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Textbook solution manual s download
Find textbook solutions and answers here! Submit Close. Ace your classes with our powerful online study tools. Get Started. Textbook Solutions. Find interactive solution manuals to the most popular college math, physics, science, and engineering textbooks. No printed PDFs! Take your solutions with you on the go. 1. 2. 3. Science direct 4. Springer, etc All the above links are for getting engineering book solution manuals. For Chegg and Scribd you need to select suitable subscription to access. Science direct and spri. Despite this, students do better in classes where homework is assigned from the textbook and graded with access to solution manuals. Figure 2. Students' performance to the class where they did not use solution manuals vs % of respondents. Do solution manuals aid student learning or only help them to get a better grade?.
Online Textbooks and Solution Manuals for Math 1, Math 2, and Math 3. Quick links: textbook, solution manual. Students using the Math 1, Math 2, and Math 3 textbooks have access to electronic textbooks and solution manuals through the online systems of the publisher, Pearson Education. If you have any trouble following. Course Text Books/Solutions Manuals - Bradenton Campus. Math. Prealgebra Text, Martin-Gay, 6th ed. Introductory Algebra Text, Martin-Gay, 4th ed. Prealgebra + Intro: Algebra Text, Martin-Gay, 3rd ed. Prealgebra + Intro: Algebra Instructor's Solution, Martin-Gay, 4rd ed. Beginning & Intermediate Algebra Text, Martin-Gay. View Notes - Textbook Solution Manual from ECO k at University of Texas. EVERY SOLUTION TO THE BOOK IS IN THE MANUAL BUT THEY ARENT NUMBERED CORRECTLY. YOU HAVE TO SEARCH BUT.
I genuinely need solution manuals to study. Unfortunately there's not a lot out there to obtain. I found [this]() and while I. I agree (as usual) with @ff Consulting an outside source is not academic dishonesty in a global sense -- academic culture does not prohibit students and faculty from reading academic sources! -- but it may be academic dishonesty in a local sense: i.e., it may be against the rules of your course as set up. Printed manuals are a print on demand item. Please allow weeks for processing and delivery. Please email your name, institution, a complete university shipping address, course name, enrollment, semester, book title, ISBN and or author to [email protected] Use subject line such as “ Solution Manual.


- Analytic Solver Upgrade 可以最多求解最多2,000决策变量的线性问题、500 variables 决策变量的非线性问题，价格是995美元
- Analytic Solver Optimization 可以最多求解最多 8,000 决策变量的问题，价格是1995美元
- Solver engines 求解问题的规模几乎没有限制，不同版本价格存在差异，在3000到10795美元之间
OpenSolver是一个开源的工具、完全免费，但是求解问题的规模没有限制。OpenSolver由新西兰奥克兰大学工程科学系（Engineering Science department, University of Auckland）的Andrew Mason及学生开发、维护；最近的开发由麻省理工学院的Jack Dunn提供。
These solvers all handle linear optimization problems in both continuous and integer variables. Their performance is not at the level of analogous commercial solvers, but can be competitive for problems that are not too large or difficult.
The solvers in this category seek solutions to problems involving smooth nonlinear functions such as powers, logs, and ratios. They differ in the algorithms that they offer, and hence in their effectiveness for different problem types. Due to the difficulty of nonlinear optimization, these solvers are effective with smaller problems than their linear counterparts.
Ipopt 3.12.13 — from COIN-OR under the Eclipse Public License; available as source code and binaries for 32-bit Linux, 64-bit Linux, OS X, 32-bit Windows and 64-bit Windows. Finds locally optimal solutions to continuous nonlinear problems, using an interior-point method.
Bonmin 1.8.8 — from COIN-OR under the Eclipse Public License; available as source code and binaries for 32-bit Linux, 64-bit Linux, OS X, 32-bit Windows and 64-bit Windows. Finds globally optimal solutions to convex nonlinear problems in continuous and discrete variables, and may be applied heuristically to nonconvex problems.
Couenne 0.5.8 — from COIN-OR under the Eclipse Public License; available as source code and binaries for 32-bit Linux, 64-bit Linux, OS X, 32-bit Windows and 64-bit Windows. Finds globally optimal solutions to nonlinear problems in continuous and discrete variables, regardless of convexity.
Constraint programming solvers
These solvers handle constraint programming problems usually in discrete variables. They support a wide variety of constraint types that may contain nonlinear and logical expressions. Constraint programming solvers can be more efficient than MIP solvers for some kinds of combinatorial optimization problems.
The kestrel program allows using remote NEOS solvers with AMPL running on your local machine. Invoked in the same way as other AMPL solvers, Kestrel sends the problem to a solver running on one of the NEOS Server’s remote computers. The results from the NEOS Server are eventually returned through Kestrel to AMPL, where you can view and manipulate them locally in the usual way. Thus you get all the benefits of using AMPL environment, without having to first obtain and install each solver you want to try. Kestrel is provided free of charge and available for download from the Run AMPL on NEOS page. It is also included in all the demo packages.


In computational theory, the efficiency and performance of an algorithm can be mathematically quantified by comparing its’ arbitrary input size against the runtime. However, an identical algorithm (or even a program) being executed on one computer may not necessarily have the same runtime on another computer. Dependencies such as processor speed, I/O speed, cache size, and etc. are without a doubt contributing factors. As such, the fundamentals behind this theory of analysis is asymptotic in nature.
Asymptotic (asymptote) is defined by their ratio as a given variable approaches infinity.
Take the Golden Ratio (φ) for example. Given its algebraic formula,


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Two years after joining in SRM University in a Computer Science Bachelors Degree, was all it took before I realized I wanted to shift towards a more data-centric career. After seeing the skillset of Data Scientist like coding ,math and statistics,Machine learning,…. was the moment when I decided where my long-term passions resided.
As per my knowledge the skills required to be a Data Scientist are:
- At least one programming language — R/ Python
- Data Extraction, Transformation, and Loading
- Data Wrangling and Data Exploration
- Machine Learning Algorithms
- Advanced Machine Learning (Deep Learning)
- Big Data Processing Frameworks
- Data Visualization
Before telling the resources where i have learnt each of the above-mentioned points, let me categorize the skills.
As a Data Scientist, you’ll be responsible for jobs that span three domains of skills.
- statistical/mathematical reasoning,
- business communication/leadership, and
The courses I have done and currently doing to achieve my Goal are :
All the above courses helps you to learn skills like python,sql,machine learning,big data and all the maths related to data science
I would also like to recommend some other valuable courses like:
“Data Science takes the guesswork/emotions out of answering business questions by applying logic and mathematics to find better solutions.”
Have a Happy Learning :)


Answer to Measurement. One meter equals about 39.37 inches. Write a function rule for converting inches to meters. Evaluate the.
Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. Learn more. Creating a function in R to convert a unit of measurement. Ask Question Asked 3 years, 7 months ago. Active 3 years, 7 months ago. Viewed 2k times 0. I would like to create a function that converts a measurement from meters to inches. The goal is to input a measurement (in.
For example, if you are converting from kilometers to millimeters, you are converting from a larger to a smaller unit. In this case, the conversion process will use multiplication or moving of the decimal point to the right. This is the same direction you will read across your chart: left to right. When converting from a smaller to a larger unit, the conversion process will involve division or.The most famous example, employed to explain conversion between basic and user defined data type is that of meters to distance class; where meter is a float type basic data type and distance is a user defined class. Some programming logic is implemented in order to convert the float to user defined class. You will be amazed to know that we will be able to do something like.The Excel CONVERT function converts a number in one measurement system to another. For example, you can use CONVERT to convert feet into meters, pounds into kilograms, Fahrenheit to Celsius, gallons into liters, and for many other unit conversions.
Access College Algebra and Trigonometry 2nd Edition Chapter 2.4 Problem 94E solution now. Our solutions are written by Chegg experts so you can be assured of the highest quality!Read More
To convert from metres to centimetres it is only necessary to multiply the number of metres by 100, since there are 100 centimetres in a metre. Inversely, to switch from centimetres to metres one multiplies the number of centimetres by 0.01 or divides the number of centimetres by 100. Length. A 2-metre carpenter's ruler. A ruler or rule is a tool used in, for example, geometry, technical.Read More
Online calculator to convert millimeters to centimeters (mm to cm) with formulas, examples, and tables. Our conversions provide a quick and easy way to convert between Length or Distance units.Read More
If you can make dinner, you can convert units in the metric system. It's that easy! In this lesson, you'll learn about the three key things you'll need to perform conversions. It's that easy!Read More
Unit conversion is a multi-step process that involves multiplication or division by a numerical factor, selection of the correct number of significant digits, and rounding. This multi-step process is presented in NIST SP 1038 - 2006 (Section 4.4), including a rounding procedure for technical documents, specifications, and other applications such packaged goods in the commercial marketplace and.Read More
Common Length and Distance Conversions. Welcome to OnlineConversion.com Common Length and Distance Conversions.Read More
Learn different units of measurement and practice changing between them using our 'Convert between different units of measure' resources for Year 4 maths lessons. These worksheets, display items and games take different metric and imperial measurements for liquids, lengths, weight and temperature and allow students to change them and convert them to solve problems.Read More
Printable worksheets for standard American linear measurement, including inches, feet, and yards. Includes using rulers to measure to the nearest inch, half inch, quarter inch, and eighth inch. Also, there are worksheets for converting between feet, yards, and inches.Read More
Metric to Imperial Conversion Tables. Author: Disabled World: Contact: disabled-world.com. Published: 2017-12-20: (Rev. 2017-12-28) Synopsis: Our handy conversion tables show you the formulas to convert from metric system measurements to the imperial system and visa versa allowing you to do your own calculations for the conversion you need. Main Digest. Our handy conversion tables show you the.Read More
To convert To convert Inch to mm - multiply by 25.4 Yards to meters - multiply by .9144 mm to inch - multiply by .03937 Meters to yards - Multiply by 1.094 feet to meters - multiply by .3048 Miles to km - multiply by 1.609 Meters to feet - multiply by 3.281 km to miles - multiply by .6214 Area - Basic unit is centare (ca) which is one square meter Weight - Basic unit is gram (g) Metric Square.Read More


Saxon Algebra 2 Homeschool Kit – Classical Conversations Bookstore Check for common scams and banned users before sending money or merchandise. A convenient package for the Algebra 2 student Audience Grades 9–12; used in Classical Conversations communities in. Saxon Alg 2 Solutions Manual.
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The mathematics curriculum at Blue Mountain School is based on methods recommended by the National Association for the Education of Young Children and standards put forth by the National Council of Teachers of Mathematics. Using a variety of rich materials and resources, teachers introduce developmentally appropriate mathematics concepts that build as students move through the program. The curriculum emphasizes mathematical thinking, problem solving and communication. Instruction includes hands-on experiences as well as practice with number facts and computation.
Our Early Childhood math program is exploratory, play-based, and encourages hands-on experience through the use of math manipulative materials such as blocks, pattern blocks, beads, natural materials, and measurement tools. Teachers model that math is a part of everyday activities by counting students during attendance, wondering if there is enough fruit for everyone, and figuring out how tall we are. Games are introduced for number recognition, geometric shape identification, quantity recognition and the development of understanding one-to-one correspondence. Teachers keep an eye out for children’s math exploration and guide them to expand their thinking.
Our Early Learning mathematics lessons and activities are based on developmentally appropriate standards, with material added when there is a need to enrich or review topics or because the children’s questions and interests inspire the group to take its explorations in different directions. In all math endeavors, children are actively engaged in the exploration and discovery of basic mathematical concepts. They develop a shared language for the communication of ideas, and they begin to build confidence in themselves as competent mathematicians. Specific topics covered in Early Learning include patterns, one-to-one correspondence, counting, introduction to place value, and introduction to single-digit addition and subtraction.
Building on basic math concepts introduced in the Early Childhood and Early Learning classes, Lower Elementary math practice continues with additional mathematical lessons and activities reflecting developmentally appropriate standards, with material added when there is a need to enrich or review topics or because the children’s questions and interests inspire the group to take its explorations in different directions. Lower Elementary mathematics also provides children with extra practice in certain skills, such as computation and memorizing number facts. At this age children continue to develop their mathematical vocabulary and communication skills, using speech, writing, drawings and other symbols to represent concepts. An emphasis of the program is on creating and articulating alternate strategies to solve problems, rather than on simply using a formula to find the predetermined “correct” answer. Specific topics covered in the Lower Elementary class include skip counting, place value, up to three-digit addition and subtraction, introduction to multiplication, and measurement.
In the Middle Elementary class, mathematics studies continue to be supplemented with additional mathematical lessons and activities that enrich or review topics, and/or to take advantage of the children’s questions and interests. Students receive extra practice in skills such as computation and memorizing number facts. At this age children are beginning to be able to think more abstractly. Hands-on activities with manipulative materials continue to be helpful, with some use of calculators. Concepts are explored in depth so that children can do more than simply follow steps; they understand why they are doing what they are doing. Specific topics covered in Middle Elementary include place value, an introduction to alternate bases and number systems, the four operations with whole numbers, an introduction to fractions and decimals, and plane geometry.
In the Upper Elementary class, students’ active participation and engagement with mathematical concepts and procedures is encouraged. Ten- to thirteen- year-olds have the ability to think more and more abstractly. Teachers help them make the connections between mathematical concepts, such as the relationships between the area of geometric figures, operation arrays, and the multiplication tables. Students work with negative numbers and expressions with variables and discover new ways of representing problems, including drawing intersecting sets and graphing equations. Specific topics covered in the Upper Elementary class include using alternate bases and number systems, the four operations with whole numbers, fractions and decimals, plane and solid geometry, an introduction to algebra, basic logic and statistics.
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Head First Statistics
O'Reilly Media, 2008
Rating: 4/5 (very good)
There are times when you really need something in the area of statistics, for your job (I'm a computer programmer and I happen to need some) or just because you'd like to know more about it. You, however, don't have time and/or find it boring to read about math and statistics on a regular text book. If this is the case, Head First Statistics might be exactly what you need.
First of all, the explanations do not start off from theory, but from practical examples. For instance, a slot machine is an entertaining way to dig into discrete probability distributions. Then, the layout makes everything clear and easy to read (and, likely, also to understand): important formulas are written in very big letters, and side notes with arrows make it straightforward to understand what is what.
Every chapter covers a topic (i.e. sampling, normal distribution, confidence intervals, ...). Explanation is what makes most of the chapter (of course), which is then closed with Q&A answer where you'll find answer to the most frequently asked questions related to the topic of the chapter. As in every good teaching book, there are also exercises (with solutions on the page following each question).
The explanation might not dig too much in depth, ad of course it lacks some of the theory. Nevertheless, this is a fine book for everybody who's interested in or needs to know something about statistics.


Period of duration of course
Requires basic notions of scheme theory. For PhD and Master students.
• The functorial point of view in algebraic geometry.
• Affine group schemes over a field. Hopf algebras.
• Homomorphisms. Faithful flatness.
• Representations. Existence of faithful representations.
• Descent theory.
• Existence of quotients.
• Group schemes of multiplicative type.
• Unipotent group schemes.
• Solvable group schemes.
Teaching the theory of group schemes.


The Golden Ratio is a good intro to photo composition.
If you're not a math whiz, no problem.... just a review of high school geometry. Nothing heavy, I promise.
When I was in school, I didn't see much value in studying math and now I'm sorry I didn't pay more attention.
Math didn't seem to apply to real life. But then I discovered a great TV show that changed my mind.
Sunflower - a perfect golden ratio
Have you ever seen Num3ers? Absolutely fascinating. Charlie is a
young mathematical professor and a genius. His brother's an FBI agent.
solves crimes for the FBI with seriously complicated math. When he
explains his theories in layman's English, I've got to admit that math
might not be so irrelevant after all. And it's actually intriguing .
Well, not long after Num3ers I learned about Fibonacci.
Fibronacci's "Golden Ratio" creates a spiral pattern that appears many places in the natural world. This sunflower right here, shows the spiral pattern clearly.
It's easy to see that the tiny flowers and seeds don't just pop up in some random order. It's all a part of Mother Nature's amazing tapestry.
You'll see the pattern in the shape of pineapples, pine cones, the branching in trees, fingerprints, DNA, the Nautilus shell, for a few examples.
Want to read more about it?
Fibonacci published a mathematical sequence in 1202 in a book called the Liber Abaci.
He wasn't the one who first stumbled on to the Golden Ratio - he came across it while he was studying East Indian mathematics. Before that, back in the 5th Century BC, Pythagoras seems to be the first one credited with discovering the divine proportion... Remember 1.6181 : 1 from school?
You only need the patterns that come from the golden ratio to make this work for your images.
The rectangle is built of squares or "iblocks".
The number of blocks that make up the sides of the squares are equal to the sum of the two numbers that come before them in the sequence.
The first two squares that initiate the rectangle are the two 1's.
Fibonacci iblocks transparency reprinted from Wikipedia Commons.
The square next to them is two blocks each side, so next to 2 and 1 is a cube of 3 blocks (3x3). Still with me?
You can just make out the the fern image I used under the iblocks transparency. This Golden Rectangle is one pattern worth using to design a picture.... and if you shoot the 2x3 ratio images (35 mm) it fits perfectly.
The fern tip cozies right into the smaller iblocks rectangle. See how the V of the fern sits right where blocks 1 and 3 meet? The whole frond falls in the left-hand side of the image.
I didn't say the
left "third" because this large rectangle doesn't quite divide into
Here's how the Fibonacci spiral is created inside the golden rectangle.
The spiral circles outward from the first iblock of 1... draw a quarter circle from the adjoining angle on the one side to the opposite side of the square. From there, continue drawing a circular arc to the opposite angle of the next square until all the squares are connected by this outward spiral.
You just drew a Golden Spiral. Now imagine the Milky Way, spinning through eternity... the large picture looks pretty much like this!
No matter which way you flip it, one of the two red poppies ends up at the beginning of the golden spiral. The partner poppy hangs along the curve at the opposite side.
I took this 35 mm slide my second year studying photography. It's one of my best. The exposure and focus are perfect but what tops it off is the composition. Took me awhile to figure out why it felt "right on"!
These poppies were blooming in the perennial garden at VanDusen Botanical Garden in Vancouver.
Now that I've added the golden spiral and triangles to this tulip photo, help me evaluate the composition.
Fibonacci spiral and golden triangles reproduced from Wikipedia Commons.
The dark foliage sits along the outside of the spiral. That was a bit of luck... I set the trees up as a "frame" with some space between the dark foliage and the tulips and it worked out well.
When I evaluate my photos, even though the focus and exposure is right on, sometimes one just doesn't click with me. There doesn't seem to be anything really wrong with it.
... but this tulip image felt comfortable to me. Look where the 4 tulips fall within the golden spiral.
They're all inside and the closest one is alone, right where the spiral begins! See?... it also fits inside the mid-sized golden triangle.
The long side of the largest golden triangle bisects the group of three tulips and they're snug inside the spiral and the other side of the largest triangle.
By the way, I didn't have a conscious checklist on my mind when I took this photo! Once you understand the concepts, they sink into your brain and eventually, your design comes automatically.
The golden ratio is just a beginning, but it's a good start if you want to improve how you compose your shots.
So here's your homework...give some thought to Fibonacci and the golden ratio - the rectangle, spiral and triangles. Go out and compose your shots so they fall into these designs.
Or find a subject that expresses the golden ratio in its natural pattern.
Read this article to get some ideas.
If you're interested in Fibonacci and understanding more about the golden ratio, there are scads of resources on these fascinating numbers.
Get a general grasp of the spiral, the iblocks, the triangles... use them to improve your image composition.


The department of Mathematics was
established in the year 1967. This is the earliest department of Quaid-I-Azam
Islamabad. The department has been developed into a leading institution of teaching and
research within and outside the country. The department consists of 19 highly qualified
faculty members. Eight faculty members have been associates of International Centre for
Theoretical Physics, Trieste, Italy. Curriculum includes courses on Pure Mathematics,
Applied Mathematics and Mathematical Statistics. Active research is pursued in Algebra,
Geometry, Functional Analysis, Astrophysics, Relativity, Fluid Mechanics,
Magnetohdrodynamics, and Acoustics.
The department has collaborative research
programs with such institutions as ICTP, MIT, and universities at Oxford, Texas and Rhode
Island. The QAU, UGC, NSRD Board and the Pakistan Science Foundation support research work
in the department.
M.Sc. Statistics program has been started
since 1994 in the Department of Mathematics. The program has achieved a great success,
which can be judged by the fact that almost all the graduates have been appointed on
various good assignments. Weekly seminars are a regular feature of the department. This
activity has provided a forum for introducing latest trends of research in Statistics for
participants from as well as outside the University.


Learn to count from 1 to 10!
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Last week, a co-worker asked if I could help her out with a Tableau table calculation. Her goal was to come up with a year-over-year (YoY) percent difference of the 4 week moving average for some key metrics in her data set. Tableau easily allowed her to find the key components individually, but she was having difficulty combining the YoY %Diff with the 4 week moving average. I’d like to share how I thought through the problem and worked it out with table calcs.
First, it’s important to understand what table calculations are… from Tableau’s website:
“Table calculations are computations that are applied to the values in the table. These computations are unique in that they use data from multiple rows in the database to calculate a value. To create a table calculation, you need to define both what values you want to compute and what values to compute along.”
The “table” refers to the data table I create in Tableau by pulling in dimensions and measures into the rows and columns shelves. The physical data table is all that I have to work with, so any values I’d like to use for a table calculation better be represented somewhere on my table! One of the neat things about this is that data can be aggregated or calculated prior to being populated in the table, and then that pre-aggregated or calculated data can be used for additional calculations. Some of the most common applications of table calculations include percent differences, running totals, weighted averages, etc.
Knowing I need all my data laid out on the table in order to use a table calc, I start with populating my data table with something like sales (measure) by date (dimension). For the purpose of this exercise, the date dimension contains dates from every Sunday of the week.
Essentially, on my data table, what I want to start with are the weekly sales figures for each Sunday. I drag my date dimension onto the rows shelf as a discrete, exact date. I then drag my sales measure onto the text mark.
Now that I have my data laid out the way I want it, I start piecing together the steps I’ll need to take to get to my final solution. First, I know I’ll need to be looking a year back in my data, so I want to figure out the calculation that gets me a data point from 52 weeks back from a given row. Essentially, I want to bring the sales value from 1/26/14 ($14,852) down to the same row as my 1/25/15 sales value ($18,697). To do this, I know I need the sum of sales. I also need a way to handle NULL sales values, so I employ the ZN() function to handle NULL values as 0. Then I insert the ZN(Sum(Sales)) as the expression of the LOOKUP() and use an offset of -52, since I need to look 52 values back in my weekly date to find last year’s weekly sales value.
I double click my “Sales 52 Weeks Prior” pill in the measures shelf to add it to my data table, then check if my 1/26/14 value is now showing as the 1/25/15 sales value.
It checks out! The next calculation I need is to find the 4 week moving average. I right click on the Sales pill in my Measure Values and create a table calculation. I select the Moving Calculation, summarize values using the average, moving down along the table since my dates are sorted ascending, and then look 3 values back from the current value.
One thing to point out here is that I could click “Perform a secondary calculation on the result” as seen in the below image, but Tableau does not provide an option for a custom number of values to look back on, which is a big part of why I’m writing this post! I only have the previous, next, first, and last values as an option, and I need to specifically look 52 values back, so let me click out of this option and go back to the table calc above.
If I click the “Customize…” button, I can check out Tableau’s automatically generated calculation based on my selections. This calculation takes the Window Average of my sales, starting 3 periods back from a given value, to the given value. I rename this calculation as the “Sales 4 Week Moving Average” to save it as a new calculated field in my measures shelf because I’ll be using it again.
When I click OK, this calculation will now replace the sum(Sales) on my chart, so I go ahead and add sum(Sales) back to the table for reference. Does the moving average calculation average out the current plus last 3 weeks of sales data for a 4 week moving average? Yup!
So now what do I do? Well, let me start with what I have… I have my weekly sales, my sales from a year back, and my 4 week moving average. I now need to find a way to get my 4 week moving average from a year back.
I have an excellent head start for this, because I not only got my 4 week moving average calc working, but I also have the lookup logic to get a value from 52 weeks back. What I need to do is create a new calculation that combines the “Sales 4 Week Moving Average” logic [WINDOW_AVG(SUM([Sales]), -3, 0)] with my “Sales 52 Weeks Prior” logic [LOOKUP(zn(sum([Sales])),-52)].
This is precisely why I replace the sum([Sales]) logic in my 1 year lookback [LOOKUP(zn(sum([Sales])),-52)] with the 4 week moving average logic [WINDOW_AVG(SUM([Sales]), -3, 0)].
I add my new calculated measure “Sales 52 Weeks Prior 4 Week Moving Average” to the data table by double clicking its pill in the measures shelf. Does this show the 4 week moving average from 1 year ago on the current row? It sure does!
Now that I have the current 4 week moving average and the 4 week moving average from 52 weeks ago, I can create a calculation that takes the ( (current 4 week average) – (4 week average from 52 weeks ago) ) / (4 week average from 52 weeks ago) to find my year-over-year 4 week moving average.
( WINDOW_AVG(SUM([Sales]), -3, 0) – LOOKUP(zn(WINDOW_AVG(SUM([Sales]), -3, 0)),-52) )
/ LOOKUP(zn(WINDOW_AVG(SUM([Sales]), -3, 0)),-52)
I add this to the data table to check if works…
It works! I have just created a YoY %Diff using 4 week moving averages to show that my 1/25/15 4 week moving average is 26.86% more than the 4 week moving average from 52 weeks back! If I play around with the Show Me options, I can chart my YoY 4 week moving average against the 4 week moving average of sales as a line graph, or whatever type of visualization will help the end users make data-driven decisions.
A few gems for you to note that played an instrumental role in my ability to work through this table calc problem in Tableau:
- Build out your base table first using dimensions and measures needed for analysis
- Maintain a level of granularity needed for the table calcs i.e. having weekly data for a 4 week moving average calculation
- Try to get any calculations needed on the given row it will impact i.e. bringing the 4 week moving sales average from 1/26/14 (52 weeks ago) to the row that displays 1/25/15 data
- Create basic calculations first, then start piecing them together to achieve what you need i.e. embedding the 4 week moving average calc into the YoY calc
- Be creative but think practically


Designed and tested by educators and parents of young children, Dominoes Number Match presents an easy and entertaining way to master a variety of numeracy skills.
Dominoes Number Match uses the concept of traditional dominoes to present game play designed especially for young learners. Because this one game actually comprises four games of increasing complexity, it can both support and challenge players at a variety of skill levels.
The first game level, called Easy Match, uses pairs of dominoes to introduce children to beginning counting and number recognition by matching numerals to corresponding sets of dots. In the Easy Match level, built-in audio supports the beginning player with both identification of numerals and counting.
Match 3 and Match 6 then help children learn to quickly identify sets and numerals while building a traditional "train" or sequence of dominoes.
Finally the Full Game allows the proficient player to develop more sophisticated math skills such as instant identification of arrays of objects and creating problem solving strategies to win a game vs. the computer.
A variety of parent options allow for individualized play, allowing control over both the degree of difficulty and the look of the game. Options include specifying the numbers covered (0-3, 0-6, or 0-9); using dominoes that display dots only, numbers only, or a combination of the two (in Match 3, Match 6, and Full Game); and choosing whether or not to allow hints during play (in Match 3 and Match 6).
Dominoes Number Match skills focus
concept of number
identification of numbers 0-9
identification of simple arrays
problem solving/ game strategy
Requires iOS 4.3 or later. Compatible with iPad.
Dominoes Number Match is a free trial software application from the Kids subcategory, part of the Education category.
The app is currently available in English and it was last updated on 2012-07-14. The program can be installed on iOS.
Dominoes Number Match (version 1.0) has a file size of 13.11 MB and is available for download from our website.
Just click the green Download button above to start. Until now the program was downloaded 0 times.
We already checked that the download link to be safe, however for your own protection we recommend that you scan the downloaded software with your antivirus.


In this software, you can calculate many calculations of mathematics or statistics. Full version Wolfram Mathematica 10.3 with serial key also available on this sides in which you can starting samplings and ending with the high level of mathematics. This software has many professional tools which make your calculations more efficient and easy. This software very useful and time saving. This software very light weight and easy to download or install in every computer and operating system. In this software, you can solve many problems of mathematics equations and algebraic formulas. Wolfram Mathematica 10.3 with activation key very useful for every one in which you can make total mathematics problems and equations very easily.
This software has large catalog of symbolic tools and numerical functions. Free Wolfram Mathematica 10.3 Crack also available in this sides very amazing for all professional and beginners as well. This software provided you awesome book maker reports makers and CDF file making easily. In this software, you can give the presentations of those file in which you can present large screen easily. As per expert’s opinions you must try this software at once, I hope you like it too much. In this software, you can display your file in 2D and 3D quality.
In this software you can also import and export your data files and videos audio easily, that is amazing software in this features and tools functions. Full version Wolfram Mathematica 10.3 with serial key has the very friendly interface with amazing functions and tools. This software has extra latest formula editor in which you and write down or edit any type or formulas very easily with one or two steps. You can also download AntiBrowserSpy Pro 2016 with keygen from this side.


KPSC Recruitment 2022: Karnataka Public Service Commission (KPSC) is hiring Junior Engineer (Civil, Mechanical) (HK), Statistical Inspector (RPC), and Assistant Statistical Officer (RPC). More than 300 vacancies are available. The commission will start the registrations of the candidates on 19 October 2022. Eligible and interested candidates can apply on or before 17 November 2022 on kpsc.kar.nic.in.
- Starting Date of Online Application – 19 October 2022
- Last Date of Online Application – 17 November 2022
KPSC Vacancy Details
- Junior Engineer (Civil) – 166 Vacancies
- Junior Engineer (Mechanical) – 03 Vacancies
- Assistant Statistical Officer in the Directorate of Economics and Statistics – 58 Vacancies
- Statistical Inspector of Economic and Statistical Directorate – 105 Vacancies
Eligibility Criteria for KPSC Recruitment 2022
- Candidates Must be a holder of a Diploma in Civil Engineering (General) and Mechanical Engineering (General) granted by the board of Technical Education, Government of Karnataka.
- Applicants also Must be holders of a Master’s Degree in any one of the subjects of Mathematics, Pure Mathematics, Statistics, Applied Statistics, Economics with Statistics / Quantitative Techniques, Pure Economics, Applied Economics, Applied Mathematics, Econometrics, or Computer Science.
18 to 40 years
Rs. 27,650 to 70,850/-
How to Apply for KPSC Recruitment 2022?
Eligible and interested candidates can apply online from 19 October to 17 November 2022.
- For general merit candidates – Rs. 600
- For candidates belonging to Category 2(A), 2(B), 3(A), 3(B) – Rs. 300
- For Ex-Serviceman Candidates – Rs. 50
- Scheduled Caste, Scheduled Tribe, Category-1, and Disabled For the candidates – Nil.


I paint math equations, their geometric forms that visually render in my mind, and how their relationships develop into geometric models that describe narratives about the human condition. I call this conceptual process Analytical Expressionism, and it expands the definition of geometry in art. In history’s long arc of artists using geometric forms in their artwork, none of it has been true geometry. Written in the universal and timeless language of mathematical equations, Analytical Expressionism allows– for the first time ever – true geometry in art.
For those without a mathematics background, I paint the geometry as I see it. However, viewers who know mathematics can read the equations in my paintings and see the geometry for themselves on the internal chalkboard in their own minds. This is a whole new way of seeing geometry in art.
Pythagoras of Samos (c. 570 BC – c. 495 BC) was a Greek philosopher, mathematician, music theorist, and someone who inspires my love of the polar coordinate system.
In these paintings, I envision Pythagoras falling into a deep sleep and dreaming of all the progenies of his original ideas. I paint the geometric forms that represent what he would have seen on the internal chalkboard of his mind. Pythagoras saw mathematics in everything. I agree. Our ability to see in this way is what I call Pythagorean Eyes.
My favorite geometric progeny of Pythagoras is the limaçon, a beautiful snail-like shape with an elegant interior and exterior curvature. This form was studied by the painter and mathematician Albrecht Durer (1471 – 1528), and I find its polar equation and curvature fascinating as well as the perfect structure for modeling human and geometric relationships. For example, by varying two parameters in the limaçon equation, I create a visual representation of the continuum of consciousness from the Swiss psychotherapist Carl Jung (1875 – 1961). Then to better understand how people see the continuum of their own consciousness and connect with each other, I use integral calculus to calculate the area enclosed by each polar curve, visualize where they intersect, and find the area enclosed by two polar curves using integration.
Once a geometric form such as a limaçon is imbued with symbolism, I call it a geometric model or geom. The geom of an orbiting limaçon is the optimal model for explaining Soul Mates: our own consciousness, that of another person, and the relationship that takes form as the interstices between them. This mapping describes how two humans orbit, first trying to find their other half and then to remain fused together over time.


The geometric mean is the average of a set of numbers.
Why It's Important
This is not to be confused with arithmetic mean. The arithmetic mean is what you learned in school when your teacher taught you about "mean". As a refresher, let's look at the following set of numbers: 3%,7%,10%,6%,4%. You find the mean by adding all the numbers together (3+7+10+6+4=30%) then dividing by the total number of records (5). The arithmetic mean in this scenario would be 6%. In contrast, a geometric mean would be calculated as (1.03x1.07x1.10x1.06x1.04)^(1/5)=~5.5015%.
Now that you have the concept, let's apply it to personal finance and investing. The geometric mean is typically used to calculate the average return on investments. You would look at the past annual rates and calculate the mean to find out what your overall return was over the time period.
For example, let's say one year you enjoyed 10%, the next 15%, and the next 8%. Your average return over the three years would be (1.10x1.15x1.08)^(1/3)=~10.627%!
Here is a Geometric Mean Calculator
For any of You Math Nerds , Its Formula is
where n is the total number of values and xi (x2, x1, ... ,xn) are the individual numbers in the data set. The formula is equivalent to:
In other words: It's the nth root of the product of n values.
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International Mathematical Olympiad
The International Mathematical Olympiad (IMO) is an annual six-problem, 42-point mathematical olympiad for pre-collegiate students and is the oldest of the International Science Olympiads.The first IMO was held in Romania in 1959.
License: Creative Commons Attribution-Share Alike 3.0 (CC BY-SA 3.0)
Image Source: https://en.wikipedia.org/wiki/File:Geo_prob_diagram.svg
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Dynamic light scattering (DLS) results are often expressed in terms of the Z-average. The Z-average arises when DLS data is analyzed by the use of the technique of cumulants (1). Since the calculation of the Z-average is mathematically stable, the Z-average result is insensitive to noise, and that makes it a preferred DLS size parameter. The purpose of this document is to clarify the meaning of this value.
Do you need to determine Z-average size? Take a look at the nanoPartica SZ-100V2 for a description of a world class tool.
The Z-average can be expressed as the intensity based harmonic mean (2,3) and is shown by the equation below:
Here, Si is the scattered intensity from particle i and Di is the diameter of particle i. Note that the result is in the form of a harmonic mean. Since this mean is calculated from the intensity weighted distribution, leading to the statement that the Z-average size is the intensity weighted harmonic mean size. For the case of sufficiently small particles known as Rayleigh scatterers, Si ~ Di6. Therefore, the Z-average can be approximated as:
There are two points about the use of the term “Z-average.” The first is that the use of the term Z-average in DLS does not match the use of the term when one is using light scattering to analyze polymers. The second is that one occasionally finds other notation, such as xDLS or dDLS. Even so, “Z-average” is the most common term.
In Figure 2 we illustrate the Z-average with a calculation showing a lognormal size distribution. A volume weighted differential size distribution is shown in blue. A discussion of different distribution types can be found in HORIBA TN154.
The example distribution’s median (Dv,50) size is indicated as 100 nm. From this distribution, we calculate the scattered intensity for each particle size (4). This intensity based distribution is then plotted in green. Finally, the harmonic mean of the intensity-based distribution is indicated at 97 nm. Note that the Z-average size is close to, but does not equal Dv,50.
The Z-average size value is calculated by the methods of cumulants (1). Since this technique relies on numerically stable least squares fitting, it is relatively insensitive to experimental noise.
In cumulants analysis the baseline subtracted autocorrelation function, C, is treated as an exponential decay of the following form:
Here, C is the baseline subtracted autocorrelation function and τ is delay time. Values for A, Γ, and µ2 can be readily obtained by a least squares fit. One then finds the intensity weighted average diffusion coefficient Dt,avg. with the relation Γ=Dt,avg. q2. Here q is the scattering vector given by q= (4πn/λ)sin(θ/2). The refractive index of the liquid is n. The wavelength of the laser light is λ, and scattering angle, θ. Finally, one uses the Stokes-Einstein relation to go from Dt to Z-average particle size, Dz.
Unfortunately, the weighting of the average is somewhat convoluted. Recall that the decay constant is proportional to the diffusion coefficient. So, by DLS one has determined the intensity weighted diffusion coefficient. The diffusion coefficient is inversely proportional to size. Therefore, the “Z-average size” is the intensity weighted harmonic mean size.
Despite the convoluted meaning, the Z-average size increases as the particle size increases. Therefore it provides a reliable measure of the average size of a particle size distribution. Also, it is easily measured. For these reasons, the Z-average size has become the accepted norm for presenting particle sizing results by DLS.
The HORIBA SZ-100V2 Nanoparticle Analyzer also presents size measurement results as a distribution table and graph and calculated mean diameter or diameters for multi-modal distributions. The methods behind those calculations are beyond the scope of this work.
(1) Koppel, D.E. “Analysis of Macromolecular Polydispersity in Intensity Correlation Spectroscopy: The Method of Cumulants” J. Chem. Phys 57 (11), pp 4814-4820, 1972.
(2) ISO 22412:2008 Particle Size Analysis – Dynamic Light Scattering
(3) Thomas, J. C. “The determination of log normal particle size distributions by dynamic light scattering” J. Colloid Interface Sci. 117 (1) pp 187-192 (1987)
(4) Here the Rayleigh-Debye-Gans approach is used and a larger average particle size is chosen to illustrate the regime where the approximations in equation 2 do not apply. This calculation is for particles in water, a 532 nm laser, and a 90 degree scattering angle.
Do you have any questions or requests? Use this form to contact our specialists.


A number that comes up frequently is the “what is the percentage of US land needed to make all our electricity with PV?”
The answer is about 0.7%: approximately a square 160 miles on a side (or 25,700 square miles); or 260 km on a side (66,800 km2).
The assumptions needed to calculate this are:
- The efficiency of the PV system (because that defines the area needed)
- The fraction of land the modules cover within the deployed system (packing factor)
- The output in kWh per installed W, which depends on the sunlight, tracking or not, and other losses within the system.
These numbers can vary quite a bit. For example, system efficiencies are between 5% and perhaps 15% at this time, and as they evolve, will almost certainly rise. Traditionally one is safe to choose 10% as the system efficiency, knowing full well it is likely to be better. (more…)


So I do not know what “Core Math” is. However I have seen it as the butt of a few jokes. So I will just toss out what I think the core of the country’s math problem is. Let’s just say we have one third of a billion people in this country. Additionally our national debt is twenty trillion dollars. Admittedly round numbers, but close. That comes out to a staggering sixty thousand dollars of debt per person. Compare that with the debt of other nations.


MathWorks offers students and teachers to have MATLAB with discount.
WHAT IS MATLAB?
MATLAB ,which is abbreviation of matrix laboratory, is a numerical computing environment and fourth-generation programming language developed by MathWorks. It is a perfect software with capabilities of matrix manipulations, implementation of algorithms, interacting with other programs written in other languages such as Python, Fortran, C , C++ and Java, creating graphics of functions and data, creation of user interfaces and more.
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Visit this link and select “For Educators” or “For Students” to explore MATLAB for students or educators. If you are a student, visit this link to get MATLAB. In that page, you can choose one of MATLAB and Simulink Student Suite including MATLAB, Simulink, and 10 of the most widely used add-on products, and MATLAB Student(unbundled) including MATLAB only. On the other hand MATLAB and Simulink Student Suite costs $89 but MATLAB Student costs $45. If you are an educator visit this page to get details of plans for educators.
- MATLAB and Simulink Student Suite includes MATLAB, Simulink, and 10 of the most widely used add-on products which are Symbolic Math Toolbox, Statistics and Machine Learning Toolbox, Optimization Toolbox, Control System Toolbox, Signal Processing Toolbox, DSP System Toolbox, Image Processing Toolbox, Data Acquisition Toolbox, Instrument Control Toolbox, and Simulink Control Design. Also it is $89.
- MATLAB Student includes only MATLAB and costs $45.


PLESD believes in using multiple assessments to determine how students are performing and how to best meet the needs of our students. There are three levels to these assessments.
The State of California mandates that all students in 2nd - 8th grade take a State Assessment each year through the Standardized Testing and Reporting (STAR) program. For almost all of our students they will take the California Standards Tests (CST). Fourth and seventh grade students also take the California Writing test. A limited number of students who qualify for Special Education are eligible to take alternative assessments, the California Alternate Performance Assessment (CAPA) or the California Modified Assessment (CMA). Please see the assessment calendar for the dates.
The district will mandate that all students take a district assessment in English Language Arts and Math each year. At this time because of the ongoing mathematics adoption, only 6 - 8th grade students will need to take the math assessments each trimester. All 1s t - 8th grade students will take the Houghton Mifflin California Summative tests each trimester. There will be a 2 week window that students may take the test each trimester to best allow the teachers flexibility in planning and implementing their curriculum. The results must be entered into the Edusoft program by the last day of the 2 week window. The 2009-2010
ELA assessment dates are:
Trimester 1- 10/26-11/6
Trimester 2- 2/22- 3/5
Trimester 3- 5/17-5/28
The results of these assessments will be used by teachers, grade level teams, and administration to best develop an academic program for our students. It will be an expectation that sites hold data meetings to analyze successes and areas of improvement.
It is expected that teachers use multiple assessments on a regular basis to continually monitor the progress of their students. These assessments can be textbook created or teacher created.
The following curriculum has been adopted by the district:
o K – 5 Math Learning Center; Bridges Mathematics, (Adopted 2016)
o 6 – 8 Houghton Mifflin Harcourt; Big Ideas, (Adopted 2016)
· Science –
o K – 5 McGraw Hill, CA Science (Adopted 2007)
o 6 – 8 McDougal Littell, CA Middle School Science Series (Adopted 2007)
· History-Social Science
o K,1 & 5 Houghton Mifflin (Adopted 2006)
o 2 – 4 McGraw Hill, California Vistas (Adopted 2006)
o 6 – 8 McDougal Littell, CA Middle School Social Studies Series (Adopted 2006)
· English/Language Arts
o K – 5 McGraw Hill, Treasures (Adopted 2011)
o 6 – 8 Holt, Literature and Language Arts (Adopted 2012)


Scott is an ESG analyst in the Multi Asset & Income team. Before joining Baillie Gifford in 2022, he was an associate analyst for the Responsible Investing team at T. Rowe Price. Prior to this role, he was a Senior Portfolio Analyst in the Fixed Income Division both in London and Hong Kong. His earlier experience includes working at Lloyd's of London as an actuarial analyst and at Lloyds Banking Group in a similar role. Scott earned a B.Sc. (with honors) in mathematics and financial economics at the University of Dundee. He is a CFA charter holder.


An illustrated counting book in which each two-page spread contains a numeral and a corresponding set of objects and animals to be counted.
|Statement||[text, Josep M. Fité ; illustrations, Luis Rizo.|
|Series||Math for children|
|Contributions||Rizo, Luis. ill.|
|LC Classifications||QA113 .F513 1998|
|The Physical Object|
|Pagination||27 p. :|
|Number of Pages||27|
|ISBN 10||0382398815, 0382398823|
|LC Control Number||96044408|
I started to read this book to her like a typical picture book, As we get to each number, I have her read the numbers and I read the text. I use this as a form of number recognition. If you are looking for a way to help your little one learn to count independently I would not recommend this by: 1. The Character of Numbers. The Book of Numbers is composed of narrative, legislation, and archival records. Its narrative begins at the point where Exodus leaves off. (Leviticus, which interrupts the flow of narration, consists almost entirely of legislation independent of historic precedent–with the exception of Lev. )Exodus ends by relating the erection of the Tabernacle on the first day. There are so many wonderful children’s books out there to help children learn various math concepts. Here are our favorite children’s books about counting and numbers!. Follow our Book Lists and Book Sets board on Pinterest!. Because we love integrating math with literature (we actually love integrating everything with literature!), I can’t wait to share some of our favorite math themed. Recently, I created some printables designed to help kids with numbers and counting. I assembled them into a book that will improve number recognition, counting skills, word recognition and even fine motor skills. All you need for this fun math activity is a copy of the book which you can download for free below and some dot stickers which I purchased at the dollar store.
26 rows Learning About Numbers is a Sesame Street video compilation, originally released . This free, printable dot counting book pictured above is available here. The free, printable dot counting book is available on the blog here. Glue Numbers. Learn how to make tactile number cards with glue that will help your students learn and retain numbers. Directions can be found on the blog HERE. Fishing for Numbers Game Freebie. Published on I Love It When It Rains. Sesame Street: Love. Licensed to YouTube by. The Orchard Music (on behalf of ABC Music), and 2 . Numbers contains many spiritual and moral lessons, and it is a book of testing and faith. We can learn such lessons as showing gratitude instead of grumbling and complaining, accepting God’s appointed leadership and following God’s instructions.
There are numerous spiritual lessons to be learned from the fourth book of the Old Testament. While many Christians may have given up on reading through the OT by the time they get to Leviticus and Numbers, perseverance is vital. This book is actually a gold mine of . See and discover other items: kindergarten books, color by number for kids, counting books for toddlers, number books, toddler activity, Best learning numbers for toddlers There's a problem loading this menu right now/5(73). How to choose a lesson about numbers from the list? When you have decided which lesson you want to view just click on the lesson of your choice. All lessons about numbers. Click on the links to choose the lesson. English Numbers 1 to learning cardinal numbers. Ordinal numbers ranking English lesson. learning Numbers 1 - 10 English lesson. 1. Recognition of numbers supports the development of other number skills, such as counting. For example, one of the most important ideas about counting that many children do not develop is this: The last counting word tells how many. Children will count three objects, but then, when asked how many, will re-count. But if they recognize groups.


Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have motivated the neural ordinary differential equations (neural ODE) architecture which garnered a lot of interest in the Machine Learning community. A widely established claim is that the Neural ODE is the limit of ResNets as the number of layers increases. A collaboration effort between InstaDeep and the University of Oxford challenges this claim by investigating the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. The conclusive research paper, the company’s first-ever submission to this conference, has been accepted to the renowned International Conference on Machine Learning (ICML) 2021 in the form of a short presentation at the event and for publication in the conference proceedings.
Significantly different scaling regimes
Our results show that ResNets do have a limit as the depth increases, however, we observe the existence of scaling regimes can be significantly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, or a stochastic differential equation (SDE), or neither of these.
These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.
Let’s take a step back and look at the methodology behind the findings. ResNet is a favourite among Deep Learning architectures that has led to huge improvements for computer vision and speech recognition especially . Below is a view of the architecture of a basic block of a residual network: it adds a convolutional transformation (\(A_k\) and \(\Delta_k\)) of the hidden state together with a skip connection \((F_k)\) of the same hidden state.
Stacking basic blocks together, we obtain below a generic representation of the residual neural network architecture for the CIFAR10 dataset. It takes as input a 3x32x32 tensor encoding an RGB image and outputs a vector in ten dimensions, where each dimension represents the probability that the image belongs to a given class.
ResNet improved standard feedforward neural network architectures (FFNN) for the following reasons:
- Gradient vanishing/explosion: adding a residual (skip) connection helps stabilize the spectral norm of the gradient of the output with respect to the hidden states. Hence, we are able to go significantly deeper with ResNets than with FFNN (1000 layers vs. 30). As some problems require depth to improve accuracy, ResNets improve the state of the art on standardised datasets.
- Information theory: At initialisation, all the weights of the ResNet are close to 0 so the input-output map is close to the identity function, as opposed to the zero function for FFNN. Hence, we don’t lose any information at initialisation, and training will be about learning a more useful representation of the data. It is arguably easier than disentangling the feature space as the FFNN must do.
Introducing a general framework to encapsulate neural ODE assumptions and beyond
Over the years, researchers started to link ResNets to differential equations. They argue that a ResNet is in fact a numerical scheme of a given differential equation, which is a well-understood topic studied by mathematicians since Euler (1750) and which motivated new deep learning architectures . This search culminated in the now-famous neural ODE model  that uses ODE schemes to train their model. We write below the (simplified) equations for the ResNet (left) and for the neural ODE (right).
To people familiar with differential equations, the link between the two equations only holds under particular conditions  that may not be satisfied in practice (see below). We may force these conditions at initialisation, but the weights trained with stochastic gradient descent (SGD) might not satisfy these conditions anymore.
The main contribution of the paper is to introduce a more general framework for the trained weights of ResNets that encapsulates the neural ODE assumptions above, but also other cases. We test our hypothesis on synthetic and real-world datasets. We found that depending on the activation function, the shape of the trained weights for a very deep network (large L) looks drastically different. Let’s consider an example:
On the left, the non-linear activation of the ResNet is tanh, and on the right ReLU.
If you are not familiar with stochastic calculus, the plot on the right-hand side looks pretty much like white noise, i.e. the “derivative” of Brownian motion. We put derivative in quotation marks because Brownian motion is a rough function, so it can’t be differentiated in the traditional sense, but nonetheless has a derivative in the distributional sense. To “integrate” white noise, we shall take the running cumulative sum of the plot on the right-hand side. We get a process that now looks like a standard Brownian motion!
In the research paper, we lay down two general assumptions that describe the behaviour of trained weights of ResNets as observed above. We prove the convergence of their limiting equations, which can be either the neural ODE, a linear ODE or a linear-quadratic SDE (below).
So what are the implications for practical training of ResNets? Knowing the scaling limit of trained weights will help you choose your initialization strategy. Also, training the limiting equation above in the neural ODE fashion will guarantee a good accuracy because of its clear connection with ResNets, and a reduced-form architecture with a low memory footprint.
Is this the end of the story? Of course not! Our results hold for fully connected networks, but we have observed that convolutional networks have a different scaling behaviour, such as a sparse limit. More on this to come so keep an eye on InstaDeep’s research space!
Research collaboration with University of Oxford
The ResNet paper is a result of close collaboration with InstaDeep’s research partner, University of Oxford. As a committed sponsor of Oxford’s Mathematics PhD programme, InstaDeep is currently supporting two PhD students with a scholarship. As part of their thesis, they both collaborate with InstaDeep’s R&D team on advanced research, such as this paper and others submitted to NeurIPS 2021. One of InstaDeep’s board members, Rama Cont, is also a Professor of Mathematics and Chair of Mathematical Finance at the University of Oxford.
As ICML is one of the three primary conferences in AI alongside NeurIPS and ICLR, this first acceptance to ICML is a true affirmation of InstaDeep’s boundary-pushing research initiatives. This year’s ICML is the thirty-eighth conference of its kind and runs from Sunday 18th July through to Saturday 24th as an online conference.
You can read the research paper in full on Arxiv.
The code for this paper can be found at https://github.com/instadeepai/scaling-resnets.
: He, K., Zhang, X., Ren, S., and Sun, J. Deep Residual Learning for Image Recognition. In 2016 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016.
: E. Haber and L. Ruthotto, Stable architectures for deep neural networks, Inverse Problems, 34 (2018).
: Chen, R. T. Q., Rubanova, Y., Bettencourt, J., and Duvenaud, D. K. Neural Ordinary Differential Equations. In Advances in Neural Information Processing Systems (NeurIPS) 31, 2018
: Thorpe, M. and van Gennip, Y. Deep Limits of Residual Neural Networks, 2018.


Heavy Duty Calculator
“The First, Last and Only Superior Calculator in the World”
This general-purpose calculator for simple and complex calculations uses the entire screen to display its content. You can click on old results to select, instead of re-typing them.
It supports fractions, repetitive parts, BIG numbers, and all these options combined. If the calculation gets lengthy, you will always receive feedback on the calculation process.
Normal & Scientific Calculations, Fractions, Repetitive Parts, BIG Numbers
Expected Release: October 2021
BIGGER is Better:
You can save the data on your screen for later use, export it or copy to the clipboard as text or as image, you can opt for just one line or the whole screen.
If you copy the data on the screen above as text to the clipboard, you will get:
1 + 1 = 2
2 ^ 3 = 8
8 ^ 8 = 16777216
1 / 3 = 0, = 1/3
1/3 ^ 2 x 0, = 0, = 2/27
100 ! = 2 ^ 97 x 3 ^ 48 x 5 ^ 24 x 7 ^ 16 x 11 ^ 9 x 13 ^ 7 x 17 ^ 5 x 19 ^ 5 x 23 ^ 4 x 29 ^ 3 x 31 ^ 3 x 37 ^ 2 x 41 ^ 2 x 43 ^ 2 x 47 ^ 2 x 53 x 59 x 61 x 67 x 71 x 73 x 79 x 83 x 89 x 97
5 types of divisions
There are 5 types of divisions:
Decimal division: no repetitive parts, goes on until finished or until the maximum number of decimals is reached.
Repetitive part division: goes on until finished or until the repetitive part is found.
Fraction division: the result is displayed as a fraction.
Remainder division: the result is displayed as a whole number + remainder, like 2 / 3 = 0 REM 2.
Plus the default division: mixed-mode
Do you want to have even more fun? Then start with BIG numbers. Not all calculations in this application can work with BIG numbers.
This is the most expanded version of the input panel:
The buttons for BIG fun with... and BIG Numbers support the big numbers.
The small fun section with functions like sine and cosine and the powers containing decimal numbers only give small fun with small results. This is like working with a normal calculator - you will get the same number of digits.
How BIG is BIG? The program crashes when the consumed memory is about 1 Gb. It will take a couple of hours until this condition is reached, depending on the type of calculations you're working with.
We have BIG numbers and we have fractions. But what about BIG fractions? Well, we can assure you that this calculator has BIG fractions too! Suppose you want to create a fraction with the result of 9999! as nominator and the result of 10000! as denominator, like:
Can you do that ? Yes you can!
How to view or edit your Biggies
Once you've created a BIG number or fraction, you can view it by clicking on the edit button. You'll find this button on the right side of the number:
How to use the Heavy Duty Calculator as a Tool Window
In some situations you just need a small always-on-top window with no buttons to perform your calculations on, while having another document open.
Something like this:
To get a window like this, go to Options
Within Options, you are able to create two types of Views: Normal View and Small View. The application can switch automatically from one view to the other, depending on the current screen size, via:
In this case, when the total surface covered by the application is less than 40 % of the total screen surface, the application switches to Small View.
Both Normal View and Small View can be customised.
In this example, if you resize your calculator window to a size less than 40 % of the surface area, the calculator's view will change from Normal View with buttons, captions, calculation numbers, bigger font to Small View, without buttons, smaller font, always-on-top, etc.
To use the Calculator without buttons, you'll need to use keyboard shortcuts for operations that are non-standard.
The Options window has the following button:
Showing the following window:
Here you can define your own shortcuts.
Export to the Clipboard as Image
When you want to display your calculations in another program, like Word, you can easily copy and export data from the calculator.
Via Edit - Copy last Line as Image to Clipboard and Copy Screen as Image to Clipboard, the calculation or screen can be copied as an image to the clipboard. This will result in an identical view as is shown within the calculator.
For example, add the fractions 1/2 and 1/3 = in the calculator, then copy line as image, paste it in Word, you will get:
This is the identical view as appeared on your calculator screen.
Export as .txt file
Via the button
Will the entire screen be copied to a .txt file. The same rules apply as under Export to Clipboard as text


One fifth of a piece of paper ( 80 gsm a4 paper weighs 4. 035274 of an ounce to 6 decimal places ( we need 28. 349523 grams to make an ounce) a kilogram is about: the mass of a liter bottle of water; very close to 10% more than 2 pounds ( within a quarter of a percent) very very close to 2. 205 pounds ( accurate to 3 decimal places) 7 apples. what weighs 1 mg? wiki user: 11: 33. a feather, a paper clip and a us dollar bill each weigh one. gram on average, one milligram is 1/ 1000 of one gram.
on earth, 1 milligram what of mass weighs 0. super green malay kratom powder. asked in math and arithmetic, units of measure, weight and mass how many milligrams are in one milligram? there are very few common objects that what weighs a milligram weigh 1 milligram. however, if you live in the us a new one dollar bill weighs about a gram, so if you can imagine a dollar bill being cut into 1000 pieces. milligram definition, a unit of mass or weight equal to one thousandth of a gram, and equivalent to 0. abbreviation: mg see more. a centigram is one hundredth of a gram.
a milligram is one thousandths of a gram. this means a centigram weighs more than a milligram. milligrams are very small measurements of solid weight in the international metric system. specifically, a milligram is one- thousandth of a gram; to put it in concrete terms, the common mosquito weighs around 2 milligrams. in imperial ( us) measurements, there are more than 28, 000 milligrams in a single ounce. a milligram is a very small unit of measurement in the metric system, which means only specific ( and tiny) things can be reasonably measured with it. it also requires very precise scales to accurate weigh out a milligram. so what are some things that weigh a milligram? here are some common things that weigh a milligram: a small feather. so, a milligram is how much something weighs, because it ends in grams.
one gram is about the weight of a penny or a big paperclip. so, you are looking for something that weighs 1/ 1000 of that, or at least less than a penny. what are some things that weigh less than a penny that you want to know the weight of? here' s a few hints. a milligram is a measure of what mass, not of weight. so there is nothing that weighs 1000 milligrams.


摘要： The Gaussian Mixture model (GMM) will be used to detect different moods in the stock market. The GMM model will be applied twice: first using price data, and subsequently with macro-economical data.
▲Photo by Element5 Digital on Unsplash
Over the last decade, the stock market has become increasingly accessible to the average layman. Moreover, the volume of money entering and exiting the market each day is at an all-time high.
As an investor, you can hone your acumen for when to buy or sell in many ways. A common approach is consulting friends or fellow investors, who quickly inundate you with conflicting opinions.
I will approach this golden, money-making question — when should I buy or sell? — with rigorous mathematical tools rather than blunt opinions. However, it is crucial to note that ultimately, people’s opinions and speculations drive the market; the mathematical tools will hopefully capture this mood or opinion.
I will demonstrate how the Gaussian Mixture Model can be used to help determine when money should enter or exit the market.
Mathematically, the mood of the market at any given time can be referred to as the “market state”. The mood can typically be interpreted as any number of concepts such as a bear or bull market; the degree of volatility; fire and ice, etc.. The way we name each state is far less important than clustering similar trading days together based on some shared characteristics.
Due to the fact that there is no clear definition for the mood of the market — and therefore, no response variable to represent the market — an unsupervised machine learning model is best to classify the market into states.
Supervised vs Unsupervised machine learning
The difference between the two approaches is the use of labeled datasets: supervised learning uses labeled input and output data, whereas an unsupervised learning algorithm does not. A labeled dataset is where the response variable, or the variable you are trying to predict, contains either numerical or categorical values. Hence, when you are using a supervised machine learning algorithm, the prediction variable is clearly defined. One very simple, but powerful, example of supervised learning is linear regression.
Gaussian Mixture Model (GMM)
The gaussian mixture model is the overlapping of multi-normal distributions in p-dimensional space. The dimension of the space is generated by the number of variables. For example, if we had one variable (S&P 500 returns), the GMM would be fit based one dimensional data. The GMM can be used to model the state of the stock market along with other financial applications. One characteristic from the stock market returns, is heavy tails, which are generated from days of high volatility. The ability to capture highly volatile days in the tails of the distribution is important for capturing information in the modelling process.
The above graph represents some multimodal data with 4 clusters. The Gaussian mixture model is a clustering type of model used to label data.
One main benefit of using the GMM for unsupervised clustering is the space encompassing each cluster can take on a ellipse shape. Gaussian mixture models take not only means into account but also co-variance to form a cluster
An advantage of the GMM approach is that it is entirely data-driven. The data given to the model will form the clusters. Importantly, the labelling of each cluster can be numerical, as the data drives the underlying characteristic, rather than human opinion. However, it can be hard to put intuition behind the resulting market conditions.
Mathematics of the GMM
The goal of the Gaussian Mixture Model is to assign data points to one of n multi-normal distributions. To do this, an Expectation Maximization (EM) algorithm is used to solve the parameters of each multi-normal distribution.
- Step 1: Randomly initialize the starting normal distribution parameters
- Step 2: Preform the E-step or the expectation step
- Step 3: Preform the M-step of the maximization step
- Step 4: Calculate the log likelihood of the joint probability of (Data given fraction of each state , mean , covariance)
- Step 5: Repeat steps 2–4 until the log-likelihood converges
The probability that each data point belongs to a certain cluster is given below. Based on the indexing, we are given a probability of each data point belonging to each induvial cluster. The size of the matrix will be the number of data points by number of clusters. Since it is a probability matrix, the values will sum to 1 under index ‘i.’
The interpretation is as follows: the index i represents each data point or vector. The index c represents that given cluster; if we were to have three clusters (c) would be 1 or 2 or 3.
▲Multivariable Gaussian Formula
The multivariable Gaussian formula is given where mu and sigma are parameters that require estimating using the EM algorithm.
An additional key concept is that each gaussian distribution in our space is unbounded and overlapping with one another. Based on the location of the data point, a probability is assigned to it from each distribution. The probabilities for each data point belonging to any of the clusters will sum to 1.
Lastly, since the EM algorithm is an iterative process, we need to gauge the progress at each step to know when to stop. To do this, we use the log-likelihood function for the model to measure when our parameters are converging.
Implementation of the GMM
This section will be broken-down into two sections each representing an application of the GMM.
- Classification of the S&P500 returns into three states using a GMM
- Classification of the American economy using Macroeconomics data fit with a GMM
Section 1 : Classification of the S&P500 returns into three states using a GMM
The first section will use daily return data from the S&P500. The data was received from yahoo finance.
Firstly I need to determine which factors to consider for detecting which market state we may be in. Secondly I need to determine how many states would best represent the market environment. Here I will assume three states — BEARISH , NEURAL, BULLISH.
I will be using the log returns of the S&P500 to fit the GMM.
The python implementation for the GMM on one dimensional data is quite simple.
The States for the Gaussian mixture model are found using the Gaussian Mixture model from sklearn and the input data is the daily return for the S&P500.
From this above analysis it may also be worth investigating two states.
One issue that may arise is convergence. Not in the sense of meeting the criteria of a certain threshold in the EM algorithm, but rather based on the initial conditions, different distributions may take shape depending on the run. Further investigation will be required here.
Section 2: Classification of the American economy using Macroeconomics data fit with a GMM
To begin and demonstrate the GMM visually, I will use two-dimensional data or two variables for simplicity. Each corresponding cluster is a multi-normal distribution in three dimensions. In this example, the first dimension is the inflation value (let’s call this X), the second dimension is the S&P500 monthly % return (let’s call this Y) and the third dimension is the joint probability of X&Y. In other words given a certain combination of X and Y what is the probability.
The graph demonstrates one of the main benefits of the GMM over other clustering algorithms. The normal distributions can produce the ellipse shape and this property comes from the covariance matrix.
Here the GMM was able to produce three different states given the two dimensional data.
Lastly we can move on to three variables. However, it should be understood that to create a meaningful model, more variables should be considered. In reality, a bevy of different indicators comprise the American economy and its performance.
We can continue and incorporate any number of dimensions, however before you go to n dimensions it is important to understand the correlation structure of the data you are feeding the model. Here, it would make sense to compare to the GDP of the American economy.
This was a simple introduction to how we can apply the GMM to financial markets and the economy. Bear in mind, this was simply an introduction and extensive research is being conducted in this field. The GMM method was introduced to improve the robustness of classifying stock market price data into states.
My recommendation for modelling the market regimes would be to use a GMM and aligning time data to understand the connection between market conditions and the economy
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In partnership with eMedia Investments, the Department of Basic Education will be broadcasting educational support for learners and teachers on the Openview HD (OVHD) platform – channel 122. This channel is available free of any subscriptions and will broadcast initially for a period of six months from 1 April to 30 September 2020.
The proposed daily schedule for the first week of the broadcast is as follows:
- The focus of the first week of the broadcast is to revise Term 1 topics.
- From 12:00 am to 7:00 am there will be revision lessons for Grade 12 learners. We cover only one subject per day to facilitate an easy recordable block.
- The subjects will rotate through a seven-week period. In the first week, Maths is on Monday but in week 2 Maths moves to Tuesday and so on.
- Between 7:00 am to 8:00 am it’s time to learn a new Indigenous African language. Each lesson is half an hour.
- From 8:00 am till 12:00 noon, the schedule is dedicated to Grade 12 learners. You can catch 60-minute lessons in Maths, Physical Sciences, Life Sciences, English (FAL), Accounting, Economics, and Geography. The focus of these lessons is initially on Term 1 topics. If you master the concepts in these lessons, you’ll be ready for Term 2 lessons which will broadcast in future weeks.
- From 12:00 pm till 2:00 pm we have 60-minute lessons for Grade 11 learners in Maths, Physical Sciences, Life Sciences, English (FAL) and Accounting.
- From 2:00 pm till 4:00 pm we have 30-minute lessons for Grade 10 learners in Maths, Physical Sciences, Life Sciences, English (FAL) and Accounting.
If you’ve missed a lesson in the morning or want to re-watch a lesson you can catch the repeat from 4 pm to 12 midnight. The lessons from 4:00pm – 8:00 pm is for Grade 12 learners, 8:00pm – 10:00 pm for Grade 11 and 10:00 – 12:00 is for Grade 10. The topics covered are aligned to the CAPS and the Annual Teaching Plan (ATP), and we will start with topics at the beginning of the ATP.


Luke Robitaille isn’t daunted by difficult math problems. In fact, when he was 4 years old, he often asked his mother to write long-division equations so that he could solve them.
By the way, the kid won the competition again and is on TV this morning. Mom says he's the third person to win the contest twice.
On Monday, Luke, 13, took first place in the Raytheon Mathcounts competition — also known as the national math bee — in Orlando, Fla. He had finished second last year.
The final question: “In a barn, 100 chicks sit peacefully in a circle. Suddenly, each chick randomly pecks the chick immediately to its left or right. What is the expected number of unpecked chicks?”
He gave the correct answer, 25, solving the problem in 0.9 second.
“I was surprised that I won,” he said. “I kind of figured that was the wrong answer.”
Luke said he competed on the local and state levels before advancing to the national competition against 224 middle school students from the United States, U.S. territories and schools serving employees of the U.S. state and defense departments.
Luke will receive a $20,000 college scholarship and a free trip to U.S. Space Camp for winning the competition.
On Wednesday morning Luke and his parents, Mary and Rob Robitaille, flew to New York, where he will be a guest on Friday’s “Live with Kelly and Ryan” show.
Besides being interviewed, Luke said he expects a math challenge from show hosts Kelly Ripa and Ryan Seacrest.
Luke’s parents said they decided to home-school him when they saw that traditional school probably wouldn’t be a good fit.
Mary Robitaille said she quit her job as a writing tutor to help home-school her son.
“We try to meet his needs,” she said. “We wish that we spoke the language of math, but he has to talk to other people. We try to understand, but he is beyond us.”
Luke started auditing college classes when he was 8. A doctoral student at the University of Texas at Arlington introduced him to math journals.
When his parents asked him what he wanted to do while on a family vacation, Luke said he wanted to visit a math library, so they took him to the one at the University of Texas at Austin.
Rob Robitaille said he is in awe of his son.
“I feel like I can do something great with my life. I feel inspired by Luke and his accomplishments,” he said.


It deserves mention that an Australian, Terence Tao has won the Fields Medal for mathematics becoming the first Australian to win the prize. Up to four Fields Medals are handed out once every four years, and it is the mathematics equivalent of the Nobel Prize.
AT THE age of two, Terence Tao could already add up and subtract using the magnetic numbers his parents stuck on the fridge.
At eight, he scored better than 99 per cent of 17-year-old prospective university students on an international aptitude test for mathematics.
The Adelaide-born prodigy was appointed a professor at 24, and now, at 31, has become the first Australian to win a Fields Medal, the mathematics equivalent of a Nobel prize.
The award was presented in Madrid yesterday by Spain’s King Juan Carlos I at a congress attended by 4000 international mathematicians.
Its a bit difficult to work out what exactly he won it for as the Medal is not awarded for specific pieces of work. His website states a fairly broad area of mathematical interest, although it is suggested here that:
It is awarded for a body of work rather than a single achievement but Professor Tao is most recently celebrated for showing, with Ben Green of Cambridge, that there are long strings of prime numbers a constant distance apart, work that is important for the coding of information such as banking details.
Well done Terence.
Of further interest is the reason why Alfred Nobel chose not to make an award in Mathematics. The Fields Institute states:
The persistent rumor that Nobel did not establish a prize in mathematics because Mittag-Leffler had an affair with Nobel’s wife is certainly incorrect. Nobel never married. But the other version of this rumor, founded on hostility between Nobel and Mittag-Leffler, may be correct though there is no documentation to support it. Certainly there appear to have been ill feelings between the two men: according to a letter from J.L.Synge to H.S.Tropp [Tropp], Fields told Synge that this was the case, and Synge remarks that he later confirmed this himself in Sweden.
I do wonder if Maths (from a publicity perspective) would have been better following the path of Economics and giving a prize in memory of Alfred Nobel to be awarded by the Nobel committee and making everyone think they had a Nobel prize as well.
A better review of his work is on the UCLA news page
Tao was awarded the Fields Medal “for his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory.” In honoring Tao, the organization said, “Terence Tao is a supreme problem-solver whose spectacular work has had an impact across several mathematical areas. He combines sheer technical power, an other-worldly ingenuity for hitting upon new ideas, and a startlingly natural point of view that leaves other mathematicians wondering, ‘Why didn’t anyone see that before?’


Now that you have performed all the calculations, see a graphical representation of gasoline prices across the USA Here
The calculators above assume the following conversion amounts:
Litre = 0.264 gallons(US)
1 gallon (imp) = 4.54609188 Litres
1 gallon (US) = 3.7854118 Litres
$1 US ~ $0.80263 CDN
$1.2459 CDN = $1 USD
at $1.059 CDN$/litre, this results in about US
$3.22 per us gal at a conversion of 1.2459 as of May 2015
looking back: US$3.72/USGAL back calculates to CDN$98.27/litre at 0.978767 CDN/US dollar conversion rate as of June 19, 2011 and we were paying about $1.35/litre at the time!
Update: as of December 12, 2012 in southern Ontario we are experiencing a
sudden drop in gasoline prices at the pump, today's price is only CDN$1.185
per litre and our CDN dollar exchange rate is above part at $1.01 USD per
CDN$ which results in US
$4.40 per us gal as
US price of gasoline is about US$3.65/USGAL back calculates to CDN$0.9739/litre at 1.01 US/CDN dollar conversion rate as of December 12, 2012
see the current US and Canadian Gasoline prices
|Year - Month||USD -> CAD||CAD -> USD|
US$/CAN$ closing rate summary
|Date||USD -> CAD||CAD -> USD|
|Past 12 months|
|From 1950 to present|
|Monthly closing, past 12 months|
Rates in above table from Bank of Canada website
Below are the exchange rates from 2007 and 2006
October 1950 - present
|1 CAD||0.6179 USD|
|1 CAD||1.1030 USD|
|1 CAD||0.9817 USD|
|1 CAD||0.9865 USD|
|Low||2013-06-14||$1 CAN = $0.9817 US|
|High||2013-06-14||$1 CAN = $0.9865 US|
Rates equal the price of 1 U.S. dollar, in Canadian dollars.
Latest closing rate is updated at about 16:30 ET the same business day.
Other Calculators found on this website:The calculator below will determine your monthly mortgage payment (principal and interest)
|Mortgage Payment Calculator | Mortgage Qualifier-Eligibility Calculator | Income Required to Qualify Calculator | Amortization Table Creator | Land Transfer Tax Calculator|
How does the Bank of Canada Set the Prime Rate & Interest Rates?
view today's mortgage interest rates
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At this Mississauga, (Erin Mills, Churchill Meadows, Sawmill Valley, Credit Mills and / or Meadowvale ) Ontario, Canada Real Estate Homes and Property Internet web site you will find relevant information to help you and your family.
|You will receive valuable Real Estate information on a monthly basis - such as: where to find the 'best' mortgage interest rates, Power of Sale Properties and graphs of current house price trends. Plus, you will pick up ideas, suggestions and excellent real estate advice when you sell or buy your next home.
Read Past Newsletters before you decide


and minimal solutions of nonlinear Nabla dynamic equations,
Proceedings of the WSEAS International Conference on APPLIED
MATHEMATICS, (with Clayton T. Brooks) (referred journal),
study of eigenvalues of an impulsive differential equation
(with D. Reid), PanAmerican Mathematical Journal, 4 Volume
14 pp. 1-10.
and convergence of stochastic approximation procedures under
Markovian perturbations, (with G. S. Ladde) Differential equations
and Dynamical Systems (Editor: D. Bahuguna), Narosa Publishing
House, New Delhi, (2004), pp. 24-48. (This is a book chapter.)
of the generalized Verhulst equation and other related dynamic
equations, WSEAS Transactions on Mathematics, 4 Volume 2 p.
joint probability density functions of discrete time iterative
processes (with G. Ladde) Mathematics and Computers in Simulation
, 63, Issue 6, (2003) pp. 629-650.
quasilinearization technique for first order nonlinear problems
on time scales, (with B. Kaymakcalan), Dynamic Eqautions and
Applications 11 (2002) pp. 191-200.
solutions and monotone iterative techniques for some nonlinear
initial value problems on time scales, (with B. Kaymakcalan)
Nonlinear Analysis: Real World Applications, 4 (2003) pp.
of eigenvalues for Strum-Liouville boundary value problems
on a measure chain (with D. Reid), Computers and Mathematics
with Applications, 45 (2003) pp.1319-1326.
variety of differentiability results for a multi-point boundary
value problem, Special Issue of the Journal of Computational
and Applied Mathematics · Dynamic Equations on Time
Scales, 141/1-2, pp.237-248, (2002).
solutions of dynamic systems on boundary matrices, Proceedings
of Dynamic Systems & Applications, Volume III, 2001, p.
problems and continuous dependence for finite difference equations,
(with J. Ehme), Pan American Mathematical Journal, 2000, vol.10,
dependence on boundary matrices of first order differential
equations, (with A. Datta), Pan American Mathematical Journal,
1998, vol.8, no. 4, 59-66.
dependence on boundary matrices, (with Johnny Henderson),
Journal of Difference Equations and Applications, 1996,vol.
and convergence of large-scale stochastic approximation procedures
(with G.S. Ladde), International Journal of Systems Science,
1995, vol. 26, no. 3, 598-618.
Return to Research Page


There is nothing wrong with the straight
bet, or a single bet, on the soccer games, but choosing the parlay would
improve your winnings a lot. We have always been pig proponents to the
parlay betting, rather than simply placing multiple single soccer bets.
And if we look at the raw numbers and compare some wagering situations,
punters would clearly see the many advantages of parlay football
betting, compared to the straight bet.
To summarize, parlay betting is
wagering on the outcome of two or more sporting events, where each of
the event must be a winner in order for the punter to collect on the
Let's do some basic math and
compare the winnings of three single soccer bets to that of just one
parlay bet. Let's say you have decided to bet on three Premier League
soccer games and you have chosen the outcome of all three games to be a
victory for the home team. To make the math much easier, we will assume
that all home team victories would pay out on 1.50 odds. We have also
chosen to bet €10
on each game and all of the three soccer games finish as winners for us.
If we placed three
separate bets on every soccer game, we would have wagered the total of
€30 and got back €45 by winning all three bets 3x(10x1.50)=45, pretty
simple and straight forward. Now, let's say that instead of betting
singles, we went with a parlay bet and wagered the entire €30 on that
parlay. If all the games came out as planned, we would have won the
whopping €101.25, 30x(3x1.50)=101.25, since in parlay betting the
winnings are calculated by multiplying the odds by each other and then
by the money wagered. As you can see by simply choosing the parlay bet
we have more than doubled our return, as compared to placing three
course, the risk is also much higher than it would be with a single bet.
As we said earlier, the parlay wager would be a winner only when all
games part of the parlay are winners, i.e. if one of the three games
don't go as planned, we would have lost the entire amount. But
mathematically speaking, the parlay betting is a much better way to win
big while wagering small on the soccer matches.