If you want to understand how digital marketing is impacting your general contractor business, you need to start by measuring the digital marketing return on investment (ROI).
Measuring your ROI helps in identifying and ensuring that your contractor marketing budget allocations are effective and delivering the best results on your marketing spending.
One of the best equations for calculating ROI is this:
(Revenue — Investment) / Investment
Supposing you invested $1000 in contractor marketing spend. Your revenue was $5,000 then your ROI would be:
($5,000 – $1,000)/$1,000. Multiply this by 100 to get a percentage value – which in this case is 400 percent.
Contractor Marketing – Key Components of Calculating ROI
Your contractor business bottom line is determined by the following:
Revenue – Expenses = Profit.
Average Revenue per Sale (or Average Job Size)
In order to calculate your average sale value, you will need to divide your revenue by the number of transactions.
So, if you earned revenue of $10,000 from 10 transactions, the average revenue per sale value will be $1,000.
Revenue ÷ Number of Transactions = Average Revenue per Sale
Lifetime Value of a Customer
The lifetime value of a customer is calculated by determining how much each customer spends (prediction of net profit) with your contractor business over time.
A simple formula to calculate this is:
Number of Transactions in a Lifetime x Revenue generated in a lifetime – Lifetime Expenses = Lifetime Value of a Customer
So, if you are a general contractor and you completed 10 transactions for a client over a period of 5 years where each transaction had a sale value of $1,000 with an operating margin of 30% – this would mean that the lifetime value of that customer is $3,000.
Calculating The Marketing Budget For Your Contractor Business
When planning your marketing budget, it is always prudent that you first spend some time researching your industry to find benchmarks which include factors such as cost per lead, cost of marketing as a percentage of revenue, closing rate, average job size.
A poignant way to calculate your marketing budget is to create a top-line annual revenue goal and then reverse engineer the math to find a path to achieving it. Here’s how you do the math:
Annual Revenue / Number of Jobs or Transactions Completed = Average Job Size
Revenue Goal / Average Job Size = Number of Jobs Needed to Reach Target Annual Revenue
Number of Jobs / Closing Rate = Number of Leads Required to Meet Your Goal
Number of Leads X Cost per Lead = Your Marketing Budget
Now you have the revenue goal, cost per lead, number of sales, and marketing budget for your business!
Best-in-class Digital Marketing for Contractors!
Are you looking for an SEO Company to help take your contractor business to the next level? If yes, Home Remodeler SEO can help you with all your SEO initiatives and improve your digital presence to get you ranking high on Google Organic Search and Google Maps. If you realize how important SEO for contractors is in this digital world we live in, call us today at (855) 235-9140.


Math Success is an easy-to-use, academic and interactive game for kids, ages 8-15, that encourages learning, keeps kids engaged and fosters their creativity. Help your student master algebra, geometry, measurement, number sense and operations, statistics, and probability.
Multiple games and activities in each subject keep students interested and learning every time they use Math Success. Your child’s confidence will soar with this effective student software program! For ages: 8-15, grades: 3-8.
- Interactive learning software for kids 8-15!
- Subjects include algebra, geometry, measurement, number sense and operations, and statistics and probability
- Concepts include angles, decimals, area, graphs, slopes, word problems, metric and standard units, and more
- An innovative approach to education and aligned with the toughest state standards
- 100% satisfaction guarantee
- Windows: Microsoft Windows XP or Vista, Pentium III or equivalent processor, 512 MB RAM, 500 MB free hard-drive space, CD-ROM drive, 1024 x 768 resolution, 16-bit color, Quicktime 5.02 or higher, microphone (optional), Internet access recommended
- Macintosh: Mac OS 10.4.x or higher, PowerPC G5 or Intel Core processor, 512 MB RAM, 500 MB free hard-drive space, CD-ROM drive 1024 x 768 resolution (millions of colors), microphone (optional), Internet access recommended


Today, it is difficult to find Science, Technology, Engineering, and Mathematics (STEM) talents. While there are greater numbers of STEM graduates worldwide than ever before, STEM jobs continue to go unfilled. Advanced and developed countries compete to attract talented students, researchers, and scientists by offering long stay visas, highest-paying jobs, scholarships, fellowships, and other benefits.
Skillsuper™ is the world’s first online learning company provides complete online skills programs and online courses for Science, Technology, Engineering, and Mathematics (STEM) talents to close the global skills gap. From a college student to a research scientist, learn essential skills to study or work in research fields; and to get the best scholarships and jobs.
The world's first complete online skills programs for talented students, researchers, and young scientists (who study or work in academia and industry).


Subject or Grade:
7th Grade Math/Honors Math/AVID
Here we learn ALL ABOUT MATH!!!! We work through the Glencoe Course 2 and Course 3.
In AVID, we focus on academic support and college readiness.
I have been teaching since 2001. I have taught Pre-K, 2nd, 3rd, 5th, 7th grades and have taught all academic areas. Math being my favorite, by far!!
7th Grade Math, 7th Grade Honors Math, AVID Elective, DRJHS Math Dept Chair


Once we take into consideration or talk about the small print and advantages of mathematical video games, we instantly assume that they’re meant for rising kids in aiding their mind energy growth. The reality is most of the mathematical video games could possibly be utilized by adults additionally for enhancing their mind capabilities, enhance reminiscence retention and recollection, and enhance processing pace in any type of scenario.
Mathematical video games offered by many web sites as on-line mind video games vary from easy mathematical issues to deep and complex ones, a few of them remaining unsolved even now. Mathematical video games could possibly be categorized as fundamental quantity video games, plain and sophisticated geometrical puzzles, combinational issues, and network-based mind video games.
Mathematical issues are believed to have began for the reason that time human settlements occurred on earth. One mathematical puzzle, often called papyrus, had been accepted as belonging to the traditional Egyptian tradition and written round 1850 BC. The puzzle is “There are seven homes in a spot, during which seven cats stay. Every cat had killed seven mice. The ears of grains eaten by every mouse in these homes are additionally seven. Each single ear of grain might have produced wheat amounting to seven hekats. What could be the entire of all these things?”
Equally, historic Greeks additionally offered a number of classical mathematical puzzles, with a lot of them by the well-known mathematician and scientist, Archimedes. The ebook often called ‘The Sandreckoner’ accommodates such mathematical mind video games, with the ‘Cattle Drawback’ being the most well-liked amongst them. The answer to the issue is a quantity with an unbelievable 206545 digits. One other nice mathematician of the previous was Fibonacci, whose ebook, ‘Liber Abaci’ was written in 1202. His rules are utilized immediately in lots of on-line mind video games, in addition to by operators in inventory markets and forex markets.
The web mind video games based mostly on mathematical puzzles provided by practically all of the web sites on this subject may be categorized as counter and board video games, card video games, domino video games, coin video games, pencil and paper video games, and scissors and paper video games. Board video games contain items or counters which might be positioned on the board, moved throughout the board, and faraway from the board. Probably the most fundamental board video games identified to all people are checkers and backgammon. The trendy on-line board video games embody Scrabble, Monopoly, and Threat. Such on-line board and counter video games could be extremely helpful each for kids, in addition to for adults in enhancing mind energy.
The web numbers video games and geometric puzzles Domino Qiu Qiu are extremely fascinating workouts. We would assume what could possibly be the wonderful thing about additions, subtractions, multiplications, divisions, and fundamental geometry. That’s underestimating the ability of arithmetic in enhancing our mind energy. For instance, many people wouldn’t be capable to multiply past 12×12 or 16×16. When you might multiply a Three-digit quantity by one other Three-digit quantity in your mind and current the reply, you can guess how a lot mind energy you possess. That is simply attainable with apply. Equally, familiarizing your self with geometrical and trignometrical patterns and fixing puzzles involving them enhance your mind energy tremendously. Such puzzles can be found in giant numbers in on-line mind video games.


One of our alumni was recently listed in USA TODAY among the AP (Advanced Placement Program) Teachers of the Year!
Amy-Karen Dougan, who received a master’s degree in education from WIU in 1972, has been selected as AP Teacher of the Year for the State of Rhode Island by the Siemens Foundation. According to the Siemens Foundation, the organization provides more than $7 million annually in support of educational initiatives in the areas of science, technology, engineering and mathematics (STEM) in the U.S.
Top Teachers of Top Students
According to the Siemens Foundation, one exceptional teacher per state is selected for this recognition each year to receive a $1,000 grant to his or her high school to support science and mathematics education.
Teachers with a minimum of five years of teaching experience in math, science or technology AP courses are selected for their exemplary teaching and enthusiastic dedication to students and the AP Program.
Sounds like the best kind of math teacher a high school kid could have. Congrats to Amy-Karen, and keep up the “advanced” work!


was wondering if Brett Craig could tell me what points "split" is required
to make a top selection a best bet, each way bet etc.....Also
can we frame an odds market with this points system?
Claude, we can work out prices if we wish. Simply add up the total points
of the main chances.
A: 80 points
B: 70 points
C: 50 points
D: 44 points
A equals 80/244, or 2/1 chance,
B equals 70/244, or 5/2 chance,
C equals 50/244, or 5/1 chance,
Horse D equals 44/244, or 9/2 chance.
A stand out, let's do it again:
A: 80 points
B: 50 points
C: 30 points
have Horse A equal to 80/160, or 50%, or EVEN MONEY.
again, to determine prices, simply divide the horse's points by the total
points of all the chances and multiply by 100 to get the horse's chance
of winning. The result of this will give a very clear guide to a horse's
fitness, ability and handicap (weights, barriers etc).
Nuss Asks: I
find your Simple Ratings for Punters a great article but I am not sure
on a few points.
For example: in the example race how do you work out the Base Rating for
the horse Asterman? Do you add only the last run (8 points) or all three
last runs including the two before the spell (1 + 10 + 8 to get 19)?
Thank you for your assistance. Regards, Allan Nuss.
the Fitness Points takes care of this situation. You always add the last
3 runs, then make additions or deductions according to the table. You will
notice that a second up run gets a deduction!
you have any questions that you would like Brett to answer, simply email


IDEA S.T.E.A.M. PRESCHOOL ENRICHMENT
Idea STEAM Enrichment for Preschoolers specializes in STEAM (Science, Technology, Engineering, Art, Math) based enrichment activities for early childhood.
At IDEA Lab, our students are encouraged to explore, observe, ask questions, predict and become intellectual, global learners while engaging in Technology, Reading, Writing, Mathematics, Science Explorations, Art classes and Cooking.
STEAM based activities encouraging Science, Technology, Engineering, Arts and Mathematics based principles
Strict 8:1 Ratio
The Fun Stuff
Chef Academy Cooking Skills
Technology incorporating pre-reading and writing skills
Science Explorations Lab
Art Studio Big Pieces
Science Lab provides both teacher-directed and child-initiated opportunities for critical thinking, science experiments and investigations. These activities reinforce simple to complex concepts and reinforce learning taking place in the homeroom.
Tech Lab allows children to experiment and explore reading, technical skills, math concepts and critical thinking programs. These applications and programs are geared to enhance the learning taking place in the homeroom and allows reinforcement of vocabulary and lessons.
Art Studio is the place for the Big messy art projects, mural and mixed media. Art Studio is full of all kinds of art materials and allows for exploration of themes and ideas through many mediums.
Indoor Gym is the place where all music and movement takes place. Spark Gym, music for aardvarks and many other tools are utilized to work on gross motor skills.


I’ve seen grown men get quite nervous and trigger their anxiety attack reflexes whenever the Decibel Math slide comes up on the screen during training courses. This makes perfect sense, most of use haven’t needed to use “higher math” functions since college, those with English degrees maybe as far back as college.*
To lower your anxiety a bit, just think of the “dB” as a set of words. Instead of reading it as “decibel” – just replace the dB with the words, “Compared To”. Decibel functions are all comparative, comparing something, to something else.
Most of what we compare in Wi-Fi are decibel to one thousandths of a watt – or mw for short. You’ll see this written as dBm – or “Compared To a Milliwatt”.
Most start teaching dB math with a formula of the actual decibel math, something like this.
This is what brings back all the anxious thoughts – seeing logarithms again. Perhaps the only thing worse would have been if we used Sine and Cosine formulas…
And yet – the actual process of doing decibel math isn’t difficult at all. I’m sure you can all pass the “Pre-Test” below.
- What is 2 times 10?
- What is 20 minus 3?
- What is 2 plus 2 plus 2 plus 2?
If you could do the easy math questions above, you have the math skills necessary to learn decibel math!
First – the Rules
In doing decibel math – all you have to do is remember two rules. These are the fixed, and immovable rules for all dB math functions. And no, we aren’t going to be using any logarithmic function. Just simple math, adding, subtracting, multiplying and dividing – things you can do in your head.
But you have to follow the rules – that’s it, just follow the rules outlined below, and you too can be a whiz at decibel math!
In decibel math, the first rule is:
The left side is the decibel math side,
and the right side is the normal math side.
That is all, nothing more to rule number one. Just remember decibel on the left, and normal on the right.
Just memorize this – no need to try to understand it – just memorize this. Don’t ask questions… don’t try to understand – just flat out memorize these!
Plus = Times
Minus = Divide
10 = 10
3 = 2
Some try to think here… resist the urge… this is a math trick, just follow the rules and everything will be fine.
That is all there is to doing decibel math. All you have to remember is these two rules above. Its easy! Lets give it a try together.
Application of Rules
Now, all we have to do in order to calculate decibel math functions is to refer to the two rules above.
To apply the first rule, I like to draw a vertical line on the paper. Specifically to give me a left side for decibel math, and a right side for normal math. Just remember. Left side is for Decibels and Right Side is for Normal.
As a reminder, I like to add the memorized details of Rule #2 at the top of my paper – something like this:
Line Down The Middle
Let’s start with a very simple example. The question at hand is what is what is the conversion from 6dB to normal math?
Since the 6dB is in decibels, we’ll have to put it on the left side of the line.
What is 6dB
Then we have to ask ourselves, “How many threes and tens are there?” – In this case, we have Two Threes in Six. So write it down on the left side of your line.
Now that we have the left side, the decibel side completed, we just need to apply Rule #2 on the right side to get our answer.
If on the left we have a “3dB + 3dB” – then on the right side we need to put the equivalents based on Rule #2. The rule says threes are equal to twos. And the rule says pluses are equal to times. Thus we will write on the right side of the line, “2 times 2”. To the normal math on the right side equation and you’ll have your answer!
Simple as that!
Perhaps now we can try one a bit more difficult: What is 29dBm?
How many Tens? How many Threes? – the left side should have something like this: “10dB+10dB+3dB+3dB+3dB” – and the right side would then be converted using Rule #2 to: “10 X 10 X 2 X 2 X 2 = 800”
That is all there is to it.
Well, you say, but what about when the number doesn’t contain Tens or Threes? My answer: the Rules stay the same. Just use your imagination a bit.
Here’s one to stretch your noggin some: What is 17dBm?
You might try adding up, one ten, plus two threes, plus… one one? The rules don’t pertain to anything except for Tens and Threes. So you can get the answer to this one by saying you have TWO tens, and 17 is 20 MINUS three… so the left side would look like this: “10dB+10dB-3dB” – and the resultant application of Rule #2 would make the right side “10 X 10 / 2”.
With the appropriate use of adding and subtracting Tens and Threes, you can get to any number you wish.
Just be sure to follow Rule #1 – and keep decibel numbers always on the left, and then apply the conversions of Rule #2 to get the converted numbers on the right.
That is all there is to decibel math!
Might I suggest you spend just a couple of minutes and try your new -found skill on the following quiz? After just a bit of practice, you’ll have decibel math down cold!
*I am obviously just teasing those of you, like my #1 daughter who can legally join the P.O.E.M. group – Professional Organization of English Majors.


Wednesday, July 21, 2010
Role-Playing Your Way to Math Mastery?
A massively multiplayer online game requiring players to employ mathematical concepts could revolutionize the teaching of mathematics at the middle school level, according to Stanford mathematician Keith Devlin.
-The importance of 'context'
-Using mathematics to achieve goals, and to see the outcome of that immediately
-Video games help students overcome that period when they haven’t seen value in the mathematics they learn
-The one thing that is missing in a math class is the meaningful environment


Lake Havasu Unified School District has adopted a new K-6 math curriculum. Known as Singapore Math, the mathematics teaching method is designed to build students’ mathematical fluency.
Math has been taught in the country of Singapore since 1981. Students
in that nation ranked the top in the world on the math portion of the
Trends in International Mathematics and Science Study. The teaching
method has been used in the United States since 2000, reportedly with
is at the heart of the instruction. The program teaches children to think mathematically versus having them memorize the mechanics of problem-solving. Students learn problem-solving with pictures and diagrams. In the classroom, students focus on fewer topics but in greater depth.


Dont be scared.
In case you didn’t hear, the Rapture will be happening 5-21-2011 at 6 PM. Â Or, for our friends across the pond, on 21-5-2011, at 6 PM. Â Somehow, it’s supposed to happen at 6 PM in every time zone. Â It makes sense…I’m sure God won’t want the pearly gates to get jammed up with too much traffic.
The prediction by Harold Camping seems to be spot on, based on biblical numerology. Â Unfamiliar? Â Here’s an excerpt from his Wikipedia article so you can see it means serious bidness.
Additionally, multiplying using the same math he uses returns an approximation of the stated results. If you use his date of April 1st, AD 33 to return 1978 years and multiply by 365.2425 you get 722,449.66. If you multiply by 265.2422 you get 722449.07. If you multiply by 265.24219 you returns 722449.05. Then if you account for leap seconds each year is slightly longer than the previous. Since 1972 to 2011 the earth rotates 24 seconds slower. This is a difference of .000276 of a year over 39 years meaning the length of each year is not consistent over 1978 years. In 1972 the resulting number would have been 1939 * 365.24246, or 708205.12. To return a result of 722500 in 2011 the length of the year would need to be 0.02575 of a day longer, or 37.06667 minutes longer than it really is.
There it is folks. Â The end is nigh.
Please ignore the fact he also predicted the same thingÂ occurringÂ in September, 1994. Â I’d suggest purchasing the book via Amazon to confirm we’re some 17 years late.
I think it’s just a power play by the Christians who decided that they want the world to end, just to prove the Mayans wrong.
edit: BREAKING NEWS. Â Here [redddit.com] is an explanation of why it’s 6 PM local time, everywhere.


Modeling + Simulation Overview
The Modeling + Simulation career academy at Bartow High School International Baccalaureate focuses on the acquisition of technology skills for rendering modeling and simulation products, which include visual simulation and engineering logistics.
Students complete a series of projects applying the tools of mathematical modeling and computer simulation to systems that change over time. Students practice data visualization and oral presentation while learning the skills essential for innovating, designing and producing prototypes.
The curriculum is integrated with hands-on activities using development tools such as Auto Desk and Solid Works.


Fractazmic is a fraction-based card game that we were able to review. There are three different “suits” of cards … sixteenths (red), tenths (green), and twelfths (blue). The main purpose of the game is to make a “hand” which is when your cards add up to one. (For example 1/2 + 1/4 + 1/16 + 1/16=1). The person with the most completed hands, wins. This deck of cards comes with 60 cards and each card is clearly labeled with the fractional amount and a pictural clue. (Such as 6 eggs in a dozen for 1/2 in the twelfth suit.)
Fractazmic is available for a reasonable $6.95. The game is for 2-4 players, although for extra practice, one child could play solitaire like, making as many hands as possible, or in a timed fashion. The game is for 1st through eighth graders.
For Tyler, he hasn’t actually been introduced to fractions yet, but with the picture clues, he was able to figure out some hands. It is great Fraction practice.
We received this game for free to provide an honest review of this product which I feel we have provided by this blog. Other people reviewed this product as well, and their review as well as mine can be found by clicking here.
We are very blessed.


Key Stage 2 SATs 2019
Please find on this page useful information to help support your child to prepare for their SATs tests in May.
The 2019 KS2 SATs Maths Organiser
On this page you can download past papers, practise arithmetic, reasoning and problem solving in a fun and interactive way. The activities have YouTube links to help your child with calculation methods for extra practise.
Key Stage 2 SATs parents information meeting - January 30th 2019
To see previous year's SATs papers and for interactive support for maths visit:


Trademinator uses the f factor to decide how much of the current balance of a given pair XXX/YYY will be operated. The idea of this factor is to operate with less than 100% of the balance. This way, if the price keeps going down/up, Trademinator will still have some balance to make a correction.
f = i / (i + 1)
- i is a variable that helps to adjust the factor
- f is the proportion of your sell
By default, Trademinator will use a factor of 0.2 when buying, and a factor of 999 when selling.
- Implemented in 0.3.0


Michael Thoreau Lacey is an American mathematician and renowned teacher at the Georgia Institute of Technology (Georgia Tech), located in Atlanta. Born September 26, 1959, Lacey is an established writer, lecturer, and researcher.
He has been at Georgia Tech since 1996. In 2004, Lacey received a coveted Guggenheim Fellowship, in partnership with his colleague Xiaochun Li. Lacey was also honored with a Simons Foundations award.
In addition to a myriad of awards, Lacey was appointed as a fellow of the American Mathematical Society in 2012. At Georgia Tech, Lacey has mentored more than ten postdoctorate students, in addition to hundreds of undergraduates. Read more: Michael Lacey | Wikipedia and Michael Lacey | GAtech
As an advocate of research, most notably harmonic analysis and probability, Lacey has directed numerous training grants in an effort to further the field of mathematics.
Lacey’s early professional years were spent in Illinois. In 1987, he received a Ph.D. from the University of Illinois at Urbana-Champaign, working under the tutelage of the late Walter Philipp, famed Austrian mathematician. Philipp was primarily known for his work in the field of probability theory and number theory.
As such, it makes sense that Lacey learned the subject from his mentor and chose the area of probability in Banach spaces for his own thesis.
In the work, Lacey worked through a problem focused on the law of the iterated logarithm using empirical characteristic functions. Through his education and extensive work in the field, Lacey has also become known for expertise in a variety of mathematical areas including ergodic theory and harmonic analysis.
Following his time at the University of Illinois at Urbana-Champaign, Lacey worked at both at the University of North Carolina (UNC) and Louisiana State University (LSU). Learn more about Jim Larkin and Michael Lacey: https://arxiv.org/a/lacey_m_1.html
Lacey and Phillip reunited at UNC and proved their work on the central limit theorem. Lacey later worked at Indiana University, where he was honored with a National Science Foundation Postdoctoral Fellowship, working on the bilinear Hilbert transform.


Another two exciting sessions are being brought to you this week.
Tech Talk Tuesdays – Aug 17th 8-9pm
Topic: Making the Impossible, Possible – Implementing a Virtual Worlds’ Program in a Traditional School Environment
Presenter: Lucy Barrow
Synopsis:- In this session we will explore one school’s journey to implement their Virtual Worlds Program. Even in a traditional school environment it is possible to bring about change to engage and motivate students in their learning. By using Quest Atlantis and OpenSim, teachers have discovered that enthusiasm and persistence are two of the key ingredients for educators looking to use virtual worlds with their students. Even those with little experience in this field can make it happen with the right support Join us as we explore the differences between virtual worlds such as Quest Atlantis and OpenSim and look at examples of student work across a number of curriculum areas.
Lucy Barrow is the innovative Staff ICT Trainer at Ballarat Grammar and responsible for the ICT Training of staff across a K-12 campus with approximately 1,300 students and 120 teachers. Prior to her current role, Lucy was the ICT Coordinator and ICT Specialist at three Catholic Primary Schools in Melbourne. She has a keen interest in web 2.0 tools and virtual worlds in education.
Link to the session
eT@lking: Wednesday 8-9pm Melbourne, Australia (gmt+10)
Topic:- Math 2.0 interest group: A year in review and brave new plans
Maria Droujkova, USA, the founder of Math 2.0 interest group, invites you to participate in the discussion of mathematical communities. During the event, we will look at different community types and discuss their accomplishments and needs. You will hear what founders of Scratch, GeoGebra, Calculation Nation, Cut the Knot, MathPlayground, ViewPoints Research, The Art of Problem Solving and many more math communities consider important tasks in mathematics education, and how they go about accomplishing the tasks. You can use the event to find math communities that will welcome your participation and add to your personal learning network. Maria will also talk about plans and dreams of the Math 2.0 group for the next year, including virtual and face-to-face conferences, the math game development forum, publishing efforts, and spin-off event series.
Link to the session:
About Maria: Maria Droujkova is the founder of Math 2.0 interest group She is the founder of natural math and mathfuture


Roger is a logician, mathematician, computer scientist, researcher, author, lecturer, science communicator, and public speaker. You can find him at UC Berkeley, California, where he is a Visiting Scholar, otherwise at the University of Oslo, where he is an Associate Professor at the Department of Informatics in the research group Logic and Intelligent Data (LogID).
Experienced and engaging, Roger enjoys giving inspiring and entertaining talks within a wide variety of topics, ranging from mathematics and computer science to philosophy and art. He challenges his audiences to question their perspectives and think differently. Roger is available to give talks both within Norway and abroad.
Roger teaches mathematics and computer science at the University of Oslo, Norway. His course, Logical Methods for Computer Science, has been well reviewed by students and peers.
Roger's academic interests are logical calculi, proof theory, mathematical logic, complexity theory, automata, combinatorics, and the philosophy of mathematics. His PhD thesis is about sequent calculi for first-order logics with free variables.
Logical Methods: The Art of Thinking Abstractly and Mathematically, The University Press (2014, in Norwegian) This book provides a solid foundation for study in the sciences with an introduction and explanation of the most important and essential concepts within mathematics and science. The book is based on lecture notes from several years of teaching introductory courses and is intended for first semester students.


In this talk, Merlin Pelz will give a quick introduction into (modern) mathematics, its techniques of developing understanding of what is not yet known and give some background needed for understanding his PhD research. Merlin will then introduce recovering pattern formation in cell systems (in other words: cell specialization in cell communities) with a foundational mathematical set-up, providing the basis for further research. Prerequisites: None (except for openness towards mathematics)
Merlin Pelz is a PhD candidate in Applied Mathematics at UBC. Merlin has majored in pure and applied mathematics since his bachelor's studies, and has additional background in engineering science, computer science and theoretical physics (at the University of Bayreuth and the Technical University of Munich). Before starting with this PhD, he obtained work and research experience at the German Aerospace Center, the University of Chicago and the Max Planck Institute for Plasma Physics, and he is now focusing on rigorously further developing mathematical biology. Specifically, his current research in collaboration with his advisor is on pattern formation in compartmental-reaction diffusion systems, which has direct implications for developmental biology. Most importantly, Merlin is enjoying living at this beautiful and open place called Green College.


I had a discussion yesterday with a skeptic that was extremely interesting to me. It was a very deep conversation that started from an extremely simple concept to understand. The number 0 (Zero).
I was asked to write a proof for 2×0=0. At first I thought this was a joke. Maybe it still is. That said really I think it serves as a good example for many of the points I have been making throughout my research.
The big take away from this conversation was the construction/structure of a proper “Mathematical Proof”. There are many different types of proofs and it is a complicated and rigorous process.
It was suggested I read “Principles of Mathematical Analysis” by Walter Rudin. This book was described in almost a God fearing way. It was really driven home that It will be extremely hard and I will get frustrated. I am not so easily deterred and I really don’t get frustrated. Of course I get stumped and there are times I do not fully understand what I am reading or looking at. I am not at all bothered by or deterred by that. I keep pushing until I do understand it. It is that simple.
At this point for me, it is not really about what I agree with or don’t agree with. I know the material I have been presenting will have to be formatted as a proper “Mathematical Proof”. This will be a requirement. I also know the skeptics will keep coming. This means I need to be fluent in the various types of proofs and how they are structured. Reading this book will no doubt help me in many ways.
So I accepted his “Challenge” with one caveat. That I would complete two proofs as a part of this exercise. One before I have read the Rudin book, and one after. This will make for a very interesting comparison at the end both in the proof itself and my opinion of the construct of Mathematical Proofs.
This may very well seem like a silly example to start with. Maybe it is. However there is a twist which I think many will not expect so I think there will be something for everyone to learn by going through this process.
I have made the argument in previous posts that all the complexity we observe both in the natural world and mathematics comes from simple numbers and the most basic of math. This ties in nicely with that. So without having read a single page of Rudin and only a general knowledge about the technical details of a proof lets begin version 1 and talk about 0. Understanding this is not a “Mathematical Proof” in the technical sense, I still feel this is a reasonable and valid proof in general and is mathematical in nature. This means it can be verified mathematically.
A Proof for Zero
Before we can prove any mathematical operation involving the number 0 we must first define and prove the existence of 0 as a number, quantity or lack there of. Further we must prove what a number is in order to classify zero itself as a number.
A number can be any natural number, integer, negative or complex. It is a notation or description of both construction and measure. A value, quantity, angle or amplitude. It is further the sum of it’s parts, prime factors or otherwise.
For example if we use the number 1 to describe an object of unit 1. Then, placing one object beside another object requires a different numerical description for the objects new plural nature. Thus we have the number 2.
Intuitively we can make the same argument for every new number being a result of the described previous numbers. This happens in a few ways. We know any number can be constructed with prime numbers. Further these described numbers create a natural number base and inherit finite properties from previous numbers. For example one number being a multiple of another.
Looking at the Fibonacci Sequence we can see this playing out.
Now we must define what we mean by number base and finite properties. The number base is a roll over position. You can think of it as a unit on a ruler. It defines a period of measure and creates powers of that measure. Think powers and multiples of 10 for a 10 base number system.
Next we must define what we mean by finite properties. By summing the digits of any number and reducing it to a single digit number in the context of it’s number base, we can look at what is called the digital root or digital sum of that number. This digital root is like a unique finger print or the DNA of a number. Even more so than primes. Any number will inherit unique behaviors and properties based on this digital root.
Looking at the digital roots of the Fibonacci Sequence
What is not so obvious when looking at the Fibonacci Sequence in digital root is that 0 and 9 are essentially the same number or position. In fact in digital root form you can start the Fibonacci Sequence with either 9 or 0 and the resulting repeating sequence will be exactly the same.
Looking at the digital roots of the Fibonacci Sequence starting with 9
9+1 = 10 (1)
1+1 = 2
1+2 = 3
2+3 = 5
3+5 = 8
5+8 = 13 (4) etc…
Further if we test this with any sequence following the same method as the Fibonacci Sequence we find there are only 9 possible digital root sequences all of which also have a 24 digit repeating pattern. These repeating sequences remain exactly the same whether you start the sequence with 0 or 9. The start position is also the only position that is not repeated. This start position can also be completely excluded and the resulting sequences are exactly the same.
These unique behaviors and properties create natural group classifications and well as polar pairs of numbers. Using a 10 base number system this looks like the following.
Any number acts according to it’s number group and polarity.
To prove this if we study these sequences we will find that each sequence reflects another. For example. If we look at sequence #1 and #8 you will note that the last 12 digits of sequence #1 is the same as the first 12 digits of the #8 sequence.
This pattern continues through out the sequences creating these polar relationships naturally.
By arranging these sequences according to their number group we find perfect mathematical alignment. Adding up the columns of digits in sequences #1,#4 and #7 in digital root produces the #3 sequence. Adding the #2, #5 and #8 sequences produces the #6 sequence. Adding all four sequences on either side will produce the #9 sequence.
These patterns take on very simple yet significant mathematic principals which apply to any number.
Principle Interactions of addition and subtraction are what allow us to define multiplication, division or any other mathematical operation beyond these 7. These 7 interactions must be empirically true for any operation to be true.
Numbers of the same group will also share factors. The digital root of any number itself can often being a factor of said number.
For example. 147 = 1+4+7 = 12 for a digital root of 3. If we divide 147 by 3 we get exactly 49.
For another example. No prime number no matter how large or number of digits will have a digital root of 3,6 or 9 with one single exception. The number 3. Put another way, all prime numbers are never a Group 9 number with the exception of the prime number 3. Further no number will ever have a digital root of 0.
We know by all of these definitions that 1+1 =2. By any description of number, value or quantity this empirically true. By default this means that 1+1+1 = 3*1 = 3 or that 3/1=3, so forth and so on.
Zero is a number absent of any value. It can be a starting point, end point or even a point between 2 or more other points. While it may not have a value it represents a state which by default has a value in any numerical or mathematical system. It is an intrinsic value that is either implied or not implied but always present. It manifests itself either through 9 or zero not metaphorically but literally and mathematically. Put another way it is the interplay between the start and end of any number base system.
Now we are ready to prove 2*0=0. Further we will prove f(n)=n*0 = 0.
With digital roots there are only 3 numbers that when squared produce no change to the value at all.
In fact these 3 numbers to any power will produce the exact same result. A unchanging digital root. This is the same as adding these numbers n number of times.
Zero specifically because it is a no value state can undergo any operation and remain unchanged digital root or not.
While is seems obvious and intuitive that 2×0=0, I feel these facts combined create an interesting space for discussion. As I pointed out at the beginning this is not a pure “Mathematical Proof” at least not in the sense of Rudin. It is a description of numerical observations which can be mathematically proven. Without any doubt a year from now when I have completed reading this book I will be able to formulate this in a way that is more in line with what is considered a Mathematical Proof.


4 edition of Group theory and its applications in physics found in the catalog.
Group theory and its applications in physics
Includes bibliographical references (p. -393) and index.
|Statement||T. Inui, Y. Tanabe, Y. Onodera.|
|Series||Springer series in solid-state sciences ;, 78|
|Contributions||Tanabe, Yukito, 1927-, Onodera, Y. (Yositaka)|
|LC Classifications||QC20.7.G76 I63 1990|
|The Physical Object|
|Pagination||xiii, 397 p. ;|
|Number of Pages||397|
|LC Control Number||91100901|
Tiling the Plane with Congruent Squares There are also regular tilings of R2 by equilateral triangles with 6 meeting at each vertex and by regular hexagons with 3 meeting at each vertex. Putting the orbital that has the lowest energy, the orbital with the fewest nodes at the bottom of the energy diagram and like wise working up form lowest energy to highest energy. However using group theory we can ignore the detailed mathematical methods. She is the recipient of the National Medal of Science and 21 honorary degrees worldwide. They are inserted throughout the text at the place where they naturally arise, making the book ideal for self-study as well as for classroom assignment. Bartholdi, R.
The only difference would be the electronic state would be the same in both the initial and final states. Group theory shows up in many other areas of geometry. Where group theory comes in to play is weather or not this transition is allowed by symmetry. Journal of Algebra. Work through the P-orbital molecular orbitals for cis-butdiene. Furthermore, for these three values of n there is essentially just one regular tiling in each case.
II, pp. The saying of "preserving the structure" of an object can be made precise by working in a category. Reviews From the reviews: "It was developed for a graduate course taught mostly by Millie Dresselhaus at MIT for more than 30 years, with many revisions of lecture notes. Ringsfor example, can be viewed as abelian groups corresponding to addition together with a second operation corresponding to multiplication. Description Group Theory and its Applications, Volume II covers the two broad areas of applications of group theory, namely, all atomic and molecular phenomena, as well as all aspects of nuclear structure and elementary particle theory.
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Seller Inventory Molecular Orbital Theory and Symmetry Molecular Orbitals also follow the symmetry rules and indeed have their own?
With this information if you have a transition from the totally symmetric HOMO orbital to the totally symmetric LUMO orbital the transition moment operator would need to have Ag symmetry using the C2h to give a result containing the totally symmetric representation.
ISBN Metric spaces of non-positive curvature. The number of transitions is dictated by 3N-6 for non-linear molecules and 3N-5 for linear molecules, where N is the number of atoms.
From the Introduction:" In the last fifteen years geometric group theory has enjoyed fast growth and rapidly increasing influence. Inventiones Mathematicae, volno. The coarse Baum—Connes conjecture for spaces which admit a uniform embedding into Hilbert space.
With appendices by Bass, L. Springer-Verlag, New York, Like the quadratic formula, the cubic and quartic formulas express the roots of all polynomials of degree 3 and 4 in terms of the coefficients of the polynomials and root extractions square roots, cube roots, and fourth roots.
Therefore, group theoretic arguments underlie large parts of the theory of those entities.
Rosenberg and J. Miller Jr. Handbook of algebra, Vol. The hyperbolic plane H2 is the interior of a disc in which the "lines" are diameters passing through the center of the disc or pieces of circular arcs inside the disc that meet the boundary of the disc in 90 degree angles.
Tanabe Y. So this IR transition is allowed by y polarized light in this molecule. Lecture Notes in Mathematics. Harmonic analysis of the cyclic group or of an elementary abelian 2-group is all over the place here.
This means a tiling of the plane by copies of congruent regular polygons, with no overlaps except along the boundaries of the polygons. Geometry and Topology. Geometric and Functional Analysis. There is no shortage of group theoretic or number theoretic thinking in telecommunications applications, but even though the apps are hi-tech, the group theory in use does not quite have the same sheen.
A torus. Symmetries form a group: they are closed because if you take a symmetry of an object, and then apply another symmetry, the result will still be a symmetry. Here is a tiling of H2 by congruent regular pentagons.
One of the reasons for this is that the really interesting groups are few and far between, but the engineers want a scalable system with a lot of flexibility in the parameters. The last chapter deals with the study of the extension, representation, and applications of Galilei group.He also includes a concise review of the linear algebra needed for group Group theory and its applications in physics book, making the book ideal for self-study.
Provides physicists with a modern and accessible introduction to group theory; Covers applications to various areas of physics, including field theory, particle physics, relativity, and much more. • Group Theory in Quantum Mechanics by Volker Heine (Dover, ).
Many other very fine books on the subject of group theory and its applications in physics are available, as well. Here is an abridged list of others you may wish to consult: • Group Theory and Its Physical Applications by L. M. Falicov (University of Chi-cago Press, ).
This book has been written to introduce readers to group theory and its ap plications in atomic physics, molecular physics, and solid-state physics. Onodera Preface to the Japanese Edition As the title shows, this book has been prepared as a textbook to introduce readers to the applications of group theory in several fields of physics.Jun 01, pdf This book is aimed at pdf students in physics who are studying group theory and its application to physics.
It contains a short explanation of the fundamental knowledge and method, and the fundamental exercises for the method, as well as some important conclusions in group theory.
The .• Group Theory in Quantum Mechanics by Volker Heine (Dover, ). Many other very download pdf books on the subject of group theory and its applications in physics are available, as well.
Here is an abridged list of others you may wish to consult: • Group Theory and Its Physical Applications by L.
M. Falicov (University of Chi-cago Press, ).This book has been written to introduce readers to group theory and its ap plications ebook atomic physics, molecular physics, and solid-state physics.
The first Japanese edition was published in The present English edi tion has been translated by the authors from the revised and enlarged.


This week we learnt about Area and Perimeter.
Miss Ashley put a grid on the carpet using masking tape and we used this to help us learn about area and perimeter.
Area is what is inside a shape - when we did this, we used real people.
Perimeter is when you count how many lines are on the outside of the shape - you can see us walking and counting to measure this.
Check out our learning!
Did this help you learn about area and perimeter?
Let us know in a comment below.


Key Stage 1 - Years 1 & 2
As children transition from Early Years into Key Stage One (KS1) their learning adventure continues. We continue to build upon the characteristics of effective learning and the children’s eagerness to be independent in their own learning.
In Key Stage 1, our primary aim is that pupils are able to confidently read, write and use mathematical knowledge, ideas and operations so they are well prepared for the demands of their future learning.
Children’s days are a carefully planned blend of teacher led sessions, small group work, independent practice tasks and time for children to demonstrate and deepen their learning by choosing how to access a range of opportunities both inside and outside.
Our KS1 classrooms are dynamic, well-resourced learning spaces. They share a large outside area which children are able to access throughout the day. Children have opportunities to; experiment with scientific concepts, engage with computing, make artwork, experience the natural world, design and create structures and models, explore scenarios through role play and learn how to cook simple recipes. Resources to support and extend the children’s reading, writing and mathematical concepts are always available to use.
We follow the National Curriculum and all KS1 Programme of Study Objectives in each subject are covered across Years 1 and 2.
Key Performance Indicators
You can find Key Performance Indicators for reading, writing and maths in Y1-6 here.
This booklet outlines the key performance indicators (KPIs) in each of the areas of reading, writing and mathematics. For pupils to have achieved the expected standard for their year group in a subject, they will have demonstrated that they have achieved all of the KPIs consistently and confidently. Evidence of achieving these KPIs will be through a variety of methods including written work, observations, discussion, performance and testing.
The Key Performance Indicators do not represent every aspect of the National Curriculum, rather they are the key indicators against which we assess pupils’ achievement and outcomes at the end of each curriculum year.
Please find below information regarding the curriculum for each year group in Years 1&2, our curriculum map and our termly curriculum overviews
Year 1 - Ash & Oak Classes
Year 1 Curriculum Map 2020 - 21 (coming soon)
Year 2 - Beech & Rowan Classes
Year 2 Curriculum Map 2020 - 21 (coming soon)


We welcome your exploration of our services as tutors in mathematics.
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Take a moment and read through our entire website. The choice you make in selecting a math tutor can be key to their academic success.
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Maria Antonopoulos, Ph.D.
Born and raised on the North Side of Chicago by her Greek immigrant parents, she pursued her degree in engineering at the University of Illinois at Urbana-Champaign, after almost two years of employment as an engineer she decided to pursue teaching. In support of her desire to teach she then pursued a Masters in Mathematics at Loyola University and a Ph.D. in Math at the University of Illinois at Chicago. Maria also studied abroad in Spain and has travelled extensively.
Maria has experience teaching at the college level for over a decade and also has experience at the high school and middle school levels through a fellowship awarded to her by the National Science Foundation (NSF)and the Chicago Public Schools (CPS). She has taught and tutored students of all ages, nationalities and backgrounds. She has experience teaching a wide variety of math courses and is well versed in the subject matter.
Maria and her family live in the western suburbs. In her spare time Maria spends time with friends and family and enjoys working out whenever she can.
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The term “percentage in point” (pip) refers to a unit of change in the rate of exchange of a currency pair that is used in finance, particularly in foreign exchange markets.
In foreign exchange, the slightest possible change in the exchange rate between two currencies is expressed as a percentage in point, commonly referred to as a pip or point. Four decimal places, or one ten thousandths, are used to calculate most major currencies. A percentage change would be a change in the fourth or last decimal point when two significant currencies are matched, such as the US Dollar and the Canadian Dollar (US/CAD).
The mathematical difference between two percentages is referred to as a percentage point. 10% represents a 1% increase over 9%.
If a country’s GDP (gross domestic product) increased by 2% in 2016 and by 1% in 2015, this indicates that GDP in 2016 increased by 2%, not by 1%, but by 100% (2% is double 1%). Something is said to be doubled when it is 100% greater.
In the pricing of the major currencies, a pip is one unit of the 4th fdecimal place, or 1/100 of a cent for dollar currencies (apart from the Japanese yen). the second decimal place is one unit of a pip. Due to the yen’s value being significantly closer to one hundredth of other major currencies.
A bigger percentage in point change in the exchange rate of a currency pair indicates that buying the base currency with the quote currency is now more expensive. Investors strive for narrower percentage point spreads between currency pairings when trading on foreign exchange markets. The profit of a currency investor can be significantly impacted by a shift of even one pip.
If the Euro/U.S. dollar currency pair When the exchange rate for the dollar (EUR/USD) changes from 1.3010 to 1.3000 (1 EUR = 1.3 USD), the price ratio rises by 10 pips.
A trader who purchases 5 standard lots of EUR/USD for US$650,000 (5 x 100,000 = 500,000) and then exits the position after the price has increased by 10 pip will receive US$650,500 with a profit of US$500 (5 standard lots x 0.0010 = US$500). The majority of retail trading by speculators is done on margin accounts, which only require a modest portion (usually 1% of the purchase price) of the transaction’s equity. Due to the Japanese Yen’s value being 0.01 versus the US dollar, there is an exception to this rule.
Another example, For macroeconomic metrics like inflation, percentage points are frequently utilized. 100 basis points are also equivalent to one percentage point. For instance, India’s inflation rate in November 2012 was 7.24%, while in December 2012 it was 7.18%. As a result, we can conclude that inflation changed by
The time value adjustment made to the spot rate is quoted in pips, FX points, or forward points in the forward foreign exchange market .
Sometimes a pip is mistaken with the tick size, which is the smallest change in a quote. Although currency pairs are frequently quoted with four decimal places, a given market’s tick size could, for instance, be 5 pips or 1/2 pip.


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1. THELMA D. OLAIVARâ€‹ - Faculty, College of Education, Polytechnic University of the Philippines.
This research is an exposition on the topic Divisibility Criteria which are the bases of the different Divisibility Rules. It is a detailed study based on the discussion on Divisibility Criteria in the book Number Theory by Sergio Ymas, with the goal of arriving at a fixed rule or test mathematically formulated as:
n a_k+a_(k+1) (mod m)
when dealing with divisibility by m where m is prime.In particular, this paper aims to show in greater detail how the easier rules on divisibility by prime numbers are obtained. This paper also aims to justify that the existing rules on divisibility by 7 and 13 are not merely obtained by trial and error but instead existing rules are based on Number Theory. Finally, this study aims to justify the existence of fixed and efficient tests for divisibility by prime numbers higher than or equal to 17.
divisibility, prime number, decimal system, modulo, congruence.


Making ChatGPT useful for Math homework with the multi-agent framework “Autogen”
Project Manager: Weikai (Kai) Huang
- Contact: email@example.com
ChatGPT(GPT-4) models perform poorly in basic reasoning, especially with regards to solving math problems. GPT models tend to forget some details when reasoning, and it doesn’t support an external math tool to help it with basic tasks (e.g. solving equations).
However, “Autogen”, a multi-agent framework released by Microsoft recently, can assign different roles to several GPTs, one GPT with a role will be called as an “agent”. We let agents interact automatically. (e.g. One GPT will be assigned as “student”, it answers the questions, and the other GPT will be assigned as “teacher”, it checks the answer and give feedback. Then the “student” will refine the answer based on feedback. This loop will continue until the answer is correct). This will hopefully greatly improve the reasoning skills of the model. What’s more, Autogen can automatically execute the AI-generated codes so we can use millions of external tools (API) to help us solve problems.
Based on multi-agent RL and code execution ability provided by Autogen, our goal is: Apply this framework to solve several complicated (multi-step) math questions from UW math homework and use multi-agent RL to let GPT self-refine the answer and use codes to generate graph or solving equations, which is impossible by directly using ChatGPT.
We have 4 steps:
- collecting the math questions datasets and transform to ideal format.
- determine our multi-agent structure, like how many agents should we have, what are their roles. How they interact with each other.
- implementation with codes and debugging.
- Result analysis.
The future of this research project:
- Visualization and web application product.
- Paper(Since multi-agent is a hot topic in academia now).
- Adapt to other field: programming, essay writing, etc.
This project embodies I2’s mission by innovating AI interactions, simulating human learning, and enhancing problem-solving intelligence.


In the video Ian and Martin Conversations 02 (on the Philosophy and Critical Thinking course page), Martin makes reference to Zeno’s paradoxes of motion, and claims that to date, there is no agreed philosophical resolution to these paradoxes.
In essence, Zeno paradoxes hinge on the concept of continuity. But of course, Zeno did not have the concept of infinitesimally small, which is the informal concept used by Leibnitz and Newton in the development of calculus in the late 1600’s. Their calculus was a technique for treating continuous motion as being composed of an infinite number of infinitesimal steps. But the calculus of Newton and Leibnitz did not have (according to the standards of the early 20th century) a sufficiently rigorous concept of continuity. Indeed, in the 19th century, infinitesimals were eliminated from standard real analysis, as the use of infinitesimals in mathematical analysis was at the time regarded as “non-rigorous”. In particular, Weierstrass developed the epsilon-delta method in which there was no longer a requirement to conceive of a quantity as actually varying (Potter, 2009). And it was this epsilon-delta method that allowed mathematicians to treat continuity of the real number line WITHOUT reference to the nebulous concept of “tending to a limit”.
In the 1960s, Abraham Robinson and others developed a non-standard analysis approach in showing that there was a conception of continuity of the real numbers, in which there are infinitesimal quantities lying in the real number line.
The crux of Zeno’s argument in the Achilles and the Tortoise Paradox is the assumption that a completed infinity of places is too many places for Achilles to go to in a finite time in order to catch the tortoise. However – as demonstrated by standard or non-standard 20th century analysis approaches, the measure (such as length) of a continuum is not a matter of adding up the measures of its points nor adding up the number of its points (Dowden, 2017). And hence the time taken by Achilles to catch the tortoise is a temporal interval, a linear continuum of instants. A finite time.
However, McLaughlin (1994) demonstrated how Zeno’s paradoxes could be treated using infinitesimals, and claimed his approach to the paradoxes was the only successful one. This claim has been challenged by other mathematicians. See for example the discussion outlined in Dainton (2010).
Dainton, B. (2010). Time and Space, Second Edition, McGill-Queens University Press: Ithaca.
McLaughlin, W. (1994). “Resolving Zeno’s Paradoxes,” Scientific American, vol. 271, no. 5, Nov., pp. 84-90.
Potter, M. (2009). Set Theory and its Philosophy, Oxford University Press
"Zeno’s Paradoxes," by B. Dowden, The Internet Encyclopedia of Philosophy, ISSN 2161-0002, http://www.iep.utm.edu/zeno-par/, 3rd August 2017.


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Next fall you will be starting a new math class. We hope that you will find the class interesting and challenging. Being successful is not an accident; it is the result of good preparation. To help you next year, please review the topics that you have studied in your previous math courses. All summer review work can be found below. Here, you will find:
1. Homework problems that are due on the first day of classes.
2. More examples and practice problems, with answers relating to each topic.
Please print out the problems, complete them as best you can, check your answers, and bring your work on the first day of school. Please note that the problems on this webpage are intended for review purposes only and should not be used as any sort of placement guide.
You will be tested on the topics related to your particular course within the first week of classes.
A TI-84+ graphing calculator is required for all math courses. It is the only model for which classroom instruction is provided.
The Math Department strongly recommends that summer homework be completed in August and a review be done in the week leading up to the opening of school.
All documents listed in the "Optional Exercises" list are optional. This is the case even if a document says it's required on the actual document.


In what seems like another life now, I tutored 3rd and 5th graders in math. Math always came pretty easy to me, which I credit to my father who would make us do complicated math problems in our heads while on family road trips. Fun, right?? What I loved about tutoring was the moment when I would see that the children finally got it—that Aha moment was priceless.
My cousin sent me this information saying:
If you, or anyone you know, might be interested in the Summer Online Learning Experience (SOLE), please take a look at this flyer and pass it on to someone who might be in need. As a former high school teacher, I know that parents and students were looking for tutoring programs at the end of the year. SOLE Math is inexpensive and easy to use.
I hope this information is helpful to you or someone you know! Is your child having problems with math?
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Who is eligible to participate in SOLE MATH?
Any 3rd through 12th grade student who would like to review old or learn new mathematics skills
during the summer
How much does it cost to participate?
SOLE MATH is $25 for three months. You only need access to a computer with the Internet.
Dr. SOLE says, “If your child comes to love Math, then your child can join SOLE MATH for
*If your child completes 30 on-task hours with the ALEKS system this summer, he/she can join SOLE MATH for FREE next summer.
What does SOLE MATH offer?
ALEKS offers individualized tutoring on a wide range of topics required for 3rd through 12th
graders, including topics required for most state standardized exams. In addition, there are
advanced mathematical concepts and topics for advanced courses, for example Advanced
Placement (AP) Statistics are covered.
How do I register my child for SOLE MATH?
Registration begins May 1st. SOLE MATH registration will take place May 1st through May 31st.
Late fees apply after May 31st. However, seating is limited, so please register soon.
For more information, please visit our website at www.s-o-l-e.org .
Phone: (901) 313-4422


Glitch Quilt Pattern (PDF)
Glitch is a bright, modern quilt inspired by “glitch art,” the serendipitous beauty that is sometimes the result of computer failures. The dynamic, striped 8” blocks come together quickly and accurately thanks to a unique foundation paper strip-piecing method, shown in detailed diagrams.
Finished Quilt: 64" by 64"
About the Designer
It took a few decades, but Bobbie Gentili finally found the right outlet for her lifelong creativity and love of mathematics when she was introduced to modern quilting. She now spends every waking moment designing quilt patterns, longarm quilting, petting curating beautiful fabrics, and sharing her quilty adventures on Instagram at @geekybobbin and on her website geekybobbin.com.
Bob's patterns feature bold, geometric designs, playing with curves and long strips to give a sense of movement. She finds inspiration in science, nature, and geeky culture.
Bob lives in Toronto, Ontario, Canada, where her husband, 2 young children, and cats enjoy any scraps of her attention that can be stolen from quilting.


Report the travelling salesman problem
Travelling salesman (2012) on imdb: movies, tv, celebs, and more imdb report this 10 /10 set piece featuring a taut claustrophobic confrontation between a team of elite mathematicians who've cracked a problem (ie the traveling salesman. Hence, can anyone simplify the problem of the travelling salesman in layman terms and also, provide a solution (if any) which is simplified and not too complicated for my level thanks alot travelling salesman problem and solution report abuse comment add a comment. Given a collection of cities and the cost of travel between each pair of them, the traveling salesman problem, or tsp for short, is to find the cheapest way of visiting all of the cities and returning to your starting point in the standard version we study, the travel costs are symmetric in the sense that traveling from city x to city y costs. Implementation of traveling salesman's problem using neural network final project report (fall 2001) ece 559 neural networks december 3, 2001 prof daniel graupe ritesh traveling salesman's problem's solution using hopfield nn. Solution to a travelling salesman problem using hamiltonian circuit i am giving a program to find a solution to a traveling salesman problem using hamiltonian circuit, the efficiency is o sorry to report. 2 applications, additional constraints such as limited resources or time windows make the problem considerably harder in this paper we are going to consider the solution of a symmetric travelling salesman problem on a. How to solve travelling salesman problems - tsp mathmathsmathematics loading need to report the video sign in to report inappropriate content travelling salesman problem using branch and bound algorithm. Abstract genetic algorithms and the traveling salesman problem bykylie bryant december 2000 genetic algorithms are an evolutionary technique that use crossover and mutation.
Tsplib tsplib is a library of sample instances for the tsp symmetric traveling salesman problem (tsp) given a set of n nodes and distances for each pair of nodes the respective report is available as gr2015pdf. The travelling salesman problem (tsp) is well known in the field of combinatorial optimization since it is an np-complete problem, there is no efficient method to solve this problem and give the best result many algorithms are used to solve travelling salesman. Report on article the travelling salesman problem: a linear programming formulation radosław hofman, poznań 2008 abstract—this article describes counter example prepared in ii. The travelling salesman problem (tsp) is a problem in combinatorial optimization studied in operations research and theoretical computer science worst-case analysis of a new heuristic for the traveling salesman problem, report 388. Orie 6300 mathematical programming i december 3, 2014 recitation 12 lecturer: chaoxu tong topic: approximation algorithms for the traveling salesman problem. If you are looking for approximation algorithms, quora user's answer to what is the optimal and best algorithm for solving the traveling salesman problem is a pretty good start what are some tools to test algorithms of travelling salesman problems.
Cs 312: algorithm analysis project #5: solving the traveling salesperson problem with branch & bound overview in this project, you will implement a branch and bound algorithm to find solutions to the traveling salesperson problem (tsp. [email protected] the travelling salesman problem and its to indicate the size of the problem instances that we\爀屮can successfully attack today\爀屮\爀屮i will also report about a \൮ew way to the traveling salesman problem and its variations.
So i have created a sort for my traveling salesman problem and i con sort by the x-coordinates and the y-coordinates i am trying to implement a greedy search, but am unable to also, each point is. Solving the travelling salesman problem using the ant colony optimization management information systems vol 6, 4/2011, pp 010-014 11 well only for solving the problems with no more. This example shows how to use binary integer programming to solve the classic traveling salesman problem.
The traveling salesman problem corinne brucato, ms university of pittsburgh, 2013 although a global solution for the traveling salesman problem does not yet exist, there are algorithms for an. P vs np is one of the deepest problems in computer science, and one of the millennium prize problems. The christofides algorithm is an algorithm for finding approximate solutions to the travelling salesman problem, on instances where the distances form a metric space (they are symmetric and obey the triangle inequality) it is an approximation algorithm that guarantees that its solutions will be within a factor of 3/2 of the optimal solution.
Report the travelling salesman problem
Travelling salesman problem the travelling salesman problem (tsp) or travelling salesperson problem asks the following question: given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city. Traveling salesman problem's heuristic this is one of the most well known difficult problems of time a salesperson must visit n cities, passing through each city only once, beginning from one of the city that is considered as a base or starting city and returns to it.
Solution of a large-scale traveling-salesman problem dantzig, fulkerson and sm johnson, solution of a large scale traveling salesman problem, technical report p-510, rand corporation, santa monica, california, usa, 1954 3. The traveling salesman problem is a well-known problem in the area of network and combinatorial optimization this problem is easy to state: starting from his home base, node 1, a salesman wishes to visit each of several cities represented by nodes 2. Solving the clustered traveling salesman problem using the lin-kernighan-helsgaun algorithm keld helsgaun may 2014 roskilde university computer science research report #142. The traveling salesman problem computer science essay print reference this published in 1954 heller published an 88 report which contains many basic solutions on the travelling salesman travelling salesman problem can be modelled as graph where as the cities are the graph. Travelling salesman problem (tsp): given a set of cities and distance between every pair of cities please write to us at [email protected] to report any issue with the above content recommended posts: travelling salesman problem | set 2. Dorigo and gambardella - ant colonies for the traveling salesman problem 2 1 introduction real ants are capable of finding the shortest path from a food source to the nest (beckers. A comparative study of tabu search and simulated annealing for traveling salesman problem project report applied optimization msci 703 submitted by.
Is it hopeless to try to compute the shortest route to visit a large number of cities not just a good route but the guaranteed shortest the task is the long-standing challenge known as the traveling salesman problem, or tsp for short. The travelling salesman problem (tsp) asks the following question: given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city and returns to the origin cityit is an np-hard problem in combinatorial optimization, important in operations research and theoretical computer science.


Lattice-based approaches are emerging as a common theme in modern cryptography and coding theory. In communications, they are indispensable mathematical tools to construct powerful error-correction codes achieving the capacity of wireless channels. In cryptography, they are used to building lattice-based schemes with provable security, better asymptotic efficiency, resilience against quantum attacks and new functionalities such as fully homomorphic encryption.
This meeting — on 18 January 2017 — is aimed at connecting the two communities in the UK with a common interest in lattices, with a long-term goal of building a synergy of the two fields. It will consist of several talks on related topics, with a format that will hopefully encourage interaction.
The existing literature contains several ring-based variants of the Learning With Errors problem, all of which are often referred to as Ring-LWE, a habit which has led to some confusion in the recent past. The main difference lies in the choice of the probability distribution from which the errors are to be sampled. We will briefly compare the main versions, such as Poly-LWE and “proper” Ring-LWE as introduced by Lyubashevsky et al., and discuss some pitfalls that arise when mixing things up. This is joint work with Ilia Iliashenko and Frederik Vercauteren.
The main goal of this talk is to discuss a variety of concepts and facts in the theory of Diophantine approximation. To motivate this discussion I will begin by exposing some (unexpected to myself) examples of the use of Diophantine approximation in a relatively recent development on interference alignment. I will discuss its link to Diophantine approximation on manifolds, a fast developing and relatively modern area of metric (probabilistic) number theory. More broadly, I will present an account of classical metric and non-metric results and techniques. Finally, I will describe a technique originating from a paper by Kleinbock and Marguis (1998) on estimating the probability that a lattice picked at random and subject to functional constraints has a small non-zero point.
We begin by introducing the context of ring-based somewhat homomorphic schemes and discuss some optimisations. This starts with introducing the RLWR hard problem and its relation to lattices. We investigate fixed-point arithmetic in ring-based homomorphic encryption schemes. Downlin et al. present two fixed-point numbers representations; we analyse and show them to be isomorphic, by presenting an explicit isomorphism between the two. Given input bounds on fixed-point numbers and scalars, we achieve lower bounds for the ring dimensions needed to support complex homomorphic operations. As an application, we investigate homomorphic image processing and, specifically, Fourier Transforms.
In this talk, I will first explain how theta functions of lattices appear in analysing which lattices are good for coset coding in wiretap channels. I will then explain what ia the secrecy gain of a lattice, and what is the conjecture of Belfiore and Sole for unimodular lattices, and how it has been generalised for l-modular lattices. I will then explain how this conjecture can be approached for both in the unimodular case, and for various values of l. Finally, I will explain about the problems in using secrecy gains in comparing lattices.
Room 611 (Dennis Gabor Seminar Room)
Department of Electrical and Electronic Engineering
Imperial College London
London SW7 2AZ
Everyone is welcome. Two caveats:


I have revised through the whole of chapter 10 again and again but I can’t seem to figure out how to get out-of-sample predictions for volatility using NUTS.
I’m trying to sample from 2000-2019 and then predict 2019-2020, could anyone help with this?
pymc3_workflow has a prediction example, perhaps this could help?
Hey Stefan, thanks for the reply. In pymc3_workflow, there was a predictive variable: the yield curve. However, for stochastic volatility, it seems we are only predicting based on sampling with the NUTS sampler. I’m not sure if we can forecast purely based on historical values for volatility?


I wrote this in 2012 in response to a twitter conversation with Mike Taylor, who was patient enough to read a draft of this post in late November and point out all the various ways it could be changed and improved. No doubt if I had taken the time to take his advice and change the post accordingly, this post would be a beautiful thing and well-worth reading. I’d like to thank him for his patient comments, and apologize for not acting on them, as I don’t foresee being able to take the time in the near future to get back to this post. I don’t really like seeing a post sit in my draft folder for months, so I’ll release it out to the world as naked and ugly as the day it was born, with the hopes that I’ll eventually sit down and write a better one that takes all of Mike’s wonderful suggestions into account. Also, John Kruschke apparently published a paper with a similar title; as it’s a paper I’ve read before but forgot about, I’m guessing I inadvertently stole his fantastic phrase. Apologies to John!
I recently [okay, at one point this was ‘recent’] got in a few discussions on Twitter stemming from a tweet about p-values. For the lucky and uninitiated, p-values are basically the go-to statistics used by giant swaths of the academic world to show whether or not their data are statistically significant. Generally, the idea is that if the value of p is less than 0.05, you have results worth publishing.
There’s a lot to unpack in p-values; a lot of history, of a lot of baggage, and a lot of reasons why it’s a pretty poor choice for quantitative analysis. I won’t unpack all of it, but I will give a brief introduction to how the statistic works. At its simplest, according to Wikipedia, “the p-value is the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true.” No, don’t run away! That actually makes sense, just let me explain it.
We’ll start with a coin toss. Heads. Another: tails. Repeat: heads, heads, tails, heads, heads, heads, heads, tails. Tally up the score, of the 10 tosses, 7 were heads and 3 were tails. At this point, if you were a gambler, you might start guessing the coin is weighted or rigged. I mean, seriously, you toss the coin 10 times and only 3 of those were tails? What’s the probability of that, if the coin is fair?
That’s exactly what the p-value is supposed to tell us; what’s the probability of getting 3 or fewer tails out of 10 coin tosses, assuming the coin is fair? That assumption that the coin is fair is what statisticians call the null hypothesis; if we show that it’s less than 5% likely (p < 0.05) that the we’d see 3 or fewer tails in 10 coin flips, assuming a fair coin, statisticians tell us we can safely reject the null hypothesis. If this were a scientific experiment, we’d say that because p < 0.05, our results are significant; we can reject the null hypothesis that the coin is a fair one, because it’s pretty unlikely that the experiment would have turned out this way if the coin was fair. Huzzah! Callooh! Callay! We can publish our findings that this coin just isn’t fair in the world-renowned Journal of Trivial Results and Bad Bar Bets (JTRB3).
So how is this calculated? Well, the idea is that we have to look at the universe of possible results given the null hypothesis; that is, if I had a coin that was truly fair, how often will the result of my flipping it yield 7 heads and 3 tails? Obviously, given a fair coin, most scenarios will yield about a 50/50 split on heads and tails. It is, however, not completely impossible for us to get our 7/3 results. What we have to calculate is, if we flipped a fair coin in an infinite amount of experiments, what percent of those experiments would give us 7 heads and 3 tails? If it’s under 5%, p < 0.05, we can be reasonably certain that our result probably implies a stacked coin. We can assume that because in only 5% of experiments on a fair coin will the results look like the results we see.
We use 0.05, or 5%, mostly out of a long-standing social agreement. The 5% mark is low enough that we can reject the null hypothesis beyond most reasonable doubts. That said, it’s worth remembering that the difference between 4.9% and 5.1% is itself often not statistically significant, and though 5% is our agreed upon convention, it’s still pretty arbitrary. The best thing anyone’s ever written to this point was by Rosnow & Rosenthal (1989):
“We are not interested in the logic itself, nor will we argue for replacing the .05 alpha with another level of alpha, but at this point in our discussion we only wish to emphasize that dichotomous significance testing has no ontological basis. That is, we want to underscore that, surely, God loves the .06 nearly as much as the .05. Can there be any doubt that God views the strength of evidence for or against the null as a fairly continuous function of the magnitude of p?”
I’m really nailing this point home because p-values are so often misunderstood. Wikipedia lists seven common misunderstandings of p-values, and I can almost guarantee that a majority of scientists who use the statistic are guilty of at least some of them. I’m going to quote the misconceptions here, because they’re really important.
- The p-value is not the probability that the null hypothesis is true.
In fact, frequentist statistics does not, and cannot, attach probabilities to hypotheses. Comparison of Bayesian and classical approaches shows that a p-value can be very close to zero while the posterior probability of the null is very close to unity (if there is no alternative hypothesis with a large enough a priori probability and which would explain the results more easily). This is Lindley’s paradox.
- The p-value is not the probability that a finding is “merely a fluke.”
As the calculation of a p-value is based on the assumption that a finding is the product of chance alone, it patently cannot also be used to gauge the probability of that assumption being true. This is different from the real meaning which is that the p-value is the chance of obtaining such results if the null hypothesis is true.
- The p-value is not the probability of falsely rejecting the null hypothesis. This error is a version of the so-called prosecutor’s fallacy.
- The p-value is not the probability that a replicating experiment would not yield the same conclusion. Quantifying the replicability of an experiment was attempted through the concept of P-rep (which is heavily criticized)
- 1 − (p-value) is not the probability of the alternative hypothesis being true (see (1)).
- The significance level of the test (denoted as alpha) is not determined by the p-value.
The significance level of a test is a value that should be decided upon by the agent interpreting the data before the data are viewed, and is compared against the p-value or any other statistic calculated after the test has been performed. (However, reporting a p-value is more useful than simply saying that the results were or were not significant at a given level, and allows readers to decide for themselves whether to consider the results significant.)
- The p-value does not indicate the size or importance of the observed effect (compare with effect size). The two do vary together however – the larger the effect, the smaller sample size will be required to get a significant p-value.
One problem with p-values (and it often surprises people)
Okay, I’m glad that explanation is over, because now we can get to the interesting stuff, and they’re all based around assumptions. I worded the above coin-toss experiment pretty carefully; you keep flipping a coin until you wind up with 7 heads and 3 tails, 10 flips in all. The experimental process seems pretty straight forward: you flip a coin a bunch of times, and record what you get. Not much in the way of underlying assumptions to get in your way, right?
Wrong. There are actually a number of ways this experiment could have been designed, each yielding the same exact observed data, but each as well yielding totally different p-values. I’ll focus on two of those possible experiments here. Let’s say we went into the experiment saying “Alright, coin, I’m going to flip you 10 times, and then count how often you land on heads and how often you land on tails.” That’s probably how you assumed the experiment was run, but I never actually described it like that; all I said was you wound up flipping a coin 10 times, seeing 7 heads and 3 tails. With that information, you can also have said “I’m going to flip this coin until I see 3 tails, and then stop.” If you remember the sequence above (heads, tails, heads, heads, tails, heads, heads, heads, heads, tails), that experimental design also fits our data perfectly. We kept flipping a coin until we saw 3 tails, and in the interim, we also observed 7 heads.
The problem here is in how p-values work. When you ask what the probability is that your result came from chance alone, a bunch of assumptions underlie this question, the key one here being the halting conditions of your experiment. Calculating how often 10 coin-tosses of a fair coin will result in a 7/3 split (or 8/2 or 9/1 or 10/0) will give you a different result than if you calculated how often waiting until the third tails will give you a 7/3 split (or 8/3 or 9/3 or 10/3 or 11/3 or 12/3 or…). The space of possibilities changes, the actual p-value of your experiment changes, based on assumptions built into your experimental design. If you collect data with one set of halting conditions, and it turns out your p-value isn’t as low as you’d like it to be, you can just pretend you went into your experiment with different halting conditions and, voila!, your results become significant.
The moral of the story is that p-values can be pretty sensitive to assumptions that are often left unspoken in an experiment. The same observed data can yield wildly different values. With enough mental somersaults regarding experimental assumptions, you can find that a 4/6 split in a coin toss actually resulted from flipping a coin that isn’t fair. Much of statistics is rife with unspoken assumptions about how data are distributed, how the experiment is run, etc. It is for this reason that I’m trying desperately to get quantitative humanists using non-parametric and Bayesian methods from the very beginning, before our methodology becomes canonized and set. Bayesian methods are also, of course, rife with assumptions, but at least most of those assumptions are made explicit at the outset. Really, the most important thing is to learn not only how to run a statistic, but also what it means to do so. There are appropriate times to use p-values, but those times are probably not as frequent as is often assumed.