Table of contents
The expression class used in iLand was originally developed for the Picus model and aims at a high performance for repeated executions. Expressions are parsed only once and converted to an internal "program" which can be executed with very little overhead. When using more complex mathematical functions (e.g. exp()), the overall performance is comparable to hard coded C++.
The meaning of a variable name within an expression depends on the context. There are three main cases:
- Expressions bound to "Objects" e.g. to Trees. In that case, the variable names are defined by the respective object. If an expression is bound to trees, one can use context sensitive variables like "dbh" or "volume" for trees. Depending on the context, this can be tree variables, resource unit variables, or sapling variables.
- named variables: the names of variables are fixed programmatically. E.g: a expression with two named parameters ("x", "n") to calculate a weight could be "x/n" or more sophisticated "x*x/n*n"
- unbound variables: In that case the name of the variable can be chosen freely. The value for the variable is set during the model execution and depends on the context. Example: the expressions for the calculation of biomass compartments (allometric equations) has one parameter (dbh). Valid expression are, e.g.: "0.1*dbh^2" or "0.1*d^2" or "0.1*fish^2".
Basically, expressions can consist of basic arithemtic operators, variables and functions. The basic operators +,-,* and / work as expected (incl. precedence rules). Additionally, the caret "^" can be used for power functions (e.g. x*x can be written as x^2). Parentheses work as expected (e.g. (a+b)*c is different from a+(b*c)).
Floating point numbers must use the dot (".") for constants (e.g. 0.001). The comma "," is used to separate arguments in function calls.
Expressions can be used to evaluate logical expressions, i.e. expressions with a result value of either "true" or "false". Operators for logcal expressions are "and" and "or". Logical expressions are typically used to filter or select from a set of objects based on a criterion. E.g.: using the expression "dbh>30 and (stress>0.5 or leafarea<1)" as a filter, would result in a list of large, but stressed trees.
Logical and "mathematical" operators can be used together: every non-zero value is evaluated as "true", zero (0) as "false". 'true' and 'false' are also available and internally converted to 1 and 0, respectively. Hence, a logical "not" can be expressed as ex
Expressions provide a basic support for constants. A constant is a system-defined name with a fixed value that can be used instead of the numerical value. Currently, the species names / IDs are available and linked to the numerical index of the species for the current run:
Therefore, you can use, e.g., 'species=Tsme' in a management-filter expression (having 'Tsme' as the ID of one tree species). Note, that no apostrophs are required. 'Tsme' is replaced with the numerical value (e.g. '1') during parsing time of the expression.
The general form of function is:
functionname(list of arguments)
Generally, mathematical functions are executed without checking for the validity of the arguments (e.g. division by 0, or tan(pi/2)).
|sin(x)||the sin of x, x as radians.||sin(x)|
|cos(x)||the cosine of x, x as radians||cos(x)|
|tan(x)||the tangens of x, x as radians||tan(x)|
|exp(x)||exponential function, e(1)=2.7182...||exp(-k*LAI)|
|ln(x)||the logarithm of base e, ln(2.7182...)=1||ln(x)|
|sqrt(x)||the square root of x (equivalent to x^0.5)||sqrt(x)|
|mod(x,y)||return the modulo (remainder) of x/y. e.g. mod(13,10)=3||if(mod(id,2), 1, 0)|
|round(x)||Returns the integral value that is nearest to x, with halfway cases rounded away from zero.||round(x)|
|min(x1,x2,...,xn)||returns the minimum value of the arguments. Argument count must be >1 and <10||min(x,0)|
|max(x1,x2,...,xn)||returns the maximum value of the arguments. Argument count must be >1 and <10||max(min(x,1),0)|
|if(condition, true, false)||logical if-then-else construct. if "condition" is true, the "true" is returned, "false" otherwise. E.g.: a abs()-function: if(x<0;-x;x). Note that both clauses are calculated in every case!||if(x<0;-x;x)|
|in(value, arg1, arg2, ... , argn)||returns true if value is in the list or arguments, false otherwise.||in(year,100,200,300)|
|incsum(fn)||when used in SQL like expressions (e.g., management, the function incsum cumulates its value over several calls. See the management functions mean and sum functions.||incsum(basalArea)<40|
|polygon(value, x1,y1, x2,y2, x3,y3, ..., xn,yn)||return is: y1 if value<x1, yn if value>xn, or the lineraly interpolated numeric y-value.||polygon(x, 0,0, 1,0.5)|
|sigmoid(x, type, param1, param2)||The value of "sigmoid" curve at x. The type of curve is designated by type with the two parameters param1 and param2. 0: logistic, 1: Hill-function, 2: 1-logistic, 3: 1-hill||sigmoid(x, 0, 10, 100)|
|rnd(from, to)||returns a uniformly distributed random function between from and to.||rnd(0,1)|
|rndg(mean, stddev)||returns a random number drawn from a Gaussian normal distribution with 'mean' as the mean value 'stddev' as the standard deviation.||rndg(0,1)|
- create an output only every 10 years:
To improve the calculation performance in certain situations, expressions can use precalculated function results to interpolate a function numerically. This works best for expressions with one variable and a defined range for the input, but also an implementation for expressions with two variables is available.
For complex mathematical expressions the linearized version is up to 10 times faster than the regular expression engine.
The linearization is globally enabled/disabled by the switch system.settings.expressionLinearizationEnabled in the project file. Note, that this feature must be explicitly enabled for each expression used in the source code.


It is a fortunate coincidence that Saturday is not just Pi Day but also Albert Einstein’s birthday. Museums and destinations across the country have created terrific ways for families to celebrate with pi parades, Albert Einstein look-a-like contests, pie eating contests, and interactive numbers games.
I think Mr. Einstein would smile at the assorted events created to honor the most memorable number sequence on the planet. If you are not following me, pi usually recognized by the Greek letter “π” is the symbol used in math to represent a constant — the ratio of the circumference of a circle to its diameter which is 3.14159265358…. and on it goes. The following events prove math can be fun for everyone and who doesn’t love pie.
Princeton, New Jersey is hosting a string of crazy events including an Einstein look-a-like contest and a Dinky Train ride with reenactors playing Einstein, his mother and their good friends.
Naturally MoMath, the National Museum of Math in Manhattan will begin the day’s festivities begin at 3/14/15 at 9:26 with a scavenger hunt through the exhibits and oodles of pi puzzles to be solved.
Any day at the Franklin Institute in Philadelphia offers exceptional rewards for families but the Museum’s National Pi Day celebration will add extra geekiness with pi reciting contests and a pie launch competition
Adler Planetarium’s daytime Pi Day activities include a pie eating contest, a parachuting pies challenge, and pie-in-the-sky solar observations.
At San Francisco’s Exploratorium the day begins at 9:26:53 and includes pi processional, light circles and pizza pie dough tossing.
If none of these work for you there’s always the excuse to bake a pie and do your own calculations per serving.
For the latest family travel news follow the Family Travel Files on Twitter (@FamTravelFiles)
Nancy Nelson-Duac, Curator of the Good Stuff


Book Title: Discovering Mathematics: Common Core, Workbook 7B
Publisher: Star Publishing
Discovering Mathematics Common Core Workbooks are designed for middle school students. Developed in collaboration between Star Publishing Pte. Ltd. and Singapore Math Inc,. these workbooks follow the Singapore Framework and also cover the topics in the Common Core State Standards.
Each workbook is written as a supplement to the textbook, Discovering Mathematics Common Core, to give students more practice in applying the concepts learned. Students may refer to the summary of the important concepts in each chapter of the textbook for a quick review before attempting the questions in the workbook. After completing the exercises, students will not only polish their own analytical skills, but also develop a stronger foundation in mathematics.
The questions in each workbook chapter are categorized into 4 pars according to the level of difficulty and the thinking skills involved:
Basic Practice: simple questions that drill comprehension of concepts
Further Practice: harder questions that involve direct applications
Challenging Practice: questions that require synthesis ability
Enrichment: questions that demand higher order thinking
These questions encourage students to think analytically, reason logically, use appropriate connections between mathematical ideas, and apply problem-solving skills in daily life situations.
We hope that these comprehensive workbooks will give students the tools and the confidence to handle mathematical questions and apply mathematical concepts to real-life situations. By achieving this, students will find learning mathematic an interesting and exciting experience.


Related info with this topic
Maurits Cornelis Escher (Leeuwarden, June 17, 1898 March 27, 1972 in Laren) was a Dutch mathematical artist known for his woodcuts, lithographs and mezzotints which feature impossible constructions, explorations of infinity, and tessellations.
Well known examples of his work include Drawing Hands, a work in which two hands are shown drawing each other, Sky and Water, in which light plays on shadow to morph fish in water into birds in the sky, and Ascending and Descending, in which lines of people ascend and descend stairs in an infinite loop, on a construction which is impossible to build and possible to draw only by taking advantage of quirks of perception and perspective.
Escher's work has a strong mathematical component, and many of the worlds which he drew are built around impossible objects such as the Necker cube and the Penrose triangle. Many of Escher's works employed repeated tilings called tessellations. Escher's artwork is especially well-liked by mathematicians and scientists who enjoy his use of polyhedra and geometric distortions. For example, in Gravity, multi-colored turtles poke their heads out of a stellated dodecahedron. One of his most notable works is the piece Metamorphosis III, which is wide enough to cover all the walls in a room, and then loop back onto itself He used lithographs and woodcuts as media. In his graphic art, he portrayed mathematical relationships among shapes, figures and space. Additionally, he explored interlocking figures using black and white to enhance different dimensions.
Integrated into his prints were mirror images of cones, spheres, cubes, rings, and spirals. In addition to sketching landscape and nature in his early years, he also sketched insects, which frequently appeared in his later work. His first artistic work was completed in 1922, which featured eight ......
[ read all story ]


Many interesting patterns in 2 dimensions can be understood as a slice through a lattice in a higher dimension. The simplest example is a slice through a three dimensional checker board. If you slice the corner off a cube at just the right angle you get an equilateral triangle. Slice at the same angle, but deeper into the cube, and you get a hexagon. So the pattern of hexagons and triangles, so common in Islamic art, is just a slice through a 3d checkerboard.
This animation illustrates the idea:


Elementary Apps for the Classroom
Check out these great apps for your students.
Arithmetic Invaders Express: Grade K-2 Math Facts - Express addition, subtraction, and multiplication games to defend the solar system and master K-2 arithmetic. Also, learn some basic facts about the Solar System.
Cloud Math Free - Excellent app for practicing and learning math." The difficulty level is easily controlled by a choice of operations, number ranges, numbers of answers to choose from, the number of problems in a set, and a Fail-safe mode. There are problems with addition and subtraction operations on numbers up to 50.
Geoboard, by the Math Learning Center - Geoboard is a tool for exploring a variety of mathematical topics introduced in the elementary and middle grades. Learners stretch bands around the pegs to form line segments and polygons and make discoveries about perimeter, area, angles, congruence, fractions, and more.
Math Puppy - Your younger students will be able to enjoy an interactive, learning environment of fun and adventure as they master basic math skills. Perfect for early childhood students.
Counting Bills & Coins - Counting Bills & Coins lets you practice identifying and solving math problems with money. Count, match, and make change with coins up to quarters and bills up to $20. Practice money skills in five unique activities: counting money, show me the money, making change, matching amounts, and show values.
Math Ninja - Use your math skills to defend your tree house against a hungry tomato and his robotic army in this fun action packed game! Choose between ninja stars, smoke bombs, or ninja magic - and choose your upgrades wisely!
Interactive Telling Time Lite - Interactive Telling Time is great for kids from ages 3 to 12 and comes in 3 difficulty levels so that it helps kids master telling time progressively (statistics are provided to help keep track of progress). Learn to set the time via interactive clocks with movable hour and minute hands, how to read a clock/to tell time, the conversion between analog clocks and digital clocks, as well as concepts such as ‘o’clock‘, ‘midnight’, ‘half past’, ‘quarter past’, ‘quarter to’, ‘past’, ‘to’, etc.
Dominoes Easy Match - Dominoes Easy Match skills focus on: concepts of numbers, identification of numbers 1-9, identification of simple arrays, rote counting, and one-to-one correspondence. This is a great app for beginning math learners.
MathTappers: Multiples - MathTappers: Multiples is a simple game designed first to help learners to make sense of multiplication and division with whole numbers, and then to support them in developing fluency while maintaining accuracy.
Teaching Number Lines: Little Monkey Apps Number Lines helps to introduce the concept of number lines through a variety of of modules such as: counters, drawings, and number lines in order to explain and physically model problems. Little Monkey Apps Number Lines aims to visualize numbers for rote counting and ordering and see the physical position of a number linking patterns and relationships. Great for student in K through 2.
K12 Equivalence Tiles - K12 Equivalence Tiles lets you compare the values of fractions, decimals, and percents up to 1 by using draggable tiles of varying values. K12 is not a calculator; it is a tool for students who have trouble understanding rational number equivalence (for example, 0.5, 1/2, 50% are all equal). This tool also allows students to visually perform simple operations like addition, subtraction, comparison, and ordering. This is a great app for upper elementary grades.
Rounding - Rounding is a great way to test your rounding skills and have fun at the same time. Select the number of problems and other options in order to correlate with your skill level.
Interactive Math Glossary -The Interactive Math Glossary App is provided by the Texas Education Agency to help teachers explore and understand mathematics vocabulary used in the grades K–8 Texas Essential Knowledge and Skills. Each glossary word is displayed in a four quadrant Frayer Model.
Science 360 - This app will allow your students to scroll the 3D sphere that is made of thumbnails of various science photos and videos. Tap on any one of those thumbnails to bring up the recent updates from National Science Foundation (NSF) or institutions funded by NSF. All contents are multimedia and are updated weekly, so you always get the most recent development of science and technology.
NASA - The NASA app carries a wealth of NASA information right on your iPad. The app collects, customizes and delivers an extensive selection of dynamically updated mission information, images, videos. It has information about the planets, live streaming of NASA TV, and on demand NASA video.
WWF Together- Experience the world's most amazing and endangered animals in one app – together. This interactive experience brings you closer to the stories of elephants, whales, rhinos and other fascinating species. Discover their lives and the work of WWF in a way you’ve never seen before. Try out “tiger vision,” stay as still as the polar bear during a hunt, and chop the panda’s bamboo. Explore the animals’ stories, then fold them up and share them with the world.
Robots for IPADS - Robots for iPad is the best, most complete guide to the world of robotics. This fun, highly interactive app lets you explore over 150 real-world robots, with hundreds of animations, photos, videos, and articles
Kids Can Match - An interactive, adaptive and fun memory game for children of all ages. This app contains amazing, one of a kind, collection of over 70 authentic animal images and sounds. The perfect way to engage children in a fun game while they learn about a broad range of animals from all over the world. Tailor made and carefully designed by experienced educators to fit the needs of small children. This educational game is a wonderful asset in any animal loving family.
Talkboard- Talkboard is the canvas for collaborative learning. Work with your students, wherever they are, on a shared whiteboard to bridge the gap in distance between you. Then harness your creativity to bring color and clarity to your lessons. Talkboard’s simple yet elegant drawing tools and integrated audio allow you to engage students in a whole new way.


Thales of Miletus (1) was born in Thebes in the year 625 BC and died in Athens, 547 BC, at age 78. He was a Greek philosopher, founder of the Ionian school and he was considered to be one of the Seven Sages of Greece. Mathematician, astronomer, and great thinker, Thales toured Egypt, where he conducted studies and was directly exposed to the mysteries of Egyptian spirituality/religion.
It is attributed to him the prediction of the solar eclipse in the year 585 BC, which was held an incredible feat. His mathematical talent was so unusual, it was able to establish accurately the height of the pyramids through the measuring of the shadow. Moreover, according to Herodotus, Thales of Miletus was the first mathematician to give a logical explanation for the occurrence of eclipses. Thales was the first to verify that the moon as in fact “illuminated” by the Sun, being the first one to count how many days a year was comprised of. According to Aristotle, this discovery was a landmark for the history of philosophy. Later, because his brilliant demonstrations of the geometric theorems, he was also regarded as the father of Geometry.


Maths and Science Tutor wanted immediately: APPLY NOW
Master Maths Morningside is currently looking for mathematics and/or physical science tutor.
Master Maths Morningside is part of a well-established franchise concern, which has been providing extra tuition for over 40 years, to learners from junior level to adults. Our successful candidate must have exceptional customer service skills, over the phone and in person. Must be computer savvy.
The closing date for applications is 1 December 2019.
Please only submit your CV if the following applies to you:
You achieved 70% or more for maths or physical science in the final matric exam, or you have a relevant tertiary qualification.
You will be required to tutor up to grade 12 level for maths and physical science.
70% or more for maths and/or physical science in the final matric exam.
Speak fluent English.
South African passport or valid work visa.
Motivated by success in your job.
A people’s person and you think you might enjoy tutoring.
Able to interact successfully with young children.
Prior experience in a maths and/or science tutoring job is an advantage.
You’re available to work between 10:00 and 19:00 on weekdays, 09:00 to 13:00 on Saturdays or times as required by the role.
Have your own transport.
You must have the ability to get on with young people. Be well-groomed with an attitude to get involved in every aspect of the business.
Requires an ability to explain mathematics or physical science pleasantly and with an enthusiastic personality.
Preparation and detailed recording of student progress for each individual student.
The position requires that you assist with admin responsibilities.
Job Type: Contract
Location: Morningside, Gauteng (Preferred)
Language: fluent English (Required)
Did you achieve at least 70% for maths or science in Gr12 (Required)


My name is Stacy Maxton, and my goal is to battle the stigma against math.
Math is fun! I first knew I loved math when I was 6 and I would hurriedly run home from school to dig in to my workbook problems. I was a nerdy kid who faced a lot of bullying; math provided me with solace and escape, while also making me feel like I was becoming smarter by the day. This problem-solving became my habit until I discovered math competitions – including the AMC and AIME – which opened many doors for me, both academically and personally as I found both resume-boosting success as well as friendship! I later dug in to computer science, finding comfort in its numbers and logical systems, but never forgetting my first love – math.
Math gave me confidence, identity, and purpose as I developed into the person I am today. I sharpened my analytical mind and power of observation using the skills I learned and the problems I solved. I built a circle of friends that only continues to grow as I find more people who love numbers. I want to give back to the next generation of youth by helping them fall in love with math… particularly as I hear so much fear and apprehension of numbers.
I tutor students who try to use rote memorization to keep math at arm’s length, never truly engaging with the problems at hand and therefore never really getting to know math. I know there are more students doing this than just the ones I instruct, and so I’ve assembled this resource of math camps as one way to inspire students to find fun in math.
Use the navigation bar above to visit the various pages I’ve built here.
If there are any camps that I’m missing here, or if you have any further resources you’d like to see added to this site, please let me know! My email is email@example.com, and I look forward to hearing from you.


Six Weeks/Months Industrial Training in MATLAB
Six Months MATLAB Industrial Training
MATLAB is a high-performance fourth generation programming language for technical computing. The name “MATLAB” stands for matrix laboratory. It accommodates visualization, computation, programming, developing and running algorithms in an easy-to-use atmosphere where the issues and solutions are conveyed in acquainted mathematical notation. It was formerly written to provide quick access to matrix program developed by the LINPACK and EISPACK projects, which collectively characterize the state-of-the-art in software for matrix computation. In university environments, it is the normal instructional tool for introductory and advanced courses in mathematics, engineering and science. In Industry, MATLAB is a tool of alternative high-productivity research, development and analysis.
The MATLAB consists of five main parts namely:
The MATLAB language:
It’s a high level matrix language with control drift statements, data, input/output, constructions and object oriented programming features. It allows both “programming in the small” to rapidly create quick throw away programming features and “programming in the large” to create complete and complex application programs.
The MATLAB working environment:
That is the set of tools and amenities that you just work with as a MATLAB user or programmer. It entails services for managing the variables to your workspace and importing and exporting information. It also entails tools for setting up, managing, debugging, and profiling M-records, MATLAB’s functions.
The MATLAB graphics system includes high-level commands for two-dimensional and three-dimensional data visualization, animation, image processing and presentation graphics. It includes low level commands that will fully customize the appearance of graphics as well as builds complete Graphical user interfaces on MATLAB applications
The MATLAB mathematical function library:
It’s an enormous collection of computational algorithms starting from elementary functions like sum, sine, cosine and complex arithmetic to more complicated functions like matrix inverse, Bessel functions an fast Fourier transforms.
The MATLAB Application Program interface (API):
MATLAB API is a type of library that empowers you to create Fortran and C programs which interacts with MATLAB. It’s basically for reading and writing the important Mat files and calling MATLAB as a computational engine
Scope of MATLAB Industrial Training From Elysian Corporation
- Our team of experts helps in providing deep knowledge which will mould you to become a skilled and successful developer
- We helps students in grasping knowledge of Complex technical concepts
- We conduct live discussions among the students to collaborate on various Topics.
- We provide free study material, PDF’s, books, sample papers and video lectures.
- We provide free interview preparations, mock sessions and 100% job assistance.
Syllabus of MATLAB
Variables, Scripts and Operation
Variables, Scripts and Operation
Basic of matrix and functions
Visualization and Programming
Image/ Surface Plot
Solving Equations and Curve Fitting
ELECTRONIC AND COMMUNICATION ENGINEERING
Modulating a Random Signal
Analog and Digital Modulation
Plotting Signal Constellation
White Gaussian Noise
– M2SE Equalizer
CONTROL SYSTEM DESIGN AND ANALYSIS
Control system Designer
Control System Tunes
Fuzzy Logic designer
SIGNAL PROCESSING AND COMMUNICATION
Bit Error rate Analysis
Radar Equation Calculators
Radar Waveform Analyzes
Sensor Array Analyzer
Control System Designer
Control System Tuner
COMPUTER SCIENCE ENGINEER
IMAGE PROCESSING TOOLBOX
Image Read and Show
Convert Images format
Image edge detection
Record and plot speech signal in matlab
Neural Net Clustering
Neural Net fitting
Neural Net pattern Recognition
Neuro Fuzzy Designer
Fuzzy logic Toolbar
Genetic Algorithm Toolbar


Mathematics deals with numbers, space, quantity, structure and change. It is a subject where patterns are formulated to create new conjectures and resolve the falsity or truth using mathematical proof. A mathematical reasoning of real phenomena provides predictions and insights about nature. Ask Assignment Help provide Mathematics assignment help and Mathematics homework help in professional manner so that students can achieve full marks in it. With the help of logic and abstraction, math expanded from shapes, physical object, measurements, counting and calculation. While, the human activity of solving math problems is called practical mathematics where in inquiry takes years or centuries to be sustained.
A lot of students find it hard to deal with mathematics such as numbers, formulas, problem solving, equations and solutions. It has the highest number of failing grades and we understand your fear repeating the subject and worst being terminated. Our Mathematics assignment help service is available 24X7 for you so that you can contact us anytime to get the solutions with our Mathematics assignment help. If you think you can no longer handle your mathematics assignment, and then consider our Mathematics assignment help service. We provide expert Mathematics assignment help on various topics such as algebraic structures, abstract, Discrete Mathematics, Advance Mathematics, Boolean, commutative and homological algebra, linear, category, ring, group and representation theory, reciprocity; complex, functional, harmonic and real analysis; multivariable calculus; geometric curve, triangle. circle and general topology; differential, algebraic, topology and metric geometry; knot, co homology, scheme and lie group theories; combinatory graph of theories; first-order theories, large cardinal and mathematical logic; number theories; dynamic differential and systems equations etc.
Mathematics Homework Help
We provide Mathematics homework help with all these branches of mathematics, different concepts and laws, Mathematics homework help experts are available to help you learn more about this subject. Our Mathematics homework help service guarantee high qualities, easy to understand output that will help you understand the structure of every mathematical problem you want us to solve for you. The good thing on our service is we aim to increase your class standing by giving you clear problem solving, problem analysis and so on. We also provide Mathematics homework help in case you need assistance on editing and revising your work.
Our Mathematics homework help experts can meet your requirements and deadlines with sustained quality. Our professional researchers and practitioner give assurance on the accuracy. We accept last-minute projects and you can reach us 24×7. Our Mathematics homework help service understand the limit of your wallet as a student so we provide a very affordable price.


The golden mean calliper is designed for symmetry. Using the rule of thirds, the golden mean eyebrow tool provides key measurements for design symmetry. The golden ratio tool is one of the most popular methods for eyebrow symmetry when mapping.
- Golden ratio tool for pmu measurement
- Made from 304 stainless steel
- Easy to use and clean
- Adjustable for all clients
Mathematicians since Euclid have studied the properties of the golden ratio. The golden ratio has also been used to analyse the proportions of natural objects, including full facial symmetry.


This riveted me; I love mental maths. To cube root a number (assuming it’s a perfect cube), here are the steps, using 250,047 as our protagonist cube:
- Ignoring the last 3 digits of the cube, find the first cube which is less than the remaining digits. 250 (ignoring 047) is the number in question, and 216 (63) is the first cube less than 250 — giving us 6.
- Find the number from 1-10 that, when cubed, ends in the last digit of your cube. 250,047 ends in 7, which corresponds to the last digit of 27 (33). This number is the last digit of the cube root.
- Voila! Those are the 2 digits of the cube root — 6 and 3 — giving us 63 as the cube root of 250,047.


Subtraction with Addition: Two's Complement
Subtracting numbers on paper is easy, but how does a computer do it? Most computer operations can be reduced to additions of binary numbers… even when the operation is subtraction. To understand how this works, let’s first think about how an odometer works.
Let’s say you’ve driven 7631 miles and really want to celebrate your 9999th mile and see the odometer return to 0000. You would have to drive 2368 miles to reach 9999 miles. When you’ve hit 9999 miles, the odometer returns to 0000 and the cycle continues.
And so the total amount of miles you had to drive was 2368 to hit 9999 and then 1 mile to hit 10000.
The formula to calculate the amount of miles you have to drive to hit 9999 miles is:
7631 + x = 9999 x = 9999 - 7631 x = 2368 2368 + 1 = 2369 miles driven in total for odometer reset.
The mind-blowing part of this is that 2369 is the negative equivalent of 7631. How?
Let’s pick another random 4-digit number and subtract 7631 from it:
9473 - 7631 = 1842
That's also equivalent to adding negative 7631:
9473 + (-7631) = 1842
Let’s substitute -7631 for its positive equivalent:
9473 + 2369 = 11842
11842 looks familiar doesn’t it? Since we’re operating in a 4-digit system, we drop the first digit and we have 1842, the correct result of the subtraction.
We can also use this negative representation of the number in other equations:
2354 - 7631 = -5277
So -5277 is the correct answer.
Let’s convert that answer back to the positive equivalent:
5277 - 1 = 5276 9999 - 5276 = 4723
Now… let’s see what happens when we only use addition with the positive equivalent number:
2354 + (-7631) 2354 + 2369 = 4723
🎉 Voila! Obviously, converting 4723 to its negative equivalent will result in -5277!
However! Instead of reversing the calculation like we just did, we can also covert a negative to a positive using the exact same procedure without reversing it:
9999 - 5277 = 4722 4722 - 1 = 4723
🎉 And the result is back to 4723.
This method is called the two's complement and is exactly how computers implement signed binary numbers! We just looked at base-10 numbers, but computers work in binary, base-2.
The same idea applies in binary. Take the binary number 0110.
The negative number of 0110 can be calculated in the same way, except the odometer resets at 1111 and not 9999.
1111 - 0110 = 1001 1001 + 0001 = 1010
With that, the negative number for 0110 is 1010. We can then do similar calculations, let’s say 7 minus 6.
7 - 6 = 1 (in decimal) 0111 - 0110 (in binary) 0111 + (- 0110) 0111 + 1010 = 10001, drop the first digit, resulting in 1!
Typically the computer uses 16-bit inputs, following this example means instead of 4-digit, computers use 16-digit binary numbers.
The system can code a total of 2n signed numbers, where 2n-1 - 1 and -2n-1 represent the number of positive values and negative values respectively. This means in a 4-bit system, the total number of numbers (haha!) represented is 24 = 16, where we can go up to positive 7 and as low as -8.
The two's complement is implemented in the hardware of the Arithmetic Logical Unit chip that makes up the CPU.


8 edition of Mathematics of the 19th century found in the catalog.
Includes bibliographical references (p. 311-346) and index.
|Other titles||Mathematics of the nineteenth century|
|Statement||edited by A.N. Kolmogorov, A.P. Yushkevich ; translated from the Russian by Roger Cooke.|
|Contributions||Kolmogorov, A. N. 1903-, I͡U︡shkevich, A. P. 1906-|
|LC Classifications||QA300 .M293713 1998|
|The Physical Object|
|Pagination||x, 353 p. :|
|Number of Pages||353|
|ISBN 10||3764358459, 0817658459|
|LC Control Number||97046763|
19TH CENTURY MATHEMATICS age of revolution France and Germany “the three L’s”: Lagrange, Laplace and Legendre advance in mathematical analysis and periodic functions Joseph Fourier's study Argand Diagrams Gauss the “Prince of File Size: KB. 19th century. The term itself is enshrined in the full title of the Sadleirian Chair, Sadleirian Professor of Pure Mathematics, founded (as a professorship) in the mid-nineteenth century. The idea of a separate discipline of pure mathematics may have emerged at that time.
The North American Arithmetic: part first, containing elementary lessons by Frederick Emerson 19th Century School Books. First Book in Arithmetic by Milton B. Goff 19th Century School Books. First lessons in numbers: oral and written on the basis of works by Benjamin Greenleaf. Henry B. Maglathlin 19th Century School Books. ISBN: OCLC Number: Notes: Translation of Vorlesungen über die Entwicklung der Mathematik im Jahrhundert. "Appendices: Kleinian mathematics from an advanced standpoint, by R. Hermann": pages
Poor Man's Rare Books We Specialize in rare and obscure books of all varieties as chance may have it. Fine leather bound books, illustrated, Religious, scholarly, 16th century etc as well as a number of Incunables from single leaves to complete works. It belonged to both. For example, the most important work on PDE in 19th century was arguably Fourier's Analytic theory of heat. You don't have to read the book, to conclude that this was applied mathematics, just from the title.
Philippine recipes and typical menus
A short history of Islam
philosophy of a politician
A Short History of Scotland
Huntingdonshire (Domesday Books (Phillimore))
Teaching for Change
The Face and The Mask
NUS welfare manual 1987/88.
Teaching strategies for improving youth fitness
Genealogical notes on the family of Cary and Carey in Somerset, England
Why we snap
The 19th Century saw an unprecedented increase in the breadth and complexity of mathematical concepts. Both France and Germany were caught up in the age of revolution which swept Europe in the late 18th Century, but the two countries treated mathematics quite differently.
After the French Revolution, Napoleon emphasized the practical usefulness 5/5(27). In contrast to the first two books of The Mathematics of the Nineteenth Century, which were divided into chapters, this third volume consists of four parts, more in keeping with the nature of the publication.
1 We recall that the first book contained essays on the history of mathemati 2 cal logic, algebra, number theory, and probability 5/5(1). Mathematics Of The 19th Century, Volume 1 book. Read reviews from world’s largest community for readers. New Edition - New in Paperback - This is the sec /5(2).
Most of the late 17th Century and a good part of the early 18th were taken up by the work of disciples of Newton and Leibniz, who applied their ideas on calculus to solving a variety of problems in physics, astronomy and engineering. The period was dominated, though, by Mathematics of the 19th century book family, the Bernoulli’s of Basel in Switzerland, which boasted two or three generations of 5/5(30).
Mathematics - Mathematics - Mathematics in the 19th century: Most of the powerful abstract mathematical theories in use today originated in the 19th century, so any historical account of the period should be supplemented by reference to detailed treatments of these topics. Yet mathematics grew so much during this period that any account must necessarily be selective.
Mathematics - Mathematics - Mathematics in the 17th and 18th centuries: The 17th century, the period of the scientific revolution, witnessed the consolidation of Copernican heliocentric astronomy and the establishment of inertial physics in the work of Johannes Kepler, Galileo, René Descartes, and Isaac Newton.
This period was also one of intense activity and innovation in. In contrast to the first two books of The Mathematics of the Nineteenth Century, which were divided into chapters, this third volume consists of four parts, more in keeping with the nature of the publication.
1 We recall that the first book contained essays on the history of mathemati 2 cal logic, algebra, number theory, and probability. 19th Century Mathematicians British American French German Indian Find out more about the greatest 19th Century Mathematicians, including George Boole, Ada Lovelace, Srinivasa Ramanujan, Lewis Carroll and David Hilbert.
This multi-authored effort, Mathematics of the nineteenth century (to be fol lowed by Mathematics of the twentieth century), is a sequel to the History of mathematics from antiquity to the early nineteenth century, published in three volumes from to 1 For reasons explained below, our discussion of twentieth-century mathematics ends with the s.
An important aim of the book is to help the student understand how any given part of mathematics first arises and comes to fruition.
for those readers with some university-level background in mathematics who are interested in the technical contours of nineteenth-century science, Gray’s book will repay careful study and is highly Cited by: 6.
The book History of Mathematics from Ancient Times to the Early Nineteenth Century [in Russian], which was published in the yearsis cited in abbreviated form as HM (with volume and page number indicated). The first volume of the present series is cited as Bk. 1 (with page numbers).
This multi-authored effort, Mathematics of the nineteenth century (to be fol lowed by Mathematics of the twentieth century), is a sequel to the History of mathematics fram antiquity to the early nineteenth century, published in three 1 volumes from to This multi-authored effort, Mathematics of the nineteenth century (to be fol lowed by Mathematics of the twentieth century), is a sequel to the History of mathematics from antiquity to the early nineteenth century, published in three volumes from to 1 For reasons explained below, our discussion of twentieth-century mathematics ends with the s: 1.
Mathematics. Throughout the 19th century mathematics became increasingly abstract. Carl Friedrich Gauss (–) epitomizes this trend. He did revolutionary work on functions of complex variables, in geometry, and on the convergence of series, leaving aside his many contributions to also gave the first satisfactory proofs of the fundamental theorem.
Development of Mathematics in the Nineteenth Century book. Read reviews from world’s largest community for readers.4/5.
Danish mathematicians born in the 19th century. Harald Bohr (–) Dutch mathematicians born in the 19th century. Brouwer (–) Gustav de Vries (–) Arend Heyting (–) Diederik Korteweg (–) Thomas Joannes Stieltjes (–) Finnish mathematicians born in the 19th century.
The Rise of Engineering and Applied Mathematics The 19th century saw an explosion of applied mathematics as the industrial revolution took hold throughout Europe. An example of this is the development of the École Polytechnique in Paris. Galois had actually applied to the École Polytechnique inbut failed his entrance exam.
Many students from. MATHEMATICS IN THE MODERN AGE – THE 19TH CENTURY: REVOLUTION OR EVOLUTION. Professor Robin Wilson. Introduction. In my last lecture, on the 18th century, we saw the devastating influence of Isaac Newton on British mathematics, holding it back for more than a hundred years while advances were being made on the Continent by such.
Page - History of. and Technology, Moscow, Russia (Eds) Mathematics in the 19th Century Mathematical Logic, Algebra, Number Theory, Probability Theory pages.
Hardcover ISBN The history of nineteenth-century mathematics has been much less studied than that of preceding periods. The historical period covered in this book extends from the. Discover the most famous 20th century mathematicians including Alexander Grothendieck, Andre Weil, Kurt Godel, Alan Turing, Hermann Weyl, John von Neumann and many more.
This list of mathematicians born in 20th century includes people from USA, France, UK, India, France, Russia and many more countries. The book History of Mathematics from Ancient Times to the Early Nineteenth Century [in Russian], which was published in the yearsis cited in abbreviated form as HM (with volume and page number indicated).
The first volume of the present series is cited as Bk. 1 (with page numbers). show more/5(2).The triple-decker novel was a standard form of publishing for British fiction from the early s until the s. The market for this form of fiction was closely tied to commercial circulating libraries, such as Mudie's and W.
H. Smith. Unlike free public libraries, these.Mathematics of the 19th century, 2 Summary: The general principles by which the editors and authors of the present edition have been guided were explained in the preface to the first volume of Mathemat ics of the 19th Century, which contains chapters on the history of mathematical logic, algebra, number theory, and probability theory (Nauka.


Measuring the area of a specific plot ought to be the very first job. It’s the irrationals that produce the actual number line so populous. Now, it is who is going to help you in the middle of the night and to top it all you have the mathematics class tomorrow when you have to submit this statistics assignment.
Now and then, math instructors have a tendency to present their students overnight assignments that should be handed in a day later. At most universities, irrespective of your major, you need to reach standard math proficiency. Maths is believed to be among the most scoring subjects.
Bearing that in mind, here are a few ideas for new year’s resolutions which can help you turn into an even greater engineer in 2018. Our experts will supply you with clear step-by-step calculations, thus royalessays.co.uk providing you with a pretty great idea of the way the task was solved and making it really easy that you explain it to your fellow students. To get the most suitable answer, which is 11, you’ve got to follow along with the appropriate order of operations.
Enrolled students of the course are eligible for a temporary matlab license. Mathematics can be rather challenging to the extent that students might be stuck with the issue and have zero clue how to proceed. Maths is believed to be among the most scoring subjects.
Top Choices of Help Me Solve This Math Problem
It’s harder than it appears even if you believe you get a good grasp of good old PEMDAS. Possessing the capacity to solve math word problem skills makes a big difference in your career and life. It is among the most frequently explained problems in computer basics.
The frequent denominator is going to be 3. On the flip side, algebra problem solvers are almost much like online algebra solver computer software programs. You are able to try out the a variety of methods in heuristics math.
You’re able to attempt breaking the issue into simpler parts. For instance, a man would like to pack 100 watermelons into boxes. You’ve got a barrel of beer and you should measure out only one gallon.
Mathematics teaching and learning is targeted at developing children’s capacity to address different mathematics problems. Math tutoring isn’t only an enjoyable approach to do and understand concepts but likewise an affordable and time-saving learning procedure. Maths is believed to be among the most scoring subjects.
The Fight Against Help Me Solve This Math Problem
They need to see that they can do the work so that they can feel confident! They can solve one problem in different ways. Before fifth grade, they really need to write things down in order to see answers.
While the issue solving materials don’t always have a focus on one specific strand of wisdom and understanding, they’ve been grouped in the tabs below in the strands that have the larger focus. Even in case you write down the factors wrong the very first time, you’ll probably see how to re-arrange them and begin. In addition, it would supply you with clues that may hint at a proof of the presence of one-way functions.
New Ideas Into Help Me Solve This Math Problem Never Before Revealed
After that, identify just what you should see in the issue. It’s these problems which make the subject mesmerizing. In order to be sure you have solved the issue correctly, plug your answer back into the original issue.
A great deal of students who are a bit confused by math see word troubles and just guess what things to do without the checking and refining part. On-line learning sessions also give students privacy and room to learn at their own speed, without worrying about needing to stay informed about their classmates. In the event your answer is incorrect, or when you sense that something is amiss, retrace your steps thoroughly, and you are certain to get the flaw.
The usage of an easy to comprehend language can assist the student feel at ease and take the next step towards solving the issue. Math word problems can be tricky but by creating a procedure and practicing on a normal basis, your son or daughter can strengthen their abilities. Explicitly teach and review the language used in mathematics so that they understand what is being asked in a problem and how the problem should be solved.
The frequent denominator is going to be 3. Other variables could be involved also. If you believe equations are pure math or physics, then you’re wrong.
Sign uphereto get INSIDER’s favourite stories right to your inbox. The terrible news is that you might have to think pretty hard. To do that you must answer each one of the easy math questions that show up in the mouth of the White Blood Cell.
The 30-Second Trick for Help Me Solve This Math Problem
Solving crossword puzzles can enhance your general knowledge also. Students may use some puzzles, which are intended on the grounds of distinct concepts of arithmetic, geometry. Students in fifth grade do most of their computations employing a pencil and paper, because they have done since they started solving math issues.
Help Me Solve This Math Problem and Help Me Solve This Math Problem – The Perfect Combination
There’s an association between the octal and the binary system, making it rather useful whilst programming computers. The exercises accelerate the cognitive retrieval and one is equipped to rapidly pick the most proper technique. The tape diagram is a good tool for building that understanding.
There’s an association between the octal and the binary system, making it rather useful whilst programming computers. So as long as human-to-machine interfacing is needed, we’ll always have the should convert one numerical system in the other. Alternately, a tape diagram enables students to visualize the issue and develop their strategy.
Characteristics of Help Me Solve This Math Problem
The entire system gets more efficient. If you’re stumped, take a look at a remedy to the issue. In addition to this, dome of the sources would show you partial solution and request that you subscribe for accessing the complete solution to the issue.


Saturday at any time
EducationM.S. in Education, Cairn University
Graduated December 2013
PA State English Ed 7-12 Certification
PA State TESOL (ELL/ESL) K-12 Certification
Experience teaching high school English (American Lit, World Lit, British Lit)
Experience tutoring high school math, SAT prep, writing
After graduating college, I was a long-term ESL substitute for 1st grade at the school that I student taught for. The following year, I was offered a Presidential Internship at my university, and I worked in the Academic Resource Center, a tutoring and support center assisting all students, especially those who needed accommodations or extra support and accountability. The following year, I was hired as a high school English teacher at the school that currently employs me.
During this summer break, I hope to begin tutoring students, not just as a part-time job, but as something that I love to do. I'd like to continue tutoring throughout the school year as well, if my services are needed. Tutoring is one of my passions and education is a field that I hope to be in for a long time.
HobbiesI enjoy music and the outdoors, and I love to read. I play the flute, and I also know a little piano and guitar as well. Writing poems is therapeutic for me, and I love to be creative with writing, art, cooking, and home decor. I also enjoy watching sports like football and basketball and am somewhat knowledgeable about some of the famous athletes. I enjoy having fun and laughing, as well as building meaningful relationships with my students. I believe that all students deserve respect and care, no matter who they are.
9th Grade math, SAT Subject Test in Literature, Medieval Literature, Literature, GRE Subject Test in Literature in English, CLEP English Literature, CLEP Analyzing and Interpreting Literature, CLEP American Literature, Flute, 9th Grade Writing, 9th Grade Reading, World Literature, 8th Grade Writing, 8th Grade Reading, 8th Grade math, 7th Grade Writing, 7th Grade Reading, 7th Grade math, 6th Grade Writing, 6th Grade Reading, 6th Grade math, 5th Grade Writing, PSAT Writing Skills, Religious Studies, SAT Mathematics, SAT Math, SAT Critical Reading, SAT, PSAT Mathematics, PSAT Critical Reading, PSAT, Writing, SAT Writing, 5th Grade Reading, Poetry Writing, Persuasive Writing, Handwriting, Fiction Writing, Expository Writing, Creative Writing, Grammar and Mechanics, ESL/ELL, English, ACT English, 11th Grade Writing, 11th Grade Reading, 10th Grade Writing, 10th Grade Reading, 10th Grade math, ACCUPLACER Arithmetic, ACCUPLACER Reading Comprehension, ACCUPLACER Sentence Skills, ACCUPLACER WritePlacer, ACT, 12th Grade Reading, ACT Math, ACT Reading, ACT with Writing, ACT Writing, Algebra 1, Algebra 2, Algebra 3/4, American Literature, AP English Language and Composition, AP English Literature and Composition, 3rd Grade, 5th Grade math, 5th Grade, 4th Grade Writing, 4th Grade Reading, 4th Grade math, 4th Grade, 3rd Grade Writing, ACCUPLACER ESL, 3rd Grade Reading, 3rd Grade math, British Literature, 2nd Grade Writing, 2nd Grade Reading, 2nd Grade math, 2nd Grade, 1st Grade Writing, 1st Grade Reading, 1st Grade math, 1st Grade, 12th Grade Writing
Inquire about this tutor
The tutor will respond if they are available/interested.


Free Online Casino Games Can Help Those With a negative Wallet
Once you hear the word “gambling,” what is the very first thing that comes into your brain? For most people, the very first thing that makes their minds are the old slots where you spin the reels and hope that you’ll hit the jackpot. Of course, the jackpot isn’t actually the only thing that casino goers can win. There are actually a lot of other activities that can be won in casino games.
You can find basically three categories of casino games: casino table games, gaming machines, and hand-held random number devices. Casino table games include roulette, craps, baccarat, poker, blackjack, and more. Gaming machines include slots along with other game devices that allow players to accomplish both gambling and table games at the same time.
The easiest method to know more about casino games is to simply head into a casino and try a few of the slots. In case you have never gambled at a casino before, then it would be wise that you should practice at the gaming tables first. This can help you get acquainted with the layout of the area as well as the way the slot machines work. By obtaining the feel of the slots first, you will be able to focus on another games at a later time. Before you lay your money on any machine, however, make certain you do your research. Learning all the statistics for each machine will assist you to make an informed decision when placing your money on the slots.
One of the most important statistics to look at when betting on casino games is the standard deviation. Standard deviation, which can also be known as the deviation of arithmetic outcomes, may be the deviation of the mean outcome of a set number of trials. When calculating the standard deviation, you take the square reason behind the number of successes or failures. The standard deviation lets you know what the expected number of results should be, after observing just how many times the game has been played in a row and some other variables.
Slots on the casino floors are one of many explanations why people enjoy playing these casino games. The main reason that casino games are fun is basically because there is always a house edge. A house edge may be the difference between your actual worth of a machine, after taking out the expense of rent and payback, and the total amount a player will probably pay if they win. Slots usually have a comparatively small house edge, but there are still some smaller variations of slots with high house edges. To obtain an idea of how much a casino is willing to bet on a machine, you can calculate the standard deviation using the average amount of wins/losses by players on that machine.
There are some games on the slots which are strictly for fun, 로투스 바카라 while there are also some games that are played with real money, but they aren’t casino games. Many people enjoy playing video poker, roulette, blackjack, baccarat, craps, along with other non-casino gambling games, such as online slots, video poker, internet bingo, etc. On a single token, many people do not consider playing free games at a common online casinos since they consider them a waste of time. However, if you are using the methods discussed in this article, then you may be able to find the best casino games online for play for free.
Most online casinos offer special promotions that give players the chance to play casino games free of charge. This is great news for many who cannot move away from gambling in real life because it allows them to save lots of money on one of these favorite casino games. This sort of promotion usually runs during certain times of the year, so it is important to sign up for it at the earliest opportunity. Typically, these promotions allows players to register around two free casino games each month, so make sure to utilize this opportunity and sign up today!
One of the oldest forms of casino games available on the web includes the classic card game, blackjack, craps, roulette, baccarat, etc. Many of these games were literally created out of an invention called the randomizer. The randomizer is a computer software program that creates random numbers and can be used to create a casino game experience. Roulette, craps, baccarat, and other casino games are available online in many different variations, so it hardly ever really matters what type of casino games you are interested in playing, since they can all be found free of charge.


- What is the role of math in poker?
- What Outs are in Poker and how do we count those?
- Using probabilities in poker math
- Pot odds in poker math
- Two ways of applying poker math
- Calculating equity outside poker tables
- Estimation of required equity at the table
- Useful literature on poker math
- Poker Math FAQ
- How is mathematics useful for a poker player?
- How to count outs correctly?
- How to use math in poker?
What are we talking about here? The mathematics of poker seems difficult to many new players. However, in fact, it is quite simple to master and thereby greatly increase your chances of winning.
What should we focus on? Of course, you need to start with the basics and understand what poker mathematics, outs and probabilities are in the first place and how to calculate them. It is also very important to be able to apply this knowledge in practice.
What is the role of math in poker?
Strategy in this game is based on probabilities of certain events. Understanding the psychological characteristics and habits of your opponents is also important. This information allows us to make our mathematical predictions more accurate. Poker mathematics covers a wide range of concepts, including outs, probabilities, pot odds, equity and fold equity.
It is necessary to analyze the chances of winning in the current hand. Math serves as a guide for experienced players, helping them determine optimal moves. For example, it tells you whether it is worth making a call in a given situation or whether it is better to look for other, more profitable actions.
What Outs are in Poker and how do we count those?
Counting outs is the most important part of poker math. Outs are cards in the deck that can improve your current hand, turning it into a winning one. Let’s take a look at an example. Let’s say you have AK of diamonds on a board with a diamond flush draw. How many outs do you have in this situation? What cards can improve our combination?
There are three aces and three kings that improve us to a top pair, which could be enough to win. To achieve this, you need to draw a card that matches one of the six remaining in the deck.
In addition, any diamond card gives us flush, which is the best possible hand here (nuts). There are 13 diamond cards in the deck. Two of them are a part of our hand and two more are on the board. Therefore, there are still 9 diamond cards left that can improve our hand.
You have 15 outs total. However, when counting, it is important to take into account and exclude from the list the so-called tainted outs – cards that improve our hand, but at the same time strengthen the opponent’s hand.
Using probabilities in poker math
Understanding outs allows you to move on to using probabilities. Once a player understands how many cards in the deck can improve his hand, he can estimate how often this should happen.
The following formula is used for calculations:
Probability = number of outs / number of hole cards (in the deck and in the opponents’ hands).
A standard poker deck contains 52 cards. Two of them are in our hand, and three more are on the table after the flop. This leaves 47 unknown cards. Let’s say we need any of two eights or four kings left in the deck. The probability of one of these hitting the turn is 6/47 or 12.76%.
If none of the eights or kings appear on the turn, the player still has one more chance to catch them on the river. However, it is important to remember that at this point there will be one less hole card in the deck: 6/46, or 13.04%.
The probability of getting the required card in one street is approximately 2%, and in two – about 4%.
Pot odds in poker math
What happens when mathematicians play poker? They start calculating the pot odds. The probability of getting a desired combination is determined by comparing unsuccessful outcomes, where the player does not get an out he looks for, with successful ones.
This chance can be represented in a form of a ratio. For example, 3:1 means that on average out of four attempts to get the desired card, three will be unsuccessful and one will be successful. Probabilities can also be expressed as percentages. For example, a ratio of 4:1 is 20%. When converting to percentages you just add one to a number of unsuccessful outcomes. Thus, 5.5 to 1 is 15.4% (1/6.5).
Pot odds are the ratio of the amount a player puts into the pot to the total size of the pot. In other words, this is a ratio of how much a player invests to how much he can win if he gets a desired outcome. For example, pot odds of 4:1 means that if we invest $1, we will get $4.
Generally, pot odds are taken into account when determining whether it is profitable to call or not. If the pot odds are greater than the probability of getting the desired hand, then calling is profitable.
Two ways of applying poker math
Calculating equity outside poker tables
When a player is at the table, there is simply no time for complex calculations. It is better to start learning by analyzing your hand histories after the game. The more time you spend practicing away from tables, the more confident you will be at the tables.
A decision that closes the action is one when there is no other options available after. For example, this can happen on the river when the villain goes all-in. You have only two possible options left: call or fold. One way or another, the hand is over after you pick one of the two.
Let’s take a look at another example, this time preflop. Let’s assume one of the players decides to go all-in. You have a choice: give up and fold, or call and answer his bet.
It is important to note that all calculations discussed below assume that there will be no action after your decision and the pot size will remain unchanged. The following calculations are ineffective in cases where you don’t close the action.
Let’s say we are on the river, pot is already 45 bb. Villain decides to bet his remaining 36bb and goes all-in. Hero has two possible options:
- Call 36bb bet;
- Fold his hand.
The question is how much equity do we need to have against villain’s perceived range for calling to be a smart decision?
To proceed with the calculation we only need two numbers. The formula takes into account the following parameters:
- AC (amount to call) – the amount of money we have to put into pot to call villain’s all-in.
- TP (total pot after bet) – the total pot after villain’s bet. Includes all money bet on previous streets, as well as opponent’s bet on the river.
- RE (Required Equity) – the parameter we are trying to calculate. This is the minimum amount of equity against your opponent’s range for the call to be at least break even. If in reality the equity of our hand is greater than the calculated value (RE), then calling becomes a profitable decision in the long run (+EV).
RE = AC / (AC + TP)
Poker mathematics follows all the standard rules of arithmetic. Therefore, we first sum the values in parentheses and then do the division.
AC = 36 (opponent bet on the river)
TP = 45 + 36 = 81 (pot before river action + opponent’s bet)
RE = 36 / (36 + 81) = 30.8%
When calling, a player must win at least 30.8% of the time at the showdown for the call to be justified.
Mathematical calculation is the first step in analyzing such spots. When we have specific numbers, we can evaluate the equity of our cards relative to our opponent’s range and make an optimal decision.
A very common mistake is when people calculate total pot as just a sum of river pot and opponent’s bet. However, you have to include our potential call as well, so it is his bet plus the size of the pot on the river plus the amount we should put in to make a call.
Estimation of required equity at the table
You are unlikely to be able to make complex calculations, even if you only play couple of tables. Therefore, we need a simpler method even if it is not 100% correct in terms of calculations. It does exist and is known as “RE scale”.
A player has to memorize four rules, which are:
- If before the bet there’s no money in the pot, it would take 50% equity to call (e.g. preflop shove, although even then there are 1.5bb in the pot from the blinds).
- Against a pot size bet, we need 33% equity.
- Half pot bet – 25% equity.
- Quarter of a pot bet – 17% equity.
Thus, we have four key points from which we can adjust. Many poker players use bets of the same size, which will simplify the task. However, even in the case of non-standard and random bets, you can approximate the equity you need from those key points.
Let’s look at a specific example. Let’s say your opponent bets 7bb into a 30bb pot. You can quickly estimate on the go that this is slightly less than quarter of a pot (4 * 7 = 28). Therefore, you need slightly less than 17% equity to call.
If we make precise calculations, we get the following:
- RE = AC / (AC + TP);
- RE = 7/ (37 + 7). Remember that this is not (30 + 7), since TP represents the size of the pot after your opponent’s bet;
- RE = 15.9%.
It turns out that our quick estimation was pretty close to the actual number.
Useful literature on poker math
One of the best books for beginner poker players is “Poker Math Made Easy” by Roy Rounder. Its only 34 pages long. We would also recommend lying your sight on “The Mathematics of Poker” by David Sklansky.
In addition, it would also be beneficial for you to reak the following books: Alan N. Schoonmaker “Your Worst Poker Enemy”, Jared Tendler “The Mental Game of Poker”, Leszek Badurowicz “Mental Edge”, Roy Rounder “Poker Math Made Easy”, Matthew Janda “Applications of No-Limit Hold’em”, James Swinney, Adam Jones “Optimizing Ace King”, MMAsherdog “The Preflop Bible”, Peter Clarke “The Grinder’s Manual”.
This library would be enough to understand the basic mathematics in poker and increase your chances of success.
Poker Math FAQ
How is mathematics useful for a poker player?
Mathematics in poker is used to evaluate the profitability of specific actions. Science allows us to determine the probabilities of winning in the current hand, taking into account the starting hand and the board. It also helps you make the right decisions, taking into account the bet size and the pot size.
How to count outs correctly?
You should count outs only after the flop and turn are dealt. Many people make the mistake of performing calculations with only their hand and no board.
Knowing outs is a critical aspect of the game. The calculation helps determine the ratio and evaluate the pot odds.
How to use math in poker?
Mathematics is a powerful tool that should be used at the right time. Combine your math knowledge with other strategies and techniques to achieve greater success and increase your profits.
Thus, poker mathematics is a set of techniques based on mathematical principles. They help you make decisions that are more accurate. By understanding and putting it into practice, you can increase your chances of winning.


Evaluating the effectiveness of a clinical weight loss program
In this study, I analyze a dataset of a 12-month clinical weight loss program to find out:
what factors affect the 12 month weight loss results;
whether an intervention was effective in increasing weight loss.
The dataset contains 234 participants of the weight loss study, and for each participant, we have information on his/her age, race, type of treatment, and the weight change 12 month after the treatment. All relevant biological information has been condensed into one variable called biomarker. The data has been processed to ensure privacies of the participants.
This project was a final project for the statistical modeling class (graduate-level) at UT Austin, Dec 2014.
I plotted every parameter against each other to have a quick look at the relationships between different parameters. The age, race, biomarker variables are self-explanatory, and the other two variables are
- wtch - 12 month weight loss in kg
- treatment - 1= control, 2 or 3 = intervention
We can see the biomarker seems to linearly correlate with the age of the subject. The total numbers of samples are very small in race 2 and 4, and the race 3 seems to have a younger population than race 1.
A quick look
First, let’s contruct a full model with all data points and all avaliable variables as covariants.
￼￼This model does not fit the data very well. The R-squared value is 0.099, which means only about 10 percent of the variations in the data is explained by the model. However, the model is still significant. With a p value of 0.001, we can safely reject the null hypothesis of no relationship all all between the weightloss and all the variables. Race 3 is the most significant covariant with a p value of 5.64e-5, and age is the second most important covariance with a p value of 0.113.
Considering the median of the weight loss is -9.89, the residuals are very large for this model, but we don’t see any strucutre in the residual vs. fittet plot. 10 points show very large leverage. This could be a problem because these 10 points can have too big influence on our accessing the model fit. We may want to exclude those data point, lower their weights, or use a different cost function.
Adding Interaction Terms
To see if including interaction terms between different variables will imporve the model fit, I construct a series of expanded models:
|1-1||Full model with race and treatment as factor variables|
|1-2||Same as 1-1 but without the treatment as a covariant|
|2-1||Add dummy variables for race to include interaction terms between age and race|
|2-2||Same as 2-1 but without the treatment as a covariant|
|3-1||Include dummy variables for both race and treatment|
The BICs and R-squared of the full model and models with interaction terms are shown below. Models with interaction terms have larger BICs and smaller R-squared compared to the full model, which means they fit the data worse than the full model. So I decided not to include the interaction terms.
As seen in exploritory analysis, biomarker has the largest P value, and it seems to correlate with age. We did a simple linear regression model for biomarker ~ age, and found R squared to be 0.4651. This means age predicts the biomarker reasonably well, but the two are not exactly the same. However, since those two variables are not independent of each other, including biomarker will greatly inflate the variance. I decided to examine a few reduced models.
|4-1||Reduced model without biomarker as a covariant|
|4-2||Same as 4-1 but without the treatment as a covariant|
|4-1c||Same as 4-1 but without the two outliers|
|5-1||Reduced model with only age and treatement as covariants|
|5-2||Reduced model with only age as the covariant|
We can see models without race doe not fit the data well (5-1 and 5-2, with larger BIC and much smaller R- squared compared to other models). On the other hand, excluding the two outliers can significantly improve our model fit (with BIC 27 smaller than the model including the outliers). So we pick model 4-1 c, the reduced model without biomarker as a covariant and without the two outliers for our analysis.
Judging from the expectaion and standard error, we are 68 percent confident that the treatment increases weightloss (a smaller wtch value). Treatment 3 has slightly larger effect than Treatment 2, with a expect (1.722 - 1.348 = 0.374) increase in weightloss.
We added dummy variables for the factor variable race and treatment, and constructed a series of models in JAGS. The general form of the model is: wtch ~ N(mu, tau) mu ~ BX
Since we don’t have any prior knowlege associate with the weightloss, we simply choose diffuse normal priors for all the betas in all of our models. We use a diffuse gamma prior for all the taus.
The covariances and DIC for each model is shown in the table below. We are using penalized deviance from dic.samples as our measurement.
|1||age + bio + race + treat||1616|
|2||age + race + treat||1614|
|3||age + race3 only + treat||1613|
|4||age + treat||1635|
|5||age + race||1619|
In model 1, the 95% interval of all the covariance includes zero, therefore we can’t constrain the importance of parameters with great confidence. In model 2, we are 95% confident that the age is a significant factor. Since we have very few samples in race 2 and 4, we decided to try only including race 3 as a covariance. As expected, excluding biomarker imporves the variance in the model parameters. In model 3, both age and race 3 are proved to be significant at 95% confident level. We tried models with no treatment, with no race as covariants, and the model only with age as the covariants. All of them have larger DIC then model 3, and they do not provide any further insight of the data. Therefore we chose model 3 for our inference.
We should note that in the frequentist approach, we included all the races in the model. However, in the Bayesian approach, we only include one dummy variable for race 3. Since we eliminated two variables that are closely dependent on existing variables (race 2, 3, and 4 are not independent of each other), the model significance is improved.
After a few experiments, we decided to thin the data by 100 to improve the mixing. We run 2 chains with 100000 sample each, so we have 2000 samples after thinning. The thinning does not change the modeled coefficients very much. The output parameters of model 3 are (in the order of ‘Inter’, ‘race3’, ‘age’, ‘treat2’, ‘treat3’):
Judging from the coefficients, we are 68% confident that treatment 3 can increase weightloss (with am expected value of -1.69). Treatment 2 is likely to increase the weightloss, but we can’t say it with 68% confidence. On the other hand, race 3 have significantly larger weighloss compared to other races, and the weighloss decreases as age increases. 10 years of increase in age leads to a decrease of 2.2 in weightloss.
Samples for betas and the PDFs of betas are shown below. We can see the mixing is generally well, and we have tighter constrain on treat 2, and treat 3 compared to other variables.


National Council of Teachers of Mathematics PRINCIPLES TO ACTIONS—Ensuring Mathematical Success for All
Two years ago, I was given the book Principles to Action, Ensuring Mathematical Success for All by a consultant now colleague. The authors included nine researchers from the National Council of Teachers in Mathematics. The text is just 117 pages long and includes summaries for guiding principles of school mathematics including; teaching and learning, access and equity, curriculum, tools and technology, assessment, and professionalism (p.5). "It's overarching message is that effective teaching is the non-negotiable core that ensures that all students learn mathematics at high levels and such teaching requires a range of actions at the state or provincial, district, school and classroom levels" (p. 4).
For two years, teachers and I have continued to reexamine our practices and beliefs about teaching and learning mathematics through ongoing professional learning. Our coach and guide frequently used Principles to Actions as a reference tool to not only examine relevant research but to bring to life the teacher moves that are needed to intentionally shift instructional practices for a more student-centered approach.
The heart of the book's content is in the Effective Teaching and Learning section. In this portion of the book, the researchers share, "Eight Mathematics Teaching Practices provide a framework for strengthening the teaching and learning of mathematics...which represent a core set of high-leverage practices and essential teaching skills to promote deep learning of mathematics" (p. 9-10). Each of these practices has been a game-changer for students and teachers in our school. Observing students persist through "productive struggle" while using "mathematical representations" on "tasks that promote reasoning and problem solving" is well, almost magical.
Although It may be magical, it is not easy. Note the image above from my copy found on page 10. I have highlighted, "Build procedure fluency from conceptual understanding." Moving away from handing out the traditional math facts worksheets for automaticity and mastery first, and then engaging "students in making connections among mathematical representation to deepen understanding" was a big switch. The change did not happen right away, but as our understanding grew, our practices evolved. Over time we learned, "A rush to fluency, however, undermines students' confidence and interest in mathematics and is considered a cause of mathematics anxiety" (Ashcraft 2002; Ramirez et al. 2013). #Truth
Also addressed in the "Essential Elements" section of Principals in Action beginning on page 11 is the unproductive and productive beliefs about access and equity in mathematics. The beliefs that have had the most significant impact at our school have included:In our continuum of growth in implementing more evidence-based instructional practices, we are moving away from the general term "all" students to becoming more specific about "each" of our students. In my opinion, this is where a mindset begins to change for teachers and leaders. When you personalize this statement, you tend to reflect inward and reexamine unproductive beliefs than can negatively impact learning or "limit student access to important mathematics content and practice" (p. 63).
- Each student's Mathematics ability is a function of opportunity, experience, and effort.
- Each student is capable of participating and achieving.
- Each student deserves support to achieve at the highest level.
- Each student receives differentiated support.
- Each student is capable of making sense of and persevering in solving challenging mathematics problems and should be expected to do so.
Finally, I must confess it took me two years to finally pick up the book and read it in its entirety. Oh, what I missed on my journey to be and become a better leader who supports teacher leaders in mathematics. My wish is for others who are trying to lead and learn will take the time to absorb the books content to impact learning for each of their students.


SEMINAR: ACTUARIAL WORLD FROM 3 DIFFERENT PERSPECTIVES
Infinitics 2 is an annual event held by Applied Mathematics UPH, consists of various mathematical competitions, seminars and workshops for high school students around different areas in Indonesia. This event aims to increase mathematics skills in order to solve mathematical problems efficiently, and to spread the knowledge about the applications of mathematics in the career world.
There were 2 seminars in Infinitics 2, and one of them is specifically talking about actuarial science. "Think about Actuarial Science", the name of the seminar. I was given a chance as a student who receives READI Project Scholarship to share my actuarial experience together with the seniors: Mr. Iwan Pasila, FSAI and Dr. Helena Margaretha, M.Sc. What an honor. This is one of the most precious opportunity for me personally, I could learn more and more about the field I am currently in with the experts. I could also meet Ms. Theresia Erni as the Communication and KM Expert from READI Project, that always support actuarial mathematics students through READI Project Scholarships and also events.
From this actuarial seminar I could see the actuarial world from different perspectives. I learned from Pak Iwan Pasila, FSAI, who is a professional actuary, about the application of the actuarial studies during our university years. He also share the difference of working as an actuary in the insurance industry and consultancy. Working in the insurance industry will gives us more in-depth skills of the actuarial skills, while working in the consultancy we will tend to communicate more with other people. This gave me wider insights about this actuarial field.
Dr. Helena Margaretha, M.Sc., an actuarial mathematics lecturer, explained how educators design the actuarial program for young potential actuaries while in their university years, especially in UPH. Whereas from me personally, I tried to share my experiences in taking professional exams (PAI and SOA) in my university years, and also the importance of support from READI Project Scholarship for me. Therefore I would also like to express my gratitude to READI Project who have support me and also other students, in lifting our spirits, confidence also financially throughout the year.
I am so grateful to be part of this event, because I still need to learn more from the seniors: Pak Iwan Pasila, FSAI, and Dr. Helena Margaretha, M.Sc. I will always treasure all of the knowledge and experience shared in this event. Thank you Pak Iwan. Thank you Bu Helena. Thank you Infinitics 2!


This toy provides a thrilling way to learn about numbers whilst building a brightly coloured wooden tower. Children can practise both number recognition and counting as they fit each wooden piece next to its individually-shaped numerical neighbour. Made from high quality, responsibly sourced materials. Conforms to current European safety standards. Age 1+ years. Height: 285mm, Width: 90mm, Depth: 90mm. Consists of 11 play pieces.
There are no reviews written yet about this product..


Seventeen Equations That Changed the World
1 in stock
This is a unique history of humanity told through its seventeen defining equations; from Pythagoras to Calculus. From Newton's Law of Gravity to the Black-Scholes model used by bankers to predict the markets, equations, are everywhere - and they are fundamental to everyday life. \"Seventeen Equations that Changed the World\" examines seventeen groundbreaking equations that have altered the course of human history. He explores how Pythagoras' Theorem led to GPS and SatNav; how logarithms are applied in architecture; why imaginary numbers were important in the development of the digital camera, and what is really going on with Schrodinger's cat. Entertaining, surprising and vastly informative, \"Seventeen Equations that Changed the World\" is a highly original exploration - and explanation - of life on earth.
Author: Stewart, Ian
Publication date: 13/06/2013
Imprint: Profile Books UK
|Dimensions||198 × 129 mm|
Only logged in customers who have purchased this product may leave a review.


2 a line on a graph representing data
3 a baseball thrown with spin so that its path curves as it approach the batter [syn: curve ball, breaking ball, bender]
4 the property possessed by the curving of a line or surface [syn: curvature]
5 curved segment (of a road or river or railroad track etc.) [syn: bend]
1 turn sharply; change direction abruptly; "The car cut to the left at the intersection"; "The motorbike veered to the right" [syn: swerve, sheer, trend, veer, slue, slew, cut]
2 extend in curves and turns; "The road winds around the lake" [syn: wind]
4 bend or cause to bend; "He crooked his index finger"; "the road curved sharply" [syn: crook]
EtymologyFrom etyl la curvus
- Bent without angles; crooked; curved.
- a curve line
- a curve surface
- a curve line
- A gentle bend, such as in a road.
- A simple figure containing no straight portions and no angles; a curved line.
- A continuous map from a one-dimensional space to a multidimensional space.
- A one-dimensional figure of non-zero length; the graph of a continuous map from a one-dimensional space.
- An algebraic curve; a polynomial relation of the planar coordinates.
- A one-dimensional continuum.
- (informal, usually in plural curves) The attractive shape of a woman's body.
- algebraic curve
- Bézier curve
- closed curve
- cosine curve
- dragon curve
- elliptic curve
- Lissajous curve
- Jordan curve
- nonsimple curve
- open curve
- pedal curve
- plane curve
- pursuit curve
- simple curve
- sine curve
- space curve
- spherical curve
geometry: one-dimensional figure
- See algebraic curve
informal: usually in plural: attractive features of a woman
- Hebrew: חיטובים (khit'uvym) m|p
informal: attractive shape of a woman's body
- To bend; to crook.
- to curve a line
- to curve a pipe
- to curve a line
- To cause to swerve from a straight course.
- to curve a ball in pitching it
- To bend or turn gradually from a given direction.
- the road curves to the right
cause to swerve from a straight course
bend or turn gradually from a given direction
- Plural of curva
- feminine plural of curvo
- Plural of curvă whores
In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. A simple example is the circle. In everyday use of the term "curve", a straight line is not curved, but in mathematical parlance curves include straight lines and line segments. A large number of other curves have been studied in geometry.
This article is about the general theory. The term curve is also used in ways making it almost synonymous with mathematical function (as in learning curve), or graph of a function (Phillips curve).
In mathematics, a (topological) curve is defined as follows. Let I be an interval of real numbers (i.e. a non-empty connected subset of \mathbb). Then a curve \!\,\gamma is a continuous mapping \,\!\gamma : I \rightarrow X, where X is a topological space. The curve \!\,\gamma is said to be simple if it is injective, i.e. if for all x, y in I, we have \,\!\gamma(x) = \gamma(y) \implies x = y. If I is a closed bounded interval \,\![a, b], we also allow the possibility \,\!\gamma(a) = \gamma(b) (this convention makes it possible to talk about closed simple curve). If \gamma(x)=\gamma(y) for some x\ne y (other than the extremities of I), then \gamma(x) is called a double (or multiple) point of the curve.
A curve \!\,\gamma is said to be closed or a loop if \,\!I = [a, b] and if \!\,\gamma(a) = \gamma(b). A closed curve is thus a continuous mapping of the circle S^1; a simple closed curve is also called a Jordan curve or a Jordan arc.
A plane curve is a curve for which X is the Euclidean plane — these are the examples first encountered — or in some cases the projective plane. A space curve is a curve for which X is of three dimensions, usually Euclidean space; a skew curve is a space curve which lies in no plane. These definitions also apply to algebraic curves (see below). However, in the case of algebraic curves it is very common not to restrict the curve to having points only defined over the real numbers.
This definition of curve captures our intuitive notion of a curve as a connected, continuous geometric figure that is "like" a line, without thickness and drawn without interruption, although it also includes figures that can hardly be called curves in common usage. For example, the image of a curve can cover a square in the plane (space-filling curve). The image of simple plane curve can have Hausdorff dimension bigger than one (see Koch snowflake) and even positive Lebesgue measure (the last example can be obtained by small variation of the Peano curve construction). The dragon curve is another unusual example.
Conventions and terminology
The distinction between a curve and its image is important. Two distinct curves may have the same image. For example, a line segment can be traced out at different speeds, or a circle can be traversed a different number of times. Many times, however, we are just interested in the image of the curve. It is important to pay attention to context and convention in reading.
Terminology is also not uniform. Often, topologists use the term "path" for what we are calling a curve, and "curve" for what we are calling the image of a curve. The term "curve" is more common in vector calculus and differential geometry.
Lengths of curves
If X is a metric space with metric d, then we can define the length of a curve \!\,\gamma : [a, b] \rightarrow X by
- \mbox (\gamma)=\sup \left\
aberrancy, aberration, arc, arch, artful dodge, artifice, bag of tricks, bear off, bend, bend back, bias, blind, bluff, bosey, bow, bowl, branch off, branching off, cast, catacaustic, catch, catenary, caustic, change of pace, change the bearing, change-up, chicanery, chouse, chuck, chunk, circle, circuit, circuitousness, circumference, coil, compass, conchoid, corner, crook, curl, curvation, curvature, curve-ball, declination, decurve, deflect, depart from, departure, design, detour, deviance, deviancy, deviate, deviation, device, deviousness, diacaustic, diffract, diffuse, digress, digression, dirty deal, dirty trick, discursion, disperse, distort, divagate, divagation, divaricate, divarication, diverge, divergence, diversion, divert, dodge, dogleg, dome, double, downcurve, drift, drifting, ellipse, embow, errantry, excursion, excursus, exorbitation, fast deal, fastball, feint, festoon, fetch, ficelle, flex, fling, flip, forward pass, gambit, gimmick, googly, hairpin, heave, heel, hocus-pocus, hook, hump, hunch, hurl, hyperbola, incurvate, incurvation, incurvature, incurve, indirection, inflect, inflection, joker, juggle, knuckleball, lateral, lateral pass, lituus, lob, loop, obliquity, outcurve, parabola, pass, peg, pererration, pitch, ploy, pull, put, rambling, recurve, reflect, reflex, refract, retroflex, rondure, round, ruse, sag, scatter, scheme, screwball, scurvy trick, serve, service, sheer, shift, shifting, shifting course, shifting path, shot-put, shy, sinker, sinus, skew, slant, sleight, sleight of hand, sleight-of-hand trick, slider, sling, spiral, spitball, spitter, stratagem, straying, subterfuge, swag, sweep, swerve, swerving, swinging, tack, throw, toss, tracery, trend, trick, turn, turn aside, turning, twist, upcurve, variation, vary, vault, veer, wandering, warp, wile, wind, yaw, zigzag


The Learning Management System (LMS) changes most students' learning trends nowadays. It provides learners with online resources intended for self–paced learning design. However, the usefulness of LMS, especially to 21st-century learners, does not guarantee effectiveness in all areas of learning, considering that not all students have the capability to adapt to this modality, predominantly in developing mathematical proficiency. Hence, this research aimed to investigate the effects of LMS on the motivation and mathematics achievement of some Junior High School students and enabled the researcher to propose some enhancements to the existing LMS implementation. Research-based survey questionnaires were administered to 126 students and eight teachers to identify their perspectives about using LMS in Math class and characterized its impact on the motivation and achievement of JHS students. The previous year's grades of the students in Math were also utilized to sufficiently satisfy the research objectives. The descriptive-correlation methods revealed that the Grade 8 students are motivated in their Mathematics achievement utilizing the LMS in full of which, significant difference were noted in their grades. Teachers were also noted being motivated by the use of LMS. No significant relationship between the student's level of motivation and their achievement during the minimal and full utilization of LMS, implying no direct effect found on mathematics achievement as a result of utilizing the LMS. Enhancements of LMS is proposed for Math Department.
Theresa Caya, De La Salle Lipa Integrated School, Philippines
About the Presenter(s)
Ma. Theresa De Ocampo - Caya is a school administrator-Math Faculty in De La Salle Lipa in the Philippines. Some of her papers include topics on Math Anxiety and Block Teaching Model and has presented papers in the national, and international forum.
Additional website of interest
See this presentation on the full schedule – Wednesday Schedule


For each of the sections, a linearized model for the furnace was derived near the midpoint of the respective section (e.g., for section4 the model was linearized near T2 = 910��Celsius).MLD hybrid model generated from the HYSDEL file for the multimodel linearized problem has 25 continuous states, 9 inputs (4 continuous, 5 binary), and 3 continuous outputs. The HYSDEL Temsirolimus model has 22 continuous auxiliary and 15 binary auxiliary variables. The optimization problem to be solved has 118 mixed-integer linear inequalities. The sampling time of the system is 0.5 minutes. If comparison to the hybrid model of the furnace linearized in one operating point whose HYSDEL representation has only 38 mixed-integer linear inequalities, it is obvious that the complexity of the optimization problem is significantly increased with the introduction of multimodel linearization.
This affects the computation time of the optimization algorithm and favors the one point linearization method for implementation if it has satisfactory behavior.3. Simulation ResultsIn order to compare the quality of the designed controllers, we have designed equivalent simulation conditions for the four algorithms. In this study, we will compare the linear MPC, multiple-model MPC, hybrid MPC, and hybrid multiple-model MPC.The disturbance signals from the front and the back hatches and the timing of the pipe entering in the first zone of the furnace are graphically represented on Figure 4. In Figure 4, the logic variable for pipes entering zone 1 is presented. The logic variables for zones 2 and 3 have deterministic dependence on this value with fixed delay.
In reality, this delay is represented through the line speed of the conveyor driving the pipes in the furnace, but this is to be done in near future. During this simulation, a fixed delay time of 10 minutes between zones is adopted. During the simulation, the continuous disturbance signal has value of 15��Celsius.Figure 4Disturbances during the experiment.The Anacetrapib main results are presented in Figures Figures5,5, ,6,6, and and77 where the temperatures in the respective zones of the furnace are presented long with the reference signal. The control signals applied to the three control valves, respectively, are presented in Figures Figures8,8, ,9,9, and and10.10. Figure 5Temperature in the first zone.Figure 6Temperature in the second zone.Figure 7Temperature in the third zone.Figure 8Control actions of the first valve.Figure 9Control actions of the second valve.Figure 10Control actions of the third valve.From the presented results, it is obvious that introducing the hybrid control approach for high consumption industrial furnace improves the quality of the control.