I am a Professor of
Mathematics at UCLA.
Before coming to Los Angeles
I enjoyed the hospitality of
Princeton University and Institute for Advanced Study.
I got my Ph.D. in 1999 from the School
of Mathematical Sciences, Tel Aviv University. My advisor was Noga Alon.
My work is supported by
NSF grant DMS-1101185, AFOSR MURI grant FA9550-10-1-0569 and USA-Israel BSF grant.
Office: Math Sciences 7911, UCLA,
Los Angeles, CA 90095.
Phone: (310) 825-1087.
Fields of interest
Algebraic and Probabilistic Methods in Combinatorics,
Graph and Hypergraph Theory,
Ramsey Theory, Random Structures, Application of
Combinatorics to Theoretical Computer Science.
I had the great pleasure of advising the following students
Keevash, Princeton University, Ph.D. 2004.
Professor of Mathematics at the School of Mathematical Sciences, Queen Mary, University of London.
Boris Bukh, Princeton University, Ph.D. 2009.
Postdoctoral fellow, Cambridge University.
Po-Shen Loh, Princeton University, Ph.D. 2010.
Assistant Professor, Carnegie Mellon University.
Jacob Fox, Princeton University, Ph.D. 2010. Assistant Professor, MIT.
Choongbum Lee, UCLA, Ph.D. 2012. Postdoc, MIT.
, UCLA, Ph.D. 2012. Postdoc, Institute for Advanced Study/DIMACS.
, UCLA, in progress.
, UCLA, in progress.
Workshops and seminars
UCLA Combinatorics Seminar.
Talks from the previous years see
Extremal and Probabilistic Combinatorics, UCLA, January 2013.
New Trends and Directions in Combinatorics
, Banff Resecrh Center, 2012.
Hypergraph Turan problem, American Institute of Mathematics, Palo Alto, California, March 2011.
Workshop on Combinatorics, Mathematical Institute, Oberwolfach, January 2011.
Extremal and Probabilistic Combinatorics, AMS 2010 Fall Western Section
Combinatorics: Methods and Applications in Mathematics and Computer Science,
Institute for Pure and Applied Mathematics (IPAM),
UCLA, September 8 - December 11, 2009.
Probabilistic and Extremal Combinatorics, Banff Resecrh Center,
August 23-28, 2009.
Workshop on Properties of Large Graphs: From Combinatorics to Statistical Physics and Back,
DIMACS, Rutgers University
Mini-symposium on Probabilistic Combinatorics:
Part I and
2006 SIAM Discrete Mathematics Conference, Victoria
Probabilistic Combinatorics, Banff Resecrh Center, 2005.
photo of participants from
Extremal and Probabilistic Combinatorics, AMS Eastern Section
Bollobas, Boris Bukh,
Alexander Kelmans, Jeong Han Kim,
Elchanan Mossel, Dhruv Mubayi,
Steven Rudich, Mike Saks,
Nick Wormald, Anders Yeo, Ayal
Zaks, Uri Zwick.


USD/CHF is the pairing of the US dollar against the Swiss franc.
It shows you how many Swiss francs you would need to purchase one US dollar. The first currency in the pair is the base currency – so in this case it would be USD. CHF is the second currency, so it is the quote currency.
For example, if the price for USD/CHF is at 0.99 this means it would cost 0.99CHF to purchase 1USD.


How to calculate a golf handicap
Your handicap is calculated based on the your most recent 20 rounds of golf. Depending on how many scores you have, a subset of those scores will be used to
determine your handicap. If you only have 5-6 scores, your best score is used. If you have all 20 then your best 10 are used. And between 1 and 10 if you have between 7 and 19 scores.
Here is an exact breakdown of how many rounds are used:
If you have less than or equal to 6 rounds: best 1 score
If you have 7 or 8 rounds: best 2 scores
If you have 9 or 10 rounds: best 3 scores
If you have 11 or 12 rounds: best 4 scores
If you have 13 or 14 rounds: best 5 scores
If you have 15 or 16 rounds: best 6 scores
If you have 17 rounds: best 7 scores
If you have 18 rounds: best 8 scores
If you have 19 rounds: best 9 scores
If you have 20 rounds: best 10 scores
If you have more than 20 scores, your 20 most recent ones are
used for handicap calculation.
Once the number of rounds to use is determined. For each round used you calculate the round differential. Which is calculated by the following formual:
((score - rating) * 113) / slope
The average of the differentials is then calculated and the result is multiplied by .96
The result is your handicap.


If you live in Spain and you are of legal age (and if you are a minor, in most cases, too) you will have a DNI that you will use for the rest of your life and that has a set of numbers and a letter at the end . Eight numbers and one letter. The letter is the check digit, an eight-digit verification system that allows you to check if you have entered the DNI correctly, for example, if you say it correctly. If you do not know it or have forgotten it, we can calculate the letter of the DNI .
The normal thing is that we know the letter of the DNI. Ours or that of the person who is under our guardianship , for example. We learn the eight digits and the final letter, which is still the easiest part of memorization. But you may have simply forgotten it, that you don’t remember it, that it is someone else’s DNI and you want to calculate it… If your classmate has told you to fill in the data for him, if your partner has told you to complete an authorization in his name but you can’t ask at the time what the letter was. In all these cases we can calculate the letter of the DNI with a series of tricks and simple processes.
The letter of the DNI, NIF or NIE is easily calculated from the numbers. “Article 11 of Royal Decree 1553/2005, of December 23, establishes that the National Identity Document will include the personal number of the DNI and verification character corresponding to the Tax Identification number”. The letter is nothing more than an eight-digit verification system. That is, it depends directly on the numbers that precede it. There are several ways in which we can calculate the letter of the DNI.
How to calculate it
There are several methods that allow us to calculate it. Applying a mathematical formula that we can do with any calculator is the most basic, but we can also use an Excel sheet or we can use a specific web page.
Applying a formula
In order to verify the DNI, we must follow a series of steps to know the control digit. We will only need a calculator or mental calculation, depending on what you are capable of doing…. We need to divide the complete number of our DNI by 23 without taking decimals, rounding the result. Once we have divided the complete number of the DNI, we use the rest of the division to calculate the letter. And this remainder will always be between the numbers 0 and 22.
Depending on the value obtained, as collected from the website of the Ministry of the Interior, we will be able to know which letter corresponds to our set of numbers by following a table provided by said ministry….
- If the remainder is 0, the letter is T
- If the remainder is 1, the letter is R
- If the remainder is 2, the letter is W
- If the remainder is 3, the letter is A
- If the remainder is 4, the letter is G
- If the remainder is 5, the letter is M
- If the remainder is 6, the letter is Y
- If the remainder is 7, the letter is F
- If the remainder is 8, the letter is P
- If the remainder is 9, the letter is D
- If the remainder is 10, the letter is X
- If the remainder is 11, the letter is B
- If the remainder is 12, the letter is N
- If the remainder is 13, the letter is J
- If the remainder is 14, the letter is Z
- If the remainder is 15, the letter is S
- If the remainder is 16, the letter is Q
- If the remainder is 17, the letter is V
- If the remainder is 18, the letter is H
- If the remainder is 19, the letter is L
- If the remainder is 20, the letter is C
- If the remainder is 21, the letter is K
- If the remainder is 22, the letter is E
For example, if the ID number is 12345678, divided by 23 gives the remainder 14, therefore, the letter would be Z: 12345678Z.
But there are exceptions. Keep in mind that, in the case of a NIE for a foreigner residing in Spain , it has a letter (X, Y or Z), seven numbers and a control digit. In this case, to do the calculation we will have to make the following substitution of letters for numbers:
- AND – 1
Using Excel to calculate it
In addition to the manual way, we can also easily know the letter of the DNI with a spreadsheet program such as Excel. Using the text function EXTRAE and the mathematical function RESIDUO, we can identify the letter of any identity document by following these steps:
- Open Excel and enter the ID number in cell A1.
- In cell B1, enter the RESIDUE function like this: =RESIDUE(A1,23). The result you should get is 14.
- You can then check which letter the number 14 corresponds to in the table shown above, but you can also use the MID function to calculate it automatically.
- So the full function you should see in cell B1 is as follows: =MID(”TRWAGMYFPDXBNJZSQVHLCK”;REMAID(A1;23)+1;1). You have to change » to quotation marks.
Although it can be a messy mess, all you have to do is copy this function and you will get the result. The only value that you will have to change if you want to calculate the letter of more documents is A1.
Use specific websites
If you don’t want to have to calculate it manually, the easiest option to do it is to use a specific website that is capable of doing the calculations for you without having to do anything else. You will simply have to enter the corresponding website in the browser and write the figures to find out or calculate the letter of the DNI…
Through the web letterenif.com you will only have to enter the numbers of the national identity document you want and press the button so that the page calculates it automatically. Although the calculation is simple, it is better not to have any errors in important documents. That is why doing it through this website gives us the security that we are not going to make a mistake.
In addition, other websites such as calculate-letter-dni.appspot.com follow the same system and we can enter the number in the box. Once you have filled it in, tap on the “Calculate ID letter” button to get the result. It is easy and very fast.


Statistics is among the most typical of the subjects for some students, but just a number play for some. The majority of the students belong to the first category only. In such cases, homework becomes a headache for the vast majority of the students and thus requires statistical homework help from a variety of sources. The college paper writing services play an important role in helping students. The homework help could be acquired from online sources, some experts, and paid services.
What is statistics?
This is a branch of mathematics which majorly deals with the number. It could be referred to as the quantity computed from the many different values. Different mathematical functions are used in the statics including mean, median, mode, variance, and standard deviation. The statistics are not limited to only these functions, but a variety of functions is the part of the branch.
How can online statistics help students?
The brilliant students even require help at any point in time in the statistics due to a variety of reasons. These reasons could include stress, the pressure of a lot of homework, or even the toughness of the homework. In such cases, the student could catch the online services available in the country. The coaching services are provided to the students and even the statistic homework help could be attained in the form of written solutions to the problems. These paid services are efficient enough to help the students to gather information and get the work done on time.
What is a stats homework solver?
The college paper writing services are there that provide homework solver, who in actuality is an expert in statistics. The helper could help you to get over the problems in statistics. The solution to the problem is cross-checked through multiple stages, to maintain the value of money paid by the student on the assignment service. These services have a variety of experts from different fields. There are services specifically for the statistics also, who dedicate their time completely on the statistics. They are efficient to provide both basic and advanced econometrics.
How does homework help for money?
The paid services are available for the students to get the homework done. These services ensure the students of the quality check of the solution and high-quality services. They serve the students with the utmost respect and the policies are completely transparent in front of students. Many fraud services are there in the market, just for making the money. These fraud companies do not value the money of the customer and thus students must go for credible sources before investing the money.
The Statistics homework help could be obtained from varied sources. Online paid services are the major contributor to help in case of western countries. The online learning platform also plays an important role in helping the students with the statistics homework. In this growing technology era, modification is the key to settle in the world.


Here are 35 maths riddles of all different levels of difficulty! We begin with fun riddles, then move to medium and challenging. Is your aim to give your brain a workout? Then you are in the right place! Enjoy but don’t think too hard and hurt yourself…
Fun Math Riddles
- What did one math book say to the other?
“I have so many problems”
- Once I’m 24. Twice I’m 20. Three times I’m inappropriate. What am I?
The letter “X”
- An apple is 40 cents, a banana is 60 cents. and a grapefruit is 80 cents. How much is a pear?
The price of each fruit is calculated by multiplying the number of vowels by 20 cents, so the answer is forty cents.
- How many bricks does it take to complete a building made entirely of bricks?
One. The last one!
- A family has five sons, each of them has a sister. How many kids are there in total?
Six children. Five sons and one shared sister.
- Give me an x, and the answer will face you. Give me a cross, It will turn its back on you. What am I?
The number nine! 9×9 is 81 and 9+9 is 18.
- How many eggs can you put in an empty basket?
One, after this the basket is no longer empty
- Where can you buy a ruler that is 3 feet long?
A yard sale
- When things go wrong, what can you always count on?
- 5 friends had to guess the exact numbers of balls in a box. Friends guessed as 31 , 35, 39 , 49 , 37, but none of them were right.The guesses were off by 1, 9, 5, 3, and 9 (not in order). How many balls are in the box?
- A train leaves from point A for point B at 80km/h. After 30 minutes, another train leaves from point B for point A at 60km/h. Which of the trains will be further away from point A when they meet ?
When the trains meet, they will be equally distant from point A.
- I have a half-cup of tea and a half-cup of coffee. I take one teaspoon of tea and mix it with my coffee, then I take one teaspoon of this mixture and mix it with the tea. Which cup contains more of its original contents?
Both are equal
- Can you put either addition (+), subtraction (-), multiplication (x), division (/) and parenthesis among five number 7s to make a target result number 50? 77777=50
((7 x 7 x 7) + 7) / 7= 50 or ((7 / 7) / 7 +7) x 7 = 50
- At 8 AM, a clock ticks 8 times. The time between first and last ticks is 35 seconds. How long does it tick at 11 Noon?
- Hunter decided to give bracelets to his friends on his Birthday. If he gives 3 bracelets to each friend, one friend will get only 1 bracelet. Also, if he gives 2 bracelets to each friend, he will be left with 13 bracelets. How many bracelets did Hunter give out on his Birthday? And how many friends are there?
43 bracelets and 15 friends
- Find the next 2 numbers in the series: 1, 8, 11, 69, 88, 96, 101, 111, 181, …
609, 619 (invertible numbers)
- If you multiply this number by any other number, the answer will always be the same. What number is this?
- My twin lives at the reverse of my house number. The difference between our house numbers ends in two. What are the lowest possible numbers of our house numbers?
19 and 91
- When shipping something, Hank can place ten small boxes or eight large boxes into a carton. A total of 96 boxes were sent in one shipment and the number of small boxes was less than large boxes. How many cartons did he ship?
- A snail is at the bottom of a 20-metre pit. Every day the snail climbs 5 meters up but at night it slides down 4 meters. How many days will it take before the snail reaches the top?
- You know 2 + 2 comes to the same as 2 x 2. Now find a set of three different whole numbers whose sum is equal to their total when multiplied.
1,2, and 3
- Sarah noticed that the amount she was paying for her lunch was a rearrangement of the digits of the amount of money she had in her pocket, and that the money she had left over was yet another rearrangement of the same three digits! How much money did Sarah start with?
- One out of 9 otherwise identical balls, one weighs 500 grams more. How can it be identified after 2 weighings?
Weigh a group of 3 balls against another group of 3. Then you’ll know which group of 3 contains the heavy ball. Pick 2 balls from that group and weigh one against the other.
- In a pond, there are some flowers with some bees hovering over them. How many flowers and bees are there if both the following statements are true: 1. If each bee lands on a flower, one bee doesn’t get a flower. 2. If two bees share each flower, there is one flower left out.
4 bees, 3 flowers
- A man dies of old age on his 25th birthday. How is this possible?
He was born on a leap year
- There is a certain club which is for men only. 600 men belong to this club, and 5% of these men wear one earring. Of the other 95% membership, half wear two earrings, and the other half wear none. How many earrings are being worn in this club?
- Stranded on a deserted island, Basil is left with only a 40 litres container of milk. To conserve his milk he decides that on the first day he will drink one litre of milk and then refill the container back up with water. On the 2nd day he will drink 2 litres and refill the container. On the 3rd day he will drink 3 litres and so on… By the time all the milk is gone, how much water has he drunk?
780 litres of water
- A bag of jelly beans was divided between Mayank and Steve. Mayank said, “Not fair! You have 3 times as many jelly beans as me.” Steve said, “OK, I will give you one jelly bean for each year of your age.” Mayank replied, “Now, you have twice as many jelly beans as I have.” “This is fair as I am twice your age”, said Steve. While Steve wasn’t looking, Mayank took apricots from Steve’s pile equal to Steve’s age. Who has more apricots now?
They both have the same number of apricots
- Jerome is six years old and his sister is half his age. How old will his sister be when he is 40?
Question 15# You are in a darkened room. Someone hands you a normal deck of 52 cards. He tells you that 13 of the 52 cards are face-up, the rest are face-down. These face-up cards are distributed randomly. Your task is to split up the deck into two piles, using all the cards, such that each pile has the same number of face-up cards. The room is dark and you can’t see the deck. How can you accomplish this?
Answer – Take the first 13 cards off the top of the deck and flip them over. This is the first pile. The second pile is just the remaining 39 cards as they started. This works because if there are X face-up cards within the first 13 cards, then there will be (13 – X) face up cards in the remaining 39 cards. When you flip those first 13 cards, X of which are face-up, there will now be X cards face-down, and therefore (13 – X) cards face-up, which, as stated, is the same number of face-up cards in the second pile.


I’ve just finished writing and submitting 246 pages of Algebra 2 content, (the first of 6 submissions), and the feeling of accomplishment and utter exhaustion is completely overwhelming.
I love math, I love numbers, and I always have. Those around me have always referred me to as a human calculator. Although I would not give myself that high esteem in regards to my computation abilities, I’m able to do things with numbers in my head that I find peculiar in most situations.
I’ve often wondered why my mind works so fast with numbers, and I’m curious if it was something that I was taught, if so I don’t remember, or rather if it’s just the way that my mind works. If it is something that I was taught, then I wish I could hone in on the specific skills and strategies that were employed to me, so that I might pass them on to my daughter.
I’m very curious about how she’ll feel about math when she’s older. My parents weren’t particularly math whizzes, so I don’t think I can simply give them the credit for my love of numbers. I do, however, hope that I’m able to pass my love of numbers on to my daughter.
I studied math in college for quite some time as an undergrad, but I decided to teach English instead. I’m not sure that my love for writing can be translated as easily. Writing is so different than math, and the teaching of writing is immensely different. I teach math to many of the students at my school, and I always find the experience very rewarding.
I often wonder why I feel so much more accomplished after I teach math skills than I do teaching writing strategies. It’s interesting because many students seem to value good lessons in math much more than writing; although they fear it much more. Why is that? I know that they see math as a much more difficult subject to approach, so is that why it seems that they value those lessons more?
What about the notion that everyone can write? I mean, most literate people write in some form on a daily basis. Do people feel more connected to writing, so they don’t see it as an equally difficult task? Is it that they see their writing as something that they could improve upon if they put in the time and effort, and they view math as some obscure entity?
Whenever students come in from ACT prep, they automatically assume that the writing and English portions will be easy; they’re mostly concerned with getting help for the math portion. I wonder why? Most of my students generally score pretty poorly on the English section initially, but they still view it as easier.
Personally, I think I enjoy teaching math more because it’s so concrete, and writing is so abstract. I can teach my students very specific steps and processes when it comes to math, but it takes so much more for me to impose strategies to improve voice in their writing. Effective writing skills are very hard to teach, but on the bright side, it seems that most students would rather write than do math, so at least we’ve got that going for us…


We Provide Homework Help for Geometry Most students do not understand geometry concepts with ease because geometry is generally tough. We make homework for geometry easy to understand by incorporating diagrams and theorems, which are well explained. Visual learning is known to be more impactful to a learner, and this is why we use these methods.
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Scarsdale International School follows the New York State Curriculum and incorporates the Common Core State Standards (CCSS) for English Language Arts (ELA)/Literacy and Mathematics in Grades K-12.
The Common Core provides a set of clear, consistent guidelines for what students should know and be able to do at each grade level in Math and English Language Arts, while stressing on and developing cognitive areas: critical thinking, problem solving, and analytical skills. Teachers tailor their instruction to the individual needs of the students in their classrooms.
These standards also ensure students are being prepared to read, write, and research across the curriculum, in other core subjects like Social Studies and Science as well. Hence, preparing all students for success in college, career, and life by the time they graduate from high school.


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LEARN Science & Math Club, a non-profit that provides kids with rich, hands-on science and math experiences, was born when we realized American kids are falling behind, ranking 17th in science and 25th in math. The solution was clear: give kids lots of time to work on fun, engaging STEM projects, and they would grow. So, we created tons of fun, hands-on classes and camps, and they worked! The kids were thrilled and clamored for more.


FINEMATIC is a young Czech project from Prague whose founders met in 2000 at the Faculty of Mathematics and Physics of Charles University. Based on the first experience with exchange trading, a project was set up in 2007 to reduce the impact of emotions on market transactions.
FINEMATIC uses a unique combination of theoretical knowledge and practical experience, which provides a competitive edge. Since its inception, FINEMATIC has been transparent, adhering to strict ethical principles, and emphasizing personal contact with the client.
Founders of FINEMATIC act as individuals providing services of collective asset management. Its activities are not subject to the supervision of the Czech National Bank.
Jan Sindelar, Ph.D. graduated in physics and mathematics at the Faculty of Mathematics and Physics of Charles University in Prague. During his studies he focused on application of mathematics to trading. At the Institute of Information Theory and Automation of the Czech Academy of Sciences he reasearched Bayesian statistics and control theory. He worked for the Estlander & Partners hedge fund in Finland. Together with programming of the FINEMATIC software platform, he is in charge of evolution of trading strategies and their optimization. He also meets with clients.
Martin Mixa, M.S. studied physics at the Faculty of Mathematics and Physics of Charles University in Prague. While working at the Department of Condensed Matter Physics, he studied computer modeling of growth of quantum dots for use in nanotechnologies. He is in charge of the design and programming of the FINEMATIC software platform, to which he still dedicates most of his time. He is also responsible for the legal organization of the project.


The annual equivalent rate (AER) is a term used to describe the interest rate that is applied to savings products on an annual basis, taking into account the effects of compounding.
It allows you to compare different savings account options and understand the true return you can expect over a year. What does interest rate mean?
Annual Equivalent Rate (AER) example:
Let’s say you have £1,000 in a savings account with an AER of 3.00%. After one year, your balance would increase to £1,030, assuming no additional deposits or withdrawals have been made.


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A while ago I made an excel sheet to calculate feeding amounts. I made a web version to share so anyone can use it :) It's especially useful for puppies since they grow so quickly it's hard to keep up with how much to feed them on a weekly basis.
Just enter your dog's weight (either in pounds OR in kg, not both) and the kcal/cup of the food you are feeding.
In the green area it tells you how much to feed your dog (use the info. from one column only). I rounded it to the nearest 1/4 cup to simplify measuring but if you want a more accurate number it's below in the purple shaded area.
*NOTE* This assumes your dog has a normal activity level and is at a healthy weight. Feeding amounts should always be adjusted depending on your dog's needs and body condition (under/overweight if applicable). If your dog gets treats in addition to kibble subtract 1/4 cup from the daily total.
If your dog is outside of the "Medium" range (either very small or very large) then the "Alternate calculations" section (on the right) is likely to be more accurate.
This calculator is made using the Resting Energy Requirements (RER) formula for caloric needs in dogs. I confirmed with my vet this is the correct formula to be using to calculate feeding amounts.
Let me know if it's working properly!


LATERAL TORSIONAL BUCKLING OF DOUBLE SYMMETRICAL I BEAM WITH VERTICAL STIFFENERS
Lateral Torsional Buckling (LTB) Formula of an I beam having a constant moment is derived using an exact mathematical approach, taking into assumption that the web is not deformed. Generally on the beam design, the vertical stiffener is only designed to increase the shear strength of the web. The effects of vertical stiffeners to the LTB moment of the beam is not taken into account in the design. In this paper, we will study the effect of the vertical stifenners to the LTB of the beam, assuming that the web is remain straight and the materials of beam is still elastic when the beam buckles. The same elementary differential equation of section rotation is used for both areas between two vertical stiffener adjacent and between the vertical stiffener and the support. The homogenous equations of the constant of integration is defined using the natural boundary conditions on the vertical stiffeners and on the support. The natural boundary condition at the vertical stiffener is nothing but the moment balance between the left flange moment, the right flange moment and the torque of the vertical stiffener. The coefficient matrix of the homogenuous equation is a function of the critical moment. By trial and error, we can then define the critical moment in which the determinant of the coefficient matrix is equal to zero. The analysis is carried out using Fortran language, validated using the existing empirical formula. The analysis shows that the vertical stiffeners increase the critical moment by up to 13%.


This applet shows some geometrical properties of K-Nearest Neighbors, Natural Neighbors (or Delaunay Neighbors) and Gamma-Observable Neighbors .
See others applets and tutorials on David Eppstein's Geometry Junkyard
- Push left button and move the mouse to move the green dot, observe its neighbors (nearest in yellow, others in red);
- Push "English/FranÁais" button to change the language;
- Select the neighborhood type in the unrolling menu;
- Use the "Mode" button to visualize and infer different geometrical properties and how they change with the green dot position;
- Use the slider to change the parameter K or Gamma.
This applet © 2001 MichaŽl Aupetit
 MichaŽl Aupetit, Pierre Couturier, Pierre Massotte."Gamma-Observable neighbours for vector quantization."
Neural Networks, Volume 15, Issues 8-9, October-November 2002, Pages 1017-1027. Elsevier


Mrs. Arthur's Web Site
This is my eleventh year teaching in Kensington Hall. I work with the fifth, sixth, seventh and eighth grade boys in math and fifth and sixth grade in science. I also work with fifth through eighth grade boys and faculty in technology. I am also the coach of the upper school combined varsity figure skating team.
This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 United States License
Based on a work at www.ashmi.org


For the purpose of the Mathematics Program Evaluation, the District administered the mathematics portions of the Stanford Achievement Test (SAT-10) to fourth graders in January 2008. The SAT-10 was selected for its ability to provide national norms on a mid-year assessment of mathematics achievement as well as an analysis of student performance on individual test items. The Stanford Achievement Test for fourth grade students is comprised of 80 multiple choice questions; 48 questions on Math Problem Solving and 32 questions on Math Procedures. The Mathematics Procedures portion of the SAT-10 is performed without a calculator. Questions are aligned with the Oregon Content Standards and BSD Learning Targets from 3rd and 4th grade. Students received a scaled score, national percentile, and grade level equivalent on the assessment. The number of items answered and correct are reported in both process (e.g., Computation in Context) and content (e.g., Geometry) clusters of skills for 76 of the 80 items.
Last Updated: Aug 14, 2008


In Math, we are learning about Number Sense and Mental Math strategies.
Students are solving problems involving the addition and subtraction of single-digit whole numbers, using lots of different mental strategies (e.g., one more than, one less than, counting on, counting back, doubles).
Dot Plates are great for practicing subitizing (recognizing numbers quickly) and then counting on.
Other subitizing videos.
Check out some great 'doubles' videos on YouTube to help students memorize their doubles facts:
Doubles, Doubles, I Can Add Doubles (1 - 5 version)
Doubles, Doubles, I Can Add Doubles (6 - 10 version)
Add 'Em Up! - one more than
Harry Kindergarten Music is great for Curriculum based songs!
I Can Write My Numbers - great if your child has reversals
Number Words Rap
I Can Count to 100
Numbers in the Teens
Adding and Subtracting
Skip Count - and then Count On! (grade 2s)
In our Room 108 Classroom Community, we foster an engaging, respectful and caring environment. I aim to balance a consistent program with flexible responsiveness to students' individual needs.


4 edition of Nonlinear evolution equations found in the catalog.
Nonlinear evolution equations
Symposium on Nonlinear Evolution Equations University of Wisconsin-Madison 1977.
|Other titles||Evolution equations.|
|Statement||conducted by the Mathematics Research Center, the University of Wisconsin-Madison, October 17-19, 1977 ; edited by Michael G. Crandall.|
|Series||Publication of the Mathematics Research Center, the University of Wisconsin-Madison ; no. 40, Publication ... of the Mathematics Research Center, the University of Wisconsin--Madison ;, no. 40.|
|Contributions||Crandall, Michael G., University of Wisconsin--Madison. Mathematics Research Center.|
|LC Classifications||QA3 .U45 no. 40, QA370 .U45 no. 40|
|The Physical Object|
|Pagination||ix, 255 p. :|
|Number of Pages||255|
|LC Control Number||78012744|
The nonlinear evolution equation depending on a real parameter A in some real Banach space E is considered. If E is finite dimensional, this equation represents an ordinary dynamical system, and if E is infinite dimensional it is the abstract version of some class of nonlinear parabolic partial differential equations. Stability, and. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate.
johnsonout.com: Solitons, Nonlinear Evolution Equations and Inverse Scattering (London Mathematical Society Lecture Note Series) () by Ablowitz, M. A.; Clarkson, P. A. and a great selection of similar New, Used and Collectible Books available now at great johnsonout.com Range: $ - $ The author investigates the global existence and uniqueness of small smooth solutions for nonlinear evolution equations, including nonlinear wave equation, nonlinear heat equation, nonlinear Author: Reinhard Racke.
*Prices in US$ apply to orders placed in the Americas only. Prices in GBP apply to orders placed in Great Britain only. Prices in € represent the retail prices valid in Germany (unless otherwise indicated). This monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schrodinger equations, nonlinear Klein?Gordon equations, KdV equations as well as Navier?Stokes equations and Boltzmann equations. This book is self-contained and may also be used as an advanced textbook by graduate students in Cited by:
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This book is divided into 13 chapters and begins with reviews of the uniqueness of solution to systems of conservation laws and the computational aspects of Glimm’s method. The next chapters examine the theoretical Nonlinear evolution equations book practical aspects of Boltzmann, Navier-Stokes, and evolution equations.
Nonlinear evolution equations arise in many fields of sciences including physics, mechanics, and material science. This book introduces some important methods for dealing with these equations and explains clearly and concisely a wide range of relevant theories and techniques.
These include the semig. Gorden equations and nonlinear Schr¨odinger equations from quantum mechanics and Cahn-Hilliard equations from material science, to name just a few, are special examples of nonlinear evolution equations. Com-plexity of nonlinear evolution equations and challenges in their theoret-ical study have attracted a lot of interest from many mathematicians.
This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the Author: Reinhard Racke.
Jul 08, · Nonlinear evolution equations arise in many fields of sciences including physics, mechanics, and material science.
This book introduces some important methods for dealing with these equations and explains clearly and concisely a wide range of relevant theories and johnsonout.com by: linear evolution equations. It contains research papers related to Benilan's work and covers a wide range of nonlinear and linear equations.
Special topics are Hamilton-Jacobi equations, the porous medium equation, reaction diffusion systems, integro-differential equations and visco-elasticity, max. Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations is devoted to inverse scattering problems (ISPs) for differential equations and their application to nonlinear evolution equations (NLEEs).
The book is suitable for anyone who has a mathematical background and interest in functional analysis, partial. Mar 16, · This is a superb book by a highly respectable scholar on nonlinear evolution equations - very clearly written and meant to serve as apt for a senior PhD student, postdoc or faculty member with a desire to learn the johnsonout.com by: This book brings together several aspects of soliton theory currently only available in research papers.
Emphasis is given to the multi-dimensional problems arising and includes inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multi-dimensions and the ∂ johnsonout.com by: Get this from a library. Nonlinear dynamics and evolution equations. [H Brunner; Xiao-Qiang Zhao; Xingfu Zou;] -- "The papers in this volume reflect a broad spectrum of current research activities on the theory and applications of nonlinear dynamics and evolution equations.
They are based on lectures given. This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations.
The book employs the classical method of continuation of local solutions with the. Nonlinear evolution equations arise in many fields of sciences including physics, mechanics, and material science. This book introduces some important methods for dealing with these equations and explains clearly and concisely a wide range of relevant theories and techniques.
These include the semigroup method, the compactness and monotone operator. Note: Citations are based on reference standards. However, formatting rules can vary widely between applications and fields of interest or study.
The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied. This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations.
The book employs the classical method of continuation of local solutions with the help of a prioriAuthor: Reinhard Racke. The Journal of Nonlinear Evolution Equations and Applications (JNEEA) is an electronic mathematical journal dedicated to rapid dissemination of high quality papers in all areas and sub-areas of evolution equations and their applications to scientific and engineering problems.
All research articles submitted to JNEEA must undergo rigorous peer. The book will be of interest to applied mathematicians and mathematical physicists working in the area of integrable and solvable non-linear evolution equations; it can also be used as supplementary reading material for general applied mathematics or mathematical physics johnsonout.com by: 8.
Part II of the book handles evolution problems and introduces every auxiliaries you will need later. Moreover, several PDEs and examples are investigated. No semigroup theory here, but the other methods. Nonlinear Evolution Equations by Zheng and Infinite-Dimensional Dynamical Systems by Robinson also fits to this description.
Book of Abstracts The Eleventh IMACS International Conference On Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory Athens, Georgia April 17—19, Sponsored by The International Association for Mathematics and Computers in Simulation (IMACS) The Computer Science Department, University of Georgia.
The book in hand is based on lectures which were given at the University of Bonn in the winter semesters of /90 and / The aim of the lectures was to present an elementary, self-contained introduction into some important aspects of the theory of global, small, smooth solutions to initial value problems for non linear evolution equa johnsonout.com: Reinhard Racke.
Aug 01, · This monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schrödinger equations, nonlinear Klein–Gordon equations, KdV equations as well as Navier–Stokes equations and Boltzmann equations.
The. Nonlinear Evolution Equations1 John K. Hunter October 1 c John K. Hunter Contents 1 Introduction 1 A central issue in the study of nonlinear evolution equations is that solutions may exist locally in time (that is, for short times) but not globally in time.May 10, · Nonlinear Evolution Equation covers the proceedings of the Symposium by the same title, conducted by the Mathematics Research Center at the University of Wisconsin, Madison on OctoberThis book is divided into 13 chapters and begins with reviews of the uniqueness of solution to systems of conservation laws and the computational Book Edition: 1.Click Download or Read Online button to get dirac structures and integrability of nonlinear evolution equations book now.
This site is like a library, Use search box in the widget to get ebook that you want. Dirac Structures And Integrability Of Nonlinear Evolution Equations.


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For this assignment use regression to complete the assignment below:
Use information from the modular background readings as well as any good quality resource you can find. Please cite all sources and provide a reference list at the end of your paper.
The following items will be assessed in particular:
Identify when the Least Squares method should be used.
Describe ANOVA and identify when the ANOVA method should be used.
Take your data and arrange it in the order you collected it. Count the total number of observations you have, and label this number N. Then create another set of data starting from one and increasing by one until you reach N. For example, if you have 10 observations, then your new set of data would be (1, 2, 3, 4, 5, 6, 7, 8, 9, 10). This set of data is called a time series. Run a regression using your original set of data as your dependent variable, and your time series as an independent variable. Use the simple regression calculation page to calculate your regression. Write a paper reporting your results and any conclusions that can be reached with it.
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While you are still in high school
- Take the appropriate college-prep English and math courses;
- Meet with your high school guidance counselor during your junior year to be sure you have the qualifications to enter one of Maine’s public universities.
If you’ve been out of school for a while
- You may be asked to take placement tests to assess your level of skill in English and math and to help you and your advisor determine the appropriate starting point for your first year at the university. The results determine whether you must take one or more remedial courses before beginning 100-level college courses.
- The Accuplacer is a self-paced, untimed computerized placement test that is used by UMA, UMFK, UMM, UMPI, and USM. The College Board publishes The Accuplacer Online Student Guide , and you can practice taking the test at this site:
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Admission Requirements for


A Basic Introduction to Regular Deviations
There are three basic sets of casino games: table games, games machines, and randomly generated games. Most table games, incorporating roulette, craps, baccarat, craps more, blackjack, etc., require more than one person to play. Some desk games such as for example bridge, joker, etc., may be played by just a few people. All the games are played by way of a team of members. The random variety game, also called slots, is among the most popular casino games nowadays.
In the progressive slot machine game, as in other casino games like poker, blackjack, craps, etc., the thing is to win real money from pay machines and get the corresponding payoff. The same type of progressive slot machine game are available in video slots. Some progressive slot machines in video casinos are equipped with their own split slot reels. When these independent reels hit the pay-line, the appropriate volume on the payoff reel pulls out and the appropriate amount on the machine next pays out.
Many slot machines can be purchased in most of the casinos. They’re categorized based on the winnings, maximum bet, reels used, locations and hrs of functioning. While playing a casino video game, there are some types of slot machines which are popular among casino goers. Included in these are regular machines, progressive equipment and bonus/progressive devices.
As mentioned earlier, regular slots can be found in almost all of the casinos. Slots in non-top quality casinos could use a random quantity generator. These machines can be found in various denominations, with regards to the casino’s minimum winning limit. They are known by various names, among them, regular, movie, combo, magnetic and spin equipment.
Progressive slots, because the name suggests, pay out a continuing amount regardless of how much the player has bet onto it. With the upsurge in house edge, the more a casino pays out, the bigger the house edge is. With a larger house edge, a internet casino is said to possess a “slot’s syndrome”, which is to say that the probability of a new player winning on a progressive slot machine is lower than in a regular equipment.
Benefit and progressive casino gambling may also be related as the latter make the gambler get more income in a shorter time period. The casinos will be able to maximize revenue through this. Basically, the more the casino pays out, the more the ball player needs to win. On the other hand, in a casino, benefit or progressive casino gambling means the same thing as good luck. This leads to casino gamblers having a “feel good” factor and feeling positive about gambling.
The random number generator, that is a device used in casinos to assign probabilities, is also related to the roulette wheel. Like the house edge, the probability of hitting a jackpot is always lower with the roulette wheel than in a device. The random quantity generator creates numbers which are independent of any regarded deterministic device. Therefore, a gambler can use this to his / her advantage. It makes the odds of hitting a more impressive jackpot or number smaller than the genuine probability on the roulette wheel and therefore increases the likelihood of a get.
Another factor that is associated with the random number generator is the payout casino games. Although some of these casinos claim that they have their own internal random generators, others just use a machine supplied by the developer. Since they depend on the manufacturer’s guarantee of quality, it isn’t surprising that the same results are again repeated again. This leads to what is referred to as the diminishing returns.
One other factor that is related to casino games available for roulette, craps, and slot machines is the reliability of the payout. Roulette, craps, and slots 엠카지노쿠폰 are known to be the most famous type of games available for casinos. Their acceptance is understandable given their ease of operation, which appeals to both the modern casino owner and the gambler. The payout from these games is frequently the highest in every casino games available for participants.
Common deviation, which is also known as mean-reverting mean, can be used in standard deviation to determine portfolio holdings of the gambler. Regular deviation can be used to measure the way the portfolio holdings of the gambler modifications as time passes. Like the binomial model, the standard deviation gives rise to the casino principle “the typical deviation” (also known as the beta distribution). Regular deviation accounts for the beta distribution in common casino games available for roulette, craps, slots, along with other standard casino video games.
In addition to the profitability of the casino game titles, another factor affecting casino play is the casino house edge (house benefits). The house edge is the difference between the expected winning number and the actual winning number at a gambling house. Standard deviations, as well as the mean deviation, are widely used in casino management and game playing to ensure that casino gaming establishments have an optimal probability of earning profits and minimizing possible losses.


Every day, we face trade-offs for how to best use our money. We constantly have to choose between competing uses of finite resources. But the cost of missed opportunities can be very high — very, very high.
In a prior business life, I was a financial adviser who was also involved in the training and development of other advisers. In doing this work, I presented a lot of seminars. A staple of basic financial seminars? An illustration of opportunity cost.
To understand the illustration, you need to understand the “rule of 72.” This rule is an approximation of how long it will take for an investor’s money to double at a given rate of return. It states that if you take the number of years it takes for the investment to double and multiply that by the rate of return, your answer will come out to 72 — approximately.
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For example, let’s say that you want to know how long it will take for your investment to double at an eight percent rate of return. The rule of 72 here says that eight times the length of time to double equals 72. So to solve for the length of time, we divide 72 by eight. The result? It will take about nine years (72 ÷ 8 = 9).
Naturally, you can also use the rule to find the approximate rate of return needed to double an investment in a given timeframe. For example, to determine the return required to double an investment in 10 years, we divide 72 by 10 to find it takes a return rate of approximately 7.2 percent to double an investment in 10 years (72 ÷ 10 = 7.2).
Now that we’re all on the same page with the rule of 72, let’s return to our discussion of opportunity cost. In this opportunity cost example, a hypothetical person — let’s call him Pat — changes jobs. Pat is 29 years old and plans to retire at age 65. That puts retirement a distant 36 years away.
He liquidates the 401(k). Unfortunately, he has to pay a 10 percent premature distribution penalty, as well as tax on the entire distribution. That leaves him with $22,000 or so for a car.
Pat is delighted to have a new car. He did not, however, consider the opportunity cost of this decision.
Let’s say that Pat had left the 401(k) investment intact and received, on average, an eight percent return between now and retirement. As we calculated earlier, the rule of 72 tells us that at eight percent, an investment will double in value in about nine years. So with 36 years until retirement, Pat’s 401(k) would have doubled four times by Pat’s age 65 (36 ÷ 9 = 4).
The money would have doubled once from $30,000 to $60,000, then from $60,000 to $120,000. The third doubling takes the $120,000 to $240,000. The fourth takes the $240,000 to $480,000.
That’s right — $480,000 in retirement money. That’s the missed opportunity of Pat’s decision to liquidate the 401(k).
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Pat “needed” a new car. Naturally, he would have had to allocate some resources to meeting this need. He'd have to balance that cost with the opportunity cost of liquidating the 401(k) — i.e. the $480,000 in retirement funds. Compare that to a car that will go to the scrap heap long before Pat retires.
We constantly have to choose between different possible uses for our finite resources. Understanding the consequences of our decisions can help us to choose wisely and avoid missed opportunities.


The company is teaming with Packet, which is offering to run the service for free on its servers. Exponential Functions — In this section we will introduce exponential functions. This web app uses machine learning to analyze and repair your technical resume, allowing you to shine to recruiters at Google, Yahoo and Facebook.
Graphing quadratic functions Video transcript We're asked to graph the equation y is equal to negative 2 times x minus 2 squared plus 5. The parabola can either be in "legs up" or "legs down" orientation.
A Summary — In this section we will summarize the topics from the last two sections.
So I care about x being equal to 1, 2, and 3, and what the corresponding y is. We know that a quadratic equation will be in the form: Logarithm Functions — In this section we will introduce logarithm functions.
Saving water and electricity essay write a essay about my best friend. Put it all together and you get a nightmare […] Posted on: I woutould like to know how to find the equation of a quadratic function from its graph, including when it does not cut the x-axis.
F4 opens the Var menu, which contains functions for dealing with variables on the calculator, and also contains the Local function, which we will use later in this tutorial. These types of equations are called quadratic in form. When x is equal to 1, 1 minus 2 is negative 1, squared is just 1.
Next, set the mode for outputting results as complex numbers in case any quadratic equations you enter result in imaginary solutions. Similarly the vertical reflection of a graph send the y-value associated to a given x-value to its negative, reflecting the graph across the x-axis.
We make the following transformations to the equation given and then show that the vertex of the resulting equation lies in the second quadrant and its graph is concave down on its domain. So let me go back to the exercise and actually put those three points in.
You will be prompted to name your new program.
First, we will start discussing graphing equations by introducing the Cartesian or Rectangular coordinates system and illustrating use of the coordinate system to graph lines and circles. The founders are marketing and HR experts who have a combined 15 […] Posted on: And now I want to find two more points so that I can really determine the parabola.
Press "1" to enter the equation calculation mode. The event will showcase the launch of 15 of the hottest startups in Africa onstage for the first time. We look at compound interest, exponential growth and decay and earthquake intensity.
Notice that the 2 is not inside the parentheses as before, and is not squared as a result. Press 3 Press "3" to select to solve a quadratic equation.
We are then asked to make a change to our equation which will move the vertex to the second quadrant.
Facebook told the regulator an estimated one million U.Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site. Step by step lessons for solving a quadratic equation can be found in this Algebra Unit.
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You have several options with this sort. Students can graph the equation then look for the matching graph, or they can take a graph find the matching equation.
Equations are in both standard and vertex form. You can also have student match the equations together.
Math homework help. Hotmath explains math textbook homework problems with step-by-step math answers for algebra, geometry, and calculus.
Online tutoring available for math help. Here is a set of notes used by Paul Dawkins to teach his Algebra course at Lamar University.
Included area a review of exponents, radicals, polynomials as well as indepth discussions of solving equations (linear, quadratic, absolute value, exponential, logarithm) and inqualities (polynomial, rational, absolute value), functions (definition, notation, evaluation, inverse functions) graphing.Download


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Rodchenkova Natalia IvanovnaSign in
Academic degree: Cand. (PhD) of Physics and Mathematics (2007)
Awards: Grant from the Russian Science Support Foundation "Candidates of Science (PhD) of the Russian Academy of Sciences" (2008); Prize of the Ministry of Education and Science of the Russian Federation in the nomination «Talented Youth» (2007); Grant from the Russian Science Support Foundation "The Best PhD Students of the Russian Academy of Sciences" (2007); Diploma for the best paper at a session of the International Conference «Lomonosov» (Moscow State University) (2005, 2007)
Scientific speciality: 05.13.18 - mathematical modelling, numerical methods and software complexes
Major research trends:
Keywords: mathematical modelling, boundary-value problems with moving bounds, numerical methods
Date of birth: 29.11.1981
1999-2003: Undergraduate student of the Faculty of Mathematics, Petrozavodsk State University.
2003: Bachelor of Math, Petrozavodsk State University.
2003-2005: Graduate student of the Faculty of Applied Mathematics, Petrozavodsk State University.
2005: Master of Science (Math), Petrozavodsk State University.
2005-2007: Postgraduate student, the Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences.
2007: PhD degree obtained, Petrozavodsk State University. PhD thesis "Numerical modelling of TDS-spectrum peak of dehydriding with moving phase bounds".


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The mathematics major prepares students for careers in the following branches of engineering, biological, meteorological, and other scientific problems. Explore applied mathematics studies and whether it's the right major for you of applied math learn how to use math and statistics to solve problems in the. The mission of the mathematics department is to prepare midshipmen for the in applying mathematics and mathematical thinking to specific naval problems. Our department has an impressive research record in both pure mathematics and fostering advanced research and creating solutions for real-world problems.
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Paik's art is grand, not only in its size which is
monumental, but also in its conception. Paik's visionary production
spans great lengths crossing tremendous heights to offer us
her magical galaxies overlaid with cathedral plans from the
medieval world. Her sacred geometry depicting harmonious proportions
and cosmologic parameters in mathematical ratios is parallel
to the cultural universal condition. Sacred geometry such
as that found in Paik's expansive surfaces covered with stars
was employed in religious architecture. Medieval churches
and temples incorporated symbolic geometry, basing it on the
design of the cross or mandala. In Cosmology the world can
be seen in terms of cosmic geometry as did Johannes Kepler.
The natural world also can be discussed in geometric terms
as seen by snowflakes, or honeycombs. In fact these geometric/natural
correspondences can be considered paradigms of cosmic significance.
Paik's tremendous canvases transport the viewer on a mystical
journey through which he discovers new dimensions not always
recognizable. Pythagorean mathematics and Sufi geometry mix
to produce realms that surround the viewer leaving him disoriented
and in total awe. Paik's huge universe envelopes the viewer,
caressing and welcoming him into a sea of alchemy.
here to see more photos of the exhibit taken by photographer
For More Information: Please contact the Exhibitions Director
Dr. Thalia Vrachopoulos at 212-691-7978 or email@example.com
or the Tenri Administrative Director Mr. Michael Yuge at 212-645-2800
or firstname.lastname@example.org .


There is no penalty for wrong answers, so it makes sense to give the best answer you can to every question, even if it is just your best guess.
The time is up. Section 2 is done, you have a 5-minute break period, then you be redirected to Section 3: Mathematics Test—Calculator 2
Math – No Calculator Tests
Mathematics Test—No Calculator 4
20 Questions. 25 Minutes to Complete
For questions 1 through 15, solve each problem, choose the best answer from the choices provided, and indicate your answer choice on your answer sheet. For questions 16 through 20, solve the problem and indicate your answer, which is to be recorded in the spaces provided on the answer sheet. Please refer to the directions before question 16 on how to record your answers in the spaces provided. You may use scratch paper for scratch work.
1 / 20
1. The use of a calculator is not permitted.
2. All variables and expressions used represent real numbers unless otherwise indicated.
3. Figures provided in this test are drawn to scale unless otherwise indicated.
4. All figures lie in a plane unless otherwise indicated.
5. Unless otherwise indicated, the domain of a given function f is the set of all real numbers x for which f (x) is a real number.
Begin skippable figure descriptions.
The figure presents information for your reference in solving some of the problems.
Reference figure 1 is a circle with radius r. Two equations are presented below reference figure 1.
A equals pi times the square of r.
C equals 2 pi r.
Reference figure 2 is a rectangle with length ℓ and width w. An equation is presented below reference figure 2.
A equals ℓ w.
Reference figure 3 is a triangle with base b and height h. An equation is presented below reference figure 3.
A equals onehalf b h.
Reference figure 4 is a right triangle. The two sides that form the right angle are labeled a and b, and the side opposite the right angle is labeled c. An equation is presented below reference figure 4.
c squared equals a squared plus b squared.
Special Right Triangles
Reference figure 5 is a right triangle with a 30degree angle and a 60degree angle. The side opposite the 30degree angle is labeled x. The side opposite the 60degree angle is labeled x times the square root of 3. The side opposite the right angle is labeled 2 x.
Reference figure 6 is a right triangle with two 45degree angles. Two sides are each labeled s. The side opposite the right angle is labeled s times the square root of 2.
Reference figure 7 is a rectangular solid whose base has length ℓ and width w and whose height is h. An equation is presented below reference figure 7.
V equals ℓ w h.
Reference figure 8 is a right circular cylinder whose base has radius r and whose height is h. An equation is presented below reference figure 8.
V equals pi times the square of r times h.
Reference figure 9 is a sphere with radius r. An equation is presented below reference figure 9.
V equals fourthirds pi times the cube of r.
Reference figure 10 is a cone whose base has radius r and whose height is h. An equation is presented below reference figure 10.
V equals onethird times pi times the square of r times h.
Reference figure 11 is an asymmetrical pyramid whose base has length ℓ and width w and whose height is h. An equation is presented below reference figure 11.
V equals onethird ℓ w h.
End skippable figure descriptions.
Additional Reference Information
The number of degrees of arc in a circle is 360.
The number of radians of arc in a circle is 2 pi.
The sum of the measures in degrees of the angles of a triangle is 180.
Salim wants to purchase tickets from a vendor to watch a tennis match. The vendor charges a onetime service fee for processing the purchase of the tickets. The equation T =15 n + 12 represents the total amount T, in dollars, Salim will pay for n tickets. What does 12 represent in the equation?
2 / 20
2. A gardener buys two kinds of fertilizer. Fertilizer A contains 60% filler materials by weight and Fertilizer B contains 40% filler materials by weight. Together, the fertilizers bought by the gardener contain a total of 240 pounds of filler materials. Which equation models this relationship, where x is the number of pounds of Fertilizer A and y is the number of pounds of Fertilizer B?
3 / 20
3. What is the sum of the complex numbers 2 + 3 i and 4 + 8 i, where ?
4 / 20
4. Question 4 refers to the following equation.
In the preceding equation, p and t are constants. Which of the following could be the value of p?
5 / 20
5. Which of the following is the graph of the equation y = 2 x – 5 in the xyplane?
Each option presents the graph of a line in the xyplane with the origin labeled O. The numbers negative 5 and 5 are indicated on each axis.
6 / 20
6. If and y = 18, what is the value of 2 x – 3?
7 / 20
7. A bricklayer uses the formula n = 7 l h to estimate the number of bricks, n, needed to build a wall that is l feet long and h feet high. Which of the following correctly expresses l in terms of n and h?
8 / 20
8. Question 8 refers to the following figure.
Begin skippable figure description.
The figure presents a 3column table with 5 rows of data. The heading for column 1 is “x,” the heading for column 2 is “w of x,” and the heading for column 3 is “t of x.” The five rows of data are as follows.
Row 1: x, 1; w of x, negative 1; t of x, negative 3.
Row 2: x, 2; w of x, 3; t of x, negative 1.
Row 3: x, 3; w of x, 4; t of x, 1.
Row 4: x, 4; w of x, 3; t of x, 3.
Row 5: x, 5; w of x, negative 1; t of x, 5.
End skippable figure description.
The preceding table shows some values of the functions w and t. For which value of x is w (x) + t (x) = x?
9 / 20
9. If , what is the value of x?
10 / 20
10. Jaime is preparing for a bicycle race. His goal is to bicycle an average of at least 280 miles per week for 4 weeks. He bicycled 240 miles the first week, 310 miles the second week, and 320 miles the third week. Which inequality can be used to represent the number of miles, x, Jaime could bicycle on the 4th week to meet his goal?
11 / 20
11. Question 11 refers to the following figure.
The figure presents a parabola labeled, y equals a x squared plus c, in the x yplane with the origin labeled O. The parabola opens upward and its vertex lies on the yaxis a short distance above the origin.
The vertex of the preceding parabola in the xyplane is (0, c). Which of the following is true about the parabola with the equation ?
12 / 20
12. Which of the following is equivalent to ?
13 / 20
13. Question 13 refers to the following equation.
In the preceding equation, t is a constant. If the equation has no real solutions, which of the following could be the value of t?
14 / 20
14. A laundry service is buying detergent and fabric softener from its supplier. The supplier will deliver no more than 300 pounds in a shipment. Each container of detergent weighs 7.35 pounds, and each container of fabric softener weighs 6.2 pounds. The service wants to buy at least twice as many containers of detergent as containers of fabric softener. Let d represent the number of containers of detergent, and let s represent the number of containers of fabric softener, where d and s are nonnegative integers. Which of the following systems of inequalities best represents this situation?
15 / 20
15. Which of the following is equivalent to ?
16 / 20
For questions 16 through 20, solve the problem and record your answer in the spaces provided on the answer sheet, as described in the following directions and examples.
1. Although not required, it is suggested that your answer be recorded in the boxes at the top of the columns to help fill in the circles accurately. You will receive credit only if the circles are filled in correctly.
2. Mark no more than one circle in any column.
3. No question has a negative answer.
4. Some problems may have more than one correct answer. In such cases, indicate only one answer.
5. Mixed numbers such as must be recorded as 3.5 or 7/2.
( is recorded in the spaces provided on the answer sheet, it will be interpreted as not )
6. Decimal answers: If you obtain a decimal answer with more digits than the spaces on the answer sheet can accommodate, it may be either rounded or truncated, but it must fill all four spaces.
The following are four examples of how to record your answer in the spaces provided. Keep in mind that there are four spaces provided to record each answer.
Examples 1 and 2
Example 1: If your answer is a fraction such as seventwelfths, it should be recorded as follows. Enter 7 in the first space, the fraction bar (a slash) in the second space, 1 in the third space, and 2 in the fourth space. All four spaces would be used in this example.
Example 2: If your answer is a decimal value such as 2.5, it could be recorded as follows. Enter 2 in the second space, the decimal point in the third space, and 5 in the fourth space. Only three spaces would be used in this example.
Example 3: Acceptable ways to record twothirds are: 2 slash 3, .666, and .667.
Note: You may start your answers in any column, space permitting. Columns you don’t need to use should be left blank.
Example 4: It is not necessary to begin recording answers in the first space unless all four spaces are needed. For example, if your answer is 201, you may record 2 in the second space, 0 in the third space, and 1 in the fourth space. Alternatively, you may record 2 in the first space, 0 in the second space, and 1 in the third space. Spaces not needed should be left blank.
If for positive integers a and b, what is one possible value of b?
17 / 20
17. Question 17 refers to the following equation.
What value of t is the solution of the preceding equation?
18 / 20
18. Question 18 refers to the following figure.
The figure presents triangle ACE, with horizontal side AC. Side AE is perpendicular to side AC such that point E is above point A. Point B lies on horizontal side AC, point D lies on hypotenuse CE, and line segment BD is drawn such that it is parallel to side AE and forms triangle CDB. Side AE is labeled 18, side BC is labeled 8, side BD is labeled 6, and a right angle symbol is at point A.
In the preceding figure , is parallel to . What is the length of ?
19 / 20
19. How many liters of a 25% saline solution must be added to 3 liters of a 10% saline solution to obtain a 15% saline solution?
20 / 20
20. Points A and B lie on a circle with radius 1, and arc AB has length . What fraction of the circumference of the circle is the length of arc AB?


Bing adds new math-based interactive answers to search results
Bing has been a bit busy recently.
After adding interactive solar system and periodic table tools to their search results, the search engine has today rolled out six maths-based interactive resources and answer boxes.
In honour of ‘Pi Day’ (14 March or ‘3/14’), Bing today announced a new multiplication table tool, separate geometry calculator and geometry shape tools, a function grapher, a polynomial equation solver, a number answer and a number converter tool.
Announcing the new set of tools, Bing said:
Today is the annual celebration of Pi Day. In honor of this day, and to help students of different ages learn and practice mathematics in an immersive way, the Bing Education team developed a number of interactive answers. These answers range from a basic multiplication tables to a more advanced polynomial-equation solver. It’s also another Bing milestone in our continuing effort to make fun, interactive tools to support students as they learn math and science.
The answer boxes on Bing work in much the same way as they do on Google, so a Bing search for [multiplication table] will bring up an interactive times table calculator to work on directly in the search results:
You can try all the new Bing tools using the dedicated links below:
Bing multiplication table: https://www.bing.com/search?q=multiplication+table&PC=U316&FORM=CHROMN&setflight=mtable
Bing geometry calculator: https://www.bing.com/search?q=area+of+a+trapezoid&PC=U316&FORM=CHROMN
Bing geometry shape: https://www.bing.com/search?q=square+shape
Bing function grapher: https://www.bing.com/search?q=sinx%2C+tanx&go=Submit&qs=n&form=QBRE&pq=sinx%2C+tanx&sc=1-10&sp=-1&sk=&cvid=12C6256C3AD9424C9DBE10ECC22EAC8D
Bing Polynomial Equation Solver: https://www.bing.com/search?q=polynomial%20solver&qs=n&form=QBRE&pq=polynomial%20solver&sc=8-17&sp=-1&sk=&cvid=B2B3ADF21F0E4CD18A50DD64A49C6E08&setflight=psolver
Bing number answer: https://www.bing.com/search?q=29+number&PC=U316&FORM=CHROMN&setflight=
Bing number converter: https://www.bing.com/search?q=20+to+binary&go=Submit&qs=n&form=CHRDEF&pq=20+to+binary&sc=0-9&sp=-1&sk=&cvid=020A3169F5A34EEAB6DD0D5FCE9FD83B
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Computer algebra systems (CAS) are well-established research tools for performing symbolic manipulation of mathematical expressions, such as algebra and calculus. CABLE is designed to be a cost-effective, online infrastructure for writing, testing and databasing lightweight and flexible mathematical learning objects.
This infrastructure allows both staff and students to interact with computer algebra for the following functions:
- Instantiation and delivery of objects with randomised parameters.
- Evaluation and feedback of answers to questions contained in these objects. Typically each object has one question associated with it.
- Generation of worked solutions from templates with reference to the instantiated parameters.
- Simple analysis of answers from cohorts of students.
Design has preferred formative learning rather than assessment.


All electrical devices have their power measured in watts. For example, a kettle might be 1,500W. To calculate the cost of the power used by an electrical item, the wattage is multiplied by the number of hours it’s used for each day, and then by the number of days per year. The total is divided by 1,000 to give us the number of kilowatt-hours (kWh). The final cost is worked out by multiplying your price per kWh by the amount of kWh’s you use.


EMS 110 Mathematics for Metalworking. A study of the material which enables the student to gain an intensive, practical, working knowledge of arithmetic, algebra, geometry, and trigonometry. This class will include challenges of solving comprehensive problems relevant to precision custom manufacturing that are similar to what will be encountered in the work environment. 3 credit hours.
EMS 120 Trigonometry for Industrial Electricity. Topics covered include solution of right and oblique triangle trigonometry; sinusoidal curves; alternating current and phase angles; complex numbers and phasors; and applications to series, parallel and series-parallel AC circuits. Prerequisite: Satisfactory placement score or MAT 051 or MAT 054 with a grade of “C” or better or SPM 050 with a passing grade. 3 credit hours.
EMS 246 Statics. Selected topics from trigonometry, force vectors, components, moments of forces, equilibrium, and parallel force systems, concurrent and non-concurrent force systems both coplanar and non-coplanar are covered. Stress in trusses by method of joints, sections, and pins will be analyzed. Prerequisites: MAT 121 or CVT 140 and MAT 071 with a grade of “C” or better. 5 credit hours.
EMS 247 Strength of Materials. Topics covered include calculation of stress and deformation caused by tension, compression, shear, temperature, torsion, bending and buckling loads. Results of these calculations are used to select appropriate structural members to support designated loads. Prerequisite: EMS 246. 5 credit hours.


We’re now ready to take the percentage error formula out for a test drive.
Let’s say you’re a bookworm with a long vacation coming up. You go to the library to grab some reading material. Before you open the front door, you assume you’ll check out three books. But instead, for whatever reason, you only take home two books. What’s the percentage error of your estimate?
In our example, the experimental value is 3 and the actual value is 2. Plug in the numbers, and you get this:
Percent Error = (3 – 2)/2 x 100
If you’re old enough to read this article, we’re guessing you already knew that 3 minus 2 equals 1. Which leaves us with:
Percent Error = 1/2 x 100
Divide 1 by 2 and you get the following:
Percent Error = 0.5 x 100
And 100 times 0.5 equals 50. But remember, we have to express our final answer as a percentage. When we do that, we learn the original guess you made had a percent error of 50%.
This example was all about quantity (i.e., the number of library books). But the percent error formula can also be applied to lots of other values — like speed, distance, mass and time.
Bearing that in mind, let’s go through the formula again.
Suppose a college athlete thinks he’ll need 45 seconds to finish a hardcore workout challenge. But when he hits the gym, the routine takes him 60 seconds to complete. What was the percent error of the time estimate he started out with (45 seconds)?
Percent error = (45 – 60)/60 x 100
Right off the bat, we’ve hit a complication. If you subtract 60 from 45, you get a negative number (-15 to be exact).
Divide -15 by 60 and you’ll get -0.25, which is another negative value. And we can’t stop there; we still need to multiply the -0.25 by 100, giving us an answer of -25. Does that mean the percent error is -25%?
The percent error between an estimated value and the actual value cannot be expressed as a negative. It’s always written out as a positive value, whether the starting estimate was way too big or way too small.
Here’s where our old friends “absolute error” and “relative error” come into play. The value of -15 is only the relative error. You need to take the absolute value of that before proceeding with the calculation. Once you have the absolute error of 15, you can divide that by 60 and multiply by 100 for a percent error of 25%.