In part 1, and part 2 of this series, I looked at overengineering 'making dots on a piece of paper' by using multiple robots. So far, I was not too concerned with finding an optimal solution, but rather with finding a solution that works well for one (in part 1) or two (in part 2) robots. Now, I want to look at how big the difference between an optimized solution, and the greedy solutions I produced so far is.
In previous posts, I looked at finding poses for robot arms to make dots, sorting the poses, and then finding paths for one robot in part 1, and for two robots in part 2. Even though this is part 3, I am not going to look at extending our approach to three robots (for now).
Instead, I am going back to only a single robot arm, and will compare the previous approach of generating a single dot-making-pose and greedily ordering the poses to generating multiple poses, and ordering them more optimally.I do not yet want to claim the optimal path, since I am still making a few approximations that impact the optimality along the way.
I am still assuming that I am getting a set of dots (2d coordinates) as input and want to output a path in joint-space of the robot that makes those dots onto the paper. I am not taking dynamics of the robot into account, i.e. I am planning geometrically only. This simplification is a valid approximation, since we have a good low lever controller, that (if we are not operating at very high speeds or with high loads) can track the path that a geometric planner produces well.
Compared to part 1, we are trying to optimize the path a little bit, instead of only looking for a reasonably good path. That is, our objective is time-optimality: Ideally, we want to find the path that makes all the dots the fastest. However, as alluded to before, finding the optimal path maps roughly to the traveling salesman problem, which is notoriously hard.
Additionally, since every dot can be made from various poses, we have multiple groups of poses which need to be visited exactly once. This is called the “Traveling Salesman Problem in Neighbourhoods”.
Instead of actually computing the time-optimal path between all poses, we use the infinity norm as distance metric between poses.I.e. the distance between two poses is the maximum absolute difference between all its elements This represents the time it takes to get from pose 1 to pose 2 fairly well, since a typical controller would steer each joint of the robot arm seprarately, i.e. the time it takes to get from pose 1 to pose 2 is the maximum time one of the joints takes.
Prior research for the traveling salesman problem with neighbourhoods are e.g. , , , or the two following here, which are concerned with robotics versions of the travelling salesman problem:  .
The problem we are tackling here is an ‘easy’ version of the two robotics papers above, since we do not have any obstacles in the environment which may make our path planning harder. The goal we have is then finding a good sequence of poses given a set of poses for each dot, i.e. finding both the sequence, and finding the right pose.
‘Solving’ the TSP for a single pose
First, we implement a ‘proper’ TSP algorithm for the single-pose case. Even though we likely have little enough poses to being able to find the exact solution, exhaustive search does not scale well, and we are thus skipping that approach directly.
We are implementing two approximation algorithms in addition to the purely greedy approach from before:
- Greedy with longer lookahead
- Simulated annealing
In both cases, I run the resulting path through an algorithm that tries to improve the result that we got. Here, I do that by locally reversing subtours and checking if that leads to a better result.
Simulated annealing is a well discussed approach for the TSP, and thus, I’ll only link to some other resources here: 1, 2. For me, an exponential cooling schedule worked well, and the transformations of the current solution I used were ‘swapping poses’ and ‘randomly reversing subtours’.
‘Solving’ the TSP for a neighbourhood
Finding a solution to the TSP with neighbourhoods can be done in various ways. However, as for the standard TSP, we are not getting the optimal solution here, but rather an approximation, since solving it is computationally not tractable.
We are going to look at a baseline of simply being greedy and simulated annealing for the neighbourhoods. I originally also planned to implement a greedy version with lookahead, but already did the experiments for a single pose, and noticed that the simulated annealing approach was much better, or said differently: The lookahead sometimes made the solution worse.
Simulated annealing for TSP with neighbourhoods: is close to the normal simulated annealing, except that we also need to include an operation that swaps poses. Thus, the transformations we use are the two from above, and swapping poses for a randomly chosen dot.
Comparison & Results
To compare the planners we produced above, we need a few testcases. We largely reuse things we have used before: a grid, a set of random points, a spiral, and part of our labs logo.
The methods I have implemented are summarized in the table below along with the pathlength of the method for each test. I marked the best result for both single-pose, and neighbourhoods italic, and the best overall in bold.
|Greedy with lookahead l=2||5.794||2.465||3.78||0.845|
And here is how the dots in the grid are ordered by the methods.
The ordering above does not seem like it makes a lot of sense from an optimality standpoint. What we are interested in is the time the robot takes for a given path. Since each joint typically has its own maximum velocity, the time each path segment takes is limited by the longest distance a single joint has to cover. We can compute the maximum velocity of each joint during the path segment, and then scale all the velocities such that the largest velocity in the segment reaches the maximum velocity. From this, we can then compute the total time each path segment would take, and thus compute the total time the robot takes for the path.
Finally, here is a side-by-side comparison of the greedy with sets and the TSP with a set of poses.
With times 1.902 and 1.422 (reload the page to restart the gifs at the same time).
I once more want to point out that the order of the dots does not necessarily seem to make sense as the ‘best’ path. The path we should get here should correspond to the shortest/best path in joint space of the robot, and thus be reasonlably close to a time-optimal path.
It came as a surprise to me that the methods with a longer lookahead do not necessarily outperform the simple methods. This likely has two reasons:
- We always perform a polishing step after we found the initial path, and some of the solutions that we obtain with a shorter lookahead might turn out better.
- The other reason is that the greedy methods are suboptimal, and it might simply be the case that a method with a longer lookahead is locally better, but turns out worse overall. (I.e. the longer lookahead digs itself into a deeper hole globally).
Further, it is clear that ‘global’ methods such as simulated annealing outperform the greedy methods on the small sets of experiments that I did here.
Sets of poses outperformed the single pose almost in all cases. In the one where it did not, I would expect that more runtime would also lead to a better solution, but I did not verify that.
- We ignored dynamics in this post. If we are truly looking for a time optimal path, this has to be taken into account.
- Additionally, we have neglected the actual path length, respectively the time it takes to traverse a path to the next pose. From experience, the use of the infinity-norm as proxy for this is reasonalble, but should be properly tested.
- Lastly, it is not completely obvious how this not translates back to multiple robots, since in addition to an ordering problem, we also need to answer the question how to assign points.


Using layouts and charts is a great method to display info and present your ideas to your viewers. They can assist you to explain complicated information with out going overboard. http://infographicsaplenty.com/best-electronic-data-rooms-for-business/ Yet , selecting the right an individual for your needs may be tricky. Thankfully, we have supplied a few guidelines to make sure your layouts and chart are when effective as possible.
A graph is one of the most common types of diagrams. It can be used to illustrate statistical data and demonstrate trends.
The graph is often used for basic numbers, while a graph and or chart is more suitable for complex info. You can also use a graph showing changes over a period of time.
Pictograms are another type of visualization which can be used to explain rate of recurrence of data. They could be used to compare two points emotionally.
A pie chart is another example of a graphical rendering of quantitative proportion. This can be a largest data type that a lot of people are familiar with.
Another prevalent type of information is the path chart. Generally, the graph and or chart has a straight axis and a side to side axis. Each axis may have a dimensions and a label.
If you are looking to choose your data take a look beautiful, you’ll want to pay attention to the aesthetics of the graph. Color coding can also be helpful.
There are numerous different types of chart, but the many popular are definitely the bar graph and or and the chart. These two are useful for displaying trends and making predictions.


- to add and subtract up to 100;
- to make, write down and solve examples and tasks;
- to acquire a graphic, sound, quantitative image of a number – the concept about structure of number is given.
The wide range of logical games and tasks is offered.
Further, the children master mathematical actions with multidigit numbers (hundred, one thousand, millions, etc.)
They master the skills of the oral counting (not only addition and subtraction, but also multiplication and division).
- the child learns names of numbers until 100, learns to write down them,
- the kid learns to make, write down and solve examples and tasks,
- the child learns to perform logical tasks of different levels of complexity.
- Age: From 4 years and older
- Number of children in the group: 7-8 kids
4 stages (8 months), the duration of each stage is 2 months (20 classes)
Accessories for classes:
A pencil, squared exercise-book, a folder for papers, indoor footwear.
Classes are held 3 times a week with each class lasting 50 min and 10 min for the Parent-Teacher talk on Sunday, Tuesday, Thursday or Monday, Saturday.
A bit about the course
The groups are formed according to the age of children and already existing skills.
As a basis we took Zaytsev’s methodology “Thousand and More” and logic games by Nikitin B.P.
The groups are formed according to the age of children, existing skills.


If you have curriculum to sell or a service related to homeschooling to offer, we will post an 'ad' for you!
Email all the details to Keri Betters at firstname.lastname@example.org.
Please remember to also include your name, email address, product/service details, and price.
Do not send photos or attachments; but rather, include all the information in the body of your email.
Reminder: Only GCA families may post ads. We reserve the right to limit the number of items allowed per seller.
All curriculum for sale can be found underneath the "Recommended Tutors/Services" section of this page.
Mark Betters (Chemical Engineering major at University of Delaware; graduated May 2017)
Any subject, especially math (any level including Calculus); Physics, Chemistry
Can tutor at GCA, RLCA, or at the student's home
$25 per hour
Leigh Ann Betters (Math/Writing/SAT/ACT Prep teacher at GCA)
Middle school math through Algebra 2; SAT/ACT prep; Writing
Will work out times/locations on a case-by-case basis
$25 per hour
Adelina (Addie) DiGiacomo
Piano accompanist - $25 fee: includes one rehearsal and one performance
Francesca Digiacomo (Violin teacher apprenticed by Kathleen Hastings)
Beginner violin lessons for students ages 4 and up.
Lessons at her home. Will work out times on a case-by-case basis.
$18 per half hour
Middle School Math -- $30/hour
High School Math -- $35/hour
Will work out times on a case-by-case basis
Change Textbook, c. 2012 - $50


As so many candidates have been asking the questions on the jamb recommended textbooks for Mathematics, it is obvious that they are preparing for the forth coming jamb exams. Using the right textbooks while preparing for jamb exam is one of the keys to exam success.
You will see some of the mathematics textbooks which will guide you while preparing for jamb exam. I hereby advise you get one, two or three of these books.
List of Jamb Recommended Textbooks For Mathematics
1. Adelodun A. A (2000) Distinction in Mathematics: Comprehensive Revision Text, (3rd Edition) Ado –Ekiti: FNPL.
2. Anyebe, J. A. B (1998) Basic Mathematics for Senior Secondary Schools and Remedial Students in Higher/ institutions, Lagos: Kenny Moore.
3. Channon, J. B. Smith, A. M (2001) New General Mathematics for West Africa SSS 1 to 3, Lagos: Longman.
4. David –Osuagwu, M. et al (2000) New School Mathematics for Senior Secondary Schools, Onitsha: Africana – FIRST Publishers.
5. Egbe. E et al (2000) Further Mathematics, Onitsha: Africana – FIRST Publishers.
6. Ibude, S. O. et al (2003) Algebra and Calculus for Schools and Colleges: LINCEL Publishers.
7. Tuttuh – Adegun M. R. et al (1997), Further Mathematics Project Books 1 to 3, Ibadan: NPS Educational.
8. Wisdomline Pass at Once JAMB.
During your study time, try to use your mathematics jamb past questions too. This will help you to get likely repeated questions.
Also See the below which you’ll find helpful
- See How 2019 Jamb Questions Will Look Like
- 20 Possible Questions from JAMB Sweet Sixteen Novel [CBT]
- JAMB 2019 Brochure For All Courses And Institutions
- How to Read And Pass JAMB 2019 Once without Cheating & Sweating
- Jamb 2019 whatsapp Group
HOT: SEE SCHOOLS THAT JUST RELEASED THEIR ADMISSION LIST
SHARE THIS NEWS


NEW 3-Hour Drop-Off Program!
Drop your kids off for 3-hours of learning and fun! STEAM Learn & Play is an engaging program for children ages 4 through 9 that includes Science, Technology, Engineering, Arts, Mathematics and, of course, physical exercise and fun.
- Every week features a new theme (e.g., Superheroes, Frozen Fun, Space Exploration, Ninja Training, and more). Each class throughout the week will feature a variety of activities and different STEAM elements, so no two classes are alike!
- Schedule: Tuesdays and Thursdays from 1:00 PM – 3:55 PM
- $168 every 4 weeks (includes a drop in playdate each week)
If you have any questions, simply complete the form below and we will contact you ASAP!


For Teachers Who Use the
TERC Math Curriculum
in their Schools
Welcome to Mr. Fier's
New York City Elementary School Teachers'
Resource Pages for Using
The Technology Portion of the TERC Math Curriculum.
These pages are for anyone who uses the TERC math curriculum in their school.
Did you know that there is at least one unit for grades Kindergarten through 5th-Grade that has a computer component you can add to your TERC classroom work?
Come explore how the technology component of TERC can help augment the Investigations in Number, Data, and Space that you do in your classroom math studies.
I have created a series of pages on the web that are meant to help any teacher, whether 1st of 50th year, whether technology savvy or novice, discover the wonderful uses of the technology component of this math curriculum.
Follow the links located bellow.
Every page has links on the
the left side of the page,
Or when you get to the bottom of the page
Just click on the
button you find there.


Ph.D. Research dissertation: Energetics and Dynamics of Internal Waves on Slopes Using Numerical Simulations (2003 - 2006)
Advisor - Professor Oliver Fringer
In this research, we present results from high-resolution 2D and 3D numerical simulations of the interaction of a first-mode internalwave field with an idealized shelf break. Our emphasis is to obtain an understanding of the partitioning of the internal wave energy over the course of the interaction process and gain insight into the dynamics of the onshore propagating internal boluses that form as a result of the interaction
Numerical Method and Setup
The Navier-Stokes equations with the Boussinesq approximation and with constant kinematic viscosity are are computed with the LES code developed by Fringer(2003) which follows the method of Zang, Street & Koseff (1994) to solve the Navier-Stokes and scalar transport equations, using a finite volume formulation on a generalized curvilinear coordinate nonstaggered grid with a rigid lid. Schematic of the computational setup that formsthe domain for the present simulations is shown in Figure 1.
Figure 1(a): Schematic of the computational setup that forms the domain for the simulations.
Figure 1(b): computational mesh for the domain shown in Figure 1(a).
Figure 2 depicts the density contours (isopycnals) for the critical case (g/s = 1) obtained by imposing a first-mode internal wave field at the left boundary of the domain shown in Figure 1.
Figure 2: Density contours of an internal wave interacting with a critical slope for the domain shown in Figure 1(a)(movie 1 movie 2) movie 3). Figure 3 shows the interaction of incoming mode-one internal wave with a critical slope.
Please visit the Movies link to see some cool animations of internal waves breaking on a slope in a continuously stratified fluid. For more really cool 3D Navier-Stokes Movies, please visit my advisor's movie page


CUDA projects: (still under constructing)
CUDA based GMRES(m) Solver for Large Scale Sparse Linear Systems
Abstract: As one popular iterative method to solve linear equations, restarted generalized minimal residual method(GMRES(m)) has the advantages of fast convergence and good stability. In this paper we implement GMRES with CUDA in parallel to solve large scale linear problems. With GPU these problems could be solved quickly. On the hardware with GeForce GTX260, the algorithm could be speed up by average 40 times compared with the according one only with Intel Core 2 Quad CPU Q9400@2.66GHz, average 20 times than the one only with Intel Core i7 CPU email@example.comGHz.
Source Code (Sponsored by NVIDIA)
Test Set of Matrices from The University of Florida Sparse Matrix Collection
Updated in 8/25/2010


Most of the games in the casions are designed so that the "house" makes money. You might get a streak of luck and win over the short term, but the house eventually wins over the long term. If you sat down at a blackjack table and played for an hour, there is a chance that you will come out ahead. If you stay there for ten hours, the chances of you coming out ahead gets smaller. Stay there for a day, a week, or a year and you will find that the chances of you coming out ahead diminishes to almost zero. The moral of the story is that the longer you spend gambling in a casino, the less of a chance you have at leaving with more money than you came with.
The stock market is just the opposite. Over the short term, there is a very real chance that you will lose money. You only have to look back a couple of years to know that! However, the numbers show that the longer you keep your money in stocks, the more likely you are to come out ahead.
In order to prove this, I looked at the price of the S&P 500 stock index going back to 1950. (The S&P 500 represents the stock price of the 500 biggest U.S. companies.) Specifically, I looked at the annual return of the S&P 500 stocks for every 1 year, 5 year, 10 year, 20 year, and 30 year period from 1950 until 2010. Then I took the average, standard deviation, min, and max of all of these periods.
As an example, for the 30 year period analysis I looked at the returns if you had invested over the following time periods:
1950 through 1980
1951 through 1981
1952 through 1982
1980 through 2010
In total, there were 31 thirty year periods. After I calculated the returns for these 31 thirty year periods, I found the average, standard deviation, min, and max of all of these returns.
(For those who aren't stat heads, the standard deviation is a measure of variability. The higher the standard deviation, the bigger the swings are from period to period.)
The results were quite interesting:
|1 Year||5 Years||10 Years||20 Years||30 Years|
|Annual Return - Average||8.39%||7.51%||7.40%||7.25%||7.17%|
|Annual Return - Std Deviation||15.86%||6.83%||4.88%||3.06%||1.42%|
|Annual Return - Min||-40.09%||-6.10%||-4.28%||2.83%||5.39%|
|Annual Return - Max||40.45%||24.28%||15.71%||13.60%||9.77%|
(Note that I annualized the returns, so that the 7.51% average return for the 5 year periods means that over the average 5 year period, you would make 7.51% on your money per year.)
Over the course of a single year, your return will average 8.39%, but there is a lot of variation from year to year. You could potentially lose over 40%, or you could gain over 40%. If you are saving for a short term goal, like a vacation or a car, you probably can't afford to have all of your money in the stock market. You could come out way ahead, or you could lose almost half of your money!
However, note how the standard deviation decreases as the amount of time you leave your money in the stock market increases. Over the average 20 year period, the least amount that you would make is 2.83% per year. In other words, if you had invested your money in the stock market and left it there for 20 years, you would always come out ahead. The 30 year numbers are even more consistent.
The lesson here is that the longer you had been able to keep your money in the stock market, the more likely you were to come out ahead. For long term investors, the stock market certainly merits consideration.


Both Math.round() and Math.ceil() refer to rounding off a number to its nearest integer. However, there is a difference in the way these methods behave. To be more precise, they differ when it comes to the direction of rounding. Let’s walk through both of these methods.
Math.round() method rounds off a number passed as parameter to its nearest integer, but always in a way to get a lower value of the number passed as parameter.
If we look at the example bellow, when a number 9.28 passed as a parameter, Math.round() rounded it to 9, which is a lower value than actual number.
console.log(Math.round(9.28)); // output is a number 9
Math.ceil() behaves a bit differently.
Math.ceil() method rounds off the number passed as parameter to its nearest integer, but in order to get a greater value of the number.
In the below example when a number 9.28 passed as a parameter, Math.ceil() rounded it to 10, which is a greater value than actual number.
console.log(Math.ceil(9.28)); // output is a number 10


- Student Enrollment
Good Afternoon Parents & Students:
I am pleased to inform you that we have finalized hiring for the teaching positions we added due to the growth of our student population:
We have hired Barb Hillstrom, a retired math educator from Erie High School, to teach three of our new math sections. Additionally, Mrs. Singh, Mr. Hicks, and Mrs. Panakhyo will each pick up one section of math, meaning that we will have experienced, veteran math teachers in the classroom with our students.
In social studies and English, I am pleased to introduce Ms. Danielle Newman and Ms. Katie Volkmar to the EHS community. Both of these teachers bring enthusiasm and high expectations to their respective classrooms.
Lastly, Ms. Gaynelle Tuck will join us as a Special Education teacher. Ms. Tuck taught previously at EHS for many years and is a standout track and field coach.
In closing, I would like to thank parents, students, and teachers for the patience exhibited during this growing process.
If you have additional questions about these updates, please feel free to contact me directly at Erie High School [303.828.4213]. Thank you for your support and GO TIGERS!Sincerely,


While many players enjoy these games for their exciting themes and big jackpots, few may realize that the physics behind them is just as fascinating. Understanding how online slots work helps players make informed decisions when playing, allowing them to better manage their bankroll and potentially increase their chances of winning big. The slots are a type of video game that uses random number generators (RNGs) to determine each spin’s outcome. RNGs are algorithms that produce a sequence of numbers or symbols without any predictable pattern. It means that each spin is entirely random and independent from previous spins. When a player clicks the “spin” button on an online slot machine, the RNG generates a random sequence of numbers or symbols that correspond to different outcomes on the reels. The game then displays these outcomes on the player’s screen. The odds of winning on an online slot machine depend on several factors.
- Number of reels
- Number of paylines
- Size of each bet
- Specific symbols and combinations required for a win
While some players believe that certain strategies can increase their chances of winning at online slots, such as betting more after a losing streak or choosing games based on their payout percentages, these strategies have no scientific basis to back them up. Despite being entirely based on chance and lacking real skill-based components, online slots remain incredibly popular among players worldwide. The reason for this popularity is their accessibility anyone with an internet connection can log onto an online casino site and start playing within minutes. Playing the games is more enjoyable when they feature bright colors, engaging animations, and pop culture references. The most significant reason why online slots are so popular is their massive jackpots. Many online casinos offer progressive jackpot slots, which can reach millions of dollars in prizes. These jackpots grow with each spin until a lucky player wins the top prize. Play online slot games to learn More about the author.
Understanding the mathematics of slots
While there is no guaranteed strategy for winning at online slots to their random nature, understanding the mathematics behind these games can help players make more informed decisions when playing. Knowing the odds of hitting specific combinations or symbols help players determine how much they should bet per spin to maximize their chances of winning big. Understanding how paylines work and how they affect payouts also be useful information for players. It’s essential to remember that even with this knowledge, every spin on an online slot machine is still entirely random and independent from previous spins. While these games may seem simple at first glance, they’re incredibly complex machines powered by RNGs and sophisticated algorithms. Understanding how online slots work from a physics perspective helps players make more informed decisions when playing these games. Remember that despite any knowledge or strategies employed while playing, every spin remains entirely random making them both exciting and unpredictable at the same time.


- Integrate Math into Daily Activities
- Use the Language of Math
- Assess What Children Understand
- Try It
- Wrap Up
- assessment: an accounting of what learners know using objective evidence. Informal assessment is ongoing as adults monitor young children’s learning each day
- math concepts: early ideas about numbers, counting, shapes, measurement, time, greater than, less than, money
- math language: commonly used math vocabulary, such as more, less, how many in all, fewer, add, take away, number, triangle, square, and circle
- open-ended questions: questions that require critical thinking, invite opinion or explanation, and result in more than a one-word answer
Use the Language of Math
Before watching this video, read the text below. When instructed, watch the video from the beginning to end.
To help children develop mathematical ideas and be able to express them naturally, you can “flood the environment” with mathematical talk and concepts, and encourage children to use math talk, too.
- Beginning and ending the day routines offer rich opportunities for math talk. For example,
- lining up (Let’s count the number of boys and girls in line.)
- sorting classroom items (How many red buttons did you find?)
- taking attendance (We have more boys than girls today.)
- Calendar routines give children daily experience in counting, number recognition, pattern recognition, and concepts of before, after, more than, less than, first, next, and last.
- Outdoor or active play promotes the use of various math words and math ideas, such as circle, line, before, after, next, triangle, more, fewer, shorter, longer, and add.
- Snack time offers many opportunities to introduce math language. Concepts of shape, size, quantity, position, length, and volume can be introduced when cutting a sandwich, pouring a cup of juice, holding a paper plate, or merely counting the children at the table.
In this video, you’ll see educators take advantage of multiple opportunities to teach and use math words and concepts throughout the day. As you watch, look for effective strategies used by the educators in the video and jot down answers to these viewing questions in your Learning Log.
- How do the educators “flood the environment” with math talk?
- How is math talk integrated into daily routines and activities?
Why is it important to “flood the environment” with math language?
- Math language gives children a way to express their growing understanding of math concepts.
- Children need multiple opportunities to use mathematical language in a variety of activities.
How can you use math talk throughout the day?
- Use daily calendar routines to engage children in patterning, number recognition, and counting to 10.
- Take attendance by counting the number of children present and graphing the results. (How many are boys? How many are girls? Do we have more boys? Fewer boys?)
- Use Snack Time to count, sort, and classify. For example, count the crackers on the plate, determine equal shares, find the longest pretzel, or talk about the shape of a sandwich or plate.
- Use concrete objects to model real world addition or subtraction. (How many crackers do we have now? What will happen if we take one away?)
- Use lining up to ask children to identify relative positions of objects in space. (Who is first in line? Who is next? Who is last in line?)
- Use the clock and a thermometer to teach mathematical vocabulary such as numbers, temperature, time, higher, lower, before, and after.
- Utilize learning centers. At the Block Center, for example, have children explore shapes, lengths, weights, and volume using words such as longer, shorter, heavier, lighter, higher, lower, more, fewer, big, bigger, and biggest.
- Use classroom chores to teach concepts such as same, different, high, low, inside, outside, on top of, and below. The task of sorting, for example, requires a basic understanding of classes or kinds of objects. (Put all the pencils in the case and all the crayons in the bucket.)
- Use nonstandard measures such as lengths of yarn or Unifix cubes to determine distance, length, or height comparisons. (How many cubes tall is your tower? What about measuring your tower now with string?)
Think about your own program as you answer these reflection questions in your Learning Log.
- What ideas or strategies would you adopt to help children learn and use math language accurately and often?
- What did you learn that you might incorporate into your program?


- Unlocking Success: The Karnataka SSLC Math Formula Lists
Mathematics is often considered a universal language, and its importance in education cannot be overstated. For students pursuing the Karnataka SSLC (Secondary School Leaving Certificate) examination, mastering mathematical concepts and formulas is a crucial aspect of their academic journey. To aid in this process, the Karnataka SSLC board provides Math Formula Lists, a valuable resource that empowers students with the tools they need to succeed in this challenging subject.
The Karnataka SSLC Math Formula Lists: An Overview
The Karnataka Secondary Education Examination Board (KSEEB) understands the significance of mathematics in a student’s academic and professional life. To facilitate effective learning and exam preparation, they have devised Math Formula Lists that cover the entire SSLC math syllabus.
These formula lists encompass a wide array of mathematical topics, ranging from basic arithmetic to advanced algebra and geometry. They serve as a comprehensive repository of mathematical formulas, equations, and concepts, all neatly organized and readily accessible to SSLC students.
Key Features of the Karnataka SSLC Math Formula Lists
1. Comprehensive Coverage: The formula lists leave no stone unturned, providing an exhaustive compilation of mathematical formulas that students are likely to encounter in the SSLC examination. Whether it’s algebraic expressions, geometry theorems, or trigonometric identities, these lists have it all.
2. Concise and Precise: The formulas are presented in a clear and concise manner, making them easy for students to understand and memorize. Each formula is accompanied by relevant explanations and examples, ensuring that students grasp the underlying concepts.
3. Systematic Organization: The formula lists are systematically organized according to the SSLC math syllabus. This logical structure enables students to locate specific formulas quickly and navigate through different mathematical topics seamlessly.
4. Accessible Language: Recognizing the diverse linguistic backgrounds of SSLC students, the formula lists are available in multiple languages, including Kannada and English. This inclusivity ensures that language barriers do not hinder a student’s understanding of mathematics.
Utilizing the Karnataka SSLC Math Formula Lists
These formula lists are more than just reference materials; they are powerful tools that can significantly enhance a student’s mathematical prowess. Here’s how students can effectively utilize them:
1. Exam Preparation:The SSLC board examinations are a crucial milestone in a student’s academic journey. The formula lists serve as a treasure trove of resources for exam preparation. Students can refer to these lists to revise important formulas and practice problems related to each concept.
2. Homework and Assignments: Completing homework and assignments is an integral part of the learning process. The formula lists offer students the support they need to tackle math-related tasks with confidence. Whether it’s solving equations, calculating areas, or working with geometric shapes, these lists have the necessary formulas at hand.
3. Concept Clarity:Understanding the underlying concepts is vital in mathematics. The formula lists provide explanations and examples that help students gain a deeper insight into each formula. This clarity of concepts is essential for problem-solving and critical thinking.
4. Self-Study:Beyond the classroom, the formula lists empower students to engage in self-study. Students can use these lists to explore advanced mathematical concepts, thereby expanding their knowledge and skills in mathematical


In finance, the “Portfolio Effect” is a term used to describe the fact that the risk in a portfolio of non-correlated investments is lower than the risk of a single investment. The portfolio returns will tend to be less volatile than that of a single investment.
In oil and gas reserves, the “Portfolio Effect” (sometimes called the “Aggregation Effect”) refers to the fact that P90 volumes (or any other probability level other than P50) can not be summed. Arithmetically summing 10 reserves at the P90 level will not yield a P90 result, because that assumes that the every one of the 10 individual items encounters its 1 in 10 “Low Case”. That would be equivalent to rolling a “1” on a 10 sided die 10 times in a row. The probability of the group total exceeding the sum of the P90 individuals will, in fact, be well over 95%. If the portfolio is increased to 1000 items, achieving the sum of the P90s is virtually certain.
In practice, the evaluator may choose to relax the level of certainty assumed for individual items, knowing that the aggregate will me more certain than the parts. For example, the Canadian Oil and Gas Evaluation Handbook COGEH
cites as a rule of thumb that an evaluator can arithmetically add entity- or field-level deterministic estimates of proved reserves of lesser probability (for instance, a judgmental > P65) that will result in a greater overall probability (P90) at the portfolio or aggregate level, provided enough entities are added together.
PRMS 2018 also speaks to this in section 18.104.22.168:
Two general methods of aggregation may be applied: arithmetic summation of estimates by category and statistical aggregation of probability distributions. There are typically significant differences in results from these alternative methods. In statistical aggregation, except in the rare situation when all the reservoirs being aggregated are totally dependent, the P90 (high degree of certainty) quantities from the aggregate are always greater than the arithmetic sum of the reservoir level P90 quantities, and the P10
(low degree of certainty) of the aggregate is always less than the arithmetic sum of P10 quantities assessed at the reservoir level. This “portfolio effect” is the result of the central limit theorem in statistical analysis. Note that the mean (arithmetic average) of the sums is equal to the sum of the means; that is, there is no portfolio effect in aggregating mean values.


If you are the type of person who has an interest in computers, software, and understanding how it all comes together, then online degrees in software engineering could be a great fit. Software engineers bring mathematics and computer science together to write and develop new computer, Web, and network software. Ultimately, software engineers need to be able to adjust to new advancements in technology, and be able to adjust their roles accordingly.
Typically, software engineers are divided into two specific fields, applications engineers and systems engineers. Applications engineers study the needs of software users and develop ways to improve existing software, or create entirely new programs. Applications engineers must know, and use, a number of different computer languages, like, C, C++, Java, and Python.Typically, they develop software for business applications, but can also work with developing databases. Systems engineers, on the other hand, coordinate a particular organization’s computer needs. They organize and develop plans to order, inventory, and care for the computer needs of a department, or in some cases, and entire business or organization.
Classes and Assignments of a Software Engineering Major
The types of courses you take as a software engineering major will vary depending on the school you attend and degree level you select. However, most software engineering majors can expect to take a majority of their courses in mathematics, computer science, and computer programing. Bachelor’s degree students can also expect basic courses in English, physical sciences, writing, and history. If you plan to develop and implement software in a science or engineering environment, you should take courses in computer or information science, mathematics, or engineering. Students hoping to work in a business settings should supplement their education with business courses like accounting or finance to help understand expenses involved for computer engineering.
Degree Levels for a Software Engineering Major
- Associate. Online associate software engineering degrees are designed to provide an introduction to computer programming, and the different languages used in creating software. Students who have an associate degree in computer engineering, or an equivalent, can find employment as entry-level software programmers, database programmers, software support technicians, and software testers.
- Bachelor’s. Online bachelors software engineering degrees provide a more in-depth study of the skills needed to work in the field, and will teach students a working knowledge of scripting for computer engineers. Graduates with a bachelor’s degree in software engineering can usually find employment as software developers, programmers, application developers, Web application developers, software engineers, software applications analysts, Web applications analysts, Web applications specialists, and software applications specialists.
- Master’s. Online masters software engineering degrees explore advanced concepts in software engineering, embedded software, software engineering management, and systems engineering. Master’s degrees in software engineering can also be specialized for designing and implementing software in specific fields such as finance, accounting, network administration, or system security. Graduates holding a master’s degree in software engineering are prepared for a wide range of careers in the field, particularly as managers or department heads.
A Future as a Software Engineering Major
Computer engineering jobs require entry-level software engineers to have a minimum education of an associate degree, or an equivalent two-year degree. Some more advanced positions will require a bachelor’s degree, or even some sort of post-baccalaureate degree or certificate. Salaries vary greatly depending on experience, location, and roles and responsibilities, but on average, computer systems software engineers earned $92,430 annually as of May 2008, according to U.S. Bureau of Labor and Statistics (BLS). The BLS also reported that those working as computer applications software engineers earned $85,430, while computer programmers earned $69,620.
Students with a degree in Software Engineering are considered well prepared for
becoming Computer software engineers, systems software.


A weir is an obstruction in an open-channel
that can be used to determine the flow rate.
a sharp-crested weir is a vertical plate with sharp edges placed across
shapes of weirs (e.g., rectangular, triangular, and trapezoidal) are
shown in the figures.
The weir discharge can be derived from Bernoulli's equation. The details of the derivation process are omitted
for brevity. The volumetric flow rate for a rectangular weir is given
where L is the width of the weir, and H is the head of the weir (see figure).
As expected, the actual flow rate deviates from that obtained
from theory (Eqn. 10). Hence, an experimentally-determined
the flow rate:
where the discharge coefficient for a rectangular channel is given by (Henderson,
Cd = 0.611 + 0.075 (H/Pw)
where Pw is the height of the weir above the channel bed, as
shown in the figure.
Similar expressions for determining the flow rate of triangular and trapezoidal
weirs can be derived, and discharge coefficients are available
for various shapes of the weirs. For more information, students are
referred handbooks on hydraulics.
[ *Reference: Henderson, F. M., "Open
Channel Flow," Macmillan, New York, 1966.]


September 20, 2018
Earlier this week, the Education Quality and Accountability Office (EQAO) released the 2017-2018 provincial testing results for Ontario’s grades 3, 6, 9 and 10 students. The Conseil scolaire catholique du Nouvel-Ontario (CSCNO) notes that its students continue to perform at a high level, especially in mathematics.
Since 2012-2013, reading results of CSCNO grade 3 students rose to 84% (an 11% increase), displaying significant improvement in that subject area. Writing results now stand at 79% (a 1% increase), while mathematics results increased to 77% (a 3% increase). The CSCNO is proud to note that the results of its grade 3 students in writing and mathematics are above the provincial average for French-language school boards, while results in reading match the average.


A method for selecting chief points in acoustic scattering
Keywords:Acoustic fields, Boundary value problems, Error analysis, Integral equations, Matrix algebra, Natural frequencies, Problem solving, Vectors, Acoustic radiation, Computational costs, Helmholtz integral equations, Surface integral equations
AbstractIn this work, the nonuniqueness problem of solving surface integral equation of acoustic scattering is considered. The solution of the acoustic scattering integral equation is not unique at some frequencies. A unique solution can be obtained by adding some constraints to the problem at some interior points of the scatterer. The primary difficulty is the lack of formalized method for the selection on the interior points to guarantee uniqueness. A simplified method for selecting interior points for CHIEF method is proposed. The new augmented surface integral equation is successful in reducing the needed number of points to solve at the characteristic frequencies of the scattering problem where a unique solution does not exist. The implementation of the method exploits the earlier computations used in selecting the interior points. Numerical results are presented at some characteristic frequencies for an axisymmetric body. A comparitive analysis is also presented to evaluate the potential of the proposed method.
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Verify by composition that one function is the inverse of another.
LE.A.2Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).High School Functions Interpreting Functions, understand the concept of a function and use function notation.To avoid it, delete all graphs, pan and zoom, and then plot the graphs again.IF.A.1Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.For example, the Fibonacci sequence is defined recursively by f(0) f(1) 1, f(n1) f(n) f(n-1) for n is greater than or equal.Solve an equation of the form f(x) c for a simple function f that has an inverse and write an expression for the inverse.
Zoom the graph in and out by holding Shift key and using the mouse wheel.
If you skip parentheses or a multiplication sign, type at least a whitespace,.e.If you need flash player installed, you will be given directions on how to install this at the time it is needed.Here are the, common Core Standards for High School Functions, with links to resources that support them.Revolutions Double-Angle Identities Evaluating trigonometric functions Evaluating inverse trigonometric functions Expressing infinite solutions for trigonometric equations Finding exact values of trigonometric functions Finding the equation given a sine or cosine graph Finding the measure of the central angle given the circumference Finding the other trigonometric.Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.Fraction Basics, addition and Subtraction, multiplication and Division, minecraft mini game teacher fraction Skills.Courses: MAT0018C, MAT0028C, MAT1033C, hobbies: Parenting sons, Family adventures, Horses, darren Lacoste.
High School Functions Linear, Quadratic Exponential Models.


2. After analyzing all data, what do you believe are the root causes of the problem you have identified? Comment on: organizational culture, external factors, organizational structure, student demographics, instruction and preparation, and curriculum.
The root causes are proving to be the most challenging to determine. From my slow progress of gathering specific data on each student through conversations with the teacher, classroom observations, looking through student cum files, and looking at math assessment scores my conclusion so far is that each of these students is struggling in math for different reasons- most having to do with family or health circumstances that prevented students from getting steady math support and instruction in years prior to sixth grade. I am not yet ready to report out for each student, as I am still looking through and sorting the data, but the family circumstances, family culture, and health issues, coupled with the fact that (in my opinion) the math curriculum hasn't been strong at our site (until the introduction of the Accellus program this January) seem to the major root causes. This means that the approaches, objectives and goals set for each student will be highly personalized. This is not in any way a bad thing, just more time consuming.
3. Based on an outcome you would like to attain for the target group, write 1 goal and 2-3 objectives that support that goal. (Create a SMART goal – specific, measurable, attainable, realistic, timely.)
Goal: Sixth grade students will improve their STAR assessment math scores.


Artificial intelligence is currently leading to one breakthrough after the other, both in public life with, for instance, autonomous driving and speech recognition, and in the sciences in areas such as medical imaging or molecular dynamics. However, one current major drawback worldwide, in particular, in light of regulations such as the EU AI Act and the G7 Hiroshima AI Process, is the lack of reliability of such methodologies.
In this lecture, we will provide an introduction into this vibrant research area, focussing specifically on deep neural networks. We will discuss the role of a theoretical perspective to this highly topical research direction, and survey the current state of the art in areas such as explainability. Finally, we will also touch upon fundamental limitations of deep neural networks in terms of computability, which seriously affects their reliability, and reveal an intriguing connection to neuromorphic and quantum computing.
Gitta Kutyniok (https://www.ai.math.lmu.de/kutyniok) currently has a Bavarian AI Chair for Mathematical Foundations of Artificial Intelligence at the Ludwig-Maximilians-Universität München. She received her Diploma in Mathematics and Computer Science as well as her Ph.D. degree from the Universität Paderborn in Germany, and her Habilitation in Mathematics in 2006 at the Justus-Liebig Universität Gießen. From 2001 to 2008 she held visiting positions at several US institutions, including Princeton University, Stanford University, Yale University, Georgia Institute of Technology, and Washington University in St. Louis. In 2008, she became a full professor of mathematics at the Universität Osnabrück, and moved to Berlin three years later, where she held an Einstein Chair in the Institute of Mathematics at the Technische Universität Berlin and a courtesy appointment in the Department of Computer Science and Engineering until 2020. In addition, Gitta Kutyniok held an Adjunct Professorship in Machine Learning at the University of Tromso from 2019 until 2023.
Gitta Kutyniok has received various awards for her research such as an award from the Universität Paderborn in 2003, the Research Prize of the Justus-Liebig Universität Gießen and a Heisenberg-Fellowship in 2006, and the von Kaven Prize by the DFG in 2007. She was invited as the Noether Lecturer at the ÖMG-DMV Congress in 2013, a plenary lecturer at the 8th European Congress of Mathematics (8ECM) in 2021, and the lecturer of the London Mathematical Society (LMS) Invited Lecture Series in 2022. She was also honored by invited lectures at both the International Congress of Mathematicians 2022
(ICM 2022) and the International Congress on Industrial and Applied Mathematics (ICIAM 2023). Moreover, she was elected as a member of the Berlin-Brandenburg Academy of Sciences and Humanities in 2017 and of the European Academy of Sciences in 2022, and became a SIAM Fellow in 2019 and an IEEE Fellow in 2024. She currently acts as LMU-Director of the Konrad Zuse School of Excellence in Reliable AI (relAI) in Munich, serves as Vice President-at-Large of SIAM, and is spokesperson of the DFG-Priority Program "Theoretical Foundations of Deep Learning" and of the AI-HUB@LMU, which is the interdisciplinary platform for research and teaching in AI and data science at LMU.
Gitta Kutyniok's research work covers, in particular, the areas of applied and computational harmonic analysis, artificial intelligence, compressed sensing, deep learning, imaging sciences, inverse problems, and applications to life sciences, robotics, and telecommunication.


An online Fraction calculator is used for various calculations including multiplication, division, addition, and subtraction. With this calculator you can calculate two or more fractions and whole numbers within no time. Online calculator fractions display the step by step solutions easily of whatever operation you have been processed. Some people call it a fraction solver as well as a multiple fractions calculator. Now it can compute up to ten both fractions and entirely mixed numbers. This online calculator is useful for all students in all grade levels and can be used as a reference to all math teachers. You can also use it in professionals that often use fractions in their workplace or in their homes.
Five Best Free Online Fraction Solver Calculators:
Here, there are five best online calculator fractions which are described below:
Fraction Calculator by Calculator-Online.net:
This free to use fraction calculator online allows you to add, subtract, multiple, and divide two or three fractions. This free online calculator will also help you in:
- Fraction similar & distinct denominators, which are added together by using the multiple fraction calculator.
- Fractions that are dis-similar & comparable denominators are added for the subtraction.
- It also simplifies the results to the most simplified terms in the divisible fractions.
- For the reduction of the simplest form by multiplying the numerator and denominator at the same time.
If you don’t have any idea about how to calculate the fractions, then you don’t have to worry about it. You can use this amazing simplify fractions calculator that can deal with various arithmetic operations and shows the step wise procedure of the calculations.
Calculator soup is an amazing addition in our list of fraction simplifier calculator. This website calculator is widely used by scholars for preparing for their exams and the reason for it is that uses the simplification technique to display the result quickly. When it comes to its calculation process, then you only need to put the denominators & numerators of both fraction into the designated places. After that you are required to select the any arithmetic operator according to your need. Then, click the calculate button and it will show you the results by making calculation for that fraction.
This subtracting fraction calculator online is the one stop solution for the users. The reason is that it can deal with the complex as well as simple operations using the fractions, mixed numbers, and decimal numbers. It will also display the detailed step by step calculation steps or instructions on how calculate fractions. The best part of this digital tool is that it has designed a special section in which you can learn about the rules for the fraction simplification. This online tool is easy to operate, there is a box in which you are required to enter fraction as many as you want. After inserting the fraction, you need to choose the operation type. Then, tap the calculate fraction button to run the calculation process. With the blink of an eye, it will show you the output for your given fractions.
Proper Fraction Calculator:
If you have a proper fraction value and you want to calculate it, use this online calculator to solve the fraction freely. Generally, a proper fraction is a normal fraction that is used as a part of a whole. When a whole fraction is divided into parts, then each part is equal to the whole parts. Keep in mind that the numerator is less than the denominator in the proper fraction. Although, this type of fraction is commonly used in different math operations. With the multiple fraction calculator online, people can add, subtract, multiply, and divide a proper fraction easily.
Improper Fraction Calculator:
Improper fraction is quietly different from proper fraction. The proper fraction is a part of a whole but on the other hand improper fraction has different value. The improper fraction value is greater than the sum of the whole parts. improper fraction is a fraction whose numerator is greater than the denominator. If you want to calculate improper fraction, the dividing fraction calculator online is the best in this way.
Mixed Number Calculator:
Mixed number is a type of fraction involving the whole number and is called the whole number plus fraction. Generally, mixed numbers are used when you need to simplify improper fractions. Although improper fractions are hard to understand. Therefore, you need it to convert to mixed numbers in order to be calculated easily. In this way, you may use a simplified fraction calculator online.
Fraction to Decimal Calculator:
Dividing numbers is easy with a dividing fractions calculator. If you need to do long division, put the top number of the fraction called “numerator” inside the division bracket and the bottom number called “denominator” outside, to the left of the division bracket.
Fraction Simplifier Calculator:
Fraction mixed number calculator is also referred to as a fraction simplifier calculator. If you are worried about how to simplify complex fractions. You do not need to worry as we brought an online calculator for you to solve the complex fraction in a couple of seconds.
In order to simplify a complex fraction, there must be:
- A number that will divide into both the numerator and denominator therefore it can be reduced, or
- The numerator must be greater than the denominator, (an improper fraction), so it can be converted to a mixed number.
There isn’t any doubt that all the parents want their child to be perfect in maths. But all the kids are not the same, some of the kids are very fast to pick the things. While there are some students that can’t get the things as faster as others. So for them, teachers need to change the method of teaching to clear the concepts of slow learners. This is why they take the help of technology like using the dividing fraction calculator online that can help the students to understand how to calculate the fractions using the basic rules of fraction calculation.
Reshaeel Sarwar is a competitive writer who is always striving to produce the most relevant articles on any subject. He delivers the most up-to-date information on the subject at hand, owing to his wealth of knowledge. In this piece of content, he has given information regarding fraction calculator online by calculator-online.net. He always emotionally engages the audience with whatever he is speaking about, and this is the only thing that propels him forward.


Preschool Mathematics Art Projects
Are you seeking a mathematics competition that will truly obtain your youngsters thrilled? If so, you have actually most likely heard about the International Math Competition, which runs each year in Cambridge, Massachusetts. The ILEX is complimentary to get in, and it is widely considered a “Internet Test.” The rules for getting in are easy: go into the obstacle within the specified amount of time, as well as submit at the very least one appropriate solution. The International Mathematics Competition is likewise referred to as the WESS Difficulty, after its makers, International Mathematics Enrollers. The competition is an online test that gauges the skills of a child in Mathematics. To be eligible for the WESS Obstacle, kids have to show the skills needed for the global phase by answering a collection of math concerns. Once participated in the WESS, a child might come back the competition approximately three times. Winning a place in the WESS Challenge is worth numerous dollars and boasting legal rights in your circle of buddies! Mathematics Contests is enjoyable for kids of every ages. The WESS uses many different degrees of mathematics contests. At the elementary degree, children will get medals for their initial effort, intermediate medals for their 2nd try, and also the gold medals for winning. At the adult degree, youngsters will receive certificates for participating and their selection of a silver or gold medal for their initiatives. These medals can be used for enhancing an office or home, or for making Xmas or Valentine presents. All gold medals received in the WESS math contest must be returned within thirty days. Each gold champion have to likewise complete a Much West Extramural Examination, an essay requiring an optimum of 500 words. For after-school activities, each participant might also have the ability to earn extra certificates. At the end of the year, there is a honors ceremony that identifies the gold medalists. WESS activities can also be bought at neighborhood area universities. For those that would rather not take part in a WESS, some neighborhood colleges use a mathematics tutoring program. Math contests permit kids to see what they are capable of, increase self-confidence, and also create analytical skills. At the same time, they create mathematics education understanding while having a good time. These contests give an outstanding method for kids to make great qualities in school. They additionally inspire trainees to apply what they learn in courses by taking part in mathematics contests. If a kid participates in a WESS as well as wins a trophy, they might have the chance to have their picture positioned on a customized leaderboard. This would make an ideal Xmas or Valentine’s Day existing for grade school kids. Parents can design their very own math contests by choosing a motif and afterwards sending out in a picture of their kid performing the activity to be made use of as the premise for the contest. Having personalized mathematics competitions at this level of difficulty urges kids to stand out, win awards, as well as develop long-term art items.


Thankfully, the process to calculate IRR in these cases can be don’t fast and easy with the help of a spreadsheet A short primer on IRR In math terms, the internal rate of return is the interest rate.
After obtaining the baseline measurements, the 61 eligible subjects were assigned in a 1:1:1 ratio to one of the three intervention groups by a computerized method (EXCEL 2010. times per week on.
The Actual/360 method calls for the borrower for the actual number of days in a month. This effectively means that the borrower is paying interest for 5 or 6 additional days a year as compared to the 30/360 day count convention. Spreads and rates on Actual/360 transactions are typically lower, e.g., 9.
· RSidhu Member. PMT is straight forward calculation on fixed loan payment schedule. And difference shows up in Rate of Interest payment to total payment. In above example. Actual/360: 48.87% is interest payment 30/360: 48.26% is interest payment In practice 30/360 and Actual/360 is.
simple and compound interest calculation in excel hindi – Duration: 6:41. IT EDUCATION IN HINDI 19,966 views
Commercial Property Insurance Calculator However, you can increase your return on investment on a property in several ways. One of them – if you borrowed money to buy it in the first place – is to refinance the loan at lower interest (use.
If they are doing an actual day (365 days per year) calculation then it is very possible that they are assuming actual days for each month rather than a month being 1/12 of a year. In that case the interest would be daily and the days between each payment would vary depending upon the number of days in the month.
How it works: the lender pretends there are 360 days in a year when calculating the daily interest rate (6% / 360 > 6% / 365), then charges.
· Interest Type = 365/360 interest rate (before adjusting because of 365/360) = 5.5%. Doesn’t have to be pretty but it would help me to know if I go off track by being able to compare your interest calculation per month to mine. 0 0 . Apr 17th, 2015, 02:19 PM #8.. 365/360 interest type amortization table payment# Days Payment Interest.
A fundamentally important task for treasurers is to oversee the organisation's cash flow and shorter-term investments. To do this successfully, the treasurer must:.
Php Calculation How Much Is A 400000 Mortgage How Much Is A 400 000 Mortgage | Jumboloanshelp – Mortgage Acceleration Calculator | FREEandCLEAR – Use our Mortgage Acceleration Calculator to determine how much money you can save and how quickly you can pay-off your mortgage by accelerating a fixed rate loan, or paying more than your required monthly payment.. what would the average payment for a 400,000 dollar loan be.PVWatts Calculator – Caution: photovoltaic system performance predictions calculated by PVWatts include many inherent assumptions and uncertainties and do not reflect variations between PV technologies nor site-specific characteristics except as represented by PVWatts inputs. For example, PV modules with better performance are not differentiated within PVWatts from lesser performing modules.
· 24 month loan. The problem is the bank uses a 360 day basis when they calculate the fixed monthly payment. Excel’s PMT formula has a 365 day basis. If you have 24 identical monthly payments, the only trick is in calculating the *effective* monthly interest rate. That is, whether you use 360, 365 or 366 day years, there are always 12 months in a year.
Commercial Loans For Dummies Remember, if there is no profit, there is no business. James Caan is chairman of the Start-Up Loans Company. Each fortnight he will be tackling a different business issue. Keep up to date by visiting.


Prof. Predrag Stanimirović
University of Niš, Serbia
Speech Title: Gradient Dynamical Systems for Solving Matrix Equations and Computing Generalized Inverses
Biography: Prof. Predrag Stanimirović has accomplished his doctoral degree from Mathematics at University of Niš, Faculty of Mathematics, Niš, Serbia. Now he is working as full Professor at University of Niš, Faculty of Sciences and Mathematics, Departments of Computer Science, Niš, Serbia. Thirty four years of experience in scientific research in diverse fields of mathematics and computer science, which span multiple branches of Numerical linear algebra, recurrent neural networks, linear algebra, symbolic computation, nonlinear optimization and others. His main research topics include Numerical Linear Algebra, Operations Research, Recurrent Neural Networks and Symbolic Computation. Within recent years, he has successfully published 245 publications in scientific journals, including 5 research monographs, 6 text-books, and 75 peer-reviewed research articles published in conference proceedings and book chapters.He is Editor-in-Chief of the scientific journal Facta Universitatis, Series: Mathematics and Informatics and section editor in Filomat and several other journals.
Abstract: The approach based on dynamical system is a powerful tool for solving many kinds of matrix algebra problems because of: possibility of defined evolution to ensure a response within a predefined time-frame in real-time applications, parallel distributed nature of initiated neural networks, convenience of hardware implementation, global convergence without restrictions, dynamical system is applicable to online computation with time-varying matrices.
As a confirmation, various dynamical systems based on the Gradient Neural Network (GNN) for solving matrix equations and computing generalized inverses have been investigated. Also, different types of dynamic state equations corresponding to various kinds of generalized inverses have been proposed and considered. Recurrent Neural Network (RNN) models arising from appropriate simplification of GNN models are also proposed. Convergence properties and exact solutions of considered GNN and RNN models are investigated.


These mathematical activities can be used with pupils aged 7 to 16. The activities can be used either by individual pupils, small groups or with the whole class using a projector or an interactive whiteboard.
algebra, games, investigations, problem solving, maths, math, mathematics, formulas, formulae, number sequences, equations, functions, nth term , interactive whiteboard, simultaneous, tile patterns, matchstick patterns,
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How to Get Better at Math
How to Improve Math Skills
Math can be a difficult subject, particularly if you don’t have the right skills in place. But once you know how to approach it strategically, you’ll likely find it less frustrating and have much higher chances of success. This article details how to evaluate, break down, and successfully complete math tasks and avoid getting stuck or overwhelmed.
Honing Your Math Brain
Play math games.Math games are good tools for honing your math skills and are designed to let you have fun while doing it. Some recommended online math games (that are in line with the new Common Core standards) include:
- DragonBox 5+ which lets you gradually build your algebra skills until you’re able to master more and more advanced equations.
- Prodigy, a game targeted at elementary-school students, that integrates math practice into a role-playing game that allows players to use math to make their way through an appealing fantasy world.
- Many other productive games are available online and as apps, so do a little looking around and find those best suited to your needs and goals.
Make math part of your life.Incorporate math equations into your daily routine to help keep your skills sharp and to help you recognize the many ways that math exists all around you.
- Take the time to apply math in common situations. For example, if, say, a sweater that’s regularly is on sale for 30% off, what is the sale price? Or if you need to double a recipe that calls for 3/4 cup of flour, how much flour will you need?
- Also take the opportunity to put your math skills to work in new and different situations outside your normal routine. For example, if you plan to hike a new trail that’s 7 miles long and it takes you 20 minutes to walk a mile, how long should you plan for your hike to take? Or if you need to drive 13 miles to pick up your friend at 1:30 and the average speed limit there is 45 mph (72 km/h), what time will you need to leave to arrive on time to get your friend?
Learn about the big picture.It’s easy to become frustrated with math when all you’re doing is memorizing a formula that, at base, means nothing to you. But if you work to truly understand the principles behind the formula, your understanding of math can become deeper and more productive.
- Start by doing some research. Say you’re learning the Pythagorean theorem. Who was Pythagoras anyway? What does he have to do with triangles? How did he discover the theorem that was named after him and why does anybody care? Having a sense of the development and broader implications of a math concept can turn it from something you simply have to memorize into something you genuinely understand and can take an interest in.
- Translate the math principle into everyday language. Staying with the Pythagorean theorem, you know that the basic definition of the Pythagorean theorem is a2 + b2 = c2, but what does that translate to in everyday language? Try to figure it out. Translating it might result, for example, in this: the square of the longest side of a triangle (c2) is the same as (or equal to) the squares of the other two sides (a2 + b2) added together. Translating the principle into everyday, non-intimidating language can help you more easily understand, remember, and apply that principle.
- Explore with that new principle--in the Pythagorean theorem example, try applying the theorem to other shapes than triangles. Can it be translated and applied to other shapes like rectangles, hexagons, squares, etc.? Why or why not? Understanding why a principle specifically applies to some instances and not others will help you better integrate and apply that principle as you go forward.
Part 1 Quiz
How can researching history help hone your math brain?
Preparing for Class
Set up a well-organized binder or notebook.Designate a separate binder or notebook specifically for math class (one binder or notebook per class if you’re taking multiple math classes).
- Set up a section for in-class notes, a section for reading notes, and a section for homework.
Schedule study time.Set aside time in your schedule for math homework and study. Otherwise you may be tempted to procrastinate, find yourself getting behind, or end up studying at inopportune times (like when you’re tired or rushed).
- Make time each day to work on math. Even if you don’t have a homework assignment every day, set aside at least 15 minutes to spend working on sample problems and reviewing your notes. Studying every day will help cement your math knowledge in place and make it easier to access when you need it.
- At the university level, you can plan to need approximately 2-4 hours of studying per week for each hour of class instruction.
- Remember that studying math, unlike some other subjects, is about doing math, so your study/practice time is the most important to your success.
Read ahead.Read ahead in the book to the chapter that will be covered in the next class.
- Knowing the main idea and general precepts of the chapter before going to class will help you better understand and keep up with the material in class.
Review notes before class.Read back through the notes from the previous class before your next class so you’ll be up to date and prepared for the new material.
- Reading your previous notes will help you make necessary connections between the old and new material and give you a more solid foundation on which to build new skills.
Part 2 Quiz
How does studying math differ from studying other subjects?
Learning While in Class
Go to class and get there on time.It should be obvious, but it’s hard to do well in a course if you don’t show up to learn the material.
- Try to sit near the front and center of the classroom. It will be easier to see and hear and harder to get distracted.
Develop good note-taking skills.Though it may seem like all you need to take notes is to write down what the instructor says, successful note-taking has as much to do with how you write them as what you write in them.
- If the material covered in the class is closely related to the material covered in the textbook, you can use what’s called the “2-3-3-2 technique”: Make a two-inch column down the left side of the page for “recall clues,” make a three-inch column down the center of the page for lecture notes, make a three-inch column down the right side of the page for text notes, and make a two-inch horizontal space at the bottom of the page for your own observations and hints.
- If the material covered in class is not closely related to that covered in the textbook, use two different sheets of paper, one for class notes and one for reading notes, and use what’s called the “2-5-1 technique” for each. Make a two-inch column down the left side of the page for “recall clues,” make a five-inch column down the middle of the page for lecture notes or reading notes, and make an inch column down the right side of the page for your own observations and hints.
- Your “recall clues” should be key words or phrases that label the kind of information in each part of your notes. These should be cues rather than extensive or repetitive notes so that you can easily glance through your notes and associate them with the relevant concepts.
Ask questions.Don’t be afraid to ask questions when you have them!
- If you’re intimidated by the idea of asking questions during the instructor’s lecture, write down your questions and speak to the instructor after class or during in-class work time.
Part 3 Quiz
Recall clues are:
Practicing after Class
Make studying math a priority.Set aside time to work on math at the same time and in the same place everyday. Doing so will help you avoid procrastinating and make it easier to get into “math” mode (rather than sitting and staring blankly at the math book for 10 minutes).
- After putting in your study time, reward yourself by doing something you enjoy. It will motivate you to get through your math work and help you associate it with something pleasurable.
- Take a break every hour. Don’t try to slog through four unbroken hours of math problems--you won’t be able to maintain necessary focus and you’ll quickly tire yourself out.Instead, take a quick break to stand up, stretch, get a drink, or use the bathroom every hour.
Create good study habits.Your study habits have a huge influence on your success in math. And it’s not just about the quantity of study time, it’s about the quality.
- Work with a tutor or study-partner. Having someone to whom you can address questions and who can help point out mistakes is often crucial to effective learning.
- If you encounter questions neither you nor your partner can answer, write them down and bring them to the instructor.
- Make note cards. Write out important concepts and formulas on note cards so that you can easily refer to them while doing problems and use them for study guides before exams.
- Study in a quiet place. Distractions, whether aural or visual, will detract both from your ability to pay attention and to retain information.
- Study when you’re alert and rested. Don’t try to force yourself to study late at night or when you’re sleep-deprived. You won’t be able to concentrate sufficiently, which leads to unwitting mistakes and frustration.
Read purposefully.When sitting down to read a math section in the textbook, read strategically.
- First gather an overview. Read the title and headings, then read the introductory remarks and summary paragraphs to give yourself a global view of the topic.
- Look for main ideas. Next, look over the section to gather the main ideas: look for and read bolded or italicized words, bulleted lists, pictures and tables.
- Read the full section. Next, read the section in full from beginning to end--this should move comparatively quickly because you already have an idea of the point and main ideas of the section.
- Read with a pencil in hand. Write down and complete each sample problem given. This will help you actively absorb what’s being demonstrated and help you recognize problem concepts early on.
- Set the section aside and write down the main idea and key ideas. Recall tends to fade immediately after reading, so taking the time to recall what you’ve just read after reading will give you a significant memory advantage.
- Make connections. Think about how the new material you’ve learned relates to and builds on what you’ve previously learned. Making these connections will help you better understand and integrate the new material.
- Review. Finally, after reading, reflecting on, and completing the new material, you’ll need to return to it as time goes on and you get closer to taking a test or exam.
Master one concept before moving on to the next.In math, each topic builds upon the next, so, much like reading, it’s difficult if not impossible to make forward progress if you haven’t mastered all of the necessary steps.
- If you’re struggling with a particular idea or concept, don’t skip it and move ahead. Instead, seek help from the instructor or a tutor until you’ve mastered the idea.
Do problems neatly and completely.Avoid trying to solve math problems in your head. Instead, write out each step of the solution without skipping steps.
- If you don’t write out each step as you go, you may miscalculate without realizing and be unable to retrace your steps when trying to fix and learn from your mistake.
- Don’t do math problems in pen and work out problems vertically and neatly, with only one step per each line.
- Not only will working neatly make it easier for you to systematically solve a problem and avoid mistakes, but many teachers also grade math exercises based on the completeness of the steps to the solution, not just the solution itself.
Have a plan to tackle each problem.It can be easy to freeze up when confronted with a math problem to solve, but having a basic strategy of attack can help get you through.
- Understand the problem. Start by reading the whole question and determining what problem it’s asking you to solve.
- Identify which skills and concepts you’ll need to solve the problem. This will give you an overall sense of what you’ll need to do to find the solution.
- For word problems, sketch out the scenario rather than try to picture it in your head. Even if the problem includes a sketch, make your own--it’s important that it makes sense to you if it’s going to help you solve the problem.
- Review your solution. Look over your work and check that you’ve answered the question and that your solution to the problem makes sense. If it seems off, go back over your work and look for mistakes or missteps.
Part 4 Quiz
True or False: If you are struggling with a topic, you can skip it and go to the next one, then come back to it once you've asked your teacher for help.
QuestionWhat is the best way to study for a math test?wikiHow ContributorCommunity AnswerWork on some problems, including past assignments. Math is a very practice oriented thing. The more you practice, the better prepared you will be.Thanks!
QuestionHow can I improve if I am a very weak student?wikiHow ContributorCommunity AnswerGo over your previous test results and look at where you made mistakes. Look at the correct solution and compare the two. Make a list of the concepts and/or formulas you do not understand and review them. Ask a teacher or peer for help if there is something specific you're having trouble with.Thanks!
QuestionHow do I avoid silly mistakes?wikiHow ContributorCommunity AnswerMake sure you're documenting every step of the problem as you solve it and make sure to check your work, go over every problem a second time before you turn in an assignment.Thanks!
QuestionI know the formulas but have trouble applying my knowledge. What can I do?wikiHow ContributorCommunity AnswerIf you understand the formulas, then create practice tests with problems using those formulas, with questions ranging from easy to hard. Then try solving those problems.Thanks!
QuestionHow can I focus on my work when there are distractions everywhere?wikiHow ContributorCommunity AnswerThanks!
QuestionWho invented mathematics?wikiHow ContributorCommunity AnswerIt's unknown. Numeracy pre-dated writing and numeral systems have been many and diverse, with the first known written numerals created by Egyptians in Middle Kingdom texts such as the Rhind Mathematical Papyrus. Between 600 and 300 BC the Ancient Greeks began a systematic study of mathematics in its own right with Greek mathematics. Also, some people consider that the principles exist regardless of human usage of them, as they underpin the universe, while others consider it to be a human construct.Thanks!
QuestionWhat is a simple average?wikiHow ContributorCommunity AnswerTo find the average of multiple numbers, add them together, then divide the answer by the amount of items you added up. For example, the average of 14, 6, and 19 is 13, because 14 + 6 + 19 = 39, which when divided by three (the number of items added) = 13.Thanks!
QuestionHow much time must I take to study for math?wikiHow ContributorCommunity AnswerTake as much time as you need in order to understand the equations and formulas. If you can explain your math homework correctly to someone else, then you know the information.Thanks!
QuestionWhat is the Pythagorean Theorem?wikiHow ContributorCommunity AnswerThe Pythagorean Theorem states that the sum of the squares of two sides of a right angle triangle is equal to the square of the hypotenuse.Thanks!
QuestionHow can I solve problems which are not in my course book?wikiHow ContributorCommunity AnswerThe same way you solve the problems in your course book. Just apply the same rules or formulas to solving the problem that you normally would. If you know the rules well, you should be able to apply them to any problem that involves them. If you're asking how to find additional problems to solve, you can search up the topic and sample problems online, or ask your teacher for extra problems.Thanks!
- Avoid buying underlined used textbooks. Books that already contain someone else’s notes and underlining can (erroneously) influence your own absorption of the material.
- Ask questions. When questions arise, ask the instructor if possible, or, if not, write down the question and bring it to them later.
- Keep up. Don’t fall behind in your studying or in your homework. Because math skills build cumulatively, the further behind you get, the harder it can be to stay on top of the skills you need to do the necessary work.
- Coolmathgames is a math website for grades 1-12. It has all sorts of games including algebra, logic, numbers, and so much more. You should try it!
Sources and Citations
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Say that you need to perform a task, and that there are 2 algorithms, say A and B for performing that task. Let A finishes the task in time TA and B finishes it in time TB. If we can show that TA is less than TB, then algorithm A is indeed faster than algorithm B.
We test both the algorithms for an input of size n0, and we see that TA(n0) < TB(n0). That means that algorithm A is indeed faster than algorithm B for input size n0. But we won’t be using the same input size n0 all the time. We need to be able to use different input sizes depending on the application. But if we can show that TA(n) < TB(n) for all values of n > 0, we can prove that algorithm A is indeed faster than algorithm B, irrespective of the input size. But we have no idea on how big or small n is, and a function is not always less than or equal to another function throughout the entire set of input sizes. To solve that, we have the asymptotic analysis.
Asymptotic analysis removes all the dependencies like hardware, OS, compiler and various other factors, and gives us a relation based purely on input size n. There are various classes of asymptotic, like the big O, theta, big Omega, little o, and little omega. Each of these can be used to calculate a relation between the running time of an algorithm (for time complexity) with its input size n. All other factors are ignored.
Big notation is used for creating an upper bound for an algorithm. It means that whatever happens, the algorithm shall not take more time than what’s shown by the big O notation. So big O notation are used mainly for worst case analysis. We shall strip off low order terms and constants to generate a relation purely on the input size n.
Say that you need to search for a telephone number from a listing of telephone numbers, What shall you do? You shall start at the top and goes down to the bottom, by comparing each telephone number with the number that you need to search for. This is what call a sequential search or linear search. If you add 1 more telephone number to the listing, you shall need to search for 1 more number only (assuming that the number you need to find has not be found). So if you add n telephone numbers, you just need to search atmost n times to find the number. So we call it linear time complexity or O(n).
Suppose you need to search for a word in a dictionary, say “Good“. Will you start at A in the dictionary and then do a linear search for every single word in the dictionary, until you find the word? No, you wont. Because linear search is time consuming in this occasion. So what shall we do? We shall try to get to the middle of the dictionary. The word we need to find shall be in either of the halves. We shall go to the either of the halves and keep dividing the dictionary, until we find our word. Since we halve the dictionary at each step, the number of steps get divided by 2 in each step. That means that its a logarithmic complexity or O(log n). In asymptotic analysis, we do not think about the base of the logarithms. The reason is because to convert from a logarithm of one base to another, we just need to multiply by some constant, and since we ignore constants in asymptotic analysis, they have no importance.
Suppose you need to find the element in an array at the index 5 (So you need to find the value of a). You do not have to search through a to a to determine the value at a. A simple lookup at the a shall get you the answer. Whatever the value of the element at a, you just need a simple lookup. It means that the time for the operation does not depend on the size, and rather needs only a constant time. This is what we call constant complexity or O(1).
When we say that the running times of 2 algorithms are asymptotically the same, it doesn’t mean that their running times are the same. For example 100n lg n and 2n lg n are asymptotically same (because the constants are ignored), though their values are not.


Posted: Sunday, January 28, 2018 10:20 PM
Job Description Mathnasium of Eden Prairie is seeking an Assistant Center Director for our Eden Prairie, MN location to become an integral part of our team! ! Every day, students around the world attend Mathnasium learning centers to boost their math skills. We are highly specialized, teaching only math using a curriculum developed over the past 40 years. We teach math in a way that makes sense to students 2nd grade to High School. Each center is independently owned and operated. The Assistant Center Director will be a bright and ambitious professional, willing to work hard and change the way students view math. The ideal candidate will be detailed oriented, have good organizational skills, be highly motivated, and very enthusiastic. This key leadership position drives quality and consistency of the center experience. You will utilize your talents to manage the classroom during instructional hours, including working directly with students and providing instruction, coaching and training a team of Instructors, and ensuring students are provided with effective and concise math instruction that makes sense to them. Assistant Center Managers are also responsible for generating leads, driving sales and assuming the Center Directors duties in his/her absence. Responsibilities: Assist the Center Director in ensuring company policies, standards and procedures are followed. · Conduct center tours and consultative sales presentations. Build rapport with parents and effectively convey the benefits of Mathnasium and our commitment to help their student be successful in Math. Schedule assessments and effectively enroll students. · Assist the Center Director in making appropriate business based decisions and resolving issues. Demonstrate good judgment in stressful situations. · Act as Manager On Duty, open/close the center as needed. · Manage the center during instructional hours, · Ensure all instructors utilize the Mathnasium Method when teaching math to students. · Review student needs and educational status with Center Director on an ongoing basis. · Provide feedback to Center Director regarding Instructor performance. · Participate in local marketing/sales events. · Perform operational and administrative functions as assigned. Qualifications: · Passion for math, and strong math skills; proficient through Pre-Calculus, and well versed in Algebra I&II, Geometry, and Pre-Calculus. · Passion for working with kids, and experience working both with kids and communicating effectively with parents. Minimum 1 year related experience, preferably in a leadership role in education, sales or customer service. · Excellent communication skills and ability to build and nurture strong relationships. · Collaborate leadership; ability to train and engage staff as well as delegating responsibilities. · Strong tact and diplomacy; interacts and works cooperatively with children, parents and staff. · Strong problem solving and conflict resolution skills. · Work independently with moderate supervision. Hours will vary, but generally are afternoon and evenings : Monday-Thursday from 3:30 pm- 8 pm and Saturdays 10 am-2 pm. About Mathnasium of Eden Prairie : When math makes sense, kids leap way ahead – whether they started out far behind or already ahead in math. Our formula for teaching kids math, the Mathnasium MethodTM has transformed the way kids learn math for over a decade across 700+ centers in the US and Canada: Company Description We have locations conveniently located in both Eden Prairie and Plymouth, MN. At Mathnasium Learning Centers, we make math make sense! Whether your child started out far behind or already ahead in math, Mathnasium will help them leap ahead because we know that any child can be successful in math—it’s a matter of teaching it in a way that makes sense to them. Our experienced math tutors utilize our proprietary teaching materials and techniques, The Mathnasium MethodTM, to deliver a customized learning plan designed to address each student's needs. Our instructional approach goes beyond traditional math tutoring to develop understanding and build a love for math. If math is a problem, Mathnasium can solve it. Students will grow more excited and confident about math—and their grades will reflect that. For students who already excel in math, the sky’s the limit. They will work to expand their math skills and, with math learning made exciting, can see all the doors that being great at math can open.
• Location: St. Cloud
• Post ID: 29247797 stcloud