Actuarial work is interdisciplinary at its core. Practicing actuaries draw upon mathematics, statistics, economics, finance, risk management, computer science, and much more to solve problems from how much insurance costs to complicated investment hedging.
Every subject/paper provides not just complete knowledge but also the helps to develop application based skills in real world situations. The actuarial course involves creating mathematical models of events and the world around us, thereby helping the company to take informed decisions which will lead to the least probability of financial losses. The actuarial education model can be likened to that of the medical education model, where the emphasis is on imparting education through the actual hospital work environment.
Since a student has to clear 13 subjects to attain fellowship, the course requires consistent efforts, dedication and strong will to attain fellowship.
Typically, the study route involves clearing the following :
- The first group comprises of the Core Principles ( CS, CM & CB) series; these involve development of theory of actuarial science and applications of mathematics and statistics to the various actuarial applications such as life insurance, general insurance, employee benefits, investment and other areas. An introduction to economics, financial economics and financial reporting is also included at this stage. Although most part of the course is somewhat theoretical, the exercises and the questions in the examination are practical in nature as they reflect real life situations of the area of work to which the subject is applicable.
- The second group comprises of Core Practices (CP series); where in CP1 paper covers strategic concepts in the management of the business activities of financial institutions and programmes, including the processes for management of the various types of risk faced, and providing appropriate solutions to business problems. CP2 subject equips the students to create models data, document the work, analyse the methods used and outputs generated. CP3 subject is meant to develop skills of communication for technical aspect of the Core Principles (CS, CM & CB) series subjects in simple language in order for it to be easily explained to non-technical persons. Here again the stress in examination questions is on demonstration of the communication skills in real life environment.
- The next group comprises of SP series, which builds on the Core Principles Stage but in individual specialism (non-jurisdiction specific). The SP series subjects are in line with the development of practices and related principles in each area of work.
- The final group is SA series, where subjects comprises of a thorough understanding of principles and application of the knowledge thus gained. It also includes demonstration of skills, professionalism and judgment in an essentially practical situation. There is no requirement to have passed the corresponding specialist principle subject, however, the Specialist Advance subjects will typically assume knowledge of the corresponding Specialist Principles subject.
The actuarial education model, therefore, is based on a combination of work with its application. As such, substantially, all these educations beyond CS,CM & CB series subjects take place in the work environment itself. The success in examinations is based on and associated with the corresponding work experience and insight, thus gained.
The career progress of an actuary is directly linked to his / her progress and performance in the examination and as a result, there is a very high likelihood that by the time a student finishes the SP series, he/she would be placed with management level of responsibilities.


I was extremely pleased to see Alan Turing being put on the UK's new £50 note. What's more impressive, however, is the attention to detail in this note.
You see the binary string that is on the note that reads 1010111111110010110011000 actually converts to the binary number 23061912 which, believe it or not, is the date Alan Turing was born - 23rd of June 1912.
I found this out from a friend who sent me the following Tweet:
I just got a nice little shiver when working out whether the binary on the ribbon of the new £50 banknote meant anything.— dan barker (@danbarker) July 15, 2019
1010111111110010110011000 is 23061912 in decimal. Alan Turing was born on the 23rd June 1912. What a nice touch.
RIP, Alan. pic.twitter.com/BUXzrT31FY


Linear Models and Effect Magnitudes for Research, Clinical and Practical Applications
Will G Hopkins
Sportscience 14, 49-58, 2010 (sportsci.org/2010/wghlinmod.htm)
Sport and Recreation, AUT University, Auckland 0627, New Zealand. Email. Reviewer: Alan M Batterham, School of Health and Social Care, Teesside University, Middlesbrough TS1 3BA, UK.
Update 2 May 2017. Figures illustrating moderator and mediator analyses now moved here from the slideshow on Research Designs.
Update 4 Jan 2017. I improved the slides on number needed to treat, odds ratio in case-control studies, and relationships between risk, hazard and odds ratios.
Update 6 June 2016. I now advise use the p value for the odds ratio in a logistic regression to get confidence limits for the corresponding proportion ratio. (I checked with simulations that this approach is accurate. Converting the confidence limits for the odds ratio to those for the proportion ratio does not work well, so I removed that advice.) A few other minor edits.
Update 23 Oct 2013. Rank transformation is now dismissed as an approach to non-uniformity, and the analysis of win-draw-lose outcomes in matches is now mentioned as an example for cumulative logistic regression.
Update 16 Sept 2012. There is now a single set of magnitude thresholds for ratios of proportions, hazards and counts. The thresholds are the same as those I proposed previously for counts and rare events. I have removed the shorter version of the slideshow.
Update 26 Sept 2011. Simplification of the introductory slides; coding of nominal predictors with dummy variables; models for controlled trials; improvements to slides dealing with nominal and count dependents, and a shorter version of the slideshow with less detail on nominal and count dependents.
Update 9 Sept 2010. Slide showing residuals vs predicteds for a dependent requiring log transformation. More information on multinomial regression (e.g., for a Likert scale with few items or skewed responses). Other minor improvements.
Update 28 Aug 2010. Odds-ratio thresholds of 1.5, 3.4, 9.0, 32 and 360 now included as an adjunct to proportion-difference thresholds of 10, 30, 50, 70 and 90 percent when modeling and interpreting common time-independent classifications. These odds-ratio thresholds, which I computed directly from the proportion differences centered on 50% (55 vs 45, 65 vs 35, etc.), agree well with a formula devised by Chinn (2000) to convert an odds ratio to a standardized difference in means (ln(odds ratio)/1.81).
After presenting the Magnitude Matters slideshow recently in several workshops, I realized that it needed more on the role played by linear modeling in estimation of effects. The additive nature of the linear model is the basis of adjustment for the effects of other factors to get pure or un-confounded effects and to identify potential mediators or mechanisms of an effect. The additive nature of linear models also explains why we should use the log of the dependent variable to estimate uniform percent or factor effects. A consideration of the error term in a linear model provides further justification for the use of log transformation, along with the use of the unequal-variances t statistic or mixed modeling in analyses where the error term differs between or within subjects. Finally, the analyses for counts and binary dependent variables make little sense without understanding how the underlying linear models require such strange dependent variables as the log of the odds of a classification or the log of the hazard of a time-dependent event. The new slideshow addresses all these issues and more, using material from the recent progressive statistics article (Hopkins et al., 2009) and a book chapter on injury statistics (Hopkins, 2009). The slideshow hopefully represents a useful combination of theory and practical advice for anyone who wants to understand and estimate effects in their research.
For more on the way we infer causality, deal with confounders, and account for mechanisms in the relationships between variables, see the slideshow/article on research designs (Hopkins, 2008). My article and spreadsheets on understanding stats via simulations (Hopkins, 2007a) are useful for learning more about log transformation, straightforward analyses, and inferential statistics. Follow this link to a slideshow that details the various approaches to repeated measures and random effects; I presented it at a conference in 2003, but it is still up to date.
When it comes to actual data analysis, you will need extra help with the practicalities of the use of a spreadsheet or stats package. Peruse the article on comparing two group means and play with the associated spreadsheet to come to terms with simple comparisons of means and adjustment for a covariate (Hopkins, 2007b). The article on the various controlled trials and the associated spreadsheets are a little more advanced and also full of useful material (Hopkins, 2017). See the item on which stats package for an overview of some of the stats packages and for a set of files that are useful for SPSS users. If you already have some experience with the SAS package but need specific advice on Proc Mixed, Genmod or Glimmix, contact me.
Chinn S (2000). A simple method for converting an odds ratio to effect size for use in meta-analysis. Statistics in Medicine 19, 3127-3131
Hopkins WG (2007a). Understanding statistics by using spreadsheets to generate and analyze samples. Sportscience 11, 23-36
Hopkins WG (2007b). A spreadsheet to compare means in two groups. Sportscience 11, 22-23
Hopkins WG (2008). Research designs: choosing and fine-tuning a design for your study. Sportscience 12, 12-21
Hopkins WG (2009). Statistics in observational studies. In: Verhagen E, van Mechelen W (editors) Methodology in Sports Injury Research. OUP: Oxford. 69-81
Hopkins WG (2017). Spreadsheets for analysis of controlled trials, crossovers and time series. Sportscience 21, 1-4
Hopkins WG, Marshall SW, Batterham AM, Hanin J (2009). Progressive statistics for studies in sports medicine and exercise science. Medicine and Science in Sports and Exercise 41, 3-12. Link to PDF.
Published July 2010


In American middle school geometry lessons, students delve into the fascinating world of shapes, sizes, and spatial relationships. Geometry, a branch of mathematics, forms a critical part of their curriculum, offering a deep understanding of the physical world around them.
Students start with the basics, exploring points, lines, and planes. They learn to measure and classify angles, from acute to obtuse, and discover the concept of right angles. Triangles become a focal point, as students differentiate between equilateral, isosceles, scalene, and right triangles. The Pythagorean Theorem emerges as a fundamental tool, connecting the sides of right triangles.
Quadrilaterals, including squares, rectangles, parallelograms, and rhombuses, are introduced, with an emphasis on their unique properties. Circles become a captivating topic as students study their components, such as radii and circumferences. They learn to calculate the area and circumference of circles, providing practical skills.
Coordinate geometry takes students into the realm of the Cartesian coordinate plane, teaching them how to plot points and graph lines and shapes. This skill is vital for understanding spatial relationships and has applications in various fields.
As geometry lessons progress, students delve into three-dimensional shapes, calculating the volume of cubes, prisms, and cylinders. Concepts of similarity and congruence are explored, enabling students to identify and work with similar and congruent shapes.
Geometry lessons also introduce geometric proofs, where students use deductive reasoning to prove theorems and geometric properties, fostering critical thinking skills.
Through middle school geometry, students acquire not only mathematical knowledge but also problem-solving skills that extend beyond the classroom. This subject forms a solid foundation for advanced math courses and has practical applications in architecture, engineering, and other fields where understanding shapes and spatial relationships is essential.


Workshop I and II
All ELL Students WILL RECEIVE A PERIOD OF cONTENT AREA sUPPORT FOR mATH AND sCIENCE. dURING THIS TIME THEY will be pre-taught or re-taught content area concepts. For this, I will work closely with science and math content area teachers to ensure that workshop lessons are aligned to the curricula they are being exposed to or will be exposed to in main stream classrooms.
Will ELL's be prepared to work with academic concepts given to them in math and science classes?
Absolutely, by being provided the target academic words and units ahead of time by the content areas teachers, I am able to differentiate instruction by modifying lessons and clarify meaning as needed by the students. In addition, students are not only learning the meaning of such vocabulary for easier transition in classrooms, they will also put their understanding of these mathematical or scientific concepts into practice.
Students will be given ample time to work on differentiated activities pertaining to lessons and also solve the old age mystery asked by many children time again, "Why do I need to know this in my life". To help answer this, after every lesson students are required to collaborate with a partner. During this time, they will strategically apply critical thinking and problem solving skills to create real life situations, where these concepts will take place.


https://en.wikipedia.org/wiki/Fourier_analysis https://en.wikipedia.org/wiki/Wavelet|Frequency domain analysis (or spectral density estimation), is the process of decomposing a complex signal into simpler parts. Many physical processes are best described as a sum of many individual frequency components. Any process that quantifies the various amounts (e.g. amplitudes, powers, intensities, or phases), versus frequency can be called spectrum analysis. The Fourier transform of a function produces its frequency spectrum by decomposing the function into its sine and cosine components. Whereas the standard Fourier transform is only localized in frequency, wavelets are localized in both time and frequency. Wavelets are handcrafted to correlate with particular frequencies in a signal; a set of wavelets is usually used for a complete analysis.


When you heard about fractions the first thing that came into our mind is mathematics, but it is an extremely important concept that we used in our day-to-day life, right from reading a clock to baking a cake. The learning of fractions forms the basis for understanding various math topics and is an essential life skill. Kids must gain an in-depth understanding of this topic to work comfortably with them. The concept of fractions usually feels confusing for kids due to its complexity. With educational resources like math puzzles and games, fractions can be made fun for kids. It also enables kids to visualize fractions in real life to understand their applications. Solving fraction puzzles also help in promoting a child’s interest in math by making it exciting and fun for them. You can also explain fractions to your kids by telling them some interesting stories which include puzzles related to fractions.
Even you can plan fun activities for kids through which you can explain fractions. These activities may include games, riddles, and many more. The kids will learn something and also they will enjoy the activities. When it comes to kids it is really important that they enjoy the activities. When they get bored, they will just ignore the main concept and their minds will get diverted. Whenever you will explain fractions make sure that you make them enjoy it otherwise, they will treat it as a boring mathematics concept. Here, we will discuss one interesting card game just like UNO which will help kids to understand fractions. You can create cards where you can write fractions on each card. Those who will collect the whole number at first will win the game. It will become more clear through example, let say A and B are playing A has two cards named half and ¼ and B has two cards named ¼, ¼, now A need one more ¼ card to win the game and B need one-half card to win the game. As the kids will calculate the numbers they will understand the fractions.
Let’s start with understanding the true meaning of the term fraction and its importance in our day-to-day life.
What is the meaning of the term fraction?
Part of a whole is called a fraction. In simple words, each whole number has two parts and a fraction represents that whole number. The number which is on upper side of the fraction is called a numerator. It represents the small part of the whole or collection that we considered. Let us understand it through a simple example when it comes to the distribution of pizza we divide it into five equal slices, every divided slice represents a fractional value of 1/5, and the remaining pizza represents 4/5.
Importance of the method Fraction in our everyday life
Learning fractions concepts enables children to gain confidence while working with fractions daily. Children who are advanced in their fraction skills can quickly figure out solutions to various complicated situations with ease, like managing their time and schedules, estimating the right proportion of ingredients to bake cookies, and so on. There are many ways you can help your child see and learn the importance of method fractions in their everyday life. Let’s discuss some real-life examples in an active way that will help them learn fractions.
Use of Fractions in our day to day life
Distributing food is a great real-life example that anyone can use to develop a child’s understanding of fractions. Dividing things among groups is a very simple application of fractions that will enable kids to grasp this concept easily. For example, you can explain to them when they divide cake slices equally amongst their friends it also requires fractions.
Dividing a single bill amount among a group of two or more people is one of the easy and helpful activities to teach fractions. For example, To divide the total amount of a restaurant bill among three or four friends, to do it properly they will require fractions.
When we go shopping, to calculate discounts and prices of various products, we have to deal with fractions. For example, when we saw the tag line of 50% off on a bag’s price the first thing we do was calculating the discount amount and here you will require fractions.
Cooking & Baking
Trying and following various recipes during cooking is also helpful in learning fractions. Following various recipes also require an understanding of fractions. For example, to estimate one and half a teaspoon of cocoa powder, ¼ quarter a tablespoon of sugar, etc. They are also useful when it comes to serving ingredients to people according to the present number of people.
Health and Fitness
Sports comes first when it comes to health and fitness. They are a great means to introduce fractions to your kids. Let’s understand it through a simple example, a football game has four equal quarters, and after two quarters, it’s a half time. We can use fractions if we want to analyze the performance of a particular/selected player or the entire team.
Tests and Assessments
Scores of any tests or exams are expressed in terms of fractions. For example, if the marks obtained by a student are 15 out of 20, it is represented in fractional form, i.e., 15/20.
Reading time is also a way of teaching fractions to kids. They can learn to represent half an hour, quarter past, and quarter with the fractions.
Fractions form the understanding of various math facts and topics. Visualizing fractions in daily life is highly beneficial for kids to learn its applications. The use of educational resources like puzzles, games, and worksheets enables kids to learn fractions better. Cuemath offers plenty of interactive resources for kids to learn and understand math in an interesting way. To find some interesting ways to teach fractions check the website.


To calculate the gradient of a straight line we choose two points on the line itself. The difference in height (y co-ordinates) ÷ The difference in width (x co-ordinates). If the answer is a positive value then the line is uphill in direction. If the answer is a negative value then the line is downhill in direction.
Also Read: How to Make Corned Beef Hash?
How to Find the Gradient of a Line?
How do you calculate a gradient?
To find the gradient you find the partial derivatives of the function with respect to each input variable. then you make a vector with del f/del x as the x-component, del f/del y as the y-component, and so on… Comment on lingling40hours’ post “To find the gradient you …”
How do you find the gradient of a line given two points?
Step 1: Find the Slope (or Gradient) from 2 Points
- subtract the Y values,
- subtract the X values.
- then divide.
What is the gradient of a straight line?
A line that goes straight across (Horizontal) has a Gradient of zero.
What is gradient Colour?
Color gradients, or color transitions, are defined as a gradual blending from one color to another. This blending can occur between colors of the same tone (from light blue to navy blue), colors of two different tones (from blue to yellow), or even between more than two colors (from blue to purple to red to orange).
What is the concentration of gradient?
The difference in the concentration of a substance between two areas is called the concentration gradient. The bigger the difference, the steeper the concentration gradient and the faster the molecules of a substance will diffuse.
What is the equation of a line given two points?
Find the Equation of a Line Given That You Know Two Points it Passes Through. The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept.
What is the two-point formula?
The two-point form formula of a line is given as,
y−y1=y2−y1x2−x1(x−x1) y − y 1 = y 2 − y 1 x 2 − x 1 ( x − x 1 )
y−y2=y2−y1x2−x1(x−x2) y − y 2 = y 2 − y 1 x 2 − x 1 ( x − x 2 ) ,
where (x1,y1) ( x 1 , y 1 ) and (x2,y2) ( x 2 , y 2 ) are coordinates of two points lying on that line.


Maths at Appleton Roebuck:
Using the first DfE recommended textbook and workbook scheme, Maths No Problem, allows us to follow a mastery approach and means our students have a clear progression across concepts and the opportunity to deepen their understanding. Lessons follow a clear progression from year to year and from lesson to lesson over units of learning. Calculation progression is modelled on the structures of MNP and ensures that pupils are moved through concrete, pictorial and abstract representations in a planned sequence and at an appropriate pace. Fluency of number is at the core of our curriculum and daily fluency sessions build this confidence through school. Problem solving is at the heart of our maths curriculum and our lessons use real-life problems as their foundation. Journaling activities and ‘Tricky Traps’ provide our learners with an opportunity to go deeper.
A Mastery Curriculum:
At Appleton Roebuck, we are of the belief that all pupils are capable of achieving high standards and challenge is part of everyday maths for all pupils. A Mastery Curriculum incorporates the 5 big ideas; Fluency, Mathematical Thinking, use of Representation and Structure, Procedural and Conceptual Variation and Coherence. Mastery teaching addresses the needs of all pupils on a daily basis. It meets the expectation that the majority of pupils will move through the programme at broadly the same pace with decisions about when to progress based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly are challenged through questioning, being offered rich and sophisticated problems in the form of a ‘Tricky Traps’ or through journaling activities which promote deeper understanding. Planning for Mastery is developing across school and is supported by the maths leader, Mastering number in EYFS – Y2 and the Maths No Problem curriculum.
Maths lessons at Appleton Roebuck follow the 5-part Maths No Problem structure. All lessons begin with fluency, ‘shape of the day’ and a recap of the previous learning before following the maths no problem lesson structure.
1.Explore - lessons start with an opportunity to explore a real-life context problem and explore the maths it contains
2.Master - master the core maths needed to achieve the learning outcome
3.Guided - working with a partner or adult to guide themselves through a problem
4.Independent - an opportunity to master the learning outcome independently
5.Journaling / Tricky trap - an opportunity for learners to go deeper if needed
We aim to ensure that all pupils become fluent in the fundamentals of mathematics over time so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately. Daily fluency sessions are a core part of our maths curriculum and ensure pupils develop the ability to retrieve number facts rapidly. Children are required to reason and make connections between calculations. The connections made improve their fluency.
For example: Don’t count, calculate
For example, with a sum such as:
4 + 7 =Rather than starting at 4 and counting on 7, children could use their knowledge and bridge to 10 to deduce that because 4 + 6 = 10, so 4 + 7 must equal 11or 7+3 = 10 so 7+4 =11.
Reasoning (mathematical thinking):
Reasoning is a core part of our curriculum. All children are expected to respond using mathematical vocabulary in full sentences explaining their thinking. Our curriculum promotes enquiry, identifying relationships and developing an argument, justification or proof using mathematical language. Children are able to extend their understanding beyond arithmetic.
Progression in reasoning can be seen in lessons by the use of carefully scaffolded and differentiated questions
- Describing – saying what happened. What do you notice? What do you see?
- Explaining – beginning to offer reasons for what was done. How did you solve it?
- Convincing – can you convince me your mathematical thinking is sound?
- Proving – providing evidence that your thinking is correct.
NCETMs Mastering Number programme aims to build firm foundations in the development of good number sense for all children in Reception, Year 1 and Year 2 in addition to the maths lesson. The aim over time, is that children will leave KS1 with fluency in calculation and a confidence and flexibility with number. During these sessions, attention will be given to key knowledge and understanding needed in reception and then continues to build on this through KS1 to support success in the future.
Maths in EYFS and Year 1
Maths in Early years follows the Number blocks long term planning. Number blocks enable our reception children to build a solid understanding of number. The daily sessions are also supported by a daily mastering number session. Dedicated maths areas are planned for in provision and allow the children to explore maths naturally.
Maths in Year 1:
Maths in Year 1 follows the maths no problem long term planning and uses the maths no problem lesson structure. Sometimes, key concepts can take longer to cover and a lesson may be taught over multiple days. The daily maths lesson is also supplemented with a mastering number session focusing on the core areas of number.
Assessment of maths:
We use PUMA for summative assessment of maths once a term. In Year 1, assessment is done by formative teacher assessment. The lesson structure of our maths lessons allows for lots of opportunities to recap and revisit key learning and identify any misconceptions. Daily fluency tasks also allow an opportunity to assess prior learning and for any intervention to be taken.


Math and Art Essays
- Math & Art | Modern Period - 8th
- Math & Art | Modern Period - 7th
- Modern Period: Non Euclidean Geometry - 7th
- How Does Math and Art Intersect? | 7th
- Art in the Renaissance period and its mathematical relation - 8th
Mathematics has changed a lot and has evolved. During the modern period a lot of mathematical topics were introduced over time. We are going to talk about how mathematics developed during the modern period and their relation with art. This takes place from the 15th century, (from the year 1400 to the present time). In this period of time in mathematical history, lots of works of art were created. We are going to talk about how modern period mathematics are really involved in famous works of art and how math really affects them. These are the Weather Project, The bean, Space and time and some artists like Leonardo da Vinci, Gego and Santiago Calatrava. Math is in most of the things we use on a daily basis as well as things we see. Whether it’s a painting, a sculpture, a shape or a museum installation.
The first artwork was named “Weather" the artist is Olafur Elliason and is at the Tate Modern art museum in London. It consists of a semi-circular screen and a set of mirrors on the ceiling and some artificial water mist to create the illusion of the sun. The semicircular screen reflects on the ceiling of mirrors and creates a full circle. Math is in this installation because geometry is used for the shape of the sun, being a semi-circle turning into a complete circle. Reflection of shapes is also used, because the semi-circle reflects on the mirror ceiling creating a complete circle. Also, the way that the light of the screen reflects on the mirror creates an angle by the light that bounces on the surface. Depending on the distance from the mirror the angle of the light changes. The intention is to create the illusion that you are looking at the sun. The light is reflected in a certain way that makes the sight of the sun more real. He was inspired by global warming and the project gave the illusion of being close to the sun. The light the fake sun sends is mono-frequency, it means it only emits one frequency. The relation with math we analyze in this artwork is related with the axis of symmetry because of the mirrors that create whole circles and reflect the light. (Images 1 to 5)
The next artwork is the “Vitruvian Man”, the ideal human body proportions are reflected in Leonardo da Vinci’s artwork. The Roman Architect Virtivius spoke in his writings about how the human body was divided into geometric shapes like the circle and square. Virtuviu’s ideas are the inspiration for the artwork. Leonardo’s interest in geometry and how it relates to the human form is evident in the picture. The idea of ideal proportions, where both the square and the circle fit, forms the foundation of the Virtuvian Man. It
illustrates the notion that particular proportions and measures are regarded as visually pleasant and harmonious. He also used geometric shapes, with the points of the finger and toes touching the circumference of the circle and the outstretched arms and legs aligning with the edges of the square. Additionally, the drawing displays bilateral symmetry. (Images 6 and 7)
Renaissance Mathematics (15th-16th century); The Renaissance period marked a revival of mathematical study. Scholars such as Leonardo da Vinci made contributions to geometry and proportion theory. The invention of the printing press allowed mathematical knowledge to be disseminated more widely.
Santiago Calatrava is a Spanish architect, considered one of the most creative architects in the world. In 1999, The New York Times organized an event in which the purpose was to create a time capsule and put documents inside it and it would be sealed until the year 3000. Calatrava was selected to do this project and he came up with an interesting design. I think this shape relates through math by analytical geometry. Analytical geometry is a branch of mathematics that combines algebra and geometry. It is concerned with the study of geometric shapes and their properties using algebraic equations. In art, analytical geometry can be used to create precise geometric shapes and designs, as well as to explore the relationships between different shapes and forms. (Images 8 to 10)
The Bean was created by Anish Kapoor, in 2006 (Chicago). Anish Kapoor got inspired to do this by liquid mercury, and wanted to reflect Chicago's view. The bean consists of an elliptical sculpture with platonic material, made out with a perfect balance. This has a very complex geometric shape that requires a very specific mathematical process. This sculpture relates to math by plane of symmetry because the figure is symmetrical if you cut it through the middle. Its shape is also similar to an ellipsoid 2D but if you look at it through the top it becomes an ellipsoid 3D. It is made out of 110 tons. The arch measures 20 meters long, 10 meters wide and 13 meters high. The curved part needed to be calculated very well to get that result. (Images 11 and 12)
The Reticularea artwork is Gego most famous sculpture. This sculpture does not represent specific objects, these sculptures are primarily concerned with exploring the interplay between light, space, and form. Gego used 2 mathematical concepts that we recognized, the first one he used was geometry. The sculpture is characterized by an intricate geometric pattern. The sculpture has straight lines, angles, and curves. Another
mathematical concept is spatial relationships, the arrangement of metal strips in the Reticularea explores the concept of space. It is a mathematical concept used to refer to all points of space and time and their relation to each other. Historically, space and time were thought of as separate entities. Time was thought to pass at the same rate for everyone, regardless of where they were or how fast they were moving. Similarly, measurements of distance were thought to be the same for everyone. When Albert Einstein developed the idea of spacetime, he showed that measurements of time and distance between the same events could differ for different observers. But at the same time, he showed that these measurements could be combined in a systematic way. Gravity feels strongest where spacetime is most curved, and it vanishes where spacetime is flat. This is the core of Einstein's theory of general relativity, which is often summed up in words as follows: "matter tells spacetime how to curve, and curved spacetime tells matter how to move". In math, time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future. Time is used to quantify, measure, or compare the duration of events or the intervals between them, and even, sequence events. (Images 13 to 16)
Throughout history, the relationship between mathematics and art has been a powerful force, providing artists with a rich set of tools to explore and express the beauty of the natural world. In the modern period, artists like Santiago Calatrava, Olafur Eliasson, Gego, and Anish Kapoor have continued to use mathematical principles to create beautiful works of art that challenge our perceptions of space, form, and texture. In conclusion, the use of mathematics in art has had a deep impact on the way we understand and appreciate the beauty of the natural world. From bridges and buildings to sculptures and installations, the artists of the modern period continue to push the boundaries of what is possible through their innovative works. By embracing the principles of mathematics and science, they have created a set of tools that allow us to see the world in new and exciting ways, inspiring us to explore the limits of our imagination and creativity.
We in the world divide time into periods to divide the advancements the world has. There exist lots of time periods that contain art advancements, but in this essay we are going to talk about the modern period. The modern period covers the period of time from 1,450 to the present day. Since 1,450 there has been a lot of art history and we are going to cover 5 highlights of art in the modern period that have a relationship with math and identifying and explaining the relationship. Art in the modern period saw a new discovery, paintings passed from being 1 dimensional to being 2 dimensional,also gave new advancements in architecture using new mathematical techniques, and the compositions present symmetry, proportion relations, perspective with a central vanishing point, the figures present volumetric treatments. There were and are lots of artists that make use of mathematics, so in the following paragraphs we are going to talk about the biggest highlights in mathematics and art.
One of the highlights is “Las Meninas de Velásquez” that embraces the change between 1 dimensional and 2 dimensional “Las Meninas de Velásquez”. This painting was finished in the year 1656, it was made by famous painter Diego Velazques. During the 18 century this painting was also known as “La Familia de Felipe VI” This painting portrays the infant Margarita from Austria surrounded by her maids, and even at the left in the painting you can even see the painter Diego Velzques presumably painting the couple that can be seen in the far through a mirror .
The painting uses a vanishing point to give an illusion of the size of the subject and the size and distance of the room.
The vanishing makes it possible to differentiate the distances between our point of view and the distances that our subjects have. The vanishing point also makes it possible for us to see subjects that are very close to us but also subjects that are more distanced from us. The painting also has an advanced use of perspective, in the painting Diego Velazques is looking at the middle presumably looking at the same couple we can see at the back of the painting in a mirror, giving the piece an advanced new look at perspective. It is clear that the painting has a big influence on mathematics that isn't looked upon.
A very famous building known as “La Sagrada Familia”. This building started construction in 1882, designed by Antonio Gaudi this is known as the masterpiece of Gaudi. It is formed by 18 towers dedicated to the 12 apostles, the four evangelists, Jesus, and virgin Mary due to the long construction of the piece it has seen the works of a wide variety of artists starting with Antonio Gaudi, Lau Feliu, Joan Flotats, Etsuru Sotoo,NUria Tortras , and lots of others. I The building is not complete but when it is finished its highest tower will measure 172.5 meters, the scheduled date for the construction of the last tower is in 2026.
Although the building encompasses a lot of mathematical thinking, one that is highlighted is in the iconic elevated conical towers. The inside of the towers are projected with a spiral staircase making use of the archimedean spiral which is a geometrical point that moves at a constant speed on a line that only rotates to a fixed point.
La Sagrada Familia also uses a rather new take on the parabolic curve using it in most of the temple but it being discreetly placed meant that it wouldn't be looked upon as much and thanks to that the math behind this curve wasn't found until years later.
Another highlight is the “Vitruvian man” by Leonardo da vinci in 1490. Leonardo da Vinci made this painting when he was an apprentice in Andrea del Verrocchio's workshop, where Da Vinci learned about architectural and technological design. The Vitruvian Man is a study of the human form visually completed by the application of mathematics and it was also Leonardo da Vinci’s we can also see the Da vinci application of pi in the attempt to solve the geometric problem of “squaring a circle.”
Da Vinci viewed mathematics as a universal constant whose proportions repeat throughout the universe. Vitruvian Man is da Vinci's study of human physiology. It was meant to be a perfectly proportionate rendering of the human form, as determined by the application of geometry and mathematics.
Vitruvius granted that a compass could be used to draw a perfect circle around a person with outstretched arms and legs, taking the person's navel as the center point. Vitruvius also noticed that for most people arm width and height match almost perfectly, and a person fits perfectly in a square.
Da vinci used proportion because in the painting from the breasts to the top of the head is a quarter of the height of a man. The distance from the elbow to the tip of the hand is a quarter of the height of a man. The distance from the elbow to the armpit is one-eighth of the height of a man. the length of the hand is one-tenth of the height of a man. The proportions 1:3, 1:4, 1:6, 1:8, and 1:10 are proportions appropriate to man.
The “The Last Supper” painting also done by Leonardo Da Vinci has an interesting take on perspective. This piece was done in 1495 to 1498. The painting is rather large, being 460cm x 880cm or 4.6m by 8.8m .
“The Last Supper” tells the story of the last supper but specifically the moments after Jesus tells the apostles that he is about to be betrayed by one of them, because the painting having a great handle on human emotions made it one of the most decorated paintings done by Da Vinci.
The painting, like others from this time period, uses a vanishing point to give the piece a new level of perspective. Leonardo used a linear perspective creating an illusion of depth in a flat surface like the canvas he used. You can see perspective on all of the faces and a depth between the background and the subjects.
On another painting by Leonardo Da Vinci “Mona Lisa” in 1503 A portrait of a seated woman set against an imaginary landscape. We can appreciate the math in the golden ratio. The golden ratio is a natural pattern that repeats itself. That is why it is so fascinating and cherished by many Renaissance artists who wished to resurrect the ideals of Antiquity while also grounding their art on scientific truth. Mona Lisa displays the golden proportion in the face as well as the neck-head ratio, indicating that the ratio between these components is 1.618. This is owing to Da Vinci's interest in both anatomy and mathematics.
All art uses math and it is connected to math in different ways. Math is what makes art complex and perfect. It is really amusing all the relationships you can find in art with math in all the periods of time. Something truly beautiful is that we can see math in places that are susceptible to the eye, meaning you have to look for it even if it is subtly shown. And we think that that is what makes this relationship beautiful
Mathematics is a fundamental part of our lives and it helps us in the areas of science, technology, and engineering. The Modern times of mathematics was characterized by the systematic synthesis of mathematical knowledge. It started from 1450 - present time. They are really complicated and sophisticated, but understanding them really makes a change in our world and lives. The characteristics about Modern Math are Applicability and Effectiveness, Abstraction and Relativity, Simplicity, Logical derivation, Axiomatic Arrangement, Precision, Correctness, and Evolution through Dialect.
The purpose of this investigation is to find the relation between non euclidean geometry and art. So, what’s non euclidean geometry?
Non Euclidean Geometry is one in which there's geometry on surfaces which are not flat, this means there's always movement or different shapes, unlike other types of art where there is a flat surface and it looks more steady. Since the surface is normally not flat and more curved like, there are basically no straight lines in it, but these distance minimizing curves known as geodesics will play the role of straight lines in these new geometries.
There can be very visual art in this type of math , and it can be seen at clear sight when it's really noticeable. An example of this can be the famous artist that is known as MC Escher, who has paintings which are known for having this type of art. This artist's work is a combination between realism and fantasy, and it is known for making “impossible constructions”, which utilize mathematical shapes, perspectives and architectures, which sometimes demonstrate Non Euclidean Geometry.
According to this context we can analyze some artists of this modern times and learn how they linked mathematics with art.
Escher “Relativity”, 1953.
Escher is known for having different geometric perspectives, like sometimes you can see how in his paintings there are three dimensional forms and two dimensional images, sometimes there's even different planes to convert a space two dimensional to three dimensional, he sometimes even plays with the images, which is a way of demonstrating geometrical perspective.
Yayoi Kusama ”The infinity room”, 2012
Yayoi Kusama is well known for having very popular art that has a lot of geometry perspective, it is basically a room with mirrors, this art is called “the infinity room.”It is known for the explanation of infinity when light reflects on the mirrors, and it is shown as if the light that bounces off is infinite, not only that, but Yayoi Kusama is also known for using patterns, this patterns are known as polka dots, and this patterns also help give the illusion that the lights within them are trailing off into the abyss, even though the room is actually quite small and people believe that it is big because of the illusion, this is a clear example of math shown on art, in this case, the reflection is a big part of this room.
Santiago Calatrava “Oculus”, 2016.
Santiago Calatrava is mostly known for his architecture but also for his sculptures. He has worked in the Lyon Airport Train Station and has sculptures in The Museum of Modern Art in New York. He likes to use perspective virtuosity. Santiago Calatrava uses folding geometry and you can see it in his work. “The L’Hemisfèric” is a good example as it shows a complete eye only having half of the structure actually built and the other half being only a reflection in the water.
Here we have the Oculus, which is located in the new World Trade Center, made by Santiago Catrava. It is a really tall structure, and it has a unique design. It is a transportation hub and a shopping mall made out of steel ribs. Something interesting is that it has 2 semicircles on the top that look like wings, and one is larger than the other. In this structure, we can see the use of a hyperbola at the front, and if you take away the semicircles on the top, we can see a semicircle on the bottom.
Remi Coulon-“Non Euclidean Geometries in Virtual Reality” 2018-2020
Remi Coulon is a talented mathematician who has also made plenty of works of art using non euclidean arts, one of the works of art is called “Non Euclidean Geometries in Virtual Reality”. It is very popular since it uses three important two dimensional geometries which are hyperbolic, euclidean, and spherical. The reason he created this was to develop accurate, real time geometries. An explanation of one of the major math is hyperbolic, this type of geometry in art replaces the parallel postulate with a type of statement that is two non-intersecting lines drawn through the point. Spherical geometry is the study of figures on the surface of a sphere, all these are examples of what Remi uses in his art.
Anish Kapoor, “Cloud Gate”, 2004.
Sir Anish Kapoor is a British-Indian sculptor. He uses geometry and biomorphic in all of his sculptures. He has done many famous sculptures like Sky Mirrors, Temenos, Cloud Gate, ArcelorMittal Orbit, etc..
He became very popular after he made the Cloud Gate in Chicago, which also looks like a bean. It reflects the city’s skyline and the green surroundings. It is made of stainless steel and weighs 80 pounds. In this structure we can see the use of analytic geometry. The kind of sphere below can be seen in the bean, except that it has kind of like a hole below.
In conclusion, mathematics can be found all over the world, and this is why it is necessary, even in art, in fact, it is possible that all art has something to do with mathematics. Some examples of this can be mainly the perspective, when changing the geometry or the figures in any painting or sculpture, the perspective changes, and gives you a different way of seeing it. Another example of this can be the analysis of symmetry and all of its ways. Finally, there may be patterns, balance, perspective, and much detail in each one. Art and math both need a balance, and when together, they can form amazing things, this is why many artists use both of them, and even try to play with them a bit.
The world is divided into time periods that are widely known. We divide history into periods to measure events, to find importance and to have a sense of control of what happens. Art and mathematics have changed through history; they developed on their own and taught us many things, but did they ever intersect? We can assume a division from the 16th century to now, which we know as the modern period. Artists consciously or unconsciously connect math with the great passion of art. Which means that many mathematical concepts are used in art during this period of time. We'll talk about two of them, the widely known golden ratio and the vanishing point.
The golden ratio’s concept is based on the Fibonacci series' use on art and architecture to create “visually appealing proportion” (Jonathan Cleveland, Expertise). What are both of these things, and how could we implement them in art? The golden ratio is the ratio between two numbers which is approximately 1.618 in decimal numbers. The golden ratio has been used by artists to get points and lines of interest in their work, the interest is in function of certain beauty or aesthetic standards. Artists divide their art in lines and rectangles through the golden ratio. The golden ratio was first mentioned by Ecluid around 300 BCE, but it was just recognized as a proportion. Through the years the golden ratio was investigated more thoroughly and praised. The ratio is associated with the Fibonnaci series or sequence.
The Fibonacci sequence is an infinite succession of natural numbers. This pattern starts in 0 and 1 following a sequence in which you add the past and new number infinitely; they end up in a spiral. (0, 1, 1, 2, 3, 5, 8, 13…) The Fibonacci sequence was discovered in the XIII century by an Italian mathematician called Leonardo de Pisa (also known as Fibonacci). It was first a formula/solution for a rabbit breeding problem which was later related to nature, and is now used in art. With this knowledge, we can now analyze different art pieces more thoroughly.
Golden Ratio - Starry Night by Vincent van Gogh.
Van Gogh painted the Starry Night while being in an asylum in 1889. He had a wide freedom in the asylum while he showed signs of recovering from the paranoia. He even had his own studio to paint. Sadly he relapsed and his work took a big change. As he did before, he began using darker colors on his paintings, the Starry Night being an example of this. How is math applied here? On the picture on the right, with enough attention, we can visualize the fibonacci spiral. Though we must note that the spiral does not cover the whole painting, just the clouds. The biggest cloud on its own is a spiral. The fibonacci spiral with help from the colors brings the attention towards the right top of the painting. The rule of third is also used, placing the ‘tree’ on the first third of the painting.
Golden ratio - Mona Lisa by Leonardo da Vinci
The fibonacci spiral can be found in many paintings. One of the most famous examples is The Mona Lisa, painted 500 years ago by Leonardo Da Vinci. Leonardo worked intermittently on the piece over the course of several years. Francis I, a french king, acquired his work after his death and it became a part of the royal collection. It was claimed during the french revolution and then hung up in Napoleon's bedroom. Then it was installed in the Louvre museum during the 19th century. Leonardo Da Vinci knew a lot about math, as he was interested in whether it could help him find ideal proportions. The tip of her nose fits in the middle of the spiral, the bottom of her chin fits the spiral and her head, shoulders, and hands also fit the spiral.
Golden ratio - Cartier Brensson
This picture was taken in 1932 by Cartier Bresson. He took it on a holiday while he was walking around his town. Cartier is a famous photographer who is well known for several reasons. One of them is using the beauty of the golden ratio. In the given photograph, on the left side, we can appreciate how Cartier applies the golden ratio to add beauty to his pictures. In the ‘center’ of the spiral, we can see the man in the bicycle while the rest is in the ‘background’.
The next concept is the vanishing point. The vanishing point refers to the space in a painting/picture which is supposed to be furthest or closest to the viewer. It's the point in which all receding parallel lines meet.
It is a single point on the horizon line of an image where parallel lines appear to intersect as they move apart and give the illusion of depth to the image. The architect Filippo Brunelleschi was the one with the most radical breakthrough with the vanishing point. In 1415, Brunelleschi made the first known drawing using the mathematical system of linear perspective to create the illusion of a building receding towards the horizon line. He devised a simple and easy system of creating a vanishing point on a horizon line and drawing diagonal lines towards it. He identified that objects and spaces are smaller when they are further from the eye.
Vanishing point - Raphael and the School of Athens by Raphael Sanzio. An example of this fascinating phenomenon is the masterpiece of ‘Raphael and the School of Athens’ by Raphael Sanzio. This painting was made between 1509 and 1511. It is from the finest examples of the linear perspective, we can see how the mathematical system is used causing an effect of depth in the painting. The vanishing point is between the two people in the middle of the painting, with the horizon line right above their heads. As an interesting fact, the two people in the center are Plato and Aristoteles. You can see how all of the people are below the horizon line, bringing attention to them. The painting has this semicircle which creates a shadow so the attention is not only on the people, but on the part with more light.
Vanishing point- The Last Supper by Leonardo Da Vinci
Another example of this phenomenon is the painting “The Last Supper”. It was painted somewhere between 1495 and 1498 for a Dominican convent in Milan. In this painting we can assume that the vanishing point was used because we can see Christ at the center of the table. The vanishing point is right in the middle of Christ’s head, and the horizon line is passing through the head of every apostle. It’s also visible how the diagonal lines match the imaginary line that the doors follow.
To conclude, math does have a purpose in our lives, especially in art. We might not notice it, but mathematics can—in certain ways be present everywhere. These forms of art are clear examples of this. We admire the Mona Lisa from the artistic point of view, and now we can admire the mathematical thinking process that went through Da Vinci’s mind while making it. While we don’t know if other artists used math intentionally, we can see different math concepts in their art pieces. This project was a way to open up our minds, and integrate a new way of viewing the world.
The relationship between math and art seems unlikely by nature since one is a more critical thinking and logical oriented discipline and the other considered as a form of expression based on aesthetic, feelings and passion.
But in reality math is everywhere in art! From the measurements in proportions to more in depth concepts like analytical geometry, art and math have been intertwined throughout history. Art in the renaissance period was a very big part of history since different artists created revolutionary art manifestations and expressions, in this essay we will highlight the works of Davinci, Arnolfo di Cambio and more. That is why their influence in the renaissance period was crucial to the development of mathematics in art.
This dome was started in 1296 and finished in 1436.
It was designed by Arnolfo di cambio, then he died and many other persons continued and made some modifications in the designs, but builded and finished the project. Between them was Fillipino Bruneleschi, who made and designed models, he worked with the construction and managed to implement a linear perspective on this and many other buildings that he did. Linear perspectives in the Florence dome : This math technique is used in the dome in the Top part (the dome), the way it works is by making lines that at the end get together in a space and this creates the vanishing point.
Another detail is that the bricks had a specific pattern to form the top part, the pattern was that they are in diagonal, this part is half sphere.
Mona Lisa / Girl with a pearl earring
In the beginning of the 14th century the renaissance period was a big contributor in the advancements of mathematics and art since more artists started to use mathematical concepts in their work. They incorporated math in their artworks because they realized that it could make their artwork more appealing and pleasing to the eye, this could be referenced with a popular math concept called the Fibonacci sequence or more famously known as the golden ratio.
This sequence was made and discovered by the mathematician Leonardo Fibonacci or Leonardo of Pisa and he is recognized as one of the greatest mathematicians of the middle ages. The golden ratio is an irrational number that is represented by the greek letter ϕ or τ, it was used by the greeks to represent the ratio of a line segment cut in two pieces of different lengths. The ancient Greeks recognized this sectioning or dividing as important since it was useful in geometry; later this golden ratio would be implemented by many artists of the renaissance period such as Davinci.
An example of the use of the fibonacci sequence is in the portrait of “The Gioconda” or best known as the Mona Lisa made by Leonardo Davinci, in this painting the fibonacci spiral made with the sequence aligns perfectly with the Gioconda's face.
Nicolaus Copernicus was a polish mathematician, astronomer and lawyer, he was born in 1473 and passed away 1543. At that time most people believed in the geocentric model of the universe which means that they thought the earth was the center of the universe. Copernicus created a model where the sun was the center and all planets moved in orbit around the sun. He studied the math of everyday objects just like games and knots, he contributed to group theory. He helped with the development of trigonometry necessitated by his sophisticated computations of the orbits of the planets. Years before Copernicus had made his discoveries, astronomer Ptolemy said the earth was the center of the universe and everything revolved around earth, he had made the best assumption of what earth is surrounded by.
Years later Copernicus came up with the theory and started investigating if he was correct. The Copernicus model allows calculation of planetary orbital periods around the sun. It shows the calculations from the distance of the sun, more distant planets have longer periods and move slower.
Perspective - The last supper & egyptians
In ancient Egypt the paintings that were made were usually made 2 dimensional, this means that the subjects in the paintings were facing at the side and there was no perspective between the background and other elements within the painting. It was until perspective in paintings was a concept introduced at the end of medieval ages by an italian painter called Giotto di Bondone and he started to introduce the concept and practice of perspective in paintings.
In the renaissance period perspective was used much more often in works of art, one of the most important concepts within perspective is the vanish point.
The vanish point is a mathematical notion that focuses on the point or points to which the extension of parallel lines meet and create perspective in a drawing; this is mostly applied in geometrical practices. Between these two paintings we can recognize the advancements in the use of mathematical concepts in art.
The Codex, Leonardo Da Vinci
The codex are ancient manuscript books created by Leonardo Davinci, these were used and created as a form of notes so he could theorize about geometrical images and it's relation with drawing of the human anatomy or even weapons. The process to create these ones is that first the animal skin is washed, hair is removed, the skin is attached to a frame, and then depending on the sheets for the final piece is the quantity you will use and take from the animal. The codex are of machines or new inventions that could be used for sketches.
For example the codex Leicester is a perfect example between the mathematical relation with art concepts, in this codex Da Vinci analyzes the relation between how the eye works and its range of vision by using geometrical figures and lines of perspective on top of eachother.
In conclusion, mathematics has been a concept used for many centuries for different purposes and people have always been a bit closed minded when it comes to learning about math, however many don't realize how much it is used in our day to day life and in our surroundings.
The ability to learn how to think critically, be rational and develop problem solving skills are some of the things math can teach you as well as having an open mind to learn new things. When it comes to art with mathematical concepts ( in this case in the renaissance period ) math played a very crucial role in the development of many artistic abilities such as perspective and the analysis of symmetry in portraits which is a concept used and studied in art very frequently today so thanks to mathematics it has given many opportunities for creativity in art and in other disciplines.
The world is currently changing at a phenomenal pace and the knowledge, tools and application of math has never been more advanced and many more ways to think critically and solve problems are bound to appear and change, so to be able to understand concepts of math and rationalize them in your day to day life even if they are not literal could be a great improvement and create a big impact in society.


The Nebraska Department of Education on Tuesday released the results of this year’s statewide exams in reading, science and math.
According to the department, 71 percent of students met or exceeded Nebraska’s proficiency standards for math this year. That’s an increase from 69 percent in 2013.
The department says 72 percent of students met or exceeded science standards, up from 70 percent last year. For reading, the percentage of students held steady at 77 percent.
The department did not release writing exam results, which were thrown out this year because of widespread computer problems for students.


On October 15th the Way Station will host our first ever event for Ada Lovelace Day! Founded in 2009 by Suw Charman-Anderson, Ada Lovelace Day celebrates the achievements on women in science, technology, engineering, and mathematics. Read more about Ada here. We’ll also have our signature games, prizes, and astro-tainment by DJ Carly Sagan & MC Tycho Brewhaha!
7 – 9:30 pm
Thursday, October 15


Brainetics a Breakthrough Math & Memory System
Brainetics a Breakthrough Math & Memory System Parents and teachers have watched and despaired over children who are struggling to learn and retain math skills. Math is often considered a hard subject for many students and the information often seems to end up lost in a myriad of other thoughts. Fortunately, Brainetics provides a solution to the struggles children face when trying to learn and memorize mathematic rules.
Brainetics is a system that is designed to help children learn math and retain the information. The main purpose of the program is improving memory skills and teaching children how to learn information that is relevant to the rules they are learning while ignoring the unnecessary information that results in confusion and misunderstandings.
The system primarily focuses on improving mental abilities like memorization and problem solving rather than giving lectures and details about specific subjects taught in school. Brainetics also helps children break away from math anxiety, which is a common concentration problem when working on the subject. The creator of the system, Mike Byster, realized that children who suffer from math anxiety end up having problems concentrating on this rule-dense subject. That lack of concentration caused by worries about learning is confronted and dealt with in the Brainetics memory system.
The system is an excellent way for children to learn life skills they will need for their school years and into their future careers. While the system does have a strong emphasis on mathematics, the memory and study skills taught along with the basic math retention aspects apply to any subject in school. Many of the lessons will even apply to careers, such as organizational skills. This system will help children reach for a brighter future as well as helping them obtain better grades and making the challenge of learning more enjoyable in the present.
Unlike math programs or programs designed to teach other necessary skills for success in school, Brainetics solves the root causes of school related learning difficulties. The root causes of learning difficulties begins with a child’s concentration and the system directly confronts concentration problems and works on methods to help children keep their mind on the subjects they are learning. The fun pattern detecting activities within the system directly relate to keeping the mind focused on the task, making concentration easier and gradually building up this necessary skill when working on retaining information.
As previously state, the system also works on getting through math anxiety. The fear and discomfort relating to math is solved and provides children with a foundation in getting past worries about studying. Eliminating fears and worries helps improve the concentration by making the subject enjoyable.
Brainetics then takes the mathematics learning a step further by showing children the reliable shortcuts that make figuring easier to remember. This is especially useful when children start learning complex mathematics and need a little help remembering the rules they’ve learned in earlier studies. The complex math shortcuts are easy to remember and make math less challenging.
Another skill Brainetics addresses is multi-tasking. During school, children are expected to learn a great deal of skills and facts all in the same day. Combined with the lessons, children also need to learn the use of current technology and managing to work through more than one task at a time. Multi-tasking skills are a necessity in the technology age and children learn the basics through the Brainetics system.
The last skill the system works on developing in school aged children is organizing thoughts, particularly as mental organization relates to mathematics. Organization is a key to success in school, especially as children get older and have more complicated lessons that require a clearly laid out train of thought. The organization skills are applied directly to mathematics building that children can use from elementary school until getting into college.
The tasks performed in the system along with the memory skills taught in the system help children succeed in school. It forms the foundation of study skills children need to build upon when they start getting into higher studies throughout their education.
Brainetics math and memory system comes with specific products that help children succeed in mathematics and improving their memory.
The system features five DVDs that break down information into manageable lessons children can start applying immediately. The DVDs are broken down into specific groupings that start with the most basic skills children need for success in math and school.
The first DVD provides children with keys to concentration. This is one of the most important skills for memory improvement. Along with the concentration lesson, the DVD will teach pattern recognition that applies specifically to mathematics.
The second DVD in the system is solely about beating math anxiety. This problem is common in childhood and requires overcoming to improve math and face the challenges of studying the subject.
The third DVD is specifically related to mathematics. It teaches common math shortcuts for complex problems.
The fourth DVD develops necessary multi-tasking skills. This skill set is vital to success in every subject as well as future careers.
The final DVD in the system provides a lesson on organizing thoughts and applies the skill to mathematics building that will carry forward into higher math and other subjects in school.
Beyond the DVDs, the program also includes a parent’s manual. The manual gives parents and educators tips and lessons to provide children with more than just the lessons on the DVD.
The playbook with the system gives problems and exercises that go along with the DVD lessons. It gives children hands on experience with the lessons.
The flashcards and playing cards are the final piece of the system and are perfect for teaching rote memorization and playing games related to the system.
The system costs $149.99. Though the cost might seem high, the results of the system are astounding to teachers and parents around the world who have discovered that their children are able to meet challenges and succeed in school.


what is the circumference of a circle with a radius of 7.8 cm
3.07 inches (7.8 centimeters) is the circumference of a circle with radius 0.49 inches (1.24 centimeters).
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Some people try to explain the Creation by coincidence. What is your answer to them?
Beneath the debate on belief, there generally lies a question: is it a matter of will or of chance? That is, whether an absolute will, an infinite knowledge, an unfathomable might has brought the universe into its recent state; or these bright beauties, these amazing works of art have come into being by coincidence.
The words coincidence / chance and coincidental / by chance are frequently mentioned in the probability theory. In this theory, there exists a multiplication rule that can be summed up as this: The total probability of realization of several independent events is equal to the multiplication of respective probabilities for those discrete events. To illustrate, let us give an example: Let us have twenty-six letters in a bag and pick letters randomly to form a word.
If we put back the letters previously drawn, the probability of picking any letter will be 1/26 each and every time. If the letter is put back, probability of picking a letter, say a, is again 1/26 just as its first turn. And this ratio will be constant. When we combine to form a word, e.g. garden, the probability for the first letter to be g is 1/26. And, if we put that g into the bag back again, the probability for the second letter to be a is still 1/26. However, the probability that the first letter to be g and that the second one to be a will be the multiplication of those discrete probabilities. In other words, it will be the square of 1/26, which is approximately equal to one in seven hundred (in other words, 1.5 out of a thousand). That is, by such drawings we can write about six hundred and fifty two-letter words like in, sg, ax, mb, eu, wk.... and so on. One of these words will be ga and the probability of writing this word by two drawings is about 1.5 in a thousand.
The probability that picking the letters g first, then a, and then r is the cube of 1/26, which is approximately 57 in one million. In short, the probability of writing the word garden by such drawings is one in twelve million.
So, let us think: if the probability of writing such a small, a six-letter word by chance is one out of twelve million; is it possible for a line or a paragraph to be written by chance, let alone for a book?
Moreover, humans ability of writing is not such a simple phenomenon. We do not pick the letters from a bag, but construct them in our mind and then write them down. In this respect, it is impossible for man to produce a word coincidentally. At first, one does not have to have a pen. If so, he does not have to move that pen, and if moves it, he does not have to write letters. He might draw lines or a picture as well. And he might order the letters randomly so that they do not have meaning. Thus, the probability of writing the word garden among almost infinite number of coincidental shapes and pictures is 1 out of infinity, or simply zero. Therefore there exist two possibilities: Either that word does not form, or if does, it is not by chance, but by will. So, if a word is written, then there must be a will to do so.
Let us give an additional example from the universe. This Earth, on which we stay and with which we travel around the Sun throughout the year, is just one of almost infinitely many celestial bodies in the universe. It is not possible to explain the existence of this globe by chance. Science teaches us that if our globe was on another orbit instead of this one and that if it turned faster around the Sun, or if did not turn, or if its axis tilted by a different degree, if it wasnt surrounded with air, coated with soil, and if so many such conditions werent arranged in their current particulars, there couldnt be life on Earth. Among thousands of factors mentioned and unmentioned here, we would like to emphasize only one, that of place. The probability for this Earth to be in its present place is one out of nearly infinity, which practically is equal to zero.
Before all, that the creation itself of the Earth requires a will to do so—just as writing a word in the previous example.
Those who know well that they cannot explain the creation of the universe with coincidence and evolution have preferred to manipulate the discussion and have attempted to make misleading and catchy assumptions. Many personal hypotheses come up. Some offered that human had descended from apes. And according to some, we were descendants of frogs; to some others, of mice. Another person alleged that man was not a product of evolution of just a single species, but offspring of two distinct species, namely bear and wolf.
Indeed, it is a matter of concern for us that where this group, who hope for help from a different animal everyday, will come to a full stop.
- The Proofs of Creation # 24: The Proof of the Absurdity of Coincidence
- The Absurdity of Coincidence
- Coincidence is unacceptable
- Does “Chance” have the chance to exist? What is the effect of Qadar (fate) in games of chance?
- The Proofs of Creation # 3: The Proof of Huduth
- First Point: It is related to unknown signs.
- Can DNAs not be shown as the unique reason for the harmony among the living beings as long as there are adequate conditions? Is it not possible that life may have existed after the coincidental formation of the first DNAs?
- Why do the Majority of Scientists Accept Evolution?
- Are there answers to questions about intraspecies and interspecies evolution?
- BASIC FALLACIES IN THE VIEW OF EVOLUTION: 2 CONFUSION OF CONCEPTS


Moon Rocks Math – with Facts Cards
I wrote my own fact cards, 1+1, 2+2, 3+3, 4+4 & 5+5 onto index cards. Then using this sheet (which I made and you can use to for FREE), he would draw a card, and place the number of moon rocks on each moon, right the numbers and the sum.
I cut out lots of shapes, a variety of rectangles, a few triangles, a square, a hexagon and a trapezoid. We talked about the shapes, their names, how many sides and angles. We sorted the shapes, rectangles v/s non-rectangles. Then he built rocket ships from them and mimicked his designs on the geoboard.


Nowadays, Quadratic Programming QP models, like Markowitz model, are not hard to solve, thanks to technological and algorithmic progress. Nevertheless, Linear Programming LP models remain much more attractive from a computational point of view for several reasons. In order to guarantee that a portfolio takes advantage from diversification, no risk or safety measures can be a linear function of the weights of the assets. Is it possible to have linear models for portfolio optimization? How can we measure the risk or safety in order to have a linear model?
In Figure 5, the red star optimiization the return and risk of the DJIA benchmark over our backtest period. The Journal of Finance. Your Practice. Stefan Mittnik" PDF. Finance and Stochastics.
Portfolio optimization model. Limitations of portfolio optimization
An evolutionary heuristic for the index tracking problem. Main article: Capital asset pricing model. American Economic Review 60 3 : — Computational Optimizatiion and Applications 51 1 : — Portfolio optimization model Practice. Portfolio optimization problem under concave transaction costs and minimal transaction unit constraints. Kelly clarkson fake sex latter component, the cost of risk, is defined as the portfolio risk multiplied by a risk aversion parameter or unit price of risk. Essentially, only the sequences in the stable region were above the "water level" of the DJIA. These results are used to derive the asset-appropriate discount rate. Koshizuka, T.
Portfolio optimization is the process of selecting the best portfolio asset distribution , out of the set of all portfolios being considered, according to some objective.
- Global investors, such as pension funds and insurance companies, need to decide how to allocate their investments across different asset classes and countries.
- Combining both elements allows us to perform portfolio optimization to determine the optimal risky portfolio.
- Portfolio optimization is the process of selecting the best portfolio asset distribution , out of the set of all portfolios being considered, according to some objective.
Modern portfolio theory MPT is a theory on how risk-averse investors can construct portfolios to optimize or maximize expected return based on a given level of market riskemphasizing that risk is an inherent part of Advice on buying fist home reward.
According to the theory, it's possible to construct an " efficient frontier " of optimal portfolios offering the maximum possible expected Portfolio optimization model for a given level of risk. This theory was pioneered by Harry Markowitz in his paper "Portfolio Selection," published in by the Journal of Modeo.
He was later awarded a Nobel prize for developing the MPT. MPT shows that an investor can construct a portfolio of multiple assets that will maximize returns for a given level of risk. Likewise, given a desired level of expected return, an investor can construct a Portfolio optimization model with the lowest possible risk.
Based on statistical measures such as variance and correlationan individual investment's return is less important than how the investment behaves in the context of the entire portfolio. MPT makes the assumption that investors are risk-averse, meaning they prefer a less risky portfolio to a riskier one for a nodel level of return. This implies that an investor will take on more risk only if he or she is expecting more reward.
The expected return of the portfolio is calculated as a weighted sum of the individual assets' returns. The portfolio's risk is a complicated function of the variances of each asset and the correlations of each pair of assets. To calculate the risk of a four-asset portfolio, an investor needs each of the four assets' variances and six correlation values, since there are six possible two-asset combinations with four assets.
Because of the asset correlations, the total portfolio risk, or standard deviationis lower than what would be calculated by a weighted sum.
Every possible combination of assets that exists can be plotted on a graph, with the portfolio's risk on the X-axis and the expected return on the Y-axis.
This plot reveals the most desirable portfolios. For example, assume Portfolio A has an expected return of 8. Portfolio A would be deemed more "efficient" because it has the same expected return but lower risk. It is possible to draw an upward sloping hyperbola Portfolio optimization model connect all of the most Porn vid trailers portfolios, Hiv prophlyaxis drugs this is known as the efficient frontier.
Investing in any portfolio not on this curve is not desirable. Risk Management. Portfolio Construction. Portfolio Management. Your Money. Personal Finance. Your Practice. Popular Courses. Optimizaiton Newsletters. Investing Portfolio Management.
Compare Investment Accounts. The offers that appear in this table are from partnerships from which Investopedia receives compensation. Related Terms Portfolio Variance Definition Portfolio variance is the measurement of how the actual returns opptimization a group of securities making up a portfolio fluctuate.
Efficient Frontier Definition Efficient frontier comprises investment portfolios that offer the highest expected return for a specific level of risk. Mean-Variance Analysis Mean-variance analysis is the process of weighing risk against expected return. Portfolio optimization model Efficient Set The Markowitz efficient set is a portfolio with returns that are maximized for a given level of risk based on mean-variance portfolio construction.
Harry Markowitz Harry Markowitz is a Nobel Memorial Prize-winning economist who devised the modern portfolio theory in Portfolip Partner Links. Related Articles.
The required inputs for the optimization include the time range and the portfolio assets. Portfolio asset weights and constraints are optional. You can also use the Black-Litterman model based portfolio optimization, which allows the benchmark portfolio asset weights to . In finance, the Markowitz model - put forward by Harry Markowitz in - is a portfolio optimization model; it assists in the selection of the most efficient portfolio by analyzing various possible portfolios of the given securities. Here, by choosing securities that do not 'move' exactly together, the HM model shows investors how to reduce their risk. The approach described here is a good starting point for a portfolio optimization model. An institutional investor using this model would probably want to incorporate transaction costs and trading constraints into the model. Nevertheless, the potential to beat the market by an average basis points with low turnover is an encouraging first step.
Portfolio optimization model. Navigation menu
The risk, return, and correlation measures used by MPT are based on expected values , which means that they are statistical statements about the future the expected value of returns is explicit in the above equations, and implicit in the definitions of variance and covariance. Journal of Portfolio Measurement 6 3 Spring : 59— International Journal of Theoretical and Applied Finance 8 1 : 13— In this case, the MPT investment boundary can be expressed in more general terms like "chance of an ROI less than cost of capital" or "chance of losing more than half of the investment". Twenty years of linear programming based portfolio optimization. Based on your location, we recommend that you select:. Its key insight is that an asset's risk and return should not be assessed by itself, but by how it contributes to a portfolio's overall risk and return. Mean-deviation analysis in the theory of choice , Risk Analysis: An International Journal, 32 8 , Journal of Risk. Hanoch, G. For given portfolio weights and given standard deviations of asset returns, the case of all correlations being 1 gives the highest possible standard deviation of portfolio return. Fabian, C. For portfolios that meet this criterion, known as efficient portfolios, achieving a higher expected return requires taking on more risk, so investors are faced with a trade-off between risk and expected return.
Modern portfolio theory MPT , or mean-variance analysis , is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. It is a formalization and extension of diversification in investing, the idea that owning different kinds of financial assets is less risky than owning only one type.
The optimization is based on the monthly return statistics of the selected portfolio assets for the given time period. The optimization result does not predict what allocation would perform best outside the given time period, and the actual performance of portfolios constructed using the optimized asset weights may vary from the given performance goal. The required inputs for the optimization include the time range and the portfolio assets. Portfolio asset weights and constraints are optional. You can also use the Black-Litterman model based portfolio optimization, which allows the benchmark portfolio asset weights to be optimized based on investor's views. You can upload a portfolio asset allocation by selecting a file below.


A visual and practical approach to learning how to create statistical graphs using R
About This Video
Learn the basics of R graphs and how to make them
Customize your graphs according to your specific needs without using overcomplicated techniques/packages
Step-by-step instructions to create a wide range of professional-looking graphs
R is a powerful tool for performing statistical analyses and drawing publication-quality graphics. This tool is ideal for organizing and graphing huge datasets. It also provides various techniques for plotting a variety of simple and more complex statistical graphs.
R Graph Essentials is a beginner’s course to learning about R graphics. This course will provide you with both a solid grounding in the so-called “base” graphics package in R as well as introducing elements from more sophisticated packages, such as lattice and ggplot2.
R Graph Essentials explains the basic functionality of R graphs in detail in order to familiarize you with how they work. The course starts with very basic R plot functions, first helping you to gain control of this function, then moving on towards various advanced plotting functions.
Different types of graphs are used to visualize different types of variables. The R Graph Essentials video course classifies these graphs and teaches them separately. This course is a compilation of tips and tricks related to the most efficient ways of drawing various types of graphs using basic R plotting functionality. Additionally, bivariate plots, time series, and high dimensional plots are also covered in this course. By the end of this course, you will be in a position to create your own ETL processes within a short amount of time.
The course offers a practical and interactive way to learn about R graphics, equipping you with the tools to draw informative statistical plots to effectively visualize your data.


RR, relative risk
The risk ratio is the probability of an outcome in one treatment comparison group divided by the probability in another.
It is commonly used as a measure of the relative effectiveness of treatments.
For example, if 20 out of 100 participants (20%) die in one treatment comparison group and 50 out of 100 (50%) die in the other group, the risk ratio is 20/50 = 0.40.
If you feel that this definition hasn't helped you to understand the term, click on our monkey to let us know.


Updated on July 14th, 2015 @ 14:00 IST by Bharathwaj Muthuswamy.
Here are some references for number theory. Note: If it is possible, I have linked the title to the book's homepage or a preview from google books.
Further references on Linear Dynamics, Nonlinear Dynamics, Electromagnetism (prereq for understanding physical memristors), Quantum Mechanics (prereq. for understanding superconductivity), Superconductivity (for understanding the ideal memristor) and Number Theory
- A Classical Introduction to Modern Number Theory. Rosen, Michael and Ireland, Kenneth. 2nd Edition, 1990, Springer. ISBN 3-540-97329-X. Many thanks to Dr. Venkat Anantharam for recommending this book to me.


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Building a strong foundation in math is essential for children in the first grade. The activities in this 3-in-1 Super Workbook are designed to help your student become familiar with math concepts like numbers and operations, solid and plane shapes, and graphs and charts. They will help your child to catch up, keep up, and get ahead—and best of all, to have lots of fun doing it! Here are some of the great features you'll find inside:
The Cupcake Eater
Counting cupcakes on a plate, and then crossing off the eaten cupcakes and counting how many are left, helps children learn subtraction.
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Children write numbers from smallest to largest or identify place-value digits to find the right combination for a safe.
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Children draw a line from each picture outside a Venn diagram to where it belongs inside the diagram, matching food and objects of different shapes.
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Review of “Thomas calculus book”
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