Dr. Dori Hargrove, Coordinator of Elementary Education and Assistant Professor of Education
101 A Knutti Hall
Ph.D. in Education– Mathematics Education Leadership, 2015; George Mason University
EDUC 352 – Integrated Math, Science, and Social Studies I
EDUC 354 –Integrated Math, Science, and Social Studies II
EDUC 341 – Math Methods for Elementary Teachers
Sterling, D.R. & Hargrove, D.L. (2014). How healthy is our pond? Examining stability and change in a local pond connects students to their environment. Science and Children 51(7) 45-51.
Sterling, D.R., & Hargrove, D.L. (2012). Is your soil sick? Students explore a new kind of testing of- soil and learn about plant needs and how to analyze results. Science and Children April/May p. 51-55.
Gallagher, M.A., Suh, J., King, L. & Hargrove, D.L. (2016). Preservice teachers’ perceptions of a hybrid fieldwork experience. Workshop Presentation at the 20th Annual Conference of the Association of Mathematics Teacher Educators. Irvine, CA.
Hargrove, D.L., Jamieson, S. & Hjalmarson, M. (2014). Elementary teachers and high cognitive demand tasks. In S. Oesterle, C. Nicol, P. Liljedahl, & D. Allan (Eds.), Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th
Conference of the North American Chapter. (Vol. 6, p. 93) Vancouver, Canada: PME.
Faculty Research Forum Committee: Spring 2016 – present
Shepherd University Professional Education Unit Council: Fall 2015 – present
Co-Sponsor of Kappa Delta Pi – Delta Psi Chapter – Fall 2015 – present
Bowling and Scrapbooking


Descriptions for the department:
· As teachers we provide an effective TEKS-based mathematics program for our students.
· As teachers we provide expertise in providing a more focused mathematics instruction to meet the needs of all our students.
· Our classrooms are safe and engage student in learning mathematics through discussion and sharing ideas.
· As teachers, we engage students using resources, tools, and technology to solve mathematically rich, real-world problems that meet
the needs of a diverse population of learners.
"Barrientes Math Teachers have the formula for Success!”


how to use linest function excel 2010
LINEST - Excel - Office.com - Office.com - Microsoft.
The LINEST (or linear estimate) function in Excel sales forecasting uses formulas to calculate a regression equation and related statistics.. Excel 2010.
LOGEST function - Excel - Office.com.
When you use the LINEST worksheet function in a worksheet in Microsoft Excel, the statistical output may return incorrect values. The Regression tool in the.
I found that I can use the LINEST function in excel but somehow it does not work for me. The spreadsheet has been build so that on every row.
Excel 2010 Formulas & Functions - For Dummies.
how to use linest function excel 2010The LINEST Function in Excel Sales Forecasting - For Dummies.
TREND function - Excel - Office.com.
Excel statistical functions: LOGEST - Microsoft Support.
Perform a regression analysis - Excel - Office.com - Microsoft.
Sep 5, 2012. It turns out that there is an Excel function called LINEST, which is what you can use to do this. In general terms, it is a least squares curve fitting.
Describes how the numeric improvements in Excel statistical functions affect the tools. Office 2013 · Office 365 Home Premium & Office 365 University · Office 2010. A second example involves an incorrect formula in Excel 2002 and in earlier .. The article on LINEST describes extensive improvements for Excel 2003 and.
how to use linest function excel 2010Excel's LINEST Function: Little Things Can Make a Big Difference | A.
Excel's LINEST() Function Deconstructed | | Que.
This article describes the formula syntax and usage of the LINEST function ... Excel 2010, Excel Web App, SharePoint Online for enterprises, SharePoint Online.
Listings 1 - 25. Microsoft Excel 2010 includes literally hundreds of functions that let you. This chart shows the information the Excel LINEST function will [more…]. In Excel 2010, you use the very familiar SUM function to total values in your.
The Excel Linest Function - Calculates the Line of Best Fit Through a Supplied. Cells D1 - E5 of the spreadsheet show the Excel Linest function, used to return.
Feb 25, 2013. Microsoft Excel's LINEST() worksheet function has a long and checkered history. . I recognize that one could use the TREND() function instead of. say, Excel 2002 to Excel 2010, or to understand how Excel 2002's results.
Jan 19, 2011. For these lines it is possible to use either the LINEST function, or the LOGEST. This is with Excel 2010, but I believe that the algorithm is.


Elementary Statistics and Probability
Student Learning Outcomes (what you should be able to demonstrate by the end of the course):
- Organize, analyze, and utilize appropriate methods to draw conclusions based on sample data by constructing and/or evaluating tables, graphs, and numerical measures of characteristics of data.
- Identify, evaluate, interpret and describe data distributions through the study of sampling distributions and probability theory.
- Collect data, interpret, compose and defend conjectures, and communicate the results of random data using statistical analysis such as interval and point estimates, hypothesis tests, and regression analysis.
|Session Title||Media Type||Status|
|Chap01 - Sampling & Data||Video|
|Chap02 - Descriptive Statistics||Video|
|Chap03 - Probability Statistics||Video|
|Chap04 - Discrete Random Variables||Video|
|Chap05 - Continuous Random Variables||Video|
|Chap06 - The Normal Distribution||Video|
|Chap07 - The Central Limit Theorem||Video|
|Chap08 - Confidence Intervals||Video|
|Chap09 - Hypothesis Testing, pt1||Video|
|Chap10 - Hypothesis Testing, pt2||Video|
|Chap11 - The Chi-Square Distribution||Video|
|Chap12 - Linear Regression & Correlation||Video|


The Galileo reading documents the process by which Galileo came up with his theories of the properties of objects in motion. He begins by defining uniform motion, then give four axioms and uses these axioms for formulate theorems. He then uses his theorems for uniform motion and applies them to accelerated motion, and walks the reader through the process by which he uses mathematical models to provide theorems for accelerated motion.
The Hazen and Trefil reading is an anecdotal walk through the early history of science, starting with the independent work of astronomers and artisans working primarily in their respective trades, and then combining these two fields to form the study of mechanics. From here, the authors summarize the findings of Galileo and Kepler, and explain how Newton used the models formed by these two scientists to form his laws of motion, detailing his process of scientific inquiry which became a frame for the modern day scientific method. The authors close by broadening the definition of modern science as an orderly study of many varieties of chaotic natural systems.
The Lehrer (2009) article presents the problem of how to educate students at developmentally appropriate levels while not underestimating their abilities to grasp scientific concepts, and gives many methods for effectively teaching science curriculum. These methods used various methodologies to develop models of scientific systems. The author suggested that physical models could be formed to represent specific ideas, and that representational models, such as mathematical theorems, would be useful to promote conceptual thinking and to build on patterns.
The Lehrer text introduced the idea of forming physical models from observations and then utilizing representational models to apply the concepts to other applications. The Hazen and Trefil text then explained how Newton used this method by taking models from other scientists and building upon them. The Galileo text gave an in depth look at how that particular scientist used observations to create physical models, then observed these physical models to form representational mathematical models. The common theme in all three of these readings was the usefulness of models to explain scientific phenomenon. While these texts were elevated, the idea of using physical models to lead into representational models is a very good method for teaching students of all ages the scientific method and giving them the tools for scientific discovery.


A biography of giuseppe peano a doctor of mathematics
Giuseppe peano and the axiomatization of mathematics mathematics, philosophy 27 graduating as doctor of mathematics in 1880 with high honours biography of giuseppe peano at mactutor on the history of mathematics. Encuentra peano: life and works of giuseppe peano (studies in the history of modern all students of mathematics know of peano's postulates for the natural numbers and his it appeared to me that the most likely person to write a biography of peano would be his devoted disciple. Giuseppe peano lived from 1858 to 1932 this 1980 biography focuses on peano's academic life, but it doesn't go far into mathematical details or include any significant discussion of the meaning or implications of his work for the development of mathematical logic or the foundations of. Life and works of giuseppe peano d reidel publishing company dordrecht: holland i boston: usa all students of mathematics know of peano's postulates for the natural of this biography, and i am grateful to them all. Formulario di analisi matematica presentations given at the international conference organized by the torino academy of sciences and the department of mathematics giuseppe peano of the torino it appeared to me that the most likely person to write a biography of peano would be. Giuseppe peano (august 27, 1858 - april 20 and returned home to study peano's text peano's followers presented papers (using peano's teachings) at the mathematics conference, but peano didn't mactutor biography de:giuseppe peano es.
Giuseppe peano (italian: collection of articles on life and mathematics of peano (1960s to 1980s) kennedy, hubert (2002) peano life and works of giuseppe peano san francisco: peremptory publications. Giuseppe peano (italian: [d u z ppe pe a no] 27 august 1858 - 20 april 1932) was an italian mathematician the author of over 200 books and papers, he w. Formulaire de mathematiques: mathematical formulary), published from 1894 to 1908 with collaborators, was intended to develop mathematics in its entirety from its fundamental postulates in giuseppe peano his formulaire de math matiques. Mathematics, logic giuseppe peano was the second of the five children of bartolomeo peano and rosa cavallo the most complete biography is hubert c kennedy, giuseppe peano are in ugo cassina, critica dei princip della matematica e questioni di logica (rome. Biography of giuseppe peano (1858-1932) giuseppe peano born: 27 aug 1858 in cuneo, piemonte, italy on 29 september 1880 peano graduated as doctor of mathematics peano joined the staff at the university of turin in 1880.
All students of mathematics know of peano's postulates for the natural numbers and his famous space-filling curve 1963, suggesting that we collaborate, meaning by this that i would write the biography, in english, using his material and advice life and works of giuseppe peano. A brief biography the peano axioms were developed by mathematician giuseppe peano giuseppe peano was born in italy in 1858 attended university of turin in 1876, graduated with a doctors of mathematics in 1933 peano's axioms origin and succession peano established a set of numbers (often. Giuseppe peano : biography 27 august 1858 - 20 april 1932 giuseppe peano ( 27 august 1858 - 20 april 1932) was an italian mathematician, whose work was of philosophical value it was to be an encyclopedia of mathematics. Peano: life and works of giuseppe peano reidel biography with complete bibliography giuseppe peano at the mathematics genealogy project hubert kennedy (2002) twelve articles on giuseppe peano (pdf) san francisco: peremptory publications. Alessandro padoa (14 october 1868 mathematics: the following description of padoa's career is included in a biography of peano: he attended secondary school in venice hc kennedy (1980) peano, life and works of giuseppe peano. Visit amazoncom's giuseppe peano page and shop for all giuseppe peano books check out pictures, bibliography, and biography of giuseppe peano.
He was giuseppe peano and was born in a farmhouse right outside cuneo, italy in 1880, peano graduated as a doctor of mathematics the university of turin promptly hired him peano published four mathematical papers during the next two years. Amazing oblivion of peano's contributions to mathematics commemorating the 150th birthday of giuseppe peano (1858-1932) abstract was due to that outstanding young man dr giuseppe peano in a cel. Biography of alessandro padoa (1868-1937) alessandro he returned to the university of turin for session 1894-95 where he attended two courses given by giuseppe peano padoa was awarded a mathematics degree from the university of turin on 26 november 1895 and he continued to study at. Find great deals for peano: life and works of giuseppe peano by springer (hardback, 1980) shop with confidence on ebay. 1 quote from giuseppe peano: 'questions that pertain to the foundations of mathematics, although treated by many in recent times, still lack a satisfactory solution ambiguity of language is philosophy's main source of problems that is why it is of the utmost importance to examine attentively.
A biography of giuseppe peano a doctor of mathematics
Peano: life and works of giuseppe peano (studies in the history of modern science) [h kennedy] on amazoncom free shipping on qualifying offers all students of mathematics know of peano's postulates for the natural numbers and his famous space-filling curve.
Gottlob frege was an eminent german mathematician of however, his true genius was recognized posthumously by bertrand russell and giuseppe peano who highlighted his work to their the primary objective of his work on logic was to prove that mathematics is deeply rooted in. In 2008 mathematics celebrated the 150th anniversary of the birth of giuseppe peano, as well as the amazing oblivion of peano's contributions to mathematics rural language, scottish church-politicks and barbarismes of john wallis, professor of geometry and doctor of divinity. All students of mathematics know of peano's postulates for the natural numbers and his famous space-filling curve it appeared to me that the most likely person to write a biography of peano would be his devoted disciple ugo cassina life and works of giuseppe peano editors h kennedy.


Take a few minutes to crunch the numbers. Our loan calculator helps to give you an estimate of what your payment might be. This calculator is for estimation purposes only. For a more precise payment, please apply with AMOCO.
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Photo credit: @delightinrain
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this is fucked up. this fucked me up. the teachers fucked up by not showing us this fuck up. fuck.
i’m 28 and never knew this
Okay, after trying this out myself, I have realized that it’s exactly the same mathematical process as when you write it out in the more familiar format. But still, I think this way of doing it is a bit faster, especially when neither of the numbers have a digit higher than about 4. And I think that teachers should show kids this trick as soon as they start working on 2-digit multiplication because it makes multiplication look less intimidating and it makes a point about place value. And, perhaps best of all, when those kids get to Algebra I, the FOIL thing is going to make perfect sense.


This paper analyzes a large-scale and long-running distance education program in Mexico. We estimate marginal treatment effects (MTEs) for learning in math and Spanish in telescundarias relative to traditional Mexican secondary schools using an empirical framework that allows for unobserved sorting on gains. The estimated MTEs reveal that school choice is not random and that the average student experiences significant improvements in both math and Spanish after just one year of attendance in telesecundarias. We find that the existing policy reduces educational inequality, and our policy-relevant treatment effects show that expanding telesecundarias would yield significant improvements in academic performance.
When school-age children work, their education competes for their time and effort, which may lead to lower educational attainment and academic achievement. This paper develops and estimates a model of student achievement in Mexico, in which students make decisions on school enrollment, study effort and labor supply, taking into account locally available schooling options and wages. All of these decisions can affect their academic achievement in math and Spanish, which is modeled using a value-added framework. The model is a random utility model over discrete school-work alternatives, where study effort is determined as the outcome of an optimization problem under each of these alternatives. The model is estimated using a large administrative test score database on Mexican 6th grade students combined with survey data on students, parents and schools, geocode data on school locations, and wage data from the Mexican census. The empirical results show that if students were prohibited from working while in school, the national dropout rate would increase by approximately 20%, while achievement would increase in both math and Spanish. Expanding the conditional cash transfer, either in terms of the magnitude of the cash benefits or the coverage, in conjunction with prohibiting working while in school is an operational policy that would greatly reduce dropout while maintaining the gains in achievement.
Work In Progress
Enrollment, Math Performance and Wages: A Coordination Model in Mexican Middle Schools, with Alejandro Sanchez Becerra and Petra Todd.
In many countries, conditional cash transfers offered by the government have been shown to increase school enrollment for the beneficiaries. However, these policies’ potential to increase overall human capital depends on the schools’ capacity to expand enrollment with sufficiently high-quality instruction, ensuring that larger classes do not negatively affect peers. We develop a structural model in which students first face an enrolment decision, and then an effort decision which will impact their achievement and the effort of their teacher. Class composition and effort choices are determined endogenously via a strategic game, which takes into consideration peer effects within the classroom. To estimate the model, we combine administrative data on test performance and cash transfers, socioeconomic surveys, and spatial data on child wages. Our model allows for heterogeneous endowments and teacher ability, and with it we can evaluate the impact of a conditional cash transfer on not only beneficiary enrollment choices and achievement, but also on their classmates.


What Misconceptions do Students Have About Gravity? Learning from TIMSS Data
This IEA Teacher Snippet is based on data from the Trends in Mathematics and Science Study (TIMSS) 2015 and can be adapted for all countries participating in TIMSS 2015. This edition is available for translation into the national language and includes the national data. To adapt this Snippet and receive all editable material, contact firstname.lastname@example.org.
TIMSS is an international assessment of student achievement in mathematics and science at fourth and eighth grades. Measuring trends in achievement since 1995, TIMSS data have enabled countries around the world to make evidence-based decisions to improve educational policies related to mathematics and science teaching and learning.
IEA offers a host of Teacher Snippets. Read the rest of this series.


Math on File: algebra by James Alexander
Publication Date: 2002-10-01
Math On File(TM): Algebra is an invaluable resource to supplement classroom instruction in a core area of the mathematics curriculum-algebra. The volume provides approximately 50 engaging problem sets, ranging from simple to challenging, that are appropriate for group work in class or individual out-of-class assignments. Covers a Wide Range of Levels and Topics Designed to support NCTM (National Council of Teachers of Mathematics) standards, this accessible volume emphasizes the systemic development of algebra skills. Opening the volume are a general introduction and an instructions for teachers section. All exercises include an introduction, as well as text and diagrams that fully articulate the ideas, and they span elementary beginning algebra to precalculus topics and modern mathematics. Subjects range from arithmetic series, balancing equations, and developing empirical laws to algebraic inequalities and interval notation, math games with numbers, statistics in practice, and parabolic motion. The exercises are all reproducible and easy to distribute for classroom use. Sections include: Basic Number Manipulations Basic Algebraic Manipulations Functions Graphing Patterns Data.


While planning a roofing project, you should compare the costs of the popular roofing materials for creating your budget. Wood shingles and asphalt are the common thatch materials used in the USA. Weather resistant metal tiling is also an alternative for homeowners.
Before you start to shingle your tiles, you should ensure the fact that you have the right amount of materials. If you estimate your needs, you will find yourself in the difficulty of having too many or too few roofing nails for accomplishing your project. Calculating the materials required by you for your tiling project could be an unnerving task due to the many angles of the roof. The tiling industry addresses this matter with a standardized system, selling its materials in a measurement called -squares’. Each square is the equal to 100 square feet of the flat area. As soon as you know the total number of squares your roof is having, you will be able to order every thing required by you.
Let’s have a look at the steps for estimating roofing materials:
Take measurements of your tiles
Climb onto the roof with the help of a tape to take the measurement. Try to take one measurement from the top of the main portion of your roof and another measurement from one end to another. Multiply the 2 measurements you have taken for obtaining the square footage. If a section of a roof is 40 feet long and 20 feet high, you could multiply the two for getting 800 square feet. Repeat this process for measuring every section of the tiles. However if you see that the areas are not square or rectangular in shape, make use of the longest span to do the calculations.
Add 10% after calculating the square footage
After calculating the total square footage, try to add 10% to it. If your roof has a total square footage of 2,000, the working number will be 2,200.You should divide that number by 100 in order to obtain the number of roofing squares. In this case, you would place orders for 22 squares of tiling shingles.
Place order for the felt underpayment
You should place orders for the felt underpayment of your tiles by making use of the same figure of the tiling square. Estimate the total number of roofing nails required by multiplying the roofing square number by 350 in order to get the nails for every tiling square.
Check out these steps for estimating your tiling materials. However if you are confused you could consult with the best South Florida Roofing contractor for executing your task.
Danl W Jones is an experienced consultant and owner of South Florida Roofing company. To know more about this and get assistance on Miami Roof Repair professionals, you may visit our website http://waterproofroofer.com/ .


I've just completed my first year of college. I've tutored for several years now, both independently and at a local math learning center, and am excited to gain more experience and improve my teaching style. I specialize in middle and high school math, the SAT, and Spanish, so if you have any interest in improving any of those skills, please feel free to reach out!
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Nutan Mathematics 12th Solution Pdf 89
Nutan Mathematics 12th Solution PDF 89: The Ultimate Guide for 12th Grade Math Students
If you are a 12th grade math student who wants to ace your exam and master the concepts of mathematics, you need Nutan Mathematics 12th Solution PDF 89. This is a comprehensive and detailed solution manual that covers all the topics and exercises in the Nutan Mathematics textbook for 12th grade. In this article, we will tell you why you need this solution manual, what it contains, and how to use it effectively.
Why You Need Nutan Mathematics 12th Solution PDF 89
Mathematics is a subject that requires a lot of practice and understanding. You cannot just memorize the formulas and rules without knowing how to apply them in different situations. You also need to develop your logical thinking and problem-solving skills to tackle the challenging and tricky questions that may appear in your exam. That is why you need Nutan Mathematics 12th Solution PDF 89. This solution manual will help you to:
Download Zip: https://miimms.com/2w3xDh
Review the concepts and theories of mathematics in a clear and concise way.
Solve the exercises and problems in the textbook with step-by-step explanations and methods.
Learn the tips and tricks to simplify the calculations and avoid common errors.
Check your answers and correct your mistakes with the help of the solutions.
Enhance your confidence and competence in mathematics.
What Nutan Mathematics 12th Solution PDF 89 Contains
Nutan Mathematics 12th Solution PDF 89 contains the complete solutions for all the chapters and exercises in the Nutan Mathematics textbook for 12th grade. The textbook covers the following topics:
Relations and Functions
Inverse Trigonometric Functions
Continuity and Differentiability
Application of Derivatives
Application of Integrals
Three Dimensional Geometry
The solution manual provides the detailed and accurate solutions for each and every question in the textbook, along with the relevant diagrams, graphs, tables, and formulas. The solutions are written in a simple and easy-to-understand language, with proper reasoning and logic. The solutions also follow the latest CBSE guidelines and marking scheme for the exam.
How to Use Nutan Mathematics 12th Solution PDF 89 Effectively
Nutan Mathematics 12th Solution PDF 89 is a valuable resource that can help you to improve your math skills and performance. However, you need to use it wisely and effectively to get the best results. Here are some tips on how to use the solution manual effectively:
Do not rely on the solutions alone. You should first try to solve the questions on your own, using the concepts and methods that you have learned in the textbook and in the class. You can use the solutions as a reference or a guide when you are stuck or unsure about your answer.
Do not copy the solutions blindly. You should understand how and why the solutions work, not just memorize them. You should also try to find alternative ways or approaches to solve the same problem, if possible. This will help you to develop your creativity and flexibility in mathematics.
Do not skip any step or explanation. You should follow the solutions carefully and thoroughly, without skipping or jumping any step or explanation. You should also check your calculations and results at each step, to make sure that you are on the right track. This will help you to avoid mistakes and gaps in your understanding.
Do not ignore the examples and illustrations. You should pay attention to the examples and illustrations that are given in the solutions, as they can help you to visualize and grasp the concepts and methods better. You should also try to apply the same examples and illustrations to other similar problems, to reinforce your learning.
Do not forget to revise and practice. You should review the solutions regularly and practice the exercises and problems frequently, to consolidate your knowledge and skills. You should also test yourself with mock exams and previous year papers, to assess your progress and performance. This will help you to prepare well for your exam and achieve your desired score.
Nutan Mathematics 12th Solution PDF 89 is a must-have for every 12th grade math student who wants to excel in mathematics. You can download it from the link below and start using it today. We hope that this article has helped you to understand the benefits and features of this solution manual, and how to use it effectively. We wish you all the best for your exam and your future endeavors.
[Nutan Mathematics RB Tripathi]
[Nutan Mathematics Solution PDF 89: The Ultimate Guide for 12]


An elliptic curve is the set of points that satisfy a specific mathematical equation. The ciphered data has been corrupted. Incryptographic algorithms were proposed based on an esoteric branch of mathematics called elliptic curves. Recently, the company RSA recalled several of their products because this random number generator was set as the default PRNG for their line of security products.
Modern browsers also support certificates based on elliptic curves. As we've written about before, it's also part of the reason that attention should be spent to ensuring that your system is using adequately random numbers. We can call this billiards move on two points "dot. Curve secpk1 bit is used for both.
Specialized algorithms like the Quadratic Sieve and the General Number Field Sieve were created to tackle the problem of prime factorization and have been moderately successful.
Here's the plot of the same curve with only the whole number points represented with a maximum of An elliptic curve is not an ellipse oval shapebut is represented as a looping line intersecting two axes lines on a graph used to indicate the position of a point.
Your IP will still be hidden. Using elliptic curve cryptography saves time, power and computational resources for both the server and the browser helping us make the web both faster and more secure.
First generation cryptographic algorithms like RSA and Diffie-Hellman are still the norm in most arenas, but elliptic curve cryptography is quickly becoming the go-to solution for privacy and security online. Small keys are important, especially in a world where more and more cryptography is done on less powerful devices like mobile phones.
For this level of security with RSA, you'd need a key with 2,bits. You can check this yourself.
If your eyes start to glaze over, you can skip way down to the section: The gap between factoring and multiplying is not sustainable in the long term. Many experts are concerned that the mathematical algorithms behind RSA and Diffie-Hellman could be broken within 5 yearsleaving ECC as the only reasonable alternative.
In a future blog post, we will go into how a backdoor could be snuck into the specification of this algorithm. ECCr1 Like ECCk1 but curve primev1 bit, also known as secpr1 is used for both key exchange and certificate.
All our certificates use SHA for signing.
The takeaway is that you can take a number, multiply it by itself a number of times to get a random-looking number, then multiply that number by itself a secret number of times to get back to the original number.
A more interesting property is that any non-vertical line will intersect the curve in at most three places. The downside It is not all roses in the world of elliptic curves, there have been some questions and uncertainties that have held them back from being fully embraced by everyone in the industry.
It has several interesting properties. In an ideal Trapdoor Function, the easy way and the hard way get harder at the same rate with respect to the size of the numbers in question.
Building blocks of a better Trapdoor After the introduction of RSA and Diffie-Hellman, researchers explored other mathematics-based cryptographic solutions looking for other algorithms beyond factoring that would serve as good Trapdoor Functions. Any calculation that results in a number larger than the maximum gets wrapped around to a number in the valid range.
It's like the original curve was wrapped around at the edges and only the parts of the curve that hit whole number coordinates are colored in. This key exchange uses much of the same field arithmetic as existing elliptic curve cryptography and requires computational and transmission overhead similar to many currently used public key systems.
He believes that ECC offers a unique potential as a technology that could be implemented worldwide and across all devices. Whitfield Diffie and Martin Hellman. If multiplication is the easy algorithm, its difficult pair algorithm is factoring the product of the multiplication into its two component primes.
Some of the more skeptical cryptographers in the world now have a general distrust for NIST itself and the standards it has published that were supported by the NSA.
Another program worth looking at is SKS, which uses a similar ECC based encryption process as the example above, but doesn't have any external dependencies so all the ECC code is right there for you to look at.
Readers are reminded that elliptic curve cryptography is a set of algorithms for encrypting and decrypting data and exchanging cryptographic keys.
By this measure, breaking a bit RSA key requires less energy to than it takes to boil a teaspoon of water. At some point we may want to validate the original text instead.
Encryption is one specific element of cryptography in which one hides data or information by transforming it into an undecipherable code. Encryption typically uses a specified parameter or key to.
How can I encrypt data using a public key from ECC X certificate douglasishere.com framework on windows? Hot Network Questions Is lift in fact a kind of drag? ECC: A Case for Mobile Encryption. Posted in General Security on January 23, Share.
Tweet They contain a special encryption card that scrambles speech and data before transmitting it. This Secusmart card uses elliptic curve cryptography to encrypt and decrypt the mobile speech.
But just because it is encrypted doesn’t mean it’s safe. IBM® Multi-Cloud Data Encryption provides a broad range of features, including data douglasishere.com has been visited by K+ users in the past month. Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields.
ECC requires smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide equivalent security.
Elliptic Curve Cryptography (ECC) is one of the most powerful but least understood types of cryptography in wide use today.
At CloudFlare, we make extensive use of ECC to secure everything from our customers' HTTPS connections to how we pass data between our data centers.Data encryption with ecc


MATH HELP CENTRE
The Math Help Centre comprises of a group of free services offered by the Department of Mathematics for all first-year students to get math students the needed help, support and resources in mathematics, and to facilitate their success.
The Help Centre is staffed by graduate students and sometimes high-level undergrads with a passion for teaching, and knowledge and experience with courses. You can avail yourself of any of the numerous Math Help Centre services if you ever need help with your math course, just bring your notes and your brains and come get help with those problems you've been stuck on!
The Help Centre offers both in-person and online help sessions. The Math Help Centre hours are:
Fall 2023 (11 Sept - 22 Dec)
MON to FRI 9:00 AM to 6:00 PM (In-person at 107 Machray Hall)
Visit the Help Centre schedule page to find out more about the Math Help Centre schedule.
MATH BOOT CAMP (For MATH 1500/1510/1520 Students)
This is a free Math Boot Camp at the beginning of each semester for students enrolled in Math 1500, MATH 1510 or MATH 1524. This Boot camp serves as a refresher on pre-calculus topics. It runs on the first Thursday, Friday, and Saturday of the term for a total of 9 hours. Over those 3 days, pre-calculus topics necessary to succeed in the upcoming calculus courses will be reviewed, with questions taken directly from the old midterm and final exams. Seating is limited so early registration is advised.
Thursday, Sept 7, 4:30 pm - 8 pm
Friday, Sept 8, 4:30 pm - 8 pm
Saturday, Sept 9, 10:00 am - 1 pm
Math Boot Camp Poster
Please use this link to register. For further information contact email@example.com
SATURDAY WORKSHOP SERIES
This is a general refresher workshop series on fundamentals to prepare all first-year math students for the upcoming semester. These run for three hours each day on three successive Saturdays. The contents of each day will be self-contained, so you don’t have to be at all three workshops, you can attend only those workshops you need. Please see the Saturday Workshop Series poster to determine which workshops will be ideal for you. Use the link below to sign up for the workshops.
Dates & Registration Links:
Saturday, Sept 16, 10 am - 1 pm (Day 1)
Saturday, Sept 23, 10 am - 1 pm (Day 2)
Saturday, Sept 30, 10 am - 1 pm (Day 3)
There are limited spots, so early registration is advised.
Saturday Workshop Series Poster
MHC WORKSHOP SEMINARS
These are free workshop seminars organized throughout the Semester on selected topics students frequently have problems with. In these workshops, problems that aid understanding of the topic, and problems that are commonly found on the midterm and final examinations are tackled. Each workshop starts with a (roughly) 20-minute demonstration, with time in the middle for participants to attempt the problems and ask questions if/when they get stuck. The problems that caused students the most difficulty are then demonstrated for the last 20 minutes. Below is a list of scheduled workshop seminars for the semester, however, you can request for workshops on topics you have difficulty in from the MHC website. Please visit the Workshop page to find out about our offerings and to register.


you can check out how she uses this review game on her blog FourthGradeRAcers. Her version is not tailored for Firsties, so I thought of how we could adapt it to fit our class needs.
I love how versatile this could be. You can use this game with anything you are teaching. I think it could also be a perfect #FIP activity. The students would be engaged the whole time.
Anyways, Alyssa writes numbers on the back of the post-its and students pick post-its when they get an answer correct. They receive positive or negative points. I think that we could use whichever team makes it to ten wins. I also think you could just use tally marks too. This would be a great review for math and ELA at the same time. WooHoo!!!! I can't wait to make my own "STAnky Foot"!!!!


The Impedance Calculator performs two way calculations between the following parameters: line width, differential line width & spacing, substrate thickness, impedance, and dielectric constant for various micro-strip and stripline configurations.
The only impedance calculator that will allow for trace etch taper and a separate dielectric constant for solder mask. The only impedance calculator that will quickly fine tune trace and substrate structures with geometry calculations based on input target impedances.
Impedance Calculator is available to add to any Designer Suites
Impedance Calculator is available as Stand-Alone software for use directly Inside Microsoft Windows™
Easy to use
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Built in Material
2 way calculations
with automatic iterations for
Stripline Single or Differential
Pair, and mixed-dielectric
differential stripline calculations
the cross section of each
Calculations are accurate up to a maximum 2GHz frequency
Various Impedance Calculations:
Microstrip with or without soldermask
Independent dielectric constant for soldermask
Microstrip and stripline rectangular or trapezoidal trace configurations
Differential and common mode impedances calculated for differential pair routing
Mixed-Dielectric Stripline configuration for accurate calculation of composite substrates.
Propagation delay calculations, Geometry Calculations,
Differential width and spacing can be calculated from the desired impedance through iterations
Accuracy correlation to within 1.0 percent of high-end field solvers on the market today!
Note box for user reference information
Print button to print out current dialog box with settings.
Impedance Calculator performs two-way calculations for various Differential Microstrip and Stripline configurations between the following parameters:
Differential line width & spacing
Impedance, and dielectric constant


Transitional Math 10F (MTT 10F)
This two-credit course will be taught from September 2022 through June 2023. MTT10F provides support for students who have struggled in math prior to Grade 9. This course comprises units designed to address gaps and reinforce skills required to develop an understanding of math and focuses on basic math strategies, numbers, patterns & relations algebra, polynomials, shape & space, graphing and statistics. Students will develop skills needed to further their math skills and strategies and beyond.


From practice your skills with answersfor use with your students discovering geometry practice your skills chapter 1 1 10 ab and cd with m as the midpoint. Discovering geometry an investigative approach practice your skills with answers ralph bothe michael serra david rasmussen judy hicks on amazoncom free . Discovering geometry worksheets showing all 8 printables worksheets are kendall hunt high school discovering mathematics practice your skills with answers . Discovering geometry practice your skills with answers michael serra on amazoncom free shipping on qualifying offers new paperback. 1b5429 discovering geometry practice your skills 2008 answers c2008 by kendall hunt practice your skills with answers as part of the teaching resources
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Muswell Hill Primary School’s vision for Mathematics is that each child will possess a confidence and positive attitude to the subject regardless of their gender or background.
Each child will move onto the next stage in their learning with a secure base of fluency and knowledge of key number facts. This knowledge will allow them to explore and solve mathematical challenges in everyday situations as maths is seen as an integral part of life.
At Muswell Hill Primary School the teaching of Maths is based on a mastery approach. The approach ensures that children learn the strategies and concepts on a deeper level rather than rushing through the objectives. Attention is paid to reinforcing their knowledge. Teachers use a teaching for mastery approach. At our school this means that the whole class will work together in some lessons, particularly those that introduce and explore a new concept. Teachers will focus on small steps, key representations, questions and misconceptions to introduce a concept, aiming for all children to become secure in the concept. In other lessons, it might be effective for the class to spend more time working in smaller groups or on independent practice; this will be based on the teacher’s assessment, from the previous lesson. Teachers will, informed by their assessments, adjust lessons and activities so that they are pitched at appropriate levels of challenge and provide the right ‘next step’. Best practice at our school is keeping the whole class working on the same concept, taking small steps to master this but also assessing progress and using ‘flexible grouping’: grouping that is informed by day to day marking and assessment of misconceptions. When appropriate, throughout the lesson, the children will be drawn together to learn from each other and share misconceptions so they can progress as a class. Children with special educational needs may well be working to an individual plan and teachers will differentiate their work, ensuring they are included in the theme of the lesson. Whatever their level of attainment, children should not experience repeated failure or effortless success; success should be encoded.
Lessons are planned from a balanced mathematics curriculum based on the National Curriculum with a strong emphasis both on fluency in number facts, calculations and place value and applying all areas through reasoning and problem solving. Teachers are expected to use precise explanations in order for children to clearly understand key concepts and strategies and assess pupils regularly to identify those requiring intervention, so that all pupils are supported in keeping up – diminishing differences and disadvantages. Specific, differentiated and deep questioning in lessons are key in order to test conceptual and procedural knowledge, as well as supporting and stretching pupils according to their needs.
Teachers at MHPS base their pedagogy on evidence from bodies such as the NCETM, NRICH and Whiterose, they gather, develop and share great lesson ideas which make maths relevant as well as those which promote problem solving with pure number. Games, reasoning and problem solving are cornerstones of our teaching and learning of mathematics. The school has worked in partnership with NCETM in recent years and is committed to approach.
The curriculum is planned so that children have regular opportunities to embed their understanding of key maths skills; such as number bonds, knowledge of +, -, x and division/multiplication tables. The progression of written methods for calculations follow the CPA approach – from concrete (actually ‘doing’ with real objects) to pictorial representations – moving to abstract concepts only when children are ready and have a secure conceptual understanding. The calculation policy with the progression of methods used across the school is attached here.
Maths @ Home
To consolidate and reinforce the maths learning carried out in school, teachers are now able to allocate online activities via the Topmarks online homework resource IXL. The children have been given their individual log in details and once logged in can access and complete their maths homework each week.
Staying Safe Online
DLC and the Internet have become integral to teaching and learning within schools, providing pupils and staff with opportunities to improve understanding. However, whilst this technology has many benefits for Muswell Hill Primary School, we recognise that clear procedures for appropriate use and the education of staff and pupils about online behaviour and potential risks are essential. Please click here to see our Online Safety Policy.
Here are a list of a few useful websites to help the children with their maths learning at home:
1) Top Marks Hit the Button: this is great for quick fire times table and number fact practice to develop the children’s fluency:
2) TT Rockstars: In KS2 each pupil has been set up with their own individual log in, which means they can access this exciting online resource at home as well as at school.


Data normal distribution and probability
2018-7-18 dealing with non-normal data: always check with a probability plot to determine whether normal distribution log-normal distribution, found with length data. Use probability distribution objects to fit a probability distribution object to sample data, or to create a probability distribution object with specified. This normal probability calculator for sampling distributions will compute normal distribution probabilities for sample means x¯, using the population mean, standard deviation and sample size.
Perform data normality tests in excel using normal probability plots and p values. A normaldistribution object consists of parameters, a model description, and sample data for a normal probability distribution. 2016-5-3 224 multivariate normal distribution from its origin in games of chance and the analysis of experimental data, probability. 2016-12-11 returns the normal distribution for the specified mean and standard deviation this function has a very wide range of applications in statistics, including hypothesis testing.
2013-6-27 4 distribution (dist) normal distribution probability calculates the probability of normal distribution data falling between two specific values. 2 天前 learn how to create probability plots in r for both r makes it easy to draw probability distributions and the fit of sample data to the normal distribution. 2014-5-11 calculate quantiles for a probability plot, and optionally show the plot generates a probability plot of sample data against the quantiles of a specified theoretical distribution (the normal distribution by default) probplot optionally calculates a best-fit line for the data and plots the results. 2008-9-3 hand-book on statistical distributions for 2 probability density functions 3 7 standard normal distribution z-values for a speciﬁc probability content.
2018-7-6 so, in summary, our assumptions tell us so far that the conditional distribution of y given x = x is involves just making a simple normal probability. A normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme. 2018-7-13 goal: this case introduces various descriptive statistics generated by forecastx tm to make statistical inference on monthly rates of return for the dow jones 30 index specifically, students will test whether monthly stock returns follow a normal probability distribution and make probability. 2018-7-19 stats_cdf_normal — calculates any one parameter of the normal distribution given of two data sets stats_dens_beta — probability density functions, a. 2017-2-3 normal distribution (probability) there are no real world examples of normally distributed distribution of a data set whether it is normal distribution or.
2012-2-10 data is position in a normal distribution then, distribute copies of the attached normal probability that a box has between 73 and 77 crackers. 2 天前 foundations of probability in r he has worked as a data scientist at stack overflow and received his phd in quantitative and the normal distribution. This normal probability calculator computes normal distribution probabilities for you you need to specify the population parameters and the event you need.
2005-2-20 converting to a standard normal distribution think of me as the measure of the distance from the mean, measured in standard deviations example: pep zone standard normal probability distribution pep zone sells auto parts and supplies including a popular multi-grade motor oil. Normal distribution definition normal distribution (also known as gaussian) is a continuous probability distribution most data is close. 2011-4-4 normal distribution table - t-2 tables probability table entry for z is the area under the 百度首页 登录 加入文库vip 享专业文档下载特权 赠共享文档下载特权.
A table for the standard normal distribution typically contains probabilities for the range of values –∞ to x (or z)--that is, p (x ≤ x)this probability is the same as. 2018-7-17 that average is one data point the normal probability distribution describes the proportion of a population having a specific in a normal distribution,. 2016-12-20 it is approximated by a normal distribution, ie probability distribution of directly measured p,(ii)an composition data through a linear relationship h.
2012-11-19 introductory textbooks in probability and statistics often introduce univariate probability ing the standard normal distribution from figure 3 are listed below. 2005-3-6 the normal distribution • the normal probability distribution is the most com-mon model for relative frequencies of a quantitative variable • bell-shaped and described by. 2016-1-11 the random normal distribution to create a normally distributed set of random numbers in excel, you now have a normally distributed set. 2017-4-25 in python, a probability plot can be generated with the command statsprobplot(data, plot=plt) if my understanding is correct, it indicates how likely the input data is in i.


2020 Advent of Code Day 1 in Go- 10 mins
About Advent of Code
(copied from here)
Advent of Code is an Advent calendar of small programming puzzles for a variety of skill sets and skill levels that can be solved in any programming language you like. People use them as a speed contest, interview prep, company training, university coursework, practice problems, or to challenge each other.
The link to the full problem is here.
To summarize the day 1 problem: we need to find the two items in a list of integers that sum to
X and then multiply those two items to recieve the correct answer.
In this case,
2020, so we need to find the items that add up to
2020 and multiply those items to get the answer.
2020 is even, we have two potential scenarios:
- Two numbers repeat and are exactly half of
- One number is greater than the other number, meaning one is greater than
1010and one is less than
After quickly looking at our input, there are no repeating numbers, so one of our values must include one greater than
1010 and one less than
If we split our input into two groups, one greater than half of
2020 and one less than half of
2020, we can create two groups which each contain one of the answers and then compare each number.
We can break down our total solution into the following steps:
- Parse the input
- Split the input into two groups, one higher than half of
2020and one lower than half
- Find the value from each which sum to
Depending on how we find the value from group, we may need to add a few steps to make it easier to find the value.
ioutil package has a nice built-in way to read our input file and convert it to an array of bytes.
We still have to convert our array of bytes into numbers that we can perform mathematical operations on and compare, so we’ll create a function to do that.
To summarize this function, we’re inputting a byte array, converting the byte array into a single string, splitting the string by line, then creating an integer array of the same size as the number of lines.
Then, we’re looping through each line and checking to make sure that the line isn’t empty. After, we’re converting each line from a string to an integer and checking that there are no errors. Finally, we’re setting the value of our current index in the integer array to our new integer value and then returning the integer array once the loop is completed.
We could do this in a less explicit way using
bufio, Go standard library’s buffered I/O, but one of my favorite parts about Go is just how explicit it is.
Categorizing our numbers
Now that we have a single array of integers that represents our input, we need to separate them into two groups, one being higher than half of
2020 and one being lower.
This function splits a single array into two and conditionally putting each integer into the upper or lower array. As a bonus, the function input is a sorted array, both of the output arrays will also be sorted.
Finding our pair of numbers
Brute-force Method (Linear Search)
We could use a nested loop to loop over both of our lists and compare every item sum to 2020 until we find the correct 2 that sum to
A basic implementation of this in Go would be:
This solution would work on small inputs, but would quickly take too long to compute as the compute-time would grow exponentially at a rate of O(n^2) compared to a linearly-growing input.
In other words, this is not a scalable solution and would quickly take too long to compute if the size of our input was large. Fortunately for us, with this problem it’s not, so we end up with our pair of numbers and can use this to quickly end up with a solution.
Generally, a well-accepted alternative to linear search is using binary search.
To summarize, rather than search each object one by one to find a match, we take a sorted array and compare the item we’re looking for with the object in the middle of the array. Depending on whether our object is greater than or less than the middle, we throw away the known incorrect half of the array and repeat the search using the correct half of the array.
If we are searching for values, we have to make one side equal to the other. We can do this by creating a
Map function which we’ll use to return custom values of the items in one of our arrays. We’ll utilize this similar to a lambda in Python, which is an unnamed function, where we’re subtracting.
In this example,
subtracted is an array of integers where the values are the difference between 2020 and the lower number. Because the lower number plus the higher number equals
subtracted array can be used in our binary search to find the same item in both.
Luckily for us, Go’s
sort package includes a binary search implementation that we can use to find our two values:
map implements a hash table, which for integers means that it would greatly improve our lookup time to find matches.
This improves our pair-finding from O(N^2) -> O(logN) -> O(1) effectively.
I have not yet implemented this solution.
A quick benchmark with our input comparing our naive approach above to Go package
Search() binary search implementation, we can see that:
Linear: 443ns Binary: 1.299µs
The benchmark shows unexpected results in favor of Linear search. After closer examination, it’s likely that my benchmark was flawed in a few ways:
- The time it takes to sort was not factored into Binary’s result, as the arrays for both had already been sorted
- Multiple benchmarks were not done (ie: the input order didn’t change), so it’s possible that the binary search was worst case vs linear best case considering that both benchmarks were trying to find a single pair of matching values in two arrays


Manage episode 348085436 series 3401073
What are Roman Numerals?
Roman numeral, any of the symbols used in a system of numerical notation based on the ancient Roman system. The symbols are I, V, X, L, C, D, and M, standing respectively for 1, 5, 10, 50, 100, 500, and 1,000 in the Hindu-Arabic numeral system. Roman numerals were employed for everyday tasks like counting and other daily operations. Roman numerals are represented by a number of letters from the Latin alphabet. They are frequently used to indicate the names of Popes and monarchs, as hour marks on a clock, as general suffixes for persons of all generations, etc. Roman numerals will be written and explained in this article. We'll also look into the various shortcuts and techniques that can be used to make this chapter simpler to learn and comprehend.
How to Convert Roman numerals to numbers and convert numbers to Roman numerals.
First, we have to know all the value of the letter in Roman.
I, V, X, L, C, D, and M, standing respectively for 1, 5, 10, 50, 100, 500, and 1,000
Example: How to Write 1999 in Roman Numerals?
Roman numerals for 1999 can be obtained by using the method given below:
In this method, we break 1999 into the least expandable form, write their respective roman letter and add/subtract them, i.e. 1999 = 1000 + (1000 - 100) + (100 - 10) + (10 - 1) = M + (M - C) + (C - X) + (X - I) = MCMXCIX.
Therefore, the value of 1999 in roman numerals is MCMXCIX.
You can find out more information about Roman Numerals here. We provide many practical examples of Roman Numerals to help you understand the knowledge of Roman Numerals.
At the same time you can learn more about variety of math formulas from simple arithmetic operations such as addition and subtraction to some more complex calculations of shape area like rectangles, parallelograms, hexagons, and even integral formulas
See detail here: https://www.calculatorful.com/math


2 edition of On the focal surfaces of the congruences of tangents to a given surface. found in the catalog.
On the focal surfaces of the congruences of tangents to a given surface.
|Other titles||Pamphlets. Mathematics. Quartos. v. 2, no. 9.|
|LC Classifications||QA608 .P38|
|The Physical Object|
|Pagination||1 p. L., 34 p., 1 L.|
|Number of Pages||34|
|LC Control Number||05033246|
Congruences associated with quad meshes are discrete versions of parametrized congruences associated with parametrized surfaces. In particular, the so-called torsal parametrizations are discussed from the integrable systems perspective by Bobenko and Suris .Cited by: 1. The tangent plane to a surface at a given point p is defined in an analogous way to the tangent line in the case of curves. It is the best approximation of the surface by a plane at p, and can be obtained as the limiting position of the planes passing through 3 distinct points on the surface close to p as these points converge to p.
oriented lines, or line congruences, which we view as surfaces in L. Thus we are lead to consider the geometry of immersed surfaces Σ ⊂ L. In the ﬁrst instance, since L can be identiﬁed with the tangent space to the 2-sphere, there is the natural bundle map π: L→ S2. If π|Σ: Σ → S2 is not an immersion, we say that Σ is ﬂat. You should prove that the tangent vector of the curve at $(1,1,1)$ is contained in the tangent plane of the surface, or is orthogonal to the normal vector to the surface at $(1,1,1)$ which is given by the gradient. You calculated the normal vector which is $(-1,-5,1)$.
The centres of those spheres having degenerate tangency with the surface (in Arnold's notation of type A2) form the focal set, and the set of points on the surface where there is a contact of type Author: Keisuke Teramoto. Focal surfaces are known in the eld of line congruences. Line congruences have been introduced in the eld of visualization by Hagen and Pottmann (see, ). Focal surfaces are also used as a surface interrogation tool to analyses the "quality" of the surface before further processing of the surface, for example in a NC-milling operation (see ).
Surface effects in controlled fusion
Souvenir of the 200th performance of The admirable Crichton ... produced under the management of Charles Frohman at the Duke of Yorks Theatre on November 4th 1902.
Information activities of major international organisations.
Bilateral cerebral activation in relation to verbal and spatial task performance, sex and handedness
fine grained database system performance model.
executive function and theory of mind performance of boys with fragile X syndrome
Procedures for the validation of courses.
Getting it togeher
Essays catholic & critical
account of church bells, with some notices of Wiltshire bells and bellfounders.
The Focal Surfaces of the Congruence Formed by the Tangents to the Lines of Curvature of a Given Surface. [Taliaferro, Thomas Hardy ] on *FREE* shipping on qualifying offers.
The Focal Surfaces of the Congruence Formed by the Tangents to the Lines of Curvature of a Given : Thomas Hardy Taliaferro. Congruences of Tangents to a Surface andi Derived Congruences. BY L. EISENHART. Given any famiily of curves upon a surface S; the tangents to these curves form a rectilinear congruence for which S is one of the focal sheets.
The other focal sheet is a determinate surface Si, and upon it there is a family of curves to. Our consideration of the focal surfaces of the congruences of the tangents to the lines of curvature of the surface (X), is based on the following two theorems given by Darboux* and Koenigs.t.
focal surface all surfaces of a congruence are tangent to each other. A surface of a congruence r¡ on which the curves Ct have an envelope is called a principal surface of Tt. It is known that each envelope curve lies on a focal surface, and that each envelope curve is.
A congruence is a surface in the Grassmannian [equation] of lines in projective 3-space. To a space curve C, we associate the Chow hypersurface in [equation] consisting of all lines which intersect C Cited by: 7. developable which is formed by the tangents of the curves v = const, on S„ constructed at the various points of the same curve u = const.
The locus of Pp, the surface S, is therefore the second sheet of the focal surface of the congruence which is composed of the tangents to the curves v = const, on S„. surfaces X. In the generic case each family consists of the tangent lines to a surface, and these two surfaces Σ,Σ are called the¯ focal surfaces of the congruence.
The congruence gives a mapping f: Σ → Σ with the property¯ that the congruence consists of lines which are tangent to both Σ and Σ and¯ join x∈ Σ to ¯x= f(x) ∈ Σ.¯ 2. In section §0, we give the basic deﬁnitions about congruences and their focal surfaces.
In section §1, we obtain the classical invariants of the focal surface. The key new technique in this section is to use the construction given in  of varieties parametrizing inﬁnitely close points of a given variety.
In general, a congruence contains two families of developable surfaces (a developable surface is formed by the tangent to a space curve). Eisenhart recognized that in all known cases, the intersections of these surfaces with the given surface and its image form a net of curves with special properties.
Moutard quadrics of the focal surfaces Sv, S. Segre-Darboux nets on the focal surfaces Sy, Sz. W congruences. Curves of the focal nets iV„, N.
Correspondences associated with the focal nets Ny, Nt. Axis congruences and ray congruences. The congruences aij, yf and the principal congruence rçf. totality of tangents to a surface from points on a given curve is a rectilinear congruence having an infinity of lines through each point of the curve.
If we establish a relation between u and v, say (2) v = 0(w) the curves of the congruence whose parameters satisfy this relation depend upon. Discrete Line Congruences for Shading and Lighting J. Wang1, C. Jiang1, P.
Bompas, ing focal surfaces of meshes with known or estimated nor-mals, have been presented by [YYG07]. There are some it is the tangent surface of a parabola). We are going to make use of these congruences in.
On the focal surfaces of the congruences of tangents to a given surface / gaev, serguei. Countries and Regions of Publication (1) View the list below for more details. SOME THEOREMS ON RECTILINEAR CONGRUENCES AND TRANSFORMATIONS OF SURFACES BY CHENKUO PA 1.
Let S be a non-developable analytic surface in ordinary space and L a rectilinear congruence with each of its generators passing through a cor-responding point of S but not tangent to S. For any given surface these con. KoG•13 (),27–S. Gorjanc: Pedal Surfaces of First Order Congruences Proposition4 An (n+1)-ple point exists on Pn+2 n iff a pole P lies on d.
The highest number of such points on Pn+2 n is two only if c n lies in the plane perpendicularto d. PROOF: If a pole P lies on d, then every circle c passing through P, and it is the (n+1)-ple point of Pn+2 n because.
The focal net of lines on every focal surface is conjugate. In a hyperbolic domain, a congruence is the set of common tangents to two focal surfaces; in the elliptic case, a congruence is formed by real common tangents to two conjugate imaginary surfaces; in the parabolic case, a congruence is formed by the tangents to a family of asymptotic lines of a unique focal surface.
Visualization and computation of freeform curves and surfaces Surfaces A paramctnc surface is a mapping X from U c into R 3 of class C'(rè 1). X is called regular if, for all u = (u, u) E U, is an invertible linear mapping. The two partial derivatives of X in u are denoted by and xo(u).
On the Line Congruences In this paper, we found general equations to determine the surfaces of a line congruence. For the convenience of some long term equations, abbreviations have been used for trigonometric functions such as: cos(u):= c(u);sin(u):= s(u) 2.
Fundamentals Line geometry In this section, we introduce some elements of the Cited by: 1. Line congruences can be viewed as surfaces in the four dimensional space of lines, a homo- geneous space of the group of Euclidean motions in R”.
Using the method of moving frames. we calculate first order invariants for line congruences with two real focal surfaces. Introduction Line congruences can be viewed as surfaces in the four dimensional space of lines, a homo- geneous space of the group of Euclidean motions in R3.
Using the method of moving frames. we calculate first order invariants for line congruences with two real focal surfaces. In Section by: 6.
contains n-ple straight line. According to , the pedal surfaces of the ﬁrst type congruence C1 n with respect to a pole P is the image of the plane at inﬁnity given by the (n + 2)-degree inversion with respect to C1 n and any sphere with the center P.
Thus, it is an (n + 2)-order surface with n-ple straight line d and contains the.Given conjugate net on a surface, it defines two new conjugate nets called the Laplace transforms of the old net; the transformations are provided by tangents to the parametric lines (see Fig.
1). The discrete version of conjugate net on a surface is given by two-dimensional quadrilateral lattice Cited by: where is a unit principal normal vector and is a nonzero curvature of the curve. Thus the focal curve or evolute of a curve is the locus of its centers of curvature.
Focal surfaces [,] can be constructed in a similar way by using the principal curvature functions of the given surface.


Middle School Academic Program
Middle school (Grades 6-8) is a transitional period for academic and social growth between the elementary and secondary levels.
The required courses are Bible, English, social studies, science, mathematics, reading, and introduction to computers. Enrichment courses such as character building, band, and art are offered. Eighth graders may begin an advanced math tract by taking Algebra I and Spanish I if they meet the qualifications based on teacher recommendation, prior grades, and test scores.


Finding your suitable readers for office calculator inches is not easy. You may need consider between hundred or thousand products from many store. In this article, we make a short list of the best readers for office calculator inches including detail information and customer reviews. Let’s find out which is your favorite one.
648 reviews analysed
1. Calculated Industries 44080 Construction Master Pro Construction Calculator
- Work in and convert between any building-math dimension; Built-in Right-Angle function
- Complete trigonometric function & D:M:S conversions
- Roof, Rafter and Framing Solutions; Complete Stair Layouts
- Calculates Weight per Volume, Footing Volume, Blocks, Roof Area
- Circular Calculations: Circumference, Arcs, Segments and More
Builders, contractors, carpenters and construction professionals use this advanced, easy-to-use Feet-Inch-Fraction, Metric and Full Trigonometric calculator to provide rapid solutions to complex construction-math problems. Work in and convert between all building dimensional formats, including square and cubic! Built-in functions include Custom and Jack Rafter keys with instant cutting angles, Rake-Wall key, complete Circular solutions, full Stair calculations, D:M:S to Decimal Degree conversions, automatic Block and Footing, three Memories, and a Preference Function for user-defined options.
The most complete construction-math calculator on the market, the Construction Master Pro desktop calculator (model 44080) from Calculated Industries is perfect for completing layouts, bids, and estimates as well as helping to save time and money by helping you figure out the right amount of needed materials. It’s ideal for or contractors, architects, builders, engineers, project managers, estimators, draftspersons, and more.
You’ll be able to work in and convert between all building dimensional formats–yards, feet-inch-fractions and metric–including area and volume, and it also comes with a full trigonometric functionality (sine, cosine, tangent, arcsine, arccosine and arctangent simplify complex design and construction-math).
The Construction Master Pro includes a number of built-in time-saving functions, including calculations for risers, treads, stringer length, and incline angle; how many 4×8, 4×9 or 4×12 sheets are needed to cover an area; jack rafter results for regular and irregular pitch roof; determining number of on-center studs for an entered length; and right angles. It also offers advanced solutions for circles, arches, columns, cones, pillars, windows and post-holes arcs, circumference, and segments.
Additional features include a large multi-position tilt display LCD, ability to custom define your preferences (such as fractional settings), a “paperless” tape that lets you review the previous 20 entries to double-check your totals, and accumulating memory with three additional memory storage locations. It’s powered by a single 3-volt CR2032 lithium battery, and the Construction Master Pro has an auto shut-off feature that turns the calculator off after about 8 to 12 minutes of non-use. It measures 6.4 x 9 x 1.4 inches, weighs 10.8 ounces, and is backed by a one-year limited warranty.
What’s in the Box
Calculated Industries 44080 Construction Master Pro desktop calculator; user guide; pocket reference guide, and battery.
2. Calculated Industries 4065 Construction Master Pro Advanced Construction Math Feet-inch-Fraction Calculator for Contractors, Estimators, Builders, Framers, Remodelers, Renovators and Carpenters
Mater Pro Advanced Construction Calculator conveniently works in and converts between all building dimensional formats for easy use minimizing mistakes. Features custom set fractions and includes protective hard case, user guide, filed guide and long life batteries.
The construction master pro (model 4065) from Calculated Industries sets the industry standard for advanced construction-math calculators. Offering powerful built-in solutions and expanded preference settings, it’s perfect for completing layouts, bids, and estimates as well as helping to save time and money by helping you figure out the right amount of needed materials. It’s ideal for or contractors, estimators, architects, builders, framers, engineers, concrete/foundation contractors, draftspersons, and more.
Quick, Accurate Solutions in the Field
You’ll be able to work in and convert between all building dimensional formats–yards, feet-inch-fractions and metric–including area and volume. The construction master pro includes a number of built-in time-saving functions, including calculations for risers, treads, stringer length, and incline angle; how many 4 by 8, 4 by 9 or 4 by 12 sheets are needed to cover an area; jack rafter results for regular and irregular pitch roof; determining number of on-center studs for an entered length; and right angles. It also offers advanced solutions for circles, arches, columns, cones, pillars, windows and post-holes arcs, circumference, and segments.
The construction master pro also includes the ability to custom define your preferences (such as fractional settings), a “paperless” tape that lets you review the previous 20 entries to double-check your totals, and accumulating memory with three additional memory storage locations. It’s powered by a two 1.5-volt batteries (LR-44/A76), and the Construction Master Pro has an auto shut-off feature that turns the calculator off after about 8 to 12 minutes of non-use. The 11-digit display measures 2.5 inches by .625 inches. Overall, the calculator measures 5.6 inches by 3 inches by .6 inches, and weighs 4.5 ounces. It’s backed by a one-year limited warranty.
What’s in the Box
One Calculated Industries 4065 construction master pro calculator, Armadillo Gear protective cover, pocket reference guide in English and Spanish, and batteries.
3. Calculated Industries 4020 Measure Master Pro Measurement Conversion Calculator
- Get professional results every time with the handy, easy-to-use tool
- It’s ideal for designers, craftsmen, tradespersons, fabricators, woodworkers
- Built-in functions make the Measure Master Pro ideal for faster, more accurate material estimates
- Work in and convert between any building dimensions, including metric
- Linear, area and volume measurements
- Find weight and weight per volume
- Instant solutions for circle area, circumference, arcs and more
Great for designers, woodworkers, craftsmen, technicians, etc. Calculates directly in feet, inches, fractions, yards, meters, centimeters, and millimeters, including square or cubic formats of each. Converts to and from all dimensional formats instantly. Instant solutions for circumference, circle area and arc lengths. 1 button solves postholes, columns, pillars, arches and much more. Weight per volume key allows you to find weight of material (i.e., tons per cubic yard, kilograms to pounds, etc.). Custom set fractions. Estimate material costs. Paperless tape allows you to review last 20 entries.
Ideal for faster more accurate material estimates (view larger).
Get professional results every time with the handy, easy-to-use tool Measure Master Pro measurement conversion calculator (model 4020) from Calculated Industries. It’s ideal for designers, craftsmen, tradespersons, fabricators, woodworkers, and technicians for on-the-spot calculations, and it fits easily in a pocket, briefcase, or tool pouch.
Built-in functions make the Measure Master Pro ideal for faster, more accurate material estimates. Work in and convert between dimensional formats including feet-inch-fractions, decimal feet-inch-fractions, yards, meters, centimeters and millimeters as well as areas and volumes. You’ll also be able to quickly find board feet for lumber estimates and solve for circumference, circle area, and arcs.
Other features include solving for cost per unit, a “paperless” tape that lets you review the previous 20 entries to double-check your totals, ability to store preferred fractional values and dimensions, and work with standard calculations.
It’s powered by two LR44 batteries, and the Measure Master Pro has an auto shut-off feature that turns the calculator off after about 8 to 12 minutes of non-use. The calculator measures 2 x 5.6 x 0.6 inches, weighs 4.5 ounces, and comes with a hard protective cover. It’s backed by a one-year limited warranty.
What’s in the Box
Calculated Industries 4020 Measure Master Pro measurement conversion calculator; protective hard slide cover; pocket reference guide (English/Spanish); batteries
4. Calculated Industries 8510 Home ProjectCalc Do-It-Yourself Project Calculator
- Great for do-it-yourselfers, woodworkers, hobbyists, decorators and gardners
- Enter feet-inch-fractions without changing to decimals
- Use it to estimate quantities and costs for paint, concrete, tile, wallpaper and carpet
- Convert between all standard math dimensions
- Includes: Easy-to-follow user’s guide and 360-degree hinged hard cover door
Designed for homeowners, do-it-yourselfers, woodworkers, hobbyists, decorators and gardeners; helps you quickly figure project material quantities, linear distances and material costs; helps you design, apply, install and finish your improvements with precision and confidence.
Tackle home improvement projects with confidence using the Home ProjectCalc calculator from Calculated Industries. Made specifically for do-it-yourselfers, woodworkers, decorators, and home-improvement hobbyists, this calculator contains dedicated functions that allow you to determine material needs and costs and quickly convert between feet, inches, fractions, decimals, yards, and meters for accurate measurements. Included is a hinged, hard, protective door that swings open fully.
Made for do-it-yourselfers, this calculator converts measurements and determines material needs and costs for home improvement projects (view larger).
Included with the calculator is a hinged, hard, protective door that swings open fully (view larger).
Make Quick Calculations for Home Improvement Projects
The Home ProjectCalc calculator is designed to help you plan and execute your home improvement projects with confidence and precision. Built-in functions allow you to calculate costs for paint, wallpaper, concrete, and tile and determine the exact amounts you need for the project. As a result, you can reduce errors and make fewer trips to the hardware store.
In addition, the Home ProjectCalc lets you type measurements in feet, inches, fractions, decimals, yards, or meters–including square and cubic formats–and make quick measurement conversions. It can also function as a standard math calculator.
This product measures 4.75 by 2.9 by 0.4 inches (H x W x D), weighs 3.2 ounces, and has an 11-digit LCD display that measures 2.25 by 6.25 inches (H x W). It is powered by a two lithium batteries (included).
About Calculated Industries
Founded in 1978, Calculated Industries (CI) is the country’s leading manufacturer and marketer of specialty construction calculators and digital measuring tools. For over 30 years, CI’s products have helped more than 8 million busy professionals work better, faster, and more efficiently with easy-to-use, portable solutions.
What’s in the Box
One Home ProjectCalc calculator, one hard cover, one user’s guide, and two lithium batteries.
|With the Home ProjectCalc, you can calculate concrete and other material needs for your project (view larger).|
5. Calculated Industries 8025 Ultra Measure Master Professional Grade U.S. Standard to Metric Conversion Calculator Tool for Engineers, Architects, Builders, Scientists and Students | 60+ Units Built-in
- INCLUDES MORE THAN 60 UNITS in both U. S. Imperial and metric units for easy and reliable data input and conversion
- enter measurements just like you say them
- you can also enter data in various formats and convert solutions to preferred read out
- you can enter feet, inch, fraction or decimal inch, other units are entered in whole or decimal numbers
- GIVES YOU OVER 400 CONVERSION combinations with no need for complex scientific calculators or memorizing conversion formulas
- for your ease the most common 43 measuring units are set as primary function keys
- the percent key also work for add-ons, discount or division percentage calculations
- Paperless Tape lets you recall your last 20 entries
- SEAMLESSLY WORKS IN AND CONVERTS BETWEEN measurement formats by pressing the conversion key and the desired unit key — it is that easy and accurate. Then you can add, subtract, multiply and divide your results to get to the solution you need.
- TIME-SAVING BUILT-IN CONVERSIONS give you all the most common physical units you need to get your job completed in an accurate fashion
- whether it’s a linear, area or volume dimensional item, weight, linear velocity, flow rate, pressure, bending moments, temperatures or another calculation you can convert it so it matches your workflow and project requirements
- INVALUABLE’ TOOL PAYS FOR ITSELF DAILY by reducing headaches, saving time, improving conversion accuracy and preventing expensive errors on your calculations from large to small units
- comes with a protective slide cover, easy-to-follow quick reference guide and handy pocket reference guide, long-life battery and a full one-year limited
The Ultra Measure Master (UMM) is the fast, easy and reliable way to handle unit conversions in the field or in the office. The UMM’s ability to convert volume, weight and weight per volume enable you to handle items from ounces to tons with the accuracy you can count on as an importer/exporter. Linear, area and volume conversions are essential for those in design and construction. Working with flow rates and pressure are critical whether you are working with a pump, a sprinkler or a dam and to succeed you need the UMM with its reliable conversions. For those who work in material production knowing the correct bending moment is critical for machine selection and costing. No matter what you are converting, using the Ultra Measure Master will enable you to get dependable answers every time. We it!
The most complete, easy-to-use conversion calculator, the Ultra Measure Master (model 8025) from Calculated Industries makes quick work of converting between imperial and metric measurements, and it’s ideal for engineers, architects, scientists, construction pros, students, and more.
Quick, Accurate Solutions in the Field
You’ll be able to convert more than 60 imperial and metric units–with over 400 conversion combinations with the touch of a few buttons–perfect for getting fast, reliable conversions in the office or out in the field. Convert between feet, inches, fractions, yards, meters, centimeters and millimeters–including square and cubic formats.
Over 400 conversion combinations (view larger).
It offers the following dedicated functions:
The Ultra Measure Master fits nicely in your hand, measuring 5.7 x 3 x 0.65 inches and weighing 4.15 ounces. In addition to using it as a standard calculator, it also offers a “paperless” tape that lets you review the previous 20 entries to double-check your totals plus a cost-per-unit function. It comes with a protective slide cover and it’s powered by a single 3-volt lithium battery (CR2016, included). The Ultra Measure Master is backed by a one-year limited warranty.
What’s in the Box
Calculated Industries 8025 Ultra Measure Master calculator; pocket reference guide; batteries
6. CALCULATED INDUSTRIES 4019 Material Estimator Calculator
- Delivers fast linear, area and volume solutions
- Efficiently displays 11 digits
- Includes a protective 360 degree hard cover door
- Works directly in yards, feet, inches, fractions and meters – including square and cubic formats. No need to convert to decimals.
- Define and store values for materials such as Grout, Fence Post Spacing, Custom Tile, Board Width, Bags of Concrete, Paint Coverage and more
- Calculate board feet and cost per unit
- Quick linear, area, and volume answers
- Dual Power – solar and battery
Material Estimator Calculator delivers fast linear, area and volume solutions directly in feet and inches, fractions, yards and metric. Designed to quickly and accurately find material requirements for studs, 4×8, 4×9, 4×10, 4×12 sheets and board feet plus the cost per unit functions estimates material costs and allowances instantly using cost and percent functions with built-in answers for material and spacing. Efficiently displays 11 digits; 7 normal and 4 fractions with full annunciators. Product includes a protective 360 degree hard cover door, 1 year limited warranty, quick reference guide and pocket reference guides in English and Spanish.
Save time and money by reducing estimating errors with the Materials Estimating Calculator (model 4019) from Calculated Industries. You’ll be able to quickly and easily calculate material costs and allowances and get exactly the materials you need. It’s designed for contractors, trades people and estimators who need to estimate materials and costs for concrete, fences, decks, bricks, tile, flooring, gravel, painting, drywall, paneling, and more.
You’ll be able to accurately find material requirements for studs, 4×8, 4×9, 4×10, 4×12 sheets, board feet, floor tiles, blocks, bricks, gravel, and paint, as well as calculate material costs and allowances using cost and percent functions. Some examples include calculating the number of standard 8-inch bricks for both face and paver applications, the number of needed concrete bags (in either 40-, 60-, or 80-pound quantities), and the number of tiles needed based on area and grout width. It works directly in yards, feet, inches, fractions, and meters, including square and cubic formats–no need to convert to decimals. Store your measurements to instantly get accurate material estimates for your jobs and projects.
The Materials Estimating Calculator can be powered by both solar and battery (CR2016 battery included). It measures 5.7 x 3 x 0.55 inches and weighs 4.15 ounces, and it’s backed by a one-year limited warranty.
What’s in the Box
Calculated Industries 4019 Materials Estimating Calculator; hard cover door; quick reference guide; pocket reference guide; battery
7. Calculated Industries 4050 Construction Master 5 Feet-Inch-Fraction, construction-math calculator
- Linear, area and volume solutions: convert dimensions, including metric
- Complete rafter, roof and framing solutions, hip/valley, jacks and rake walls
- Stair solutions are nearly automatic
- risers, treads, stringer, incline
- Built-in right-angle solutions
- automatic square-ups
- Circular and arc calculations
- areas, diameters, circumference
The Construction Master 5 is fun to use. Quickly find solutions to building and dimensional problems that seem to come-up and you haven’t used the math formulas for years. Enter the numbers, just as you would say them, and the solutions appear in an instantthey’re built-in to your Construction Master 5. Reduce the risk of expensive errors when estimating dimensions, costs and materials. Save time, money and frustration!
8. OFFDIX Large Office Calculators Office Desktop Black Calculator for 2018 Gift, Solar and Battery Dual Power Electronic Calculator Portable 12 Digit Large Office Calculator LCD Display Desk Calculator
- Energy saving: Solar Function works in daytime or even in the dim light without battery
- 12 Digital: Offidix Black Calculator (ANSIN:B06ZZ57F4Q)Allow large number calculations.
- Comfort-fit design: Ergonomic design comfortable button, wide keyboard with raised keys and increased pressure sensitivity
- Easy to carry: Handheld, perfect choice for office and home
1. Use Japan LCD, its letters are legible and striking.
2. 75¡ãANTI REFLECTIVE DESIGN
3. The tilted display makes viewing the numbersso much easier than typical flat desktop calculators.
1.American optoelectronic technology, high photoelectric conversion efficiency,long serving life, able to provide adequate electrical energy, moreenvironmentally friendly.
1.In accordance with ergonomic shapes and configurations to conform to naturalfinger movements.
2. Large Buttons, with the large buttons you will neverbe hitting the wrong numbers again. They are really easy to press and make the perfect clicking sound.
3. Imported silicone conductive rubber, resist fatigue, comfortable hand feeling, more accurate.
4. long serving life, the use of frequency up to 1 million times.
1.With antiskid silicone pads, not easy to slide on the desktop.
*Dimension (LxWxH):5.83*4.69*1.57 inch
1 x Calculator
1 x User manual
9. Basic Calculator: Catiga CD-8185 Office and Home Style Calculator – 8-Digit – Educational – Suitable for School and Destop-use (Purple)
- Easy-to-use Design – With a large screen this CATIGA calculator is made for convenient comfortable everyday use. Its tough titled display can even increases visibility from any angle.
- Large Applied Button – Comfortable and durable buttons make use easy for people of any age including children.
- Robust Build – With a hard plastic body the CATIGA Office Calculator is built with everyday use in mind. Its 6×4 size ensure comfort with use.
- Standard Functions – With 6 functions including addition, subtraction, fractions, percentages and tax conversions this calculator is able to perform efficiently for everyone.
- Dual-power source – with use of battery and solar power it supports constant use throughout your day everyday.
The CATIGA CD-8185 is built to serve simple home tasks while also accommodating business needs. It offers solar and battery power. Its large 8 digit LCD screen reduces stress on the eyes after constant use. Its sleek 6×4 design takes up little space and can be taken on the go for an style of work. The extra-large buttons make for a comfortable work experience for any level user.
10. Calculator,Vilcome 12-Digit Solar Battery Office Calculator with Large LCD Display Big Sensitive Button, Dual Power Desktop Calculators (Black)
- 【SOLAR & BATTERY DUAL POWER】Solar powered and battery back-up make the desktop calculator keep working in low light conditions(AA battery NOT included).Solar calculator has an automatic power-off function.
- 【12 DIGITS CALCULATOR】12 digits make the calculator most useful for large calculations. Suitable for any businessman, worker, teacher, student or anybody that needs make any sort of calculation from time to time.
- 【BIG BUTTON DESIGN】Electronic desktop calculators adopt scientific big button design in line with the use of human habits and comfortable for touch.
- 【NOTE】Some buyer may use office calculator in the early morning or night. The screen maybe difficult to read in low light without battery power. Please insert our AA battery for continuous and accurate usage.
- 【WHAT YOU GET】1 x Basic Calculator,1 x User Manual, 12 months warranty and plus lifetime technical support.
By our suggestions above, we hope that you can found Office Calculator Inches for you.Please don’t forget to share your experience by comment in this post. Thank you!


Intel Math Kernel Library (MKL)
Intel MKL includes a wealth of routines to accelerate application performance and reduce development time. Today's processors have increasing core counts, wider vector units and more varied architectures. The easiest way to take advantage of these features is to use a carefully optimized math library designed to harness that potential.
Core math functions in MKL include BLAS, LAPACK, ScaLAPACK, sparse solvers, fast Fourier transforms and vector math. For information about MKL, go to the Intel MKL web site.


This “modern multiplication primer” takes readers through various scenes in a school year, all set to the lilt of a rhyming multiplication table. From “Back to School” (the 2× tables) through “End of the Year” (the 9× tables) and plenty of moments in-between, Markel highlights the minutiae and milestones of the classroom with humor. In the chapter dedicated to the Winter Pageant, “6 × 4 is 24/ The babies cry. The parents snore,” and “6 × 5 is 30/ These risers don’t feel sturdy.” Liddiard’s accompanying spot illustrations, drawn with an expressive, inky line, convey entertaining moments throughout (“4 × 1 is 4/ Sam pukes. Sam pukes some more”). The rhymes are at times clunky, but the overall mnemonic effect remains engaging, and the book closes with a simplified multiplication chart, making this a valuable resource for the reluctant mathematician. A charming addition to any math teacher’s toolkit, and a diverting prompt for students learning their not-so-terrible times tables. Ages 6–9. (Aug.)
Reviewed on : 08/01/2019 Release date: 08/01/2019 Genre: Children's
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Two new members for BILTIR
Amy Ponnampalam, CEO. Athora Life Re
The Bermuda International Long-Term Insurers and Reinsurers (BILTIR) has gifted 750 books to P4 students (those in the fourth year of primary school) in all 27 schools across the island. The donations are part of BILTIR’s tenth anniversary and aim to introduce the concepts of probability, risk and actuaries.
The Magic School Bus Takes a Risk was written in collaboration with the American Academy of Actuaries. Students were also invited to join a Zoom presentation, including custom-written probability songs and videos. The event included Taiyana Allen, the recipient of a $30,000 BILTIR scholarship to study data analytics and actuarial science at Georgia State University, who now works as an actuarial analyst at Wilton Re,
Minister of Education Diallo Rabain welcomed the git: “In Bermuda, we have international business partners such as BILTIR who are genuinely committed to helping our communities to thrive and prosper. International business offers fantastic career opportunities for Bermudians. I hope that these books contributed by BILTIR enhance the joy of reading and help to persuade some of these young students to join the industry.”
Amy Ponnampalam, CEO of Athora Life Re Ltd. and chair of BILTIR’s Social Impact Committee, said: “We are delighted to be able to help our school students learn the mathematical skills which will be so important for them throughout their lives. One of BILTIR’s key objectives is to support educational causes in the community, and we hope that some of the students using the book will go on to be the next generation of Bermudian life insurance and reinsurance professionals.”
The book distribution was launched through a live virtual event hosted by Planet Math, a Bermuda-based tutoring service.
“Planet Math was set up to help our school students improve their math skills, and this wonderful donation from BILTIR is a massive contribution to that mission,” said its founder Sergio.
BILTIR, risk,, Reinsurers, science, Academy, North American, probability