make use of matrix algebra, but only at the level of matrix multiplication. Finally, an exposure to digital signal processing or Fourier analysis will give you a better intuition for some topics, but it is not required.


My dad sent me this little blurb in an email today and I thought it was worth sharing. Enjoy nerds!
Yesterday afternoon, per the Census Bureau, the U.S. population reached a milestone that is very meaningful to mathematicians: 314,159,265 residents, or pi (3.14159265) times 100 million. Pi is a mathematical constant that is the ratio of a circle’s circumference to its diameter. “This is a once in many generations event…so go out and celebrate this American pi,” said Census Bureau Chief Demographer Howard Hogan.


Click on Sudoku Index of videos, then click on video number. This is an Excel file. It will appear at the bottom of your screen click on it to open it.
Attention all teachers looking for valuable resources for the classroom. These are lessons using PowerPoint, videos and printable activities designed as a step-by-step approach to teach students how to do sudoku puzzles.
1 Q What is the goal of Sudoku?
A All rows, columns and blocks need to have the numbers 1 to 9. You cannot have a number repeated in a row, column or block.
2 Q What are the values of solving Sudoku puzzles.
A Sudoku offers relaxation and fun while enhancing brain fitness. It improves memory and encourages logical thinking. With patience and a touch of humility, players can tackle increasingly difficult puzzles. The challenge is satisfying and a positive way to use spare time. Solving a puzzle correctly motivates you to try another and to move from easy to ever harder levels.
3 Q Can I guess?
A Not a good idea. You may be lucky; however, usually it doesn’t work. Avoid guessing. Sudoku is based on logic.
4 Q Can you suggest a book to purchase?
A I don’t recommend any specific book because publishers use different guidelines for what they term easy or hard. One book may call certain puzzles easy that are actually medium or difficult according to another publisher’s standards. If you purchase a book, use its designations of difficulty with caution.
5 Q I use the puzzles in the local newspaper and find the grids so small I end up with a mess.
A Yes, you are right. Here are 3 suggestions. First, copy the puzzle onto a large grid that you make up your self. Second, as you solve numbers, erase the small numbers instead of just crossing them out. Third, look for books with only one puzzle per page. I find these less messy.
6 Q Today I solved a puzzle. It was hard. I think it has more than 1 solution. At the end, I had four matching 4/5 pairs, two in one column, two in another. They lined up like a rectangle. It didn’t matter where I put the first 4, the others worked out perfectly. Is that possible?
A You have a good question. That situation is possible but so rare. It is more likely you overlooked an earlier mistake. Purists claim only a mistake or a poor puzzle allows for that scenario. If you have 4 matching pairs, of the same numbers, which make up a rectangle, something is likely wrong. Technically this type of puzzle is not a true puzzle. That should NOT happen in a legitimate puzzle. Watch a future tutorial on this topic.
7 Q Is it true that a puzzle with more starting numbers is always easier than one with fewer numbers?
A Generally, the more numbers, the easier the puzzle. However, this is not always the case. It depends on the algorithm used to create the number configuration. One book I am familiar with has an average of 26 numbers per puzzle, which should be difficult but not overly so. The puzzles in the book are fiendish.
8 Q Why do you underline all pairs?
A As you progress towards more difficult puzzles, an underlined pair reminds you that only those 2 numbers can go into that cell.
9 Q What should I do if I get stuck.?
A Go over the steps I cover in the course in order. If you don’t see any solution, take a break and come back later. It is amazing how often you come back to the puzzle later and suddenly see something you missed earlier.
10 Q Is the aim to complete the puzzle quickly?
A Not necessarily. Some online programs encourage you to time your performance and compare your time with others. However, the choice is yours. Rushing often leads to mistakes. Competitive players try for speed, which can be fun. It’s up to you.
11 Q What do TMB and LCR stand for?
A TMB Top Middle Bottom. This refers to horizontal blocks. Each block has a top, middle and bottom row of numbers. The three horizontal blocks have a top, middle and bottom row which correspond to each block as well. In a horizontal set of blocks you should NEVER have a number repeated. That is, you cannot have any number in a top middle or bottom row twice within a horizontal set of 3 blocks.
LCR Left Centre Right. This refers to vertical blocks (3 blocks) Each block has a left, centre and right column of numbers. In a vertical set of blocks you should NEVER have a number repeated. That is you cannot have any number in a left, centre or right column twice within vertical set of 3 blocks.
This is a fundamental technique and procedure of my course. It is used throughout the whole course extensively. And now it is used worldwide. Makes me feel good seeing it was me who developed it.
12 Q When should we look at the answers?
A Hopefully never!!! If you complete the puzzle you can check yourself easily whether it is correct. The only time I look at the answers is to check to see if when trying new logic I am correct. This is dangerous.
Why? It is so easy to look at another number nearby, which is really cheating and the temptation to put that number in is great. You need lots of self-discipline. Avoid entering any number you have seen until you have worked out the logic for it.
13 Q What do you suggest to do if you have only 2 or 3 numbers left to solve and realize that you have made a mistake.
A You have several options.
1 Put a line through the puzzle . Try another puzzle. Above all SMILE. It’s not the end of the world.!!!
2 Erase all the answers and try again. This can be messy.
3 Look over what you have done and see if you can find a number repeated in a row, column or block.
4 Take a blank grid and transfer the original numbers. Try again.
5 Look at the answer sheet.
14 Q Is it possible to solve a puzzle different ways?
A. Yes. The more techniques you learn the more the possibility of you missing a procedure or a technique. 5 people doing the same puzzle can come up with the correct answer, but each may have gone a different route depending what they did or didn’t see or what procedure they used or missed out. It is possible that you can solve a puzzle without doing certain techniques. E.g. You may be able to solve a puzzle using the Xwing technique while someone else solves the same puzzle using another technique.
My course gives you a basic procedure to get going, then as you get into more difficult puzzles you may go a different direction.
The procedures I suggest are such that you can avoid missing opportunities and at the same time self correct as you go by using another technique.
15 Q Does it always happen that if you solve a new number that will enable you to complete the puzzle?
A Not necessarily
16 Q Lesson 6. Can you elaborate more on the Rule of Exclusion.
A If you are using the technique of only putting small numbers in only 2 cells of a row, column or block, then you can exclude any other small numbers that may appear in that row, column or block. I have prepared an addendum to show this more clearly.
17 Q In lesson 7 is there a discrepancy. Re 3 small similar numbers in a block?
A No there isn’t. I may have not made it clear. If a small number can go in a block in a line. (either vertical or horizontal) then it is OK. If the small number can go in a block but it is not in a line, then I suggest you don’t put any small numbers in. One of the powerful features of Sudoku solving is keeping small numbers to 2 cells. The advantage is that if you solve one number then you know the other number. If there are more choices once you have solved one cell, it may become more difficult to know what the other 2 cells should be. There are times when you get to the very difficult puzzles where you will need to put in more than 2 small numbers in a row, column or block.
18 Q In lesson 21, is it possible to solve that puzzle without using Xwing?
A. Yes. There are many ways to solve a puzzle once you have many procedures and techniques.. I suggest Xwing as only an option if you get stuck. Xwing , skyscraper and swordfish patterns are hard to spot.
19 Q I noticed that you missed several ramifications. Is this deliberate?
A Sometimes yes, sometimes no. I some cases I want to show that you can miss something but find it later, and sometimes you simply miss it by mistake. It is not the end of the world. Everybody does it including me. Later in the course I show you techniques to check yourself to see if you did miss something.
20 Q Do you cover every technique possible to solve Sudoku puzzles.
A. No I don’t. There are many ways to solve these puzzles. For example: you can use another similar “When all else fails” technique. I’ll explain….if you have a small number, which can only go in 2 cells in a row column or block, you can chose one cell with that number in one of the 2 cells and see if it works. If it doesn’t work, then the other one should, providing all your numbers solved so far are correct. This is another “if not this then that” scenario. Thanks to my friend Margaret for showing me this technique.
At the advanced level, you will find some quite complicated techniques. These are for the fiendish level puzzles and are seldom needed in puzzles that are “just” very difficult. These techniques are easier to identify if you use a computer program that enables you to put in all the possible numbers with a click.
One of the skills of Sudoku solving is to correctly work out all possible numbers in a cell. This takes time in the advanced puzzles and can be tedious, and messy. Having the computer software program fill them in for you keeps the puzzle neat, but you lose the chance to learn why each number is needed. The purist will say do your own small numbers. It is your choice.
21 Q From your experience what do you see as the biggest problem of beginning Sudoku players?
A They try harder puzzles too soon.
22 Q Can I do ram (ramifications( if I see them when doing the first step, which is horizontal blocks.
A Yes you can. The reason I introduce ram in the second lesson is that this is a step by step course and beginners do not need too many steps at once, and they also need to understand the LCR principle as well.
Once you have had plenty of practice using ram, then by all means if you see the opportunity to get a number put it in, and then look for more ram.. Now you need to remember where you were in the procedure and go back to it where you left off. For me that is a test of memory!!!
23 Q How many different Sudoku puzzles are there?
A 16,930,529,280. This has been refuted by others, however the number is still very high
24 Q Can you solve Sudoku puzzles without putting in any small numbers?
A. Yes you can. In fact it provides a good system for you to use your memory.
25 Q, Do the video tutorials cover the same techniques and hints as you provide in the other courses.
A. Yes and no. I cover the same techniques and procedures, however I add many more techniques, scenarios, hints and procedures.
26 Q Can you do the “video tutorials without having done the other Sudoku Guy courses?
A Yes you can, however having had the previous courses will help. It does cover more sophisticated solving however an experienced Sudoku player would find it no problem.
28 Q Why should I avoid putting all possible numbers in an empty cell
A Thanks Guys, Just taught Jeanette not to put all possible numbers in a cell but to put small numbers in only if they can only go in 2 cells in a row, column or block. If a small number can go in more than 2 cells in a row, column or block then DON'T put them in. In the advanced puzzles this may not be the case. I use this procedure for all puzzles to begin with. Why do I suggest this?..... 1 it can become very messy particularly if the grid has small cells.....2 when you do solve a number you need to be careful to eliminate all of those numbers in that block, row or column.
Debbie H "If Robin Jarman can teach me not just to play Sudoku but to truly enjoy it, He can teach anyone. I may have been his most challenging student, questioning the value of every new technique. He is born teacher, patient and clear every step of the way. Thanks to him, I've gone from skeptic to fan and do Sudoku every day
.ajCosta "You are an excellent teacher”
Vernon Osier “Great demonstrations for beginners. Thank you.
Suresh Ife "Thank you Mr. Robin for your great videos. I learnt many many techniques from your videos"
Ramchander "Just wonderful. Great teacher. Kept me confident to solve puzzles."
CWellner "Sudoku had no appeal for me until Robin got me started. Now I'm addicted and can tackle challenging puzzles, thanks to his clear, step-by-step guidance."
I say to myself "I love your teaching style"
Jyoh Bilat "You're just awsome"
J aune "Oh my this is the best video yet"
Burton Hennig Very Very Good. thankyou Robin. That helped a lot.
Jim W "Sudoku guy...thanks for still doiing these videos. I really enjoy them."
Louise Mans "Sudoku Guyy ou are brilliant. Sometimes you are funny and I laugh with you. sometimes you are clumsy and I relate to that (Lessson 7) but you never gave up on the cardboard strips!"
Sangeetha Dhakshab "Your way of teaching is so easy to understand."
Bridgendesar "it's a wonderful way to keep the brain sharp"
Bryson Xias "Cool ...another trick to think about"
Anasta3d ""Thanks very much for your lessons...very helpful and nice to watch"
Tom Markson " I prefer putting in my pencil marks rather than let the app do it for me"
Amy Koo "Great for me learning step by step"
petla bhavya "I like the way you teach and it is not boring"
Jason Power " A joy to watch"
Graeme McGregor "Those who say they can do sudoku without putting in small numbers are either geniuses in which they don't need your help or they have not yet got into very difficult puzzles."
Rosario Strano "thank you for a step by step procedure that fine tunes the search for a missing #"
Marisa Robertson. "thanks for teaching me how to do sudoku in a straight forward fashion"
Vishal Gaur "Your knowledge means a lot."
Ay Samuel "I was smiling and learning. This is awsome."
Grace Smith "Very good teaching on how and where to place numbers in rows, columns and blocks."
Barbara Cronkite " Great job explaining"
Van Ster " your techniques got me interested in Sudoku again."
Nica Q "I looked at every lesson. You are clever, funny, and an enjoyable guy. I hope you never lose your enjoyment of life."
Mukund Verma "kudo to you for explaining Sudoku in a lucid way."
Anthony Vincent "I watch all of your videos thanks to you"


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Ngo Bao Chau is a mathematician who is best known for his proof of the Fundamental Lemma, an intricate problem in number theory. He has been awarded with the Fields Medal in 2010, which is generally regarded as the highest distinction in mathematics. He teaches in the University of Chicago and also serves as the scientific director of the Vietnam Institute for Advanced Study in Mathematics. He is an editor of Inventiones Mathematicae, one of the best mathematical journal.
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