reasoning and verification
Language models for mathematics and codeOur research uses mathematics as a testbed for reasoning, and integrates language models with interactive proof assistants such as Lean. Moving forward, we are interested in enabling strong reasoning capabilities, verified code synthesis and mathematics, and furthering the science of scaling in these domains.
Foundation models for mathematics
As part of a multi-lab collaboration we developed Llemma and ProofPile II, a foundation model for mathematics and 55 billion token dataset with 1.5 billion tokens of formal code.
Neural and symbolic theorem proving
We develop theorem proving methods that leverage informal and formal representations. For example, Draft Sketch Prove uses language models to sketch formal proofs based on informal proofs, then fills in the gaps.
Iterative improvementWe aim to develop machine learning systems that improve over time. In the context of language, we have viewed this problem as one of interleaving search and learning, which requires new inference-time algorithms and algorithms for learning from feedback. Moving forward, we are particularly interested in iterative improvement in the context of reasoning and code, along with core algorithmic development.
Iterative refinement algorithms
We develop algorithms for iteratively refining outputs at inference time, allowing for efficient search that takes advantage of feedback. Examples include Self-Correction and Self-Refinement.
Search and decoding algorithms
We develop inference-time algorithms that search for sequences guided by constraints. Examples include A* lookahead decoding and Maeutic inference.
science of llms
Science of neural language modelsWe analyze neural language models, including formalizing their behavior, studying their ability to generalize, and evaluating their learned distributions. Moving forward, we are broadly interested in basic research related to large language models, scalable evaluation, and efficient methods for generating sequences.
We aim to understand how language models generalize, including out-of-distribution generalization in formal reasoning and the role of memorization. Examples include Symbolic Brittleness, Limits of Transformers, and Llemma.
We aim to reduce the human effort needed to evaluate large language models. For example, Mauve enables automatic evaluation of text at a distributional level using information divergences.


CC BY-NC-SA 4.0 License.
A: It’s not easy being a circle.
B: Too true!
A: If you’re a polygon, you’re living on easy street. All you need to define yourself is to figure out the angles of your corners and the number of sides you have.
B: Which is easy.
A: But do circles get that? Do circles get a simple mathematical representation of their essence, nay, of their very souls?
B: No, we get an irrational number.
A: The ratio of our circumference to our diameter.
A: We hate Pi.
B: Take that, Internet!


Download Cool Math Games for Kids For Android
Cool Math Games for Kids Apk Review
✅ This cool maths App for kids eliminates the suffering in teaching kids because it makes them happy with solving quick math exercises in a funny way and generates endless questions with random numbers.
✅ Our cool maths software contains most lessons you expect to find in grade 2 math apps for kids. Lots of parents wrote in comments that our Arabic version of the App is one of the best math apps for kids or math game for children.
✅ Cool Math Games for Kids Apk is one of the best cool math games, it offers wonderful interesting quick math lessons of the second grade math for kids (grade 2 math).
✅ One of Flash Toons goals is to produce learning games for kids or educational games for kids to encourage e-learning.
✅ There are interesting math methods that resembles Eureka Math curriculum.
✅ In this App, there is multiplication games and fun math drills. we designed it to be cool math games for kids, in order to make kids encourage in learning.
✅ This game is one of math free games, and all games inside it are free for better kids math.
✨ Cool math app contains two types of second-grade math lessons which cover basic educational skills for kids with property of maths play:
⭐ Compare numbers and determine the correct signal (You can adjust numbers within 99 and numbers within 999 up to second grade math level)
⭐ Sum two numbers within 99 or within 999 with the choice of whether to sum with carry without carry. In addition, there is a freehand drawing tool to give the player the freedom to write on the screen. Also, there is a possibility of displaying portrait or landscape.
⭐ Subtract two numbers with the choice of whether to subtract with the borrow or without borrow. In addition, there is a freehand drawing tool to give the player the freedom to write on the screen. Also, there is a possibility of displaying portrait or landscape.
⭐ Two lessons to teach kids to calculate division and multiplication, with a simulation of these operations using the game of dragging plates on towers.
⭐ The game of place values, which make kids put a set of plates on towers and read the number.
⭐ Selecting the correct fraction (Half, one-third, one-fourth, one-fifth, one-eighth)
⭐ Writing the previous or next numbers.
⭐ Sort three ascending or descending numbers in two modes: Teaching or Practising exercises.
⭐ You can also choose to view numbers either in Arabic or Indian numeric to make fun math games suitable for all curricula.
⭐ You can change the range of randomly generated numbers for all App tests.
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👉 The good opportunity you may get is that teachers can use this App to generate fun math sheets for 2nd grade. They can use them to teach addition sums for class 2.
👉 You can use the free-hand drawing tool to extract the common core for practicing math 2nd grade for solving 2nd grade subtraction or 2nd grade addition.
👉 2nd grade multiplication can be in the landscape of a portrait view.
👉 There are lots of grade 2 math lessons that kids can learn in this math App, it can play the role of grade 2 math sheets.
✅ Teacher can generate unlimited math workout sheets for their kids using this App.
✅ We also provide a set of games about math for kindergarteners, you can open our developer page to download more. there is “Math Drills” kids math app with five free math games for kids including drills about fractions for kids. Find it here: Math Drills App
Our mathematic apps are also linked to Flash Toons’ educational and entertainment services on YouTube at: YouTube Channel


Complexity Theory (CxT)
- Tuesday from 14:15 to 17:00
In this course we will give a thorough and self-contained introduction to the area of computational complexity theory. Starting off from the abstract computational model of a Turing machine, we will discuss deterministic and non-deterministic time- and space complexity classes with regard to their structural and algorithmic properties. We will address numerous relevant examples while putting some emphasis on the complexity classes P and NP as well as to the theory of NP-completeness. Some keywords: dynamic complexity measures; deterministic and nondeterministic polynomial time; the P versus NP problem and its relativization, NP completeness; the polynomial hierarchy and PSPACE.
On successful completion of this course, you will be able to:
- Classify algorithmic problems into complexity classes
- Determine the known relationships between complexity classes
- Show that an algorithmic problem in NP-complete
- Understand the P versus NP problem
- Discuss problems whose complexity is beyond NP
- Understand problems with polynomial space complexity
To be announced.


Students will learn to see mathematics as a language, a tool, and an art form with which they can communicate ideas, solve problems, and explore the world around them. By the end of eighth grade, students will be taught to see multiple ways of expressing mathematical ideas, to make multiple connections to real life situations, and to work with others in exploring possibilities. Students will have an understanding of how numbers are used and represented. They will be able to estimate and use basic operations to solve everyday problems and confront more involved calculations in algebraic, geometric, and statistical settings.
As a result of the Math Common Core implementation, our curriculum has shifted to become more rigorous and focused K-8. Rigor includes fluency, application and deep understanding of the mathematics. Focus allows teachers the opportunity to help students develop a deep understanding of the concepts. With the shifts it is most important that children master the grade level curriculum. It is equally important that children are exposed to another major shift: a shift in student mathematical practices. Kindergarten through eighth grade classrooms across District #37 are implementing mathematical practice standards through tasks and projects, which include the following:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
Mathematicians in kindergarten through fifth grade focus on operations and algebraic thinking, numbers and operations in base ten, geometry, and measurement and data, in addition to the mathematical practices. Materials used for math instruction for kindergarten through fifth grade are based upon the unit math targets. The following domains are the focus of the content.
Operations and Algebraic Thinking
The progression in Operations and Algebraic Thinking deals with the basic operations—the kinds of quantitative relationships they model and consequently the kinds of problems they can be used to solve as well as their mathematical properties and relationships. Primary students develop meanings for addition and subtraction as they encounter problem situations in kindergarten, and they extend these meanings as they encounter increasingly difficult problem situations in grade 1. They represent these problems in increasingly sophisticated ways. And they learn and use increasingly sophisticated computation methods to find answers. By grade 3 students focus on understanding the meaning and properties of multiplication and division and on finding products of single-digit multiplying and related quotients. Fourth graders extend problem solving to multi-step word problems using the four operations posed with whole numbers. As preparation for the Expressions and Equations Progression in the middle grades, students in grade 5 begin working more formally with expressions.
Number and Operations in Base Ten
Students’ work in the base-ten system is intertwined with their work on counting and cardinality, and with the meanings and properties of addition, subtraction, multiplication, and division. Work in the base-ten system relies on these meanings and properties, but also contributes to deepening students’ understanding of them. Work with computation begins with use of strategies and “efficient, accurate, and generalizable methods.” In Kindergarten, teachers help children lay the foundation for understanding the base-ten system by drawing special attention to 10. In first grade, students learn to view ten ones as a unit called a ten. At grade 2, students extend their base-ten understanding to hundreds. At grade 3, the major focus is multiplication, so students’ work with addition and subtraction is limited to maintenance of fluency within 1000 for some students and building fluency to within 1000 for others. At grade 4, students extend their work in the base-ten system; they use standard algorithms to fluently add and subtract. In grade 5, students extend their understanding of the base-ten system to decimals to the thousandths place, building on their grade 4 work with tenths and hundredths. They become fluent with the standard multiplication algorithm with multi-digit whole numbers. They reason about dividing whole numbers with two-digit divisors, and reason about adding, subtracting, multiplying, and dividing decimals to hundredths.
Fractions (grades 3-5)
In grades 1 and 2, students use fraction language to describe partitions of shapes into equal shares. In grade 3 they start to develop the idea of a fraction more formally, building on the idea of partitioning a whole into equal parts. The whole can be a shape such as a circle or rectangle, a line segment, or any one finite entity susceptible to subdivision and measurement. In grade 4, this is extended to include wholes that are collections of objects. grade 4 students learn a fundamental property of equivalent fractions: multiplying the numerator and denominator of a fraction by the same non-zero whole number results in a fraction that represents the same number as the original fraction. This forms the basis for much of their other work in grade 4, including the comparison, addition, and subtraction of fractions and the introduction of finite decimals. In grade 4, students have some experience calculating sums of fractions with different denominators in their work with decimals, and grade 5 students extend this reasoning to situations where it is necessary to re-express both fractions in terms of a new denominator.
Students in kindergarten, grade 1, and grade 2 focus on three major aspects of geometry. Students build understandings of shapes and their properties, becoming able to do and discuss increasingly elaborate compositions, decompositions, and iterations of the two, as well as spatial structures and relations. In
grade 2, students begin the formal study of measure, learning to use units of length and use and understand rulers. Measurement of angles and parallelism are a focus in grades 3, 4, and 5. At grade 3, students begin to consider relationships of shape categories, considering two levels of subcategories (e.g., rectangles are parallelograms and squares are rectangles). They complete this categorization in grade 5 with all necessary levels of categories and with the understanding that any property of a category also applies to all shapes
in any of its subcategories. They understand that some categories overlap (e.g., not all parallelograms are rectangles) and some are disjoint (e.g., no square is a triangle), and they connect these with their understanding of categories and subcategories. Spatial structuring for two- and three-dimensional regions is used to understand what it means to measure area and volume of the simplest shapes in those dimensions: rectangles at grade 3 and right rectangular prisms at grade 5.
Measurement and Data
As students work with data in grades K-5, they strengthen and apply what they are learning in arithmetic. Kindergarten work with data involves counting and order relations. First- and second-graders solve addition and subtraction problems in a data context. In grades 3–5, work with data is closely related to the number line, fraction concepts, fraction arithmetic, and solving problems that involve the four operations. In geometric measurement, second graders learn to measure length with a variety of tools, such as rulers, meter sticks, and measuring tapes. Second graders also learn the concept of the inverse relationship between the size of the unit of length and the number of units required to cover a specific length or distance. Third graders focus on solving real-world and mathematical problems involving perimeters of polygons. Students in grade 3 learn to solve a variety of problems involving measurement and such attributes as length and area, liquid volume, mass, and time. In grade 4, students build on competencies in measurement and in understanding units that they have developed in number, geometry, and geometric measurement. Students also combine competencies from different domains as they solve measurement problems using all four arithmetic operations, addition, subtraction, multiplication, and division. In grade 5, students extend their abilities from grade 4 to express measurements in larger or smaller units within a measurement system. Grade 5 students also learn and use such conversions in solving multi-step, real world problems.
Mathematicians in fifth through eighth grade focus on units specific to course placement in addition to the mathematical practices. Materials used for math instruction for fifth through eighth grade are based upon the unit math targets.
Students working with the grades 6-8 learning targets in Grades 6-8 Math focus on the following general domains: Ratio and Proportional Relationships; the Number System; Expressions and Equations; Geometry; and, Statistics and Probability. Grades 7 and 8 Algebra content and units include the Number System; Expressions and Equations; Geometry; Statistics and Probability as well as an introduction to Functions. The general descriptions about these domains are described below. Grade 8 Geometry content and units include Circles; Congruence; Geometric Measurement and Dimension; Expressing Geometric Properties with Equations; Modeling with Geometry; and Similarity, Right Triangles, and Trigonometry.
Ratio and Proportional Relationships
The study of ratios and proportional relationships extends students’ work in measurement and in multiplication and division in the elementary grades. Students in grade 6 focus on understanding the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. They also build an understanding of the concept of a unit rate associated with a ratio and use rate language in the context of a ratio relationship.
In grade 7, students extend their reasoning about ratios and proportional relationships in several ways. Students use ratios in cases that involve pairs of rational number entries, and they compute associated unit rates. They identify these unit rates in representations of proportional relationships. They work with equations in two variables to represent and analyze proportional relationships. They also solve multi-step ratio and percent problems, such as problems involving percent increase and decrease.
The Number System
Within the grades 6-8 learning targets, students build on two important conceptions which have developed throughout K–5, in order to understand the rational numbers as a number system. The first is the representation of whole numbers and fractions as points on the number line, and the second is a firm understanding of the properties of operations on whole numbers and fractions. As grade 6 begins, students have a firm understanding of place value and the properties of operations. On this foundation they are ready to start using the properties of operations as tools of exploration, deploying them confidently to build new understandings of operations with fractions and negative numbers. They are also ready to complete their growing fluency with algorithms for the four operations. In grade 6 students learned to locate rational numbers on the number line; in grade 7 they extend their understanding of operations with fractions to operations with rational numbers. Students must rely increasingly on the properties of operations to build the necessary bridges from their previous understandings to situations where one or more of the numbers might be negative. In grade 7 students encountered infinitely repeating decimals, and in grade 8 they understand why this phenomenon occurs, a good exercise in expressing regularity in repeated reasoning. In addition, they glimpse the existence of irrational numbers.
Expressions and Equations
In grades 6-8, students start to use properties of operations to manipulate algebraic expressions and produce different but equivalent expressions for different purposes. This work builds on their extensive experience in K–5 working with the properties of operations in the context of operations with whole numbers, decimals and fractions. In grade 6 they begin to work systematically with algebraic expressions, and they start to incorporate whole number exponents into numerical expressions. In grade 7 students start to simplify general linear expressions with rational coefficients. Building on work in grade 6, where students used conventions about the order of operations to parse, and properties of operations to transform, simple expressions, students now encounter linear expressions with more operations and whose transformation may require an understanding of the rules for multiplying negative numbers. In grade 8 students add the properties of integer exponents to their repertoire of rules for transforming expressions. They prepare in grade 8 by starting to work systematically with the square root and cube root symbols. They begin to understand the idea of a function. Students in grade 8 also start to solve problems that lead to simultaneous equations.
Students working through the grade 6 learning targets work with problems involving areas and volumes to extend previous work and to provide a context for developing and using equations. Students’ competencies in shape composition and decomposition, especially with spatial structuring of rectangular arrays should be highly developed. These competencies form a foundation for understanding multiplication, formulas for area and volume, and the coordinate plane. Using the shape composition and decomposition skills acquired in earlier grades, students learn to develop area formulas for parallelograms, then triangles. They learn how to address three different cases for triangles: a height that is a side of a right angle, a height that “lies over the base” and a height that is outside the triangle.
Composition and decomposition of shapes are used throughout geometry from grade 6 to high school and beyond. Compositions and decompositions of regions continues to be important for solving a wide variety of area problems, including justifications of formulas and solving real world problems that involve complex shapes. Decompositions are often indicated in geometric diagrams by an auxiliary line, and using the strategy of drawing an auxiliary line to solve a problem are part of looking for and making use of structure. Recognizing the significance of an existing line in a figure is also part of looking for and making use of structure. This may involve identifying the length of an associated line segment, which in turn may rely on students’ abilities to identify relationships of line segments and angles in the figure. These abilities become more sophisticated as students gain more experience in geometry. In grade 7, this experience includes making scale drawings of geometric figures and solving problems involving angle measure, surface area, and volume.
Statistics and Probability
Through the grade 6 learning targets, students build on the knowledge and experiences in data analysis developed in earlier grades. Students working through the grade 7 standards move from concentrating on analysis of data to production of data, understanding that good answers to statistical questions depend upon a good plan for collecting data relevant to the questions of interest. The grade 8 mathematics standards have students apply their experience with the coordinate plane and linear functions in the study of association between two variables related to a question of interest.
Before they learn the term “function,” students begin to gain experience with functions in elementary grades. In kindergarten, they use patterns with numbers to learn particular additions and subtractions. A trickle of pattern standards in grades 4 and 5 continues the preparation for functions where a rule is explicitly given. The grades 4–5 pattern standards expand to the domain of Ratios and Proportional Relationships in grades 6–7. In grade 6, as they work with collections of equivalent ratios, students gain experience with tables and graphs, and correspondences between them. In grade 7, students recognize and represent an important type of regularity in these numerical tables—the multiplicative relationship between each pair of values—by equations of the form y = cx , identifying c as the constant of proportionality in equations and other representations. The notion of a function is formally introduced in Grade 8 Math. Linear functions are a major focus, but students are also expected to give examples of functions that are not linear.
Grades 7 and 8 Algebra is a combination of domains of the Grade 8 Algebra content and High School domains, and these include the following: Geometry; Statistics & Probability; Seeing Structure in Expressions; Creating Equations; Reasoning with Equations & Inequalities; Building Functions; Interpreting Functions; Quantities; Interpreting Categorical & Quantitative Data; Linear, Quadratic, & Exponential Models; Arithmetic with Polynomials & Rational Expressions; and, the Real Number System.
Grade 8 Geometry is a combination of the following High School domains: Circles; Congruence; Geometric Measurement and Dimension; Expressing Geometric Properties with Equations; Modeling with Geometry; and Similarity, Right Triangles, and Trigonometry. The Geometry sequence is currently being developed, and the resources used for the program are aligned with the Grant High School Geometry course.
The Illinois Learning Standards are correlated with the Common Core State Standards: Common Core State Standards. District 37's learning targets are aligned with the Illinois Learning Standards.
The Math Proficiency maps below show the math standards and learning target sequences for each course. Assessments are aligned to these proficiency maps.


Weight Watcher Point Calculator
To get assistance in determining food-related smart points per the diet, you take for a whole day, you can use the Weight watcher points calculator.
What is WW (Weight Watchers)?
In the world, It is one of the best weight-loss programs. Jean Nidetch organized it in the early 1960s.To get assistance from each other to initiate and follow good lifestyle choices, like having healthy food to earn interests such as losing weight and glowing skin, and growing hair quality.
To simplify this program, it's divided into unique smart points. Every participant in this program can monitor its progress by noting each meal they eat in an app.
Interestingly, more than 290,000 products are listed already in this program. Which monitors their progression, so a participant can see how close they are to reaching their goals. There are already more than 290,000 products listed. But still, we designed this WWP calculator to find the points in any meal by only getting the content of protein, sugar, saturated fats, and calories.
Table of Contents
Formula of Weight Watcher Point Calculator
To find Weight Watchers Points, the Weight Watchers freestyle formula is used in our calculator. You can use it to determine the number of points in each meal contains:
Weight Watchers Points = (calories * 0.0305) + (saturated fat * 0.275) + (sugar * 0.12) - (protein * 0.098)
You only need to put the values of calories, saturated fat, sugar, and protein to get your meal points.
To know about power-to-weight ratio, you can use our Power To Weight Ratio Calculator.
For better understanding, let us have an example here;
Imagine a girl who wants to lose weight, decides to obey the Weight Watchers diet, and begins scoring her points. On Wednesday, she intakes 800 kcal, sugar of 8g, saturated fat of 2g, the protein of 5g. find the weight watcher point scored by her.
Calories = 800 kcal
Sugar = 8g
Saturated fat = 2g
Protein = 5g
Weight Watcher Point = ?
We will find the WWP by using the formula given below:
WWP = (calories * 0.0305) + (saturated fat * 0.275) + (sugar * 0.12) - (protein * 0.098)
Putting values in the formula:
WWP = (800 * 0.0305) + (2 * 0.275) + (8 * 0.12) - (5 * 0.098)
The weight Watcher Point scored by that girl is 25.
How to use Weight Watcher Point Calculator?
The steps to use the weight watcher point calculator are as follows:
Step 1: Enter the values of calories in the first required input.
Step 2: Enter the values of sugar in the second required input.
Step 3: Enter the values of protein in the third required input.
Step 4: Enter the values of saturated fat in the fourth required input.
Step 5: The calculator will automatically display an answer on the screen.
To get your meal points from our free online Weight Watchers Points Calculator, enter the value. After this, our calculator will appear as the precise solution on the screen.


Opened 7 Apr 2014
WHAT IS IT ABOUT?
Catherine has cared for her father Robert, a renowned mathematician, through his mental illness for the past five years. His ex-student, Hal, discovers a ground-breaking proof in Robert's office but the question is posed: who is the real author of this brilliant work? Catherine struggles to solve this as well the most perplexing problem of all: how much of her father's madness - or genius - has she inherited?


Completely factor and solve the expression 3x - 9y + 12
when factor 2 out of 3x-9z+12 you get 3(x-3y+4)
Which of these types of income is taxed?a)federal tax refunds
c)interest from municipal bonds
B. Stock dividends. Stock dividends are taxable under certain conditions. If the shares are from a retirement account, stock dividends are not taxed. Concerning any other accounts, any income that has been acquired is taxable in the year that it was received.
Answer: interest on saving account
Please help! I'll mark your answer as brainliest if right <3
dowload the snap slove aap and then crop ans it give u a correct ans
The correct answer should be y = (-8/3)x + 9
Evaluate b^2 + 5a – 20
Answer: it cant even be factored
If total employee benefits are calculated as a percentage of their gross pay, which of the following employees receives the largest percentage of their gross pay in employee benefits?
For this type of question, all you need to do is the following
- Find out the amount of Gross pay - Find out the amount of total employee's benefit. - Find out the difference between the two of them - Find the percentage of that difference and compare it with the others


HOME OF THE DRAGONSLAYERS
Charter High School in St. George & Washington, UT
Individualized University Program (Grades 8-12)
Accelerated programs in Math, Science, Technology, Language Arts, and Social Science
Philosophy & Vision
St George Academy comprehensively prepares students for a demanding college experience through an academically rigorous high school education. We provide our students more advanced, educational challenges in pursuit of their academic and life goals.
Leader In Me
Enroll your student for the 2023-2024 school year.
Digital submissions should be emailed to email@example.com. Printed enrollment forms can be dropped off at the office on Weekdays 9:00 am – 3:30 pm.
The St. George Academy Difference
We offer accelerated programs in Math, Science, Technology, and Language Arts for all of our students.
We emphasize Honors, Advanced Placement, and Concurrent Enrollment for all of our students.
STEM opportunities include VEX robotics and advanced computer programming Career Pathways.
Who We Are
St. George Academy is a tuition-free, charter high school in Washington Fields, serving grades 8-12. SGA offers a college preparatory education to our students in a unique learning environment. Students can earn college credit while attending SGA Classes.
Individualized College Preparation Plan
College Attendance Rate
Challenging Our Students
St. George Academy courses are designed to challenge students with college-level and AP content.


[iframe_loader type=’open_link_in_new_window’ href=’http://ignitelearning.net/wp-content/uploads/articulate_uploads/ELC71_Teaching_Math/story.html’]
The challenge for this week was to design a short lesson to teach one or more math concepts. I immediately knew I wanted to create something that aligned with the Common Core State Standards for K-12 education. I choose to focus on working with time and money, which aligned with Grade 2 Common Core standard CCSS.MATH.CONTENT.2.MD.C.8.
I browsed various worksheets and exercises to get some inspiration. There is a wealth of teacher resources on the internet for applying Common Core in the classroom. I came across this free download on Jason’s Online Classroom. The Money I Have, Who Has? game is intended to be printed and played with one or more students. I adapted the game into a short lesson using Articulate Storyline 2. Learners are tasked with helping the main character, Bob, find the thieves who stole money from his piggy bank. They’re given a line-up of three suspects and must identify who has the correct amount of money by identifying the coins presented. They must also identify $ and ¢ signs appropriately.


Learn Excel division with 7 formulas! Explore practical examples for efficient calculations at excel-learn.com.
The SUBTOTAL function in Excel is used to return the subtotal in terms of sum, average, count, max, min etc. for the specified list, named range or database.
if you require the count of cells that contain numbers only, use the Excel COUNT function.
To get the count of all cells with numbers, text, dates etc except the blank cells, use the COUNTA function. Similarly, for returning the count of cells based on certain criteriause the COUNTIFS function. To get the count of blank or empty cells, use the COUNTBLANK function.
There is no Excel SUBTRACTION function. Instead, you may accomplish the task of subtracting numbers or a cell’s value from the other by using the minus arithmetic operator (-).
You may simply use the ‘*’ operator e.g. 10*5, A2 * B2 or use the multiple operators in various functions. The PRODUCT function can also be used for multiplication of numbers and ranges.
Formulas to Calculate Age in Excel In Excel, you may calculate the age in a…


Amazon.com: Student Solutions Manual, Chapters 1-6 for Epp's ... Amazon.com: Student Solutions Manual, Chapters 1-6 for Epp's Discrete Mathematics with Applications, 4th Edition: SoftwareEssentials Of Discrete Mathematics Solutions Manual - Buy Discrete Mathematics, Student Solutions Manual: Mathematical Reasoning and Proof with Puzzles, Patterns, and Games on Amazon.com FREE SHIPPING on qualified orders. Written for the one-term course, Essentials of Discrete Mathematics, Third Edition is designed to serve computer science and mathematics majors, as well as students from a wide range of other disciplines.. Delegation strategies for the NCLEX, Prioritization for the NCLEX, Infection Control for the NCLEX, FREE resources for the NCLEX, FREE NCLEX Quizzes for the NCLEX, FREE NCLEX exams for the NCLEX, Failed the NCLEX - Help is here.
64 Journals in JSTOR Date Range American Journal of Mathematics. Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag.The books in this series, like the other Springer-Verlag mathematics series, are yellow books of a standard size (with variable numbers of pages).. Five Plays: Kamala, Silence! The Court is in Session, Sakharam Binder, The Vultures, Encounter In Umbugland.
There are 2 types of software engineer: those who understand computer science well enough to do challenging, innovative work, and those who just get by because. Study.com has been an NCCRS member since October 2016. The mission of Study.com is to make education accessible to everyone, everywhere. Students can save on their education by taking the Study.com online, self-paced courses and earn widely transferable college credit recommendations for a fraction of the cost of a traditional course.. Mar 12, 2008 · 171 Comments: Ben said. Thanks, Steve; that was very helpful, although it would've been more helpful before I had a phonescreen with you guys last fall and totally brainlocked on a.
Free textbooks (aka open textbooks) written by knowledgable scholars are a relatively new phenomenon. Below, find a meta list of Free Math Textbooks, part of our larger collection 200 Free Textbooks: A Meta Collection.Also see our online collection, 1,300 Free Online Courses from Top Universities. Abstract Algebra: The Basic Graduate Year by Robert B. Ash, University of Illinois. Search the world's information, including webpages, images, videos and more. Google has many special features to help you find exactly what you're looking for.. NMCC is accredited by the Commission on Institutions of Higher Education, the same agency that accredits Harvard..
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Exciting News From DDCES
For over 30 years, the Dade County Council of Teachers of Mathematics organization has promoted the love for learning mathematics through various events, but none more so than the Math Bowl. The annual event brings hundreds of local students from both the public and private sectors to compete in various activities involving mathematics. Downtown Doral Charter Elementary School was proud to be a participant in this year’s 2021-2022 DCCTM competition. As a result of hard work and dedication, the students were able to excel and won 1st place for the category of Team Problem Solving. This particular category was special because, in addition to utilizing their academic knowledge, the students also had to use key social skills to ensure proper communication with one another in order to complete their tasks.


David Hilbert Biography, Life, Interesting Facts
Died On :
Birth Place :
David Hilbert was a mathematician who created a new field: metamathematics. He had formulated the theory of Hilbert Spaces, which later became a foundation for functional analysis.
Childhood And Early Life
David Hilbert was born on 23rd of January 1862, in Province of Prussia then. He said that he was born in Königsberg, but his parents were living in its neighbor Wehlau, where his father Otto worked as a city judge. David Hilbert had a younger sister Elsie, six years younger. His mother Maria Therese Erdtmann homeschooled him until he attended school at eight. Eight- year- old David Hilbert was enrolled junior section of Collegium Fridericianumin, before entering the gymnasium of the Royal Friedrichskolleg in 1872. He transferred to Wilhelm Gymnasium for his final year in 1879, where he was encouraged to think and do mathematics and science. After graduating from school, David went to The Albertina of the University of Königsberg in 1880.
In Albertina, David Hilbert worked under mentor Ferdinand von Lindemann and met Adolf Hurwitz and Hermann Minkowski in 1884, and it was the start of development in mathematics. David presented his thesis: Über invariant Eigenschaften specially binärer Formen, insbesondere der Kugelfunctionen (translation: ‘On the invariant properties of particular binary forms, in particular, the spherical harmonic functions). David obtained his doctoral degree and passed the Staatsexamen in quality as a teacher.
David Hilbert became a lecturer at the University of Königsberg after he passed his Ph. D, he also traveled to Paris on invitation from Felix Klein. In Paris, he met with French mathematicians such as Henri Poincaré, Charles Hermite, and others. David Hilbert returned to Germany, visiting Göttingen and Berlin before returning home to Königsberg to teach. He was promoted to Extraordinary Professor in 1892 and became a full professor in the following year. He proved the Basis Theorem in 1888 by showing the theorem in a different but abstract way.
Two years later he listed twenty- three problems that remained unsolved at the International Congress of Mathematicians in Paris. In 1897, David Hilbert wrote treatise Zahlberich, unifying algebraic number theory. In 1902 he was co-editor of Mathematische Annalen, with Felix Klein and Otto Blumenthal. After being a pure mathematician for years, David Hilbert delved into physics around 1912. He had a physics tutor and corresponded with Albert Einstein about fundamentals of the theory of gravity and field equations. David Hilbert developed integral equations, trying to make physics more natural and more elegant for mathematicians.
When Richard Courant wrote Methoden der mathematischen Physik (Methods of Mathematical Physics), he credited David as he used some of the ideas, despite David did not contribute to the writing. David Hilbert developed pernicious anemia in 1925; he was sixty- three years old then. Five years later he retired from the University of Göttingen. In 1933, the Nazis forced out Jewish or those who were married to Jewish people, resulting in ending of the Institute.
In 1910, David Hilbert won the Bolyai Prize and was made a fellow of the Royal Society of London in 1928. He won the first Mittag-Leffler prize of the Swedish Academy in 1939, sharing it with French mathematician Émile Picard.
David Hilbert married Käthe Jerosch in 1892; they had one son together. Unfortunately, Franz Hilbert was born in 1893 was born with an undiagnosed mental illness, and was a disappointment to the father. David Hilbert broke his arm while walking in 1942; it was the precursor of his spiral downwards. He passed away 14 February 1943, but the news only made public six months after he had died.
David Hilbert famous quote: Wir müssen wissen. Wir Werden wissen. (We Must Know, We Will Know) Was written on his epitaph in Göttingen. It was spoken during his retirement speech to the Society of German Scientist and Physicians in 1930


MASU hosts a mathematics festival for students from local schools
MASU Mathematics and Natural Sciences Faculty held Polar Coordinates, a popular science festival of maths for students of Murmansk region's schools. More than 130 students attended the Festival and took part in various educational events.
Vera Levites, Dean of Faculty, and 2nd year students organized a mathematical game for eighth and ninth-graders. Children were solving mathematical speed puzzles and challenging tasks.
At the workshop led by Victoria Lazutina, a 3rd-year student, high school students learned how to count faster and do unusual maths calculations. At the same time, the youngest participants of the Festival, third and sixth-graders, wrote mini-essays discussing the role of mathematics in their lives.
The Festival also included two open lectures: Georgy Wolfson, a mathematics teacher at St. Petersburg Physics and Mathematics Lyceum no. 366, told the audience about the paradoxes of probability theory. Later, Natalia Nedelko, an associate professor of MASU Mathematics, Physics and IT Department, demonstrated the tricks of the Excel spreadsheet software for calculating profits and making forecasts about the projects' development.
The organizers of the Festival thank all the participants, MASU students and volunteers, as well as maths and elementary school teachers for their help in organizing the Festival.


Recently there have been several posts on the interwebs supposedly demonstrating spurious correlations between different things. A typical image looks like this:
taken from here.
The problem I have with images like this is not the message that one needs to be careful when using statistics (which is true), or that lots of seemingly unrelated things are somewhat correlated with each other (also true). It’s that including the correlation coefficient on the plot is misleading and disingenuous, intentionally or not.
When we calculate statistics that summarize values of a variable (like the mean or standard deviation) or the relationship between two variables (correlation), we’re using a sample of the data to draw conclusions about the population. In the case of time series, we’re using data from a short interval of time to infer what would happen if the time series went on forever. To be able to do this, your sample must be a good representative of the population, otherwise your sample statistic will not be a good approximation of the population statistic. For example, if you wanted to know the average height of people in Michigan, but you only collected data from people 10 and younger, the average height of your sample would not be a good estimate of the height of the overall population. This seems painfully obvious. But this is exactly analogous to what the author of the image above is doing by including the correlation coefficient . The absurdity of doing this is a little less transparent when we’re dealing with time series (values collected over time). This post is an attempt to explain the reasoning using plots rather than math, in the hopes of reaching the widest audience.
Correlation between two variables
Say we have two variables, and , and we want to know if they’re related. The first thing we might try is plotting one against the other:
They look correlated! Computing the correlation coefficient value gives a moderately high value of 0.78. So far so good. Now imagine we collected the values of each of and over time, or wrote the values in a table and numbered each row. If we wanted to, we could tag each value with the order in which it was collected. I’ll call this label “time”, not because the data is really a time series, but just so it will be clear how different the situation is when the data does represent time series. Let’s look at the same scatter plot with the data color-coded by whether it was collected in the first 20%, second 20%, etc. This breaks the data into 5 categories:
The time a datapoint was collected, or the order in which it was collected, doesn’t really seem to tell us much about its value. We can also look at a histogram of each of the variables:
The height of each bar indicates the number of points in a particular bin of the histogram. If we separate out each bin column by the proportion of data in it from each time category, we get roughly the same number from each:
If plot the histograms of each 20% separately on the same axes, we get histograms that look pretty similar. Here are the histograms overlapped:
Alright, now let’s see what happens is we finally plot the data as time series.
There might be some structure there, but it looks pretty messy. It should look messy, because the original data really had nothing to do with time. Notice that the data is centered around a given value and has a similar variance at any time point. If you take any 100-point chunk, you probably couldn’t tell me what time it came from. This, illustrated by the histograms above, means that the data is independent and identically distributed (i.i.d. or IID). That is, at any time point, the data looks like it’s coming from the same distribution. That’s why the histograms in the plot above almost exactly overlap. Here’s the takeaway: correlation is only meaningful when data is i.i.d.. [edit: it’s not inflated if the data is i.i.d. It means something, but doesn’t accurately reflect the relationship between the two variables.] I’ll explain why below, but keep that in mind for this next section.
Correlation between two time series
Now let’s look at an example of two time series that seem correlated. This is meant to be a direct parallel to the ‘suspicious correlation’ plots floating around the internet.
I generated some data randomly. and are both a ‘normal random walk’. That is, at each time point, a value is drawn from a normal distribution. For example, say we draw the value of 1.2. Then we use that as a starting point, and draw another value from a normal distribution, say 0.3. Then the starting point for the third value is now 1.5. If we do this several times, we end up with a time series in which each value is close-ish to the value that came before it. The important point here is that and were generated by random processes, completely independently from each other. I just generated a bunch of series until I found some that seemed correlated.
Here’s a plot showing the time series of and :
Hmm! Looks pretty correlated! Before we get carried away, we should really make sure that the correlation measure is even relevant for this data. To do that, make some of the plots we made above with our new data. With a scatter plot, the data still seems pretty strongly correlated:
Notice something very different in this plot. Unlike the scatter plot of the data that was actually correlated, this data’s values are dependent on time. In other words, if you tell me the time a particular data point was collected, I can tell you approximately what its value is. That means that the data is not identically distributed (the time series lingo is that these time series are not “stationary”).
To make the point a little clearer, let’s make a histogram of the data.
Looks pretty good. But now let’s again color each bin according to the proportion of data from a particular time interval.
Each bin in this histogram does not have an equal proportion of data from each time interval. Plotting the histograms separately reinforces this observation:
If you take data at different time points, the data is not identically distributed. This means the correlation coefficient is misleading, as it’s value is interpreted under the assumption that data is i.i.d.
We’ve talked about being identically distributed, but what about independent? Independence of data means that the value of a particular point does not depend on the values recorded before it. Looking at the histograms above, it’s clear that this is not the case for the randomly generated time series. If I tell you the value of at a given time is 30, for example, you can be pretty sure that the next value is going to be closer to 30 than 0.
One way to formalize this relationship is by looking at a time series’ autocorrelation. As the name suggests, it’s a way to measure how much a series is correlated with itself. This is done at different lags. For example, each point in a series can be plotted against each point two points behind it. For the first (actually correlated) dataset, this gives a plot like the following:
This means the data is not correlated with itself (that’s the “independent” part of i.i.d.). If we do the same thing with the time series data, we get:
Wow! That’s pretty correlated! That means that the time associated with each datapoint tells us a lot about the value of that datapoint. In other words, the data points are not independent of each other.
If we plot the autocorrelation function at all lags from the first dataset, we get the following:
The value is 1 at lag=0, because each data is obviously correlated with itself. All the other values are pretty close to 0. If we look at the autocorrelation of the time series data, we get something very different:
Again, the height of each bar tells how correlated each time point is, on average, with other points lag away.
But why does this matter? Because the value we use to measure correlation is interpretable only when the autocorrelation of each variable is 0 at all lags.
If we want to find the correlation between two time series, we can use some tricks to make the autocorrelation 0. If we do this, the will be interpretable as the correlation between the time series (explained in the next section). The easiest method is to just “difference” the data - that is, convert the time series into a new series, where each value is the difference between adjacent values in the nearby series. If we do this to our time series, the autocorrelation function becomes:
What happens if we plot the differenced data against time? We get:
They don’t look correlated anymore! How disappointing. But the data was not correlated in the first place: each variable was generated independently of the other. They just looked correlated. That’s the problem. The apparent correlation was entirely a mirage. The two variables only looked correlated because they were actually autocorrelated in a similar way. That’s exactly what’s going on with the spurious correlation plots on the website I mentioned at the beginning. If we plot the non-autocorrelated versions of these data against each other, we get:
The time no longer tells us about the value of the data. As a consequence, the data no longer appear correlated. This reveals that the data is actually unrelated. It’s not as fun, but it’s the truth.
A criticism of this approach that seems legitimate (but isn’t) is that since we’re screwing with the data first to make it look random, of course the result won’t be correlated. However, if you take successive differences between the original non-time-series data, you get a correlation coefficient of , same as we had above! Differencing destroyed the apparent correlation in the time series data, but not in the data that was actually correlated.
Samples and populations
The remaining question is why the correlation coefficient requires the data to be i.i.d. The answer lies in how is calculated. The mathy answer is a little complicated (see here for a good explanation). In the interests of keeping this post simple and graphical, I’ll show some more plots instead of delving into the math.
The context in which is used is that of fitting a linear model to “explain” or predict as a function of . This is just the from middle school math class. The more highly correlated is with (the vs scatter looks more like a line and less like a cloud), the more information the value of gives us about the value of . To get this measure of “cloudiness”, we can first fit a line:
The line represents the value we would predict for given a certain value of . We can then measure how far each value is from the predicted value. If we plot those differences, called , we get:
The wider the cloud the more uncertainty we still have about . In more technical words, it’s the amount of variance that’s still ‘unexplained’, despite knowing a given value. The compliment of this, the proportion of variance ‘explained’ in by , is the value. If knowing tells us nothing about , then = 0. If knowing tells us exactly, then there is nothing left ‘unexplained’ about the values of , and = 1.
is calculated using your sample data. The assumption and hope is that as you get more data, will get closer and closer to the “true” value, called Pearson’s product-moment correlation coefficient . If you take chunks of data from different time points like we did above, your should be similar in each case, since you’re just taking smaller samples. In fact, if the data is i.i.d., itself can be treated as a variable that’s randomly distributed around a “true” value. If you take chunks of our correlated non-time-series data and calculate their sample correlation coefficients, you get the following:
where the line represents the sample correlation coefficient for the entire sample. The important thing is that gives you a reasonable idea of what the population is, and becomes a better estimator the more data you get. If you do the same thing for our time series data, you get something very different:
As you can see, the sample correlation coefficient varies a LOT depending on what data subset you’re using. Why, then, should we assume that the particular sample value we’ve estimated for our time series is a good estimation of the “true” population correlation coefficient ? That’s right, we shouldn’t.
The main takeaway here is that the correlation coefficient is NOT an estimator of the population correlation coefficient when the time series are autocorrelated. You can find correlations between time series, but first you have to use some method to “de-trend” the data and take out any autocorrelation. If you do that, the sample value can then be interpreted as an estimator of the true population value.
Since the true value for unrelated variables like the ones in our time series is 0, looking at subpopulations of the differenced, de-trended data should give us correlations of 0. Critically, each sub-group of the data should have a correlation coefficient that’s near the value of the correlation coefficient of the entire sample.
I hope this helps clear up the confusion a little.


All Volume Calculator is a basic Calculator that calculates the volume of 7 shapes (Cube, Cylinder, Prism, Rectangular Prism, Sphere, Pyramid, Cone). It runs on all Windows Machines via the Command Prompt. It aids children by calculating the volumes without them needing to know the calculations required.
All Volume Calculator is a basic calculator that runs on all Windows Machines and does not take any knowledge to install and use. It offers advance features on an basic interface.
All Volume Calculator is used for children studying volumes as well as people who require to know the volume of an object.


Many of our customers frequently ask “how do I calculate how much wood I need for a project?” They want to install paneling or hardwood flooring in a room and they have the price per square foot for the material they want to purchase. Without calculating the total square footage of the project though, they are still left wondering the total cost of the project. So, how do you measure the square footage so you can calculate the amount of material or square footage you need?
Let’s start with walls, as they have the challenge of windows and doors to measure around. The easiest method is usually to measure the walls, ignoring the windows and doors for now, as you can subtract them out later. Measure the length and the height of each wall, and multiply the height times the width. This gives you the square footage. For example, a 8 feet high wall that is 10 feet long is 80 square feet. Do that for each wall, and determine the total.
Now measure each door and window for height and width. Multiply height times width to get the square footage of each, and total all the doors and windows. Subtract that total from the your initial square footage total for the walls and you have your net square footage for the project.
Measuring Vaulted Ceilings
What if you have a area on the wall that is a triangle, like the part of a wall that meets a vaulted ceiling? Going back to our high school geometry tells us that the area or square footage of a triangle is the height time the width, divided by two. For example, a triangle that is 5 feet tall and 6 feet long has 15 square feet, (5X6 divided by 2). Measure each triangle you have in this manner.
Flooring presents a different challenge than walls. While there are no doors or windows to contend with, there are many other items like cabinets, fireplaces and odd nooks. The easiest method usually is to try to divide the floor into a series of squares. Start with the largest area that is a square and measure the length and width of the square. Again, multiply length times width for square footage. Measure each of the succeeding smaller squares and total all areas. Treat triangles, if any, just like we did above.
Accounting for Waste
So you now have calculate the actual square footage of the walls or floors for your project. Is this the amount of material you need then? Not quite yet. We need to discuss including an amount for waste. When cutting the wood flooring or paneling you will encounter some waste when you get to the ends of the walls or cut around objects like doors, windows, cabinets or fireplaces. Adding 5% additional square footage to account for waste is plenty for most projects. We may add 10% if there are a lot of angles or odd cuts. We can help you determine what amount to use for your individual project.


Select Awards & Fellowships
- Professor Lee H. Armstrong Award for Distinguished Teachers, Department of Mathematics, UCF, 2017.
- Outstanding Dissertation Award, Department of Mathematics, UCF, 2016.
- Selected as one of 15 student recipients of UCF’s Graduate Dean’s Dissertation Completion Fellowship, Spring 2016.
- Graduate Research Assistantship, Fall 2016, Center for Research in Computer Vision (CRCV), University of Central Florida (UCF).
- Graduate Teaching Assistantship, University of Central Florida.
- Graduate Research Assistantship 2011 and Summer 2012, for Gauss project, a Computational Science Training for Undergraduates in Mathematical Sciences funded by NSF.
- Merit scholarship for graduate studies, Indian Institute of Technology, Dhanbad, 2007-08.
- “Ila Mukhopadhyay Memorial Medal-2003” for Best in Human Qualities, Presidency College, 2003-04.
- KAUST travel grant to attend SIAM Conference on Imaging Science 2018 at Bologna, Italy, June 2018.
- IMA Travel Award (international airfare and ground transportation, lodging, food) for Integrating Machine Learning and Predictive Simulation: From Uncertainty Quantification to Digital Twins Workshop, March 2018.
- KAUST travel grant to attend Applied Machine Learning Days workshop and conference, EPFL, Lausanne, Switzerland, January 2018.
- KAUST travel grant to attend ICCV, Venice, Italy, October 2017.
- KAUST travel grant to attend American Mathematical Society’s Sectional Meeting, Orlando, Florida, September 2017.
- SAMSI Optimization Summer School travel and lodging award, August 2016, September 2016.
- UCF Mathematics department’s conference registration and travel award, January 2015, Novem- ber 2015, September 2016, January 2017.
- IMA Travel Award (travel, lodging, food) for Math Modeling in Industry Workshop, August 2014 and August 2015.
- Student Government Association’s conference registration and travel award, University of Central Florida, August 2014, August 2016.
- Graduate Travel Fellowship, University of Central Florida, December 2013.


A measure of the extent to which there is a correspondence between the observed values of a Dependent Variable and the predicted values from a Predictive Model. There are two commonly-used and equivalent ways of computing the variance:
- The ratio of the varianceof the predicted values to the variance of the observed values. (This formula only works where the predicted values are, in some sense, optimal.)[note 1]
- The square of the Pearson's Product-Moment Correlation coefficient.
Also known as
- Proportion of variance explained.
- For example, Maximum Likelihood estimates.
A more up-to-date version of this content is on www.displayr.com.


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Projectile problems - Nuffield Foundation Practice Problems - PROJECTILE MOTION Problem 1: A shotput is thrown. For the each of the indicated positions of the shotput along its trajectory, draw and label the following vectors: the x-component of the velocity, the y-component of the velocity, and the acceleration. Explain why you
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How To Solve Any Projectile Motion Problem (The Toolbox Method): Introducing the “Toolbox” method of solving projectile motion problems! Here we use kinematic equations and modify with initial conditions to generate a “toolbox” of equations with which to solve a classic three-part projectile motion problem. Bookmark File PDF Projectile Motion Worksheet Answers Projectile Motion Word Problems Worksheet #3 Kennedy 100 The projectile hits the incline plane at point M. a) Find the time it takes for the projectile to hit the incline plane. b)Find the distance OM. Solution to Problem 2. Problem 3 A projectile is to be launched Principles and Problems . Title: Worksheet 11 (Projectile - Horizontal Launch).pdf Author: okmteacher Created Date: 10/15/2010 11:54:17 AM ...
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Nov 23, 2020 · Hand out the worksheet with problems, each solving for a different kind of variable, such as time, initial velocity or distance. (Worksheet answers and solutions are provided on the Projectile Motion Problem Worksheet Answer Key. Review answers with students, ensuring that students can explain why they used certain equations and can explain step by step how to use the equations to solve each problem. Problem Solution Sample Essay. Global warming is one of the biggest threats humans face in the 21st Century and sea levels are continuing to rise at alarming rates.
Suppose that a projectile of mass is launched, at , from ground level (in a flat plain), making an angle to the horizontal. Suppose, further, that, in addition to the force of gravity, the projectile is subject to an air resistance force which acts in the opposite direction to its instantaneous direction of motion, and whose magnitude is ... Physics worksheet – Projectile motion (g = 9.8 ms-2, no air resistance) Q1 A golf ball is projected vertically with a speed of 15 ms-1. Calculate the maximum height reached by the ball. Q2 A tennis ball is projected from a height of 1.5 m parallel to a horizontal ground. Physics 01-01 Intro and Units.pdf: 663.09kb; Physics 01-02 Displacement and Vectors.pdf: 601.43kb; Physics 01-03 Velocity and Graphs.pdf: 721.67kb; Physics 01-04 Acceleration and Graphs.pdf
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First find the time for projectile #1: Δy = 0 = (v o sin45)t + ½gt 2 t = (v o sin45)/4.9 Find the range called D: D = (v o cos45)t D = (v o cos45)(v o sin45)/4.9 = (0.1)v o 2 t 1 = Time for projectile 2 to hit the first time. Δy = 0 = (v o sinθ)t + ½gt 2 t 1 = (v o sinθ)/4.9 t 2 = Time for projectile 2 to hit the second time. Δy = 0 = ((v o /2)sinθ)t + ½gt 2 t 2 = (v o sinθ)/9.8 Projectile Motion Simulator Worksheet. Description. Answers Included.Hypothesis Worksheet Pdf
You may change the projectile's launch angle and initial speed by using the text boxes and clicking "set values and play." Find the relationship between v 0 and θ such that the projectile will always hit the car. When you determine the relationship, make sure to test it with a few values of v 0 and θ. Restart. Oct 29, 2003 · I need to learn how to do projectile motion properly before tomorrow's quiz and we got this worksheet.. with all these problems on this worksheet found on...
Benefits of NEET MCQs for Physics Kinematics and Projectile Motion. a) NEET Physics Kinematics and Projectile Motion MCQs will help the kids to strengthen concepts and improve marks in tests and exams. b) These multiple choice questions for Kinematics and Projectile Motion Physics will help to improve analytical and complex problem decoding skills. Jul 10, 2016 · On this page you can read or download projectile motin in two dimension worksheet with answers dpf in PDF format. If you don't see any interesting for you, use our search form on bottom ↓ . Unit 5 General Physics Projectile Motion Practice
Error Correction Worksheet - Correct the errors in this sample "My Hobby" essay. Assignment: "My Hobby" - Use the grammar and sentence patterns from Unit 1 to write an essay titled "My Hobby".Problem 1. Determine the muzzle velocity of your projectile launcher for a given angle: θ = _____ Use the NCR paper to measure the distance of the shot. Shoot 5 times and use the average for any measurement. Use the attached worksheet and complete all of the sections. The lesson on Freefall: Projectiles Released at an Angle will help you complete this worksheet. You should also take advantage of the help buttons if you need additional guidance. Remember to have your calculator mode set to "degrees" not "radians."
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11 VOCABULARY WORKSHEET #4 Application Forms. 12 VOCABULARY WORKSHEET #5 Employment. Living in English. Vocabulary Worksheet #3. Review of personal qualities.Worksheet: Have students solve the problems on the Projectile Motion Problem Worksheet. Once they are finished, review the solutions as a class. This is a good indicator of whether students grasp the mathematical concepts behind projectile
projectile-motion-worksheet-gina-wilson 1/4 Downloaded from ny.hearstfdn.org on December 29, 2020 by guest [eBooks] Projectile Motion Worksheet Gina Wilson Thank you very much for downloading projectile motion worksheet gina wilson.Maybe you have knowledge that, people have see numerous period for their favorite books in imitation of this ... Environment worksheets and online activities. Free interactive exercises to practice online or download as pdf to print.
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Projectile Motion Problems Projectile motion problems: Solutions Thursday, October 31, 2013 9:56 AM HONORS PHYSICS Page 1 Projectile motion problems: Solutions - Beaver Dam, WI Projectile Problems with Solutions 5 Written By Physics Lessons and Course. Saturday, November 16, 2019 Add Comment Edit. Projectile Motion I Problems ( 1-5 ) We finished Time Elapsed graph and The Trajectory of a Projectile Worksheet, through the answers given to us by Ms. K. The 1-5 problems (Projectile Motion I Problems Worksheet) can be solve using the formulas that Kristin posted on the blogs before me (^_^), and it will be corrected tomorrow.
AP Physics Projectile Motion Example Problems #26836 Worksheet Projectile Problems Key - Livinghealthybulletin #26837 physics 12 projectile motion worksheet 2 #26838 Worksheet projectile problems key This lab will answer whether or not initial speed affects the time that a projectile is in the air. Also, it will be determined if there is a direct
Projectile Worksheet #2 Name _____ Hour _____ For your solutions to these problems draw a picture of the situation described and label it with the given information. Neglect any air resistance. 1. A girl runs at a speed of 3.9 m/s off a high dive and hits the water 1.8 seconds later. a. How high was the diving board? b.
May 21, 2019 · Some of the worksheets below are Projectile Motion Worksheet with Solutions Worksheets, Projectile Motion Presentation : Contents – What is Projectile Motion?, Types of Projectile Motion, Examples of Projectile Motion, Factors Affecting Projectile Motion and exercises with solutions, …
Projectile Motion Worksheet - ephysics.net Projectile Motion activity — Projectile Motion Problem Worksheet Answer Key 4 5.) Drop a ball from a height of 2 meters and, using a stopwatch, record the time it takes to reach the ground. Repeat this two more times and record all the times in the table below, then find the average time. May 31, 2019 · If you found these worksheets useful, please check out Uniform Circular Motion Questions and Answers, Atwood Machine Problems and Solutions, Vector Sums Magnitude and Direction Independent Practice Worksheet Answers, How Does the Coriolis Effect Affect Ocean Currents, Coefficient of Fr iction Problems Worksheet with Answers, Pascal’s ...
Projectile Motion Worksheet. Due No Due Date. Points 100. This assignment was locked Apr 14, 2013 at 10:59pm. Upload the punting and projectile motion worksheet here.Oct 21, 2013 · Figure 1. This graphic shows a typical setup for a projectile motion problem. A projectile at height h above the ground (y=0) is launched with an initial velocity v 0 at an angle θ with respect to the horizontal (the x-axis). Gravity ( g) is in the negative y direction. We want to calculate the position of the ball at any time, t. Another kind of projectile problem is picture below. The ground is flat throughout the trajectory of the projectile. Also suppose 1. the magnitude of the initial velocity is V 0 = 35mês and 2. the direction is initially an angle q=30° above the horizontal direction. (Obviously, these numerical values can be different.) X Y V 0 q path of the ...
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Jul 10, 2016 · On this page you can read or download projectile motin in two dimension worksheet with answers dpf in PDF format. If you don't see any interesting for you, use our search form on bottom ↓ . Unit 5 General Physics Projectile Motion Practice
Enter the distance of an object and the height of an object. The calculator will evaluate and display the angle of elevation. This calculator assumes a flat distance and does not take into account the curve of the earth. Collection of Mathcad worksheets Miron Kaufman 's MathCAD Course Labs The list below comprises computer labs, part of courses I teach: University Physics I, University Physics II, Thermal Physics, Statistical Physics, Environmental Physics.


Klein and Marple on Math Education
While you're over at the Los Angeles Times website, you can check out this op-ed from yesterday's edition. The article is by David Klein and Jennifer Marple, an education professor and high school math teacher respectively. The subject is math education in the Los Angeles Unified School District:
What accounts for the low achievement in middle and high school mathematics in the district? A standard explanation is lack of funds. Certainly more money could — if spent wisely — improve education in the LAUSD, but unfortunately the district uses scarce resources in ways that undermine student achievement.
Take professional development. The district requires math teachers to attend in-service meetings to learn more math and better ways to teach it. No one would quarrel with those goals, but the quality of professional development programs is often so poor that they are likely to cause more harm than good.
LAUSD teachers and math coaches are wrongly instructed not to use time-tested, standard methods of arithmetic. High school teachers are steered away from conventional and powerful techniques in algebra and directed to use unreliable “guess and check” methods and physical objects instead. Even elementary school teachers are discouraged from following their high-quality state-approved math books and from teaching the best methods of calculation, the standard algorithms of arithmetic.
Confirming our own observations, the head of one of the stronger LAUSD high school math departments lamented: “The mandatory 40-hour algebra training was worthless. We had to teach the trainers how to do algebra … the people in charge of making final decisions on math [in the LAUSD] don't know math!”
Too often, the math that teachers are taught at district training sessions is just plain wrong. For instance, middle school teachers are erroneously taught that fraction division is repeated subtraction. This makes sense only for special examples such as 3/4 divided by 1/4 . In this case, 3/4 may be decreased by 1/4 a total of three times, until nothing is left, and the quotient is indeed 3. Understanding division as repeated subtraction, however, is nonsensical for a problem like 1/4 divided by 2/3 because 2/3 cannot be subtracted from 1/4 even once. No wonder students have trouble with fractions in high school.
All of this matches well with my own experiences.


Corner pieces are pieces with 3 sides. There are 8 corner pieces.
Edge pieces are pieces with 2 sides. There are 12 edge pieces.
Center pieces are pieces with 1 side. There are 6 center pieces.
Center pieces don't move.
White is always opposite to Yellow.
Blue is always opposite to Green.
Red is always opposite to Orange.
Every move is clockwise, unless it has an i after it or an apostrophe ('). In this case, you move it counter clockwise.
Hold the cube as it says on the picture. Gray pieces mean the pieces don't matter. Each move is a 1/4 turn rotation.Next-->


MathWood - Jouet éducatif de mathématiques
Age Range:>3Year old
1. Learn simple addition and subtraction calculations to lay the foundation for learning mathematics in the future.
2. Exposing mathematics to the preschool baby game can make learning mathematics easy and simple, and mathematics learning in the future will be more effective.
3. During the play, the baby can exercise the cognitive ability of the baby's hand-eye coordination ability and the ability to recognize the number.
4. Can help the baby to draw conclusions through reasoning, let the baby feel a sense of accomplishment


“It is not about the answer you get, but the journey you took to get to the answer.”
At St. John’s we follow the White Rose Scheme of Learning. This is to ensure mathematics is taught to a mastery level showing depth and understanding of concepts taught. This approach to learning ensures small steps of progress are made towards the National Curriculum objectives, so that children have time to fully grasp a concept before moving on. This approach can take time to embed this understanding and knowledge but is vital in ensuring children are grasping key concepts in learning.
Lessons taught should mainly follow the structure outlined below:
Our approach to teaching maths at St. John’s ensures children are taught at their year group level and for those children who need stretching, further opportunities are provided to provide the depth in their learning. This could be in the form of ‘Odd One Out’ tasks, ‘How many ways?’, ‘Explain’, ‘I know…So…’. These tasks give children the chance to apply their understanding and problem solve and reason their way through the tasks.
At St. John’s, we recognise that mathematics is all around us and makes up part of the foundations of everyday life. Therefore, we believe that it is vital for children to be fully equipped with a variety of skills and the ability to adapt these skills to different situations.
From the Early Years Foundation Stage, we follow a mastery approach where children learn a concept in depth, moving through small progressive steps to develop a deep, lasting understanding and confidence. This is taught through a variety of fluency, reasoning and problem-solving tasks. The idea is that all children begin in the same place and learn the same content. Those that are quicker at grasping a concept or skill will be pushed to think more mathematically and explore the ‘why’ of the concept, whereas additional support and scaffolding is given to those who take a little longer to grasp a learning objective.
All year groups begin their learning with place value which is vital to underpinning the number system, followed by calculation and other mathematics strands including measure, fractions and geometry. A strong foundation of number knowledge enables children to access and progress through the maths curriculum confidently.
Across the school, the children complete daily recall tasks to develop their fluency in arithmetic and solidify their understanding of mathematical methods. This helps to build their resilience and confidence in their own abilities.
Maths lessons should also:


* 1811, † 1882
Li Shanlan was born 1811 in Haining, Zhejiang Province, China. Li Shanlan was the greatest Chinese mathematician of the 19th century who translated Western works and gave many summation formulas. Li Shanlan died in 1882 in China.
| | | | created: 2016-08-26 21:54:42 | modified: 2018-05-24 21:27:18 | by: bookofproofs | references:


Timothy R Field
McMaster University, Canada
Timothy R Field studied undergraduate mathematics at King’s College, Cambridge University, and went on to receive a Doctorate in mathematics from New College and the Mathematical Institute, Oxford University in 1997, where he studied mathematical physics under Sir Roger Penrose. He is an Associate Professor in the Departments of Electrical & Computer Engineering and Mathematics & Statistics at McMaster University. He is fellow of the Institute of Physics and the Institute of Mathematics and its Applications, and twice recipient of NSERC Discovery Awards for research into electromagnetic scattering from random media and related phenomena.
The dynamics of a spin system is usually calculated using the density matrix. However, the usual formulation in terms of the density matrix predicts that the signal will decay to zero, and does not address the issue of individual spin dynamics. Using stochastic calculus, we develop a dynamical theory of spin relaxation, the origins of which lie in the component spin fluctuations. This entails consideration of random pure states for individual protons, and how these pure states are correctly combined. Both the lattice and the spins are treated quantum mechanical. Such treatment incorporates both the processes of spin-spin and (finite temperature) spin-lattice relaxation. Our results reveal the intimate connections between spin noise and conventional spin relaxation. These developments in theoretical aspects of spin noise and relaxation and their interrelationship reveal a modified spin density, distinct from the density matrix, as the necessary object to describe fluctuations in spin systems. These fluctuations are to be viewed as an intrinsic quantum mechanical property of such systems immersed in random magnetic environments and are observed as spin noise in the absence of any radio frequency excitation. With the prospect of ultrafast digitization, the role of spin noise in real-time parameter extraction for spin systems, and the advantage over standard techniques, is of essential importance, especially for systems containing a small number of spins. In this presentation we outline prospects for harnessing the recent dynamical theory in terms of spin-noise measurement, with attention to real-time properties.


Rob Vingerhoets is a well-renowned educator in Melbourne, Australia. He has taught in many school settings and was a Principal for a prestigious Melbourne private school for a while too. He is an author of many educational texts, presents to educators on a regular basis and works with schools to help schools and educators improve the delivery of math classes, as well as the engagement level and understanding of mathematical concepts of students.
Last month, I was fortunate to have Rob visit my classroom and work with my year 6 students. My class isn’t the easiest class for visiting educators to work with and engage, but within minutes, Rob had my students eating out of the palm of his hand. He introduced my class to a game called ‘Date Maths’, where you create equations to equal the numbers 1 through to 20 using only the digits in that day’s date. The activity is timed and if all 6 digits are used in an equation, a bonus is awarded; that being 30 seconds off the total time. My class had never played this game before and within minutes, they were applying order of operations across to equations so all 6 digits were included. Some students also noted that if you multiplied or divided a number by one, the total remained the same; however, if you multiplied a number by zero, the value was wiped.
I was amazed by the deep level of thinking this game promoted. Each student shared an equation. It is definitely a game that caters for all mathematical abilities.
The one thing I admired whilst Rob was playing this game with my class, was that whenever he could, he would relate a score to a mathematical concept, i.e. “You have completed 5 out of 20 equations. How do you write that as a fraction? percentage?” These incidental teaching points provided concrete examples for my students to relate to. I truly believe my students will remember fraction to percentage conversions now as a result of this game. It was fun, it was challenging, there was a clear purpose and it involved the class working together as a team.
It was a pleasure to meet and work with Rob. My students adored him and we look forward to working with him again in the future.


Tablets reveal Babylonian math skills
Old Babylonian "hand tablet" illustrating Pythagoras' Theorem and an approximation of the square root of two.
A New York exhibition of ancient tablets has revealed the highly sophisticated mathematical practices and education in central-southern Mesopotamia.
Before Pythagoras: The Culture of Old Babylonian Mathematics displays thirteen Babylonian tablets which show that people of the region were math experts more than 1,000 years before Greek mathematicians were even born.
Held at the New York University's Institute for the Study of the Ancient World (ISAW), the event exhibits tablets dating from the Old Babylonian Period (ca. 1900-1700 BCE) along with supplemental documentary material.
"It has long been widely recognized that many of the critical achievements of Western Civilization, including writing and the code of law that is the basis for our present-day legal system, developed in ancient Mesopotamia," Artdaily quoted ISAW director for exhibitions and public programs Jennifer Chi.
"By demonstrating the richness and sophistication of ancient Mesopotamian mathematics, Before Pythagoras adds an important dimension to the public knowledge of the history of historic cultures and attainments of present-day Iraq," she added.
The tablets, collected from the Columbia Rare Book and Manuscript Library, the University of Pennsylvania Museum of Archaeology and Anthropology, and the Yale Babylonian Collection, will be on display until December 17, 2010.
"The evidence we have for Old Babylonian mathematics is amazing not only in its abundance, but also in its range, from basic arithmetic to really challenging problems and investigations," said exhibition organizer Alexander Jones.
The modern knowledge of Babylonian mathematics is based on the work of scribes, who were young wealthy men formally trained in reading and writing.
The scribes learned and practiced mathematics while working in fields such as accounting, building-project planning, and other professions in which mathematics is essential.
"Since the documents are the actual manuscripts of the scribes… we feel as if we were looking over their shoulders as they work," said Jones.
"We can even see them getting confused and making mistakes."
The exhibited tablets are in cuneiform script and cover the full spectrum of mathematical activity from arithmetical tables copied by scribes-in-training to sophisticated work on topics today classified as number theory and algebra.
Many of the solutions used by scribes to solve the mathematical problems depended on principles that were believed to have been discovered by Greeks in the sixth century BCE and later.


Up to this point we have worked with unsigned integers, i.e. whole numbers which are zero or bigger than zero. Much like it happened with endianness, the interpretation of the value of several bytes as a negative number depends on the specific interpretation.
In computing there are two main ways to interpret the values of a group of bytes as a negative number: one’s complement and two’s complement.
At the moment GNU poke supports the two complement interpretation, which is really ubiquitous and is the negative encoding used by the vast majority of modern computers and operating systems.
We may consider adding support for one’s complement in the future, but only if there are real needs that would justify the effort (which wouldn’t be a small one ;)).
Unsigned values are never negative. For example:
(poke) 0UB - 1UB 0xffUB
Instead of getting a -1, we get the result of an unsigned underflow, which is the biggest possible value for an unsigned integer of size 8 bits: 0xff.
When using type specifiers like
uint<16> in a
map, we get unsigned values such as 0UB. It follows that we need
other type specifiers to map signed values. These look like
For example, let’s map a signed 16-bit value from foo.o:
(poke) .set obase 10 (poke) int<16> @ 0#B 28515H
Note how the suffix of the value is now
H and not
This means that the value is signed! But in this case it is still
positive, so let’s try to get an actual negative value:
(poke) var h = int<16> @ 0#B (poke) h - h - 1H -1H
Adding two signed integers gives you a signed integer:
(poke) 1 + 2 3
Likewise, adding two unsigned integers results in an unsigned integer:
(poke) 1U + 2U 3U
But, what happens if we mix signed and unsigned values in an expression? Is the result signed, or unsigned? Let’s find out:
(poke) 1U + 2 3U
Looks like combining an unsigned value with a signed value gives us an unsigned value. This actually applies to all the operators that work on integer values: multiplication, division, exponentiation, etc.
What actually happens is that the signed operand is converted to an unsigned value before executing the expression. You can also convert signed values into unsigned values (and vice-versa) using cast constructions:
(poke) 2 as uint<32> 2U
Therefore, the expression
1U + 2 is equivalent to
1U + 2
(poke) 1U + 2 as uint<32> 3U
You may be wondering: why not doing it the other way around? Why not converting the unsigned operand into a signed value and then operate? The reason is that, given an integer of some particular size, the positive range that you can store in it is bigger when interpreted as an unsigned integer than when interpreted as a signed integer. Therefore, converting signed into unsigned before operating reduces the risk of positive overflow. This of course assumes that we, as users, will be working with positive numbers more often than with negative numbers, but that is a reasonable assumption to do, as it is often the case!