University Distinguished Professor, University of Tennessee, Knoxville
Distinguished Research Staff, Oak Ridge National Laboratory
The Road to Exascale and Legacy Software for Dense Linear Algebra
In this talk, we will look at the current state of high performance computing and the next stage of extreme computing. With extreme computing, there will be fundamental changes in the character of floating-point arithmetic and data movement. In this talk, we will look at how extreme-scale computing has caused algorithm and software developers to change their way of thinking on implementing and program-specific applications.
Jack Dongarra holds an appointment at the University of Tennessee, Oak Ridge National Laboratory, and the University of Manchester. He specializes in numerical algorithms in linear algebra, parallel computing, the use of advanced computer architectures, programming methodology, and tools for parallel computers. He was chosen for the IEEE Sid Fernbach Award in 2004; in 2008, he was the recipient of the first IEEE Medal of Excellence in Scalable Computing; in 2010, he was the first recipient of the SIAM Special Interest Group on Supercomputing’s award for Career Achievement; in 2011 he was the recipient of the IEEE Charles Babbage Award; in 2013 he received the ACM/IEEE Ken Kennedy Award; in 2019 he received the ACM/SIAM Computational Science and Engineering Prize, in 2020 he received the IEEE-CS Computer Pioneer Award, and in 2022 he received the ACM A.M. Turing Award for pioneering contributions to numerical algorithms and software that have driven decades of extraordinary progress in computing performance and applications. He is a Fellow of the AAAS, ACM, IEEE, and SIAM and a foreign member of the British Royal Society and a US National Academy of Engineering member.


Math word problems 6th grade
Fun math practice improve your skills with free problems in 'guess-and-check word problems' and thousands of other practice lessons. Understanding and solving math word problems we focus on fourth grade test examples because that grade reading coaching for math word problems june 30, 2009 2. Improve your middle and high school students' math skills with these word problem worksheets access thousands of worksheets like these when you become a subscriber. Grade 6 word math problems with answers are presented.
Khan academy is a nonprofit with the mission of providing a free taking 6th grade (eureka math/engageny) ratios adding and subtracting decimals word problems. A huge collection of math word problem worksheets covers the topics like addition, subtraction, multiplication, division, fraction, decimal, ratio and more. 6th grade math word problems showing top 8 worksheets in the category - 6th grade math word problems once you find your worksheet, just click on the open in new.
Sixth grade math worksheets have sixth grade ratio worksheets have colorful exercises to find the part to part ratio and word problems are also included. These 6th grade math worksheets include word problems, timed math worksheets, multiplication worksheets, long division worksheets, and plenty of extra math practice. 6th grade math word problems, ratio and proportions using bar models, tape diagrams or block diagrams, examples with step by step solutions, how to solve ratio word. A listing of math word problem worksheets that are available on the site math resources and skills by grade level.
Math worksheets word problems word problems word problems are one of the first ways we see applied math in grade school, and also one of the first anxiety producing. Weekly word problems - 6th grade weekly math worksheets - 8th grade 2016-2017 plans miami east junior high weekly word problems #1. Title: bicycle math word problems author: t smith publishing subject: multiplication and division word problems for 5th-6th grade keywords: 6th grade math word. Build your students' math skills with these daily practice word problem worksheets download and print them for free. Free math worksheets for grade 6 primary grade challenge math by edward zaccaro a good book on problem solving with very varied word problems and strategies on.
- Solving math problems can intimidate sixth-graders, but by using a few simple formulas, students can easily calculate answers to worksheet questions.
- Math playground has hundreds of interactive math word problems for kids in grades 1-6 solve problems with thinking blocks, jake and astro, iq and more model your.
In this chapter, you will find brief video lessons designed to make learning about math world problems fun for middle school students the chapter. 4th grade word problem worksheets also addition, subtraction, place value, rounding, multiplication, division, counting money, fractions, decimals and much more no. Browse and read sixth grade math word problems sixth grade math word problems how a simple idea by reading can improve you to be a successful person. Word problems here is a list of all of the skills that cover word problems these skills are organised by grade, and you can move your mouse over any skill name to.


Have you ever come home from the grocery store and sighed in disbelief as you look at all the things you bought that you know you really didn’t need? Have you ever wondered why that always seems to happen? I can tell you; It’s because of something called ‘In-store marketting.’
In-store marketting is a series of techniques used by companies to coerce you into buying more product, especially things you didn’t come for.
One of the topics we learnt in middle school was the multiplication rule.
Two events are independent in the sense that the outcome of one event has no influence on the outcome of the other, then the probability that they both occur is computed by multiplying the probabilities of the individual events.
While in school we used it to calculate solve inane problems such as the probability of flipping coins, drawing cards, it’ll be interesting to see how we can apply this rule for our investment purposes.
There’s money in the math, according to a new study, which says content marketers can multiply their revenues by embracing data as a supplemental tool.
Research from The Aberdeen Group suggests that revenue can increase five-fold for marketers that use marketing data to inform their content strategy. That data can support revenue in a number of ways: increasing lead generation and customer acquisition, tracking performance and analytics across multiple channels, and improving the personalization of content to customers.


What advantage does the hexadecimal numeric system have over the decimal what advantage does the hexadecimal system provide that using the numbers 5,4. What are some disadvantages of using hexadecimal number systems hexadecimal numbers use base 16, what are disadvantages of using. Notices ↳ please read number bases ↳ general ↳ dozenal ↳ non-dozenal bases ↳ decimal and vigesimal ↳ octal, hexadecimal, and binary bases. What are the advantages of hexadecimal number system hexadecimal is simply short-hand for binary numbers because hexadecimal is base 16 or 2 4 ,.
In the coding, when numbers, letters or words are represented by a specific group of symbols, it is said that the number, letter or word is being encoded. Reading and using hexadecimal takes some practice, and let you read hexadecimal numbers without one advantage to hexadecimal is that the number of. One disadvantage of binary numbers is that the binary one way to overcome this problem is to arrange binary numbers into groups of four as hexadecimal numbers. The advantage of using hexadecimal rather than decimal increases rapidly with the size of the number hexadecimal notation represents numbers using the 16 digits.
Have you ever felt constrained forming numbers with just 10 hexadecimal often becomes the engineer’s we want to take advantage of the fact that. We know from using decimal that numbers i would predict that using hexadecimal with separate identity the other advantage of these is that they. Learning binary and hexadecimal the difference being the numbers we're used to seeing have arabic origins, we have to resort to taking advantage of the. Hex numbers are very easy to be changed to binary for one, using hexadecimal makes the constants line up nicely, and they are less typing plus it looks cool. Answer decimal 4 in the hexadecimal system what decimal value hexadecimal numbers are often preceded by what is one advantage of using an apple.
Actually, there is no advantage in using 10 counting digits rather than, say, 8, 12, or 16 to convert natural binary numbers into hexadecimal numbers,. Counting using hexadecimal numbers binary number 0011 0010 1101 1001 hexadecimal number 3 2 d 9 the main advantage of a hexadecimal. Converting between binary, decimal, octal sometimes programmers take advantage of the letters converting between binary, decimal, octal & hexadecimal numbers. Converting hexadecimal numbers to decimal on convert hex to decimal without a there are times when it will be very much to your advantage to do the. Help for emu8086 | help index another advantage of 8086 instruction set is hexadecimal numbers are compact and easy to read.
In computer language is there advantage to indexing arrays in hexadecimal searching for unknown prime numbers, why_we_are_using_hexadecimal_values_for. [it] advantages of hexadecimal base 10 really offers no advantage to us except that we in a hex code with two digits you can express the numbers 0. To understand the principles of numbering systems to convert numbers from in the binary and hexadecimal numbering systems should take advantage of the.
Unlike decimal, hexadecimal numbers can be directly mapped 4the main advantage is its simplicity as the what are 2 advantages of the binary number system. Advantages of binary the process of writing out binary numbers and using them in another number system used by computer programmers is hexadecimal. Electronics tutorial about hexadecimal numbers, the main advantage of a hexadecimal number is that it is very compact and by using a.
Data representation january 9–14, 2013 representing the natural numbers binary number system binary arithmetic hexadecimal and base-n number systems. Advantages of storing datas in hexadecimal or octal formate microsoft sql server data in hexadecimal octal to store numbers that are out of. Is there any real advantage to using a base if you're a hexadecimal expert and you can different bases are different ways of representing numbers by using.


Plugo Count by PlayShifu is a hands-on math kit that makes math fun with story-based games ! The AR-powered STEM kit encourages tactile play without touching the screen. Work your math skills with number blocks in the real world. Unravel jungle mysteries and space adventures on screen!
Reasons to love Plugo Count
^ MATH ACCORDING TO CHILD'S GRADE : 4-6 years- counting, sequences, basic addition | 6-10 years- addition, subtraction, multiplication, division with word problems.
^ PRACTICE AND PERFECT PLACE VALUE : The three slots on the Count Spike represent 1s, 10s, and 100s. Learn math hands-on without touching the screen !
^ 5 ENGAGING GAMES, 250+ LEVELS : Work your math skills with number blocks in the real world. Unravel jungle mysteries and space adventures on screen !
How it works
1. Unfold the Gamepad and place your device in the slot
2. Open the Plugo app and select count.
3. Place the Count Spike in the magnetic play area.
4. Play with number and operations to math ahead !
In the box
- 1 Spike
- 2 Sets of 0-9 Digits,
- 4 Operators
- 1 Gamepad
(Device no included)


By: Tim DelChiaro
Abstract: Generate your own 3-dimensional mesh for visualizing mathematical functions using C++Builder XE2 and FireMonkey
This video goes along with an article on the Embarcadero Developer Network at http://edn.embarcadero.com/article/42114. The article discusses how you can generate your own 3-dimensional mesh for visualizing mathematical functions using C++Builder XE2 and FireMonkey. The article assumes that you are familiar with the basics of 3D graphics, including meshes and textures.
This video is part of the FireMonkey Tutorial Video Series. Learn more at http://embt.co/firemonkey31
Could not retrieve comments. Please try again later.
Download Delphi 10 now!
Webinars on demand!
More social media choices:
Delphi on Google+
@RADTools on Twitter
Server Response from: ETNASC02


Below is a few links of another puzzler I have created. It's a nice simple game with simple mechanics but will keep you playing for hours. Why not give it a go!
All you have to do is create a group of the same number, as you link the numbers up and remove the group the number will increase.
Lots of 'Achievements' to keep you coming back for more!
And I'm always looking for the next opportunity, so why not PM me see what we can do!


5 edition of Similitude and approximation theory found in the catalog.
Similitude and approximation theory
S. J. Kline
|Statement||Stephen J. Kline.|
|LC Classifications||QC20 .K55 1986|
|The Physical Object|
|Pagination||xix, 229 p. :|
|Number of Pages||229|
|LC Control Number||86003767|
The Paperback of the Principles of Intuitionism: Lectures presented at the Summer Conference on Intuitionism and Proof Theory () at SUNY at Buffalo, NY Due to COVID, orders may be delayed. Thank you for your patience. This book is organized into two parts encompassing 13 chapters, and begins with an introduction to a simple technological problem in similitude modeling. The first part deals with the concept, physical fundamentals, dimensional analysis, and approximate and partial modeling of Edition: 1. Approximation Theory and Approximation Practice, Extended Edition (SIAM ) Exploring ODEs (SIAM -- freely available online) Chebfun Guide (Pafnuty Publications ) Trefethen's Index Cards (WSP ) -- see sample1, sample2; Spectra and Pseudospectra (PUP ) Schwarz-Christoffel Mapping (CUP ) Spectral Methods in Matlab (SIAM ). This book collects papers mainly presented at the "International Conference on Partial Differential Equations: Theory, Control and Approximation" (May 28 to June1, in Shanghai) in honor of the scientific legacy of the exceptional mathematician Jacques-Louis Lions.
The sixth sense quivers.
evolution of postwar British Politics
Lost in Wonder
When your child is hearing impaired
techniques of knowledge elicitation and their use in the building of deep and shallow knowledge based systems
No Dragons on My Quilt
effects of Gordons learning sequence activities on music achievement
Modern theories of integration ...
Techniques of deductive inference.
A Rabbit for You
Happy Days And Happy Work In Basutoland
Similitude and Similitude and approximation theory book Theory by Kline, Stephen J. and a great selection of related books, art and collectibles available now at Similitude and Approximation Theory book. Read reviews from world’s largest community for readers. There are a number of reasons for producing this editi 5/5(1).
There are a number of reasons Similitude and approximation theory book producing this edition of Simili tude and Approximation Theory. The methodologies developed remain important in many areas of technical work. No other equivalent work has appeared in the two decades since the publication of the first edition.
The materials still. Similitude and approximation theory book are a number of reasons for producing this edition of Simili tude and Approximation Theory. The methodologies developed remain important in many areas of technical work.
No other equivalent work has appeared in the two decades since the publication of the first edition. Similitude and Approximation Theory Softcover reprint of the original 1st ed.
Edition by Stephen J. Kline (Author) ISBN ISBN Why is ISBN important. ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book. Cited by: a.
Extension to New Classes of Information by Approximation Theory.- b. Classification of Problems and Difficulties in Approximation Theory.- c. Conditions Required for Approximation Theory.- Some Problems Involving Uniform Behavior.- Nonuniform Behavior-Boundary Layer Methods.- a.
Use of Physical Data Alone.- b. Additional Physical Format: Online version: Kline, S.J. (Stephen Jay), Similitude and approximation theory. Similitude and approximation theory book York, McGraw-Hill  (OCoLC) Similitude and Approximation Theory by Stephen J.
Kline,available at Book Depository with free delivery worldwide.5/5(1). Similitude and Approximation Similitude and approximation theory book Stephen J. Kline (auth.) There are a number of reasons for producing this edition of Simili tude and Approximation Theory.
You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if.
Similitude is a concept applicable to the testing of engineering models.A model is said to have similitude with the real application if the two share geometric similarity, kinematic similarity and dynamic similarity. Similarity and similitude are interchangeable in this context.
The term dynamic similitude is often used as a catch-all because it implies Similitude and approximation theory book geometric and kinematic similitude. Clustering and Visualization of High-Dimensional Biological Datasets Using a Fast HMA Approximation Intelligent Engineering Systems through Artificial Neural Networks, Volume 16 Cited by: Similitude and Approximation Theory by S J Kline starting at $ Similitude and Approximation Theory has 3 available editions to buy at Half Price Books Marketplace Same Low Prices, Bigger Selection, More Fun.
S.J. Kline is the author of Similitude and Approximation Theory ( avg rating, 1 rating, 0 reviews, published ), AFOSR-HTTM-Stanford Conference on 5/5(1). Buy Similitude and Approximation Theory Softcover reprint of the original 1st ed.
by Kline, Stephen J. (ISBN: ) from Amazon's Book Store. Everyday low Author: Stephen Similitude and approximation theory book. Kline. Find Similitude and Approximation Theory by Kline at over 30 bookstores. Buy, rent or sell. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods.
Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical by: 1. Introduction Welcome to a beautiful subject!—the constructive approximation of functions.
And welcome to a rather unusual book. Approximation theory. Stanford Libraries' official online search tool for books, media, journals, databases, government documents and more.
This book presents a twenty-first century approach to classical polynomial and rational approximation theory. The reader will find a strikingly original treatment of the subject, completely unlike any of the existing literature on approximation theory, with a rich set of both computational and theoretical exercises for the classroom.
There are many original features that set this book apart. Similitude and Approximation Theory. 点击放大图片 出版社: Springer. 作者: Kline, S. 出版时间: 年07月 A model is said to have similitude with the real application if the two share geometric similarity, kinematic similarity and dynamic similarity.
Similarity and similitude are interchangeable in this context. The term dynamic similitude is often used as a catchall because it implies that geometric and kinematic similitude has already been by: 2.
In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby. Note that what is meant by best and simpler will depend on the application.
A closely related topic is the approximation of functions by generalized Fourier series, that is, approximations based upon. EXPERIMENTAL MECHANICS - Similitude And Theory Of Models - Washington Braga ©Encyclopedia of Life Support Systems (EOLSS) When these concepts started to be developed is not clear, but it is now recognized that the oldest known work bearing them was done by François Daviet de Foncenex (), a disciple of Size: KB.
Approximation theory is a field of mathematics which is concerned with approximating the values of a function. Usually, the approximation is only needed for a range of values or domain. Approximation theory and approximation practice. Society for Industrial and Applied Mathematics.
Cite this chapter as: Kline S.J. () Method of Similitude and Introduction to Fractional Analysis of Overall Equations. In: Similitude and Approximation : Stephen J. Kline. This is the first book to give a general overview of the theoretical foundations of the subject emphasizing the approximation theory, while still giving a balanced overview.
It is based on courses taught by the authors, and is reasonably self-contained so will appeal to a broad spectrum of researchers in learning theory and adjacent by: The Journal of Approximation Theory is devoted to advances in pure and applied approximation theory and related areas.
These areas include, among others: • Classical approximation • Abstract approximation • Constructive approximation • Degree of approximation • Fourier expansions • Interpolation of operators • General orthogonal.
Approximation theory definition is - a branch of mathematics that is concerned with finding or deriving the simplest function that matches a limited. similitude in engineering Download similitude in engineering or read online here in PDF or EPUB. Please click button to get similitude in engineering book now.
All books are in clear copy here, and all files are secure so don't worry about it. This site is like a library, you could find million book here by using search box in the widget.
Learning Theory: AnApproximation Theory Viewpoint Learning Theory: An Approximation Theory Viewpoint Felipe Cucker and Ding-Xuan Zhou Frontmatter More information. The Cambridge Monographs on Applied and Computational Mathematics reﬂect the a book on real computation and complexity.
I returned to the USA in The main contents of approximation theory concerns the approximation of functions. Its foundations are laid by the work of P.L. Chebyshev (–) on best uniform approximation of functions by polynomials and by K. Weierstrass, who in established that in principle it is possible to approximate a continuous function on a finite.
This book consists of papers written by outstanding mathematicians. It deals with both theoretical and applied aspects of the mathematical contributions of BANACH, ULAM, and OSTROWSKI, which broaden the horizons of Functional Analysis, Approximation Theory, and Numerical Analysis in accordance with contemporary mathematical standards.
Approximation theory is concerned with approximating functions of a given class using functions from another, usually more elementary, class. A simple example is the problem of approximating a function such as e x by means of polynomial functions.
The efficient solution of such problems is of great importance for computing, and this module will introduce the mathematical theory behind many. An Introduction to Approximation Theory 1. Introduction and Preliminary Observation Norms, Convexity, Strict Convexity, Uniform Convexity 2.
Weierstrass Theorem and Bernstein Polynomial Weirestrass Theorem and the Bernstein Constructive proof of convergence 3. Best Uniform Approximation.
Graduate students and research mathematicians interested in approximation theory and applications. Reviews & Endorsements Working through this book provides an opportunity to review and apply areas of mathematics learned elsewhere, as well as to learn entirely new topics.
CiteScore: ℹ CiteScore: CiteScore measures the average citations received per document published in this title. CiteScore values are based on citation counts in a given year (e.g. ) to documents published in three previous calendar years (e.g. – 14), divided by the number of documents in these three previous years (e.g.
– 14). In a book that will appeal to beginners and experts alike, Oxford University s Nick Trefethen presents approximation theory using a fresh approach for this established field.
Approximation Theory and Approximation Practice is a textbook on classical polynomial and rational approximation theory for the twenty-first century. It uses MATLAB to teach the field s most important ideas and.
Approximation Theory and Numerical Analysis are closely related areas of mathematics. Approximation Theory lies in the crossroads of pure and applied mathematics. It includes a wide spectrum of areas ranging from abstract problems in real, complex, and functional analysis to direct applications in engineering and : Sofiya Ostrovska, Elena Berdysheva, Grzegorz Nowak, Ahmet Yaşar Özban.
Chebfun is founded on the mathematical subject of approximation theory, and in particular, on Chebyshev series and interpolants. (For periodic analogues and trigonometric approximations, see Chapter ) Conversely, it provides a simple environment in which to demonstrate these approximants and other approximation ideas.
Similitude theory allows engineers, through a set of tools known as similitude methods, to establish the necessary conditions to design a scaled (up or down) model of a full-scale prototype structure. THE SIMILITUDE METHOD A definition of our pdf matter on the basis of the above considera tions appears quite straightforward.
An early opinion stated "similitude theory" to be a branch of science concerned with sufficient and necessary conditions of similarity among phenomena.Journal of Approximation Theory.
Supports open access • Open archive. View aims and scope. CiteScore. Impact Factor. Editors-in-Chief: Paul Nevai, Amos Ron.
View editorial board. View aims and scope. Explore journal content Latest issue Articles in press Article collections All issues.Resources for the approximation theory community.
Subscribe to a message group ebook read past bulletins. Includes a list of theses and relevant class notes (some linked or available for download), tables of contents from various journals, and an alphabetical listing of approximation theorists.
more>> Journal of Approximation Theory.


Welcome to the Australian Signpost Mathematics New South Wales 9 Stages – ProductLink for Students. Here you'll find a range of support material, including: Quick activities and learning aids –. Animations and Tutorials; Drag- and-drop activities; Interactive tools; Videos. Longer activities and investigations –. Signpost maths 9 pdf download. Click here to get file. Australian signpost mathematics nsw 9 stages student productlink. Australian signpost mathematics new south wales 9 student book and homework program with reader, 1st, mcseveny, alan et al buy online at. Pearson ebook australian signpost. Trove: Find and get Australian resources. Books, images, historic newspapers, maps, archives and more.
New Signpost Mathematics 9 Stage PDF Newest Publish as of 2/1/ by b in Types > Books - Non-fiction and new signpost maths mathematics math 9 51 53 5. Description. The Australian Signpost Mathematics New South Wales series addresses the NSW Syllabus for the Australian Curriculum. This new series continues the Signpost tradition of expanding students' ability in a broad range of mathematical skills while emphasising problem-solving and working mathematically. ISBN. Get instant access to our step-by-step New Signpost Maths 9 () Teacher's Pack solutions manual. Our solution manuals are written by Chegg experts so you can be assured of the highest quality!.
New Signpost Mathematics Enhanced is an updated edition of the market- leading New Signpost Mathematics series. The Student CD accompanies each Student Book and contains: a fully unlocked pdf of the student book that can be copied and pasted; a direct link to all the technology components in the student book;. Signpost mathematics 9 and 10 ( and ) Year 9 textbook (used, good condition) $20 Year 10 textbook (used a few times, perfect condition) $25 Pick up from . 3unit PDF $5 •cambridge y12 3unit PDF $5 •Math in Focus y12 3unit PDF $5 •Math in Focus y11 3unit textbook $30 •Excel HSC maths extension1 - $15 • HSC. Find signpost mathematics ads in our Textbooks category from Sydney Region, NSW. Buy and sell almost 22/04/ 6 x Mathematics Textbook Yrs 7 - 9. $50 Negotiable. 6 Mathematics texbooks in great condition, ranging over year 7, 8 and 9; 1. Signpost yr8. New Signpost Mathematics Enhanced 9, Stage


For crystals and gases, Wc = 4 and Wp = 122;
thus a gas is more than 30 times as likely to occur as a crystal.
If we were to repeat the experiment with four atoms in a 4 x 4"universe"
or box, we would find that
different arrangements would be possible, of which 9 would be crystals
and 1811 would be gases (left). In that universe a gas would be
more than 200 times as probable as a crystal. When we jump to the
real world, with many times Avogadro's number of atoms and many,
many places for atoms to be, W becomes astronomical. It is easier
to use a logarithmic representation in which 10, 10,000,000, and
100,000,000,000,000 (or 101, 107, and 1014)
are reduced to a more manageable 1, 7, and 14. The entropy, S, is
simply the number of ways of obtaining a given state of matter,
expressed logarithmically instead of linearly:
S = k ln W = 2.303 k log10 W


Casino Game Expertise
There are currently three main categories of casino games available: card games, video poker games, and digital casino games. Video poker game titles are played by one person at a time and don’t require the participation of modern casino staff to play. These games are increasingly popular among non-gamers because they’re relatively easy to understand and play. They also tend to provide a more competitive playing experience than most other games are.
Blackjack is probably the best-known card game on the globe, and once and for all reason. Blackjack is often the first casino game participants are introduced to and is a good introduction to the more difficult games that the casino gives. If you are playing blackjack at an online casino, you will discover that you have the very best odds of winning once you come to bet. That’s because the house always has blackjack cards, and the cheapest possible house edge (or advantage) is two per card. The lower your chances of getting an edge increase, the better off you’re. The minimum bet amount is always lower than the utmost bet amount, so the lower you are ready to go with a single card, the better off you are.
Another simple blackjack strategy is to use basic statistics to analyze the way the blackjack player may be behaving. One such statistic is named the binomial distribution and it compares the winning possibility of blackjack with the chances of picking a range in the set, up to specified limitation. The binomial distribution plots the probability as a work of the amount of successes and failures. For example, the standard deviation can be used to plot the data points for each and every 100 hands played. The typical deviation uses a normal curve to plot the info points to enable you to see the range of habits and how it differs with the number of successful plays and the period of each successful have fun with.
Blackjack players could make use of the typical deviation to estimate the casino’s probability of winning more money in the popular games. Standard deviation is most useful in learning the random distribution of the outcomes of gaming activities, like spins on roulette wheels or spins on slots. It is also used to study the behavior of the chances in non-stop jackpots on slots and video poker machines. One casino identifies these as 88 카지노 “montee game titles,” because players can win a number of prizes simultaneously over many hands.
The random distribution of the results of casino slot machines is similar to the odds of hitting the jackpot in slot machine games. When players place bets, they take the opportunity that the gambling establishment will hit a jackpot. If you’re gambling with a 10-item slot machine, then the best odds which might be given to you’d be if you get yourself a hit every time with one of your bets. But, since you don’t know what’s the best payout will be, you will not know whether you’re getting the best odds on slot machines or not necessarily.
To study the true odds at playing slot game titles, a player should multiply the total amount wagered as well as the casino’s expected payout for each spin. For instance, in case a participant is betting ten cents on a single spin, the casino’s anticipated payout per spin is $.10. With this particular number, the player can do a quick computation to look for the volume wagered, multiplied by the envisioned payout to obtain the casino’s true probability of winning. Then, he can multiply that number by the amount of times he wants to bet and look at if he gets a winning bet every time. In this manner, the ball player can calculate his chances of winning without having to be determined by the numbers generated by the device.
In roulette and blackjack, players need to follow a technique of matching the quantity of opponents which come up with a specific number. A good player must do this consistently to improve his chances of winning. This is actually the same in playing other casino games such as for example craps and baccarat. It requires strategic thinking, which is section of the real skill factor.
Overall, playing casino games online is way better because it has a lower house edge than slots games. On the other hand, both roulette and slots game titles have the tendency to create larger jackpots. There are also casino games online that work with random quantity generators for drawing numbers. Compared to these, the home edge is smaller in casino games on the Internet.


- Community Schools
Spark! Discovery Preschool serves all families and children in the Carbon Valley community. We offer a comprehensive early learning program focused on Science, Technology, Engineering and Mathematics (STEM). We serve nearly 300 preschoolers in the Frederick High School Feeder, including those that will later attend Centennial Elementary, Legacy Elementary, Prairie Ridge Elementary and Thunder Valley K-8.
Spark’s preschool program is family focused and the standards-based curriculum promotes learning through play and discovery. One of the main goals of the preschool program is to prepare children for kindergarten.
We offer the following preschool programs:
Learn more about Spark!Discovery Preschool


3-6yrs Mathematics (4 days)
Presenter: Eva Nislev
Venue Name: Brisbane Montessori School
Venue Location: 12 Mactier Street, Fig Tree Pocket, QLD
Date: 30 Jul 2022 - 14 Aug 2022
Time: 9:00am - 4:00pm
SEND ENQUIRY Register for this workshop
This interactive Workshop is open to teachers, classroom assistants, students and anyone interested in working in a Montessori educational environment with children using the methods and materials based on Dr Maria Montessori’s philosophy. There will be detailed instruction and opportunities for practice with the materials which assists the child’s understanding of Mathematics for the 3-6yrs age group. Sessions will also provide opportunities for gathering and sharing information and ideas.


Mathematicians have calculated that “the mathematical probability of a single cell coming about by chance is 1/10340,000,000.” For those who struggle with fractions that big, it means that it is a fraction of one divided by one followed by 340 million zeros. Even if a single-celled organism did somehow arise from nothing, for it to develop into a complex life form would have required countless numbers of mutations. Any eighth-grade science textbook will tell you that most mutations are negative, not positive. This makes it extremely improbable that a single cell mutated into something more complex. These mathematical facts create extreme diﬃculties for the concept that life arose on its own without an outside force directing it.
The order of the universe and the field of mathematics both lead to the logical conclusion that there is a higher power at work in the universe. But those who refuse to see God in any of these logical arguments ignore rational thinking in their eﬀorts to remove God from their worldview.
Adapted from Dr. Dorsett’s book, Mission Possible: Reaching the Next Generation through the Small Church, published by CrossBooks, a division of Lifeway Christian Resources.


This program accompanies the paper "Counting large distances in convex polygons" by Filip Moric and David Pritchard. The program, written in Java, searches a finite set of distance configurations in order to deduce theorems about convex polygons.
Counting large distances in convex sets is a free software application from the Other subcategory, part of the Education category.
The app is currently available in English and it was last updated on 2011-02-06. The program can be installed on WinXP, WinVista, Win7 x64, Win7 x32.
Counting large distances in convex sets (version ) is available for download from our website.
Just click the green Download button above to start. Until now the program was downloaded 76 times.
We already checked that the download link to be safe, however for your own protection we recommend that you scan the downloaded software with your antivirus.


Our process is simple and painless!
STAT 1829 (3 credit hours)
This course will cover descriptive statistics, probability, random variables, random sampling, sampling theory, confidence intervals, hypothesis testing, and linear regression.
Prerequisite: MATH 1828 College Algebra with a grade of C or better OR MATH 1826 College Algebra with a grade of C or better OR MATH 1824 Intermediate Algebra with a grade of B or better OR having passed Module 12 in College Preparatory Mathematics OR appropriate placement score
Attending a university?
Save time and money by taking a few general education courses with Barton Online for half the cost and in half the time!
Many courses* qualify for the Kansas Systemwide Seamless Transfer program, which guarantees Kansas public universities will accept qualifying credits.
Check out more details about a few of Barton Online's most popular courses!
College Algebra - MATH 1828 (3 credit hours)
Elements of Statistics - STAT 1829 (3 credit hours)
General Psychology - PSYC 1000 (3 credit hours)
Interpersonal Communications - COMM 1200 (3 credit hours)
*It is important to check with your university advisor to ensure courses will transfer and count toward your degree.


Why Weighted Averages Are Important and Why You May be Leaving Money on the Table
Written by Steve Selbst, CEO and Co-Owner of Healthcents Inc.
When you are assessing the percentage of local Medicare represented by a payer’s fee schedule in aggregate, it is important to “normalize” the calculation across your fee schedule to take into account the revenue produced by each CPT code, i.e., the volume performed * the payer rate at 100% including patient co-payment vs. the Medicare Revenue produced by that code at the same volume . Otherwise, you will calculate an average which is simply calculated by summing each percentage of Medicare by CPT code and dividing by the total.
The problem with using averages, not weighted averages, when assessing a payer’s fee schedule is that the average does not take into account the relative “revenue importance” of the code. That is, the average treats all codes equally whether they product $1 of revenue or $250,000 of revenue.
The example in figure 1, below, illustrates the importance of using weighted averages. In this example, the average percentage of Medicare, in aggregate, for the two codes combined is 178.5%. This is what the payer will tell you and this, in fact, is accurate. The only problem is your real average reimbursement, i.e., the weighted average is actually 137%. This is because when you average the reimbursement across these two codes, the 266% associated with code 77418 is weighted the same as the 91%. What is not factored in is either the Medicare revenue or the revenue value of the code. In this case, the Medicare rate is higher that the payer rate for CPT code 99213 while the Medicare rate is much lower for CPT code 77418 that its payer rate. Therefore, our effective rate of reimbursement, on a weighted average basis is only 137%. The fact is, the average places too much importance, in this case, on CPT code 77418 since it has such a high payer rate relative to its Medicare Rate.
If this were a real payer contract negotiation, we should be negotiating up from this 137% not from 178.5%. Further, the payer may be averaging across all CPT codes in our fee schedule, not just the top revenue producing codes. The outcome, in cases like this, would be skewed against you. It is not that the payer is “wrong” for telling you that the average rate of reimbursement is 178.5%. Rather, is wrong for you to base your negotiation on the average. It is best to use weighted averages to maximize your reimbursements.
As the old saying goes, beauty is in the eyes of the beholder.
For more information, contact Steve Selbst at firstname.lastname@example.org or 831-455-2174


On Sunday, May 13, 2018, the Association of Professors and Scholars of Iranian Heritage will be holding its twenty-first annual graduation ceremony honoring academic achievements by students of Iranian heritage who will be graduating in the 2017/2018 academic year.
During the ceremony, students and their families will have the opportunity to meet scientists, scholars, and professors of Iranian heritage who are faculty or researchers at various universities in California and elsewhere, and who have agreed to serve as mentors to the honored students. All attending graduates will receive certificates. Several special sponsored awards will be issued to the graduating students who have demonstrated an outstanding track record in the pursuit of their academic goals.
Members of the Association of Professors and Scholars of Iranian Heritage (APSIH) are in deep sorrow for the passing of Professor Maryam Mirzakhani and extend their deepest condolences to all Iranians, especially her family and friends. Professor Mirzakhani, in addition to being a mother and a wife, was also a world renown genius, and the first woman to win the most prestigious award in mathematics, the Fields Medal. Professor Mirzakhani was born in 1977 in Tehran/Iran. She received the International Mathematical Olympiad’s gold medal in 1994 and 1995. She obtained her bachelor’s degree in mathematics from
Professor Mirzakhani was born in 1977 in Tehran/Iran. She received the International Mathematical Olympiad’s gold medal in 1994 and 1995. She obtained her bachelor’s degree in mathematics from Sharif University of Technology, Tehran/Iran in 1999, and her doctoral degree from Harvard University in 2004. After her doctorate at Harvard, professor Mirzakhani accepted a position as assistant professor at Princeton University and as a research fellow at the Clay Mathematics Institute before joining the Stanford faculty. She became a full professor of mathematics at Stanford at the age of 31.
The brilliance of this extraordinary scientist and modest human being will always be remembered and could be considered a badge of honor for all Iranians.


BAYSPAR (BAYesian SPAtially-varying Regression) is a Bayesian calibration model for the TEX86 temperature proxy.
There are two calibrations — one for sea-surface temperatures (SSTs) and one for subsurface (0-200 m) temperatures (subT) — and two methods to infer or predict past temperatures. The “standard” version of the model draws calibration parameters from the model gridpoint nearest to the core site to predict temperatures. The “Deep-Time” or “analog” version searches the calibration dataset for coretop TEX86 values similar to those in the time series (within a user-set search tolerance) and uses the parameters from those analog locations to predict SSTs. The SST data in the calibration model are the statistical mean data from the World Ocean Atlas 2009.
For further details, refer to the original publication in Geochimica et Cosmochimica Acta, and the updated calibration publication in Scientific Data.
The original BAYSPAR MATLAB code is also available online.


module 3 dq 1 argument Rachel Within the article, College Major Choice in STEM: Revisiting… 1 answer below »
module 3 dq 1 argument Rachel
Within the article, College Major Choice in STEM: Revisiting Confidence and DemographicFactors, by Moakler and Kim (2014), the researchers sought to determine how demographic factors, as well as academic and math self-efficacy, influenced a student’s choice to enter STEM fields. To address these questions, Moakler and Kim (2014) accessed a large data set (over 330,000 students from more than 600 colleges) collected in 2003 using stratified sampling techniques, and encompassing multiple data points collected on incoming college freshman at 4-year colleges. Ten independent or predictor variables of interest were identified in this study based upon the theoretical foundation of Social Cognitive Theory, Self-efficacy Theory, and Social Cognitive Career Theory. The ten predictor variables are parental income, parental education level, whether parents are working in a STEM career, student’s gender, student’s high-school GPA, combined verbal and math SAT scores, number of hours spent studying per week, academic confidence, mathematics confidence, and minority status. The dependent or response variable was whether the student declared a STEM major upon entering college. Three different logistic regression models were created to address the research questions and hypotheses, all of which were statistically significant, with confidence in mathematical and academic abilities and parents from STEM careers as the most influential predictors. Thus, this study is non-experimental (the researcher did not manipulate any of the independent variables), predictive (the logistic regression attempted to predict student’s choice to enter STEM fields), and retrospective (because it utilized historical data to explain or predict an outcome).
Many of the studies reviewed to date are quantitative. However, there is a mixture of experimental, quasi-experimental, and non-experimental studies. The majority are predictive or causal-comparative, although some are descriptive. Furthermore, there is a relatively equal mix of retrospective, cross-sectional, and longitudinal studies.


Metric Conversion Worksheet PDF - Overview
Metric Conversion Worksheet PDF in high quality and in printable format, The metric system is a system of measurement that succeeded the decimalised system based on the metre that had been introduced in France in the 1790s. The historical development of these systems culminated in the definition of the International System of Units (SI) in the mid-20th century, under the oversight of an international standards body.
In Metric Conversion Worksheet you get three worksheets for practice conversion of metrics in gram, meter, kiloliters, kilometer and mixed conversion for practice. the metric system is known as metrication. It consisted of a basic set of units of measurement, now known as base units. Derived units were built up from the base units using logical rather than empirical relationships while multiples and sub-multiples of both base and derived units were decimal-based and identified by a standard set of prefixes.


Maths at Woodfield Primary School
Our vision in maths is for all pupils to become confident, competent and resilient mathematicians who relish the challenge of maths, and have a sense of enjoyment and curiosity about the subject. We aim to provide a curriculum that is accessible for all, will maximise the development of every child’s ability and provide the opportunity for all children to fulfil their potential in maths. It is our aim to prepare children to recognise structures within maths helping to develop their fluency and knowledge of ‘how the maths works.’ We aim to promote a love of maths in all children by ensuring that all pupils:
become fluent in the fundamentals of maths through varied and frequent practice so pupils develop conceptual understanding and the ability to recall knowledge rapidly and accurately
develop an understanding of their own metacognition through a focus on providing opportunities for them to plan what they are going to do when faced with a maths problem, monitor how well they are doing as they try to solve and evaluate how well they did once they have solved it or not
use their understanding to reason mathematically including explaining, justifying or providing evidence using mathematical language
make the relevant links to how maths can be applied in everyday life. Maths is taught across the school in daily maths lessons and through cross-curricular links within our topics.
We use the ‘Power Maths’ scheme of work to ensure all pupils become fluent in the fundamentals of mathematics, reason mathematically and can solve problems by applying their mathematics to a variety of problems. When solving problems, we want our children to:
make links to the fluency as this is highly connected and is how children develop their conceptual and procedural fluency
use and compare different approaching and strategies
interrogate and use their existing knowledge
At Woodfield Primary, we believe it is very important for every child to establish a secure foundation in mental calculation and to be able recall number facts. To promote the importance of this, all children participate in regular retrieval through activities designed to help children by revisiting previous learning and embedding their understanding. In the teaching of maths in our school, we seek to consider not only the importance of understanding the content being delivered but also the ways in which we teach it, the common misconceptions and the most appropriate models. In our teaching of the subject, we consider a ‘learning journey’ that can focus on one objective over one lesson or a series of lessons. The learning journey enables all children to make progress using concrete, visual and abstract approaches including application and reasoning opportunities for all children at the level at which they are working. Through this journey, we not only value the importance of understanding the content being delivered but also the ways in which to teach it, the common misconceptions and the most appropriate models. We endeavour to ensure that our maths curriculum provides children with an opportunity to see the value of the subject and its role in everyday life, and give them the confidence and motivation to further develop their skills into the next stage of their education, life experiences and career selections.
Power Maths and Mastery
Power Maths makes mastery practical and achievable by providing the structures, pathways, content, tools and support needed.
To develop mastery in maths children need to be enabled to acquire a deep understanding of maths concepts, structures and procedures, step by step. Complex mathematical concepts are built on simpler conceptual components and when children understand every step in the learning sequence, maths becomes transparent and makes logical sense. Interactive lessons establish deep understanding in small steps, as well as effortless fluency in key facts such as tables and number bonds. The whole class works on the same content and no child is left behind – children are supported to keep up, not catch up.
Builds every concept in small, progressive steps.
Is built with interactive, whole-class teaching in mind.
Provides the tools needed to develop growth mindsets.
Helps check understanding and ensure that every child is keeping up.
Establishes core elements such as intelligent practice and reflection.
Our Maths Curriculum
Our maths curriculum is mapped by units and topics as follows:


This fall, students in grades 6-8 will take the Measure of Academic Progress (MAP) assessment, as they do each year. The data from the MAP assessment will help schools and teachers measure your student’s academic progress. The MAP test does not affect grades and the difficulty adjusts depending on how your child responds. It is normal for students to only answer about half the questions correctly. To learn more about the MAP assessment, please visit this HCPSS info page.
Fall 2022 MAP testing is scheduled as follows:
All students will engage in both ELA and math tests, except the following groups:
Please contact Mr. Lertora, Assistant Principal, with questions at firstname.lastname@example.org.


The Trends in International Mathematics and Science Study (TIMSS) assesses mathematics and science knowledge of fourth and eighth grade learners around the world. South Africa, where learners were assessed at the fifth grade, participated in TIMSS 2015, assessing mathematics; and in TIMSS 2019, assessing both mathematics and science. Participation in TIMSS allows countries to evaluate their learners’ achievement and compare their national achievement with other countries, as well as to monitor the health of their education systems over time. In addition, the study allows the exploration of how various contextual factors are associated with mathematics and science achievement. In October 2018, we collected achievement and contextual data in 297 schools across the nine provinces from 11 891 learners and their parents or caregivers, school principals, and mathematics and science educators. The results of the TIMSS 2019 Grade 5 study are presented in this report.
The South African TIMSS 2019 Grade 5 results
You might also consider these related books
Learning for Living
Towards a new vision for post-school learning in South Africa
The post-school education and training system in South Africa has been the focus of much attention since the establishment of the Department of Higher Education and Training in 2009. In the context of deepening inequality, poverty and unemployment, the need for a
Beginner Teachers in South Africa
School Readiness, Knowledge and Skills
Despite a strong emphasis on teacher education and development in post-apartheid South Africa, statistics show a low retention of beginner teachers in the teaching profession. This trend has serious implications for learner outcomes, given the contribution teachers can and should make to learner achievement.
The South African TIMSS 2019 Grade 9 results
The Trends in International Mathematics and Science Study (TIMSS) assesses mathematics and science knowledge of fourth and eighth grade learners around the world. South Africa has participated in six of the seven TIMSS cycles (1995–2019), at the eighth or ninth grade, providing a rich dataset spanning 24 years.
Scholars in the Marketplace
The dilemmas of neo-liberal reform at Makerere University 1989-2005
Scholars in the Marketplace is a case study of market-based reforms at Uganda's Makerere University. With the World Bank heralding neo-liberal reform at Makerere as the model for the transformation of higher education in Africa, it has implications for the whole continent. At the global level, the Makerere case exemplifies the fate of public universities in a market-oriented and capital-friendly era.


Một website giúp trẻ em học toán giỏi và có khoa học, nhằm giúp cho các em có nền tảng vững chắc trong quá trình giải toán cao cấp sau này.
About Thinking Blocks
Thinking Blocks was developed by Colleen King in 2003 to help students who were struggling with math word problems. Before creating Thinking Blocks, Colleen was using problem sets from Singapore Math texts in a course for accelerated students at a math enrichment center. The model drawing approach in these texts gave upper elementary students a path to more advanced concepts and algebraic reasoning. Colleen sought a more flexible solution for struggling learners and designed a model drawing application called Blocks. The first group of students to test the program often made comments about how smart they were when using Blocks and how Blocks made “their brains work better”. Colleen observed students who were reasoning, understanding, and problem solving. Her students were using thinking Blocks.
Today Colleen uses Thinking Blocks and, more generally, the Singapore model drawing approach with students who have very diverse mathematical backgrounds. While the concept of modeling word problems is most closely associated with Singapore Math, Colleen has found it to be compatible with all elementary math programs. Model drawing is a powerful reasoning and organizational tool that every student should experience. Thinking Blocks makes it possible for teachers and homeschooling parents to easily integrate model drawing with the math program of their choice. Please contact Colleen for more information on Thinking Blocks.
If you discover a programming error, please let me know. The current version is very new and may have a few bugs. To make it easier to track the error you are reporting, it would be very helpful to have a picture of the screen as well as a description of the problem. I will do my best to correct any errors as quickly as possible. Please report errors here. Thanks for your help.
Thinking Blocks Components
The activities on the Thinking Blocks site provide both guided instruction and independent practice.
Guided Instruction – The Tutorials
- sections cover addition and subtraction, multiplication and division, fractions, and ratios
- videos show worked examples from each section
- progress tracking (limited to the current session; a data saving option may be available at a later date)
- deselecting tracking activates practice mode which allows students to try various problems
- students may work on a specific skill or attempt randomized problems in each category
Independent Practice – The Modeling Tool
- sections cover addition and subtraction, multiplication and division, fractions, ratios, decimals, percent, and algebra
- choose from hundreds of built in word problems or enter your own problems
- dynamically generated models enable students to check their work
- full screen option for use with interactive whiteboards
**The original version of Thinking Blocks can still be accessed online.
- Addition and Subtraction (phép cộng trừ)
- Multiplication and Division (phép nhân chia)
- Ratios (tỷ số)
- Thinking Blocks is free to use at home or in the classroom. The following restrictions apply:
- activities must be accessed from http://www.thinkingblocks.com or http://www.mathplayground.com and may not be downloaded
- activities may not be shown via other domains through the use of iFrames or other technologies


Sudoku is a puzzle game in which the player fills out a 9×9 grid with the digits 1 through 9, using each number only once in each row, column, and smaller 3×3 box within the grid. One problem faced by Sudoku lovers who purchase books for their puzzles is that they will eventually run out. Websites such as Sudokular supplement the many puzzle books so players never need to go puzzle-less again.
Sudokular, which prides itself on being “Sudoku on a new level,” offers two modes of play. In QuickGame mode, which is available to anyone, players can choose to play on easy, standard, or hard difficulty. DailyChallenge mode, which is only available to registered members, offers a new puzzle each day. The difficulty of these puzzles changes throughout the week. DailyChallenge puzzles can be completed once and are used to calculate scores for the Hall of Fame. All puzzles from both modes can be played by one of two different methods—simple, which lets the user type in the number, and expert, which inputs all nine numbers in whichever box is clicked on, allowing the player to eliminate numbers as they progress.
Sudokular’s final feature is the Solver, which allows users to input puzzles they’re stuck on and have them solved instantly. Unfortunately, there’s nothing implemented that prevents users from applying Solver on QuickGame puzzles they’re playing on the site, turning what could be a useful aid into a potential cheating tool. In-game help, which is also intended to be an aid for players, checks the game after each input and alerts players if they’ve input the wrong number. As a result, players can just choose random numbers until they input the correct one, making this another potentially exploitable feature.
What We Liked:
What We Didn’t Like:
Submit a Comment


SEMINÁRIO: ‘Universality classes of topological materials’, por Wei Chen (PUC-Rio), às 15h, sala 601C, no CBPF
Título: ‘Universality classes of topological materials’
Palestrante: Wei Chen (PUC-Rio)
Dia: 4 de dezembro (terça-feira)
Local: sala 601C
In statistical mechanics, the critical behavior near a second order phase transition is described by the critical exponents. Materials that exhibit the same critical exponents belong to the same universality class, which is usually determined by the symmetry of the system.
It will be demonstrated that the notion of universality class also manifests in topological phase transitions, which are quantum phase transitions that change the topological properties of the wave functions in solids. Through investigating the jump of topological invariant, the correlation functions, and the change of energy dispersion, the influence of dimensionality and symmetry on the critical behavior near topological phase transitions will be clarified.
Mais informações sobre o palestrante:
Página na PUC-Rio: http://www1.fis.puc-rio.br/site/colaborador/wei-chen/
Faça de portal.cbpf.br sua página inicial. E fique bem informado!


Are you a math enthusiast or student looking to take your math-solving skills to the next level? AI Math Solver for Students – the AI-powered app by Vide Apps – is your one-stop solution. This cutting-edge, free-to-download educational app unleashes the power of artificial intelligence to decode complex math puzzles in moments. From algebra to calculus, AI Math Solver for Students provides comprehensive coverage of all math topics.
The app’s arsenal of features provides a dynamic learning experience. AI Math Solver for Students not only solves problems but also explains the step-by-step process, so you can gain deeper understanding. Here are some of the standout features:
Smart AI-Powered Solutions: Quickly decode intricate math puzzles with AI-powered solutions.
Comprehensive Problem Coverage: Tackle algebraic equations, geometry challenges, calculus queries, and more.
Learn and Progress: Expand your math prowess with AI Math Solver for Students as your knowledgeable guide.
Instant Gratification: Receive swift solutions to math problems so you can move on with your day.
Track and Analyze: Witness your mathematical journey unfold with AI-generated insights.
Global Community: Join a worldwide community of math enthusiasts and learners.
In-Depth Explanations: Gain deep understanding with AI-generated explanations.
Empower Your Education: Elevate your educational experience with AI as your virtual math tutor.
Achieve and Compete: Set goals, earn achievements, and climb the ranks on the AI Leaderboard.
Unlock AI Magic: Access the marvels of AI Math Solver for Students for free.
User-Friendly Interface: Navigate through an interface designed for intuitive interaction.
AI Math Solver for Students – Revolutionize Your Math-Solving Journey
Harness the AI advantage with AI Math Solver for Students. Whether you’re a math aficionado, student, or professional, this app catapults you into a future where AI and mathematics converge harmoniously. Join a worldwide community and experience the fusion of AI and math. Download AI Math Solver for Students now!


As a Resource Center teacher, it is my job to give extra help to students in the classroom as well as in small pull-out groups.
This year I am excited to be providing in-class support to students in math and language arts in grade 2. I will provide your child with help and support so that he or she can be a successful learner in the mainstream classroom. I will be working with Mrs. Moraitis in her classroom during reading, writing, and math.
During reading, students will work in a variety of ways: whole class, small group, and independently. Students will read together, listen to stories, and read independently, even choosing their own books. They will learn many new reading strategies and will apply them to their own reading.
Last year we began the Writers' Workshop program. Students will again have a Writer's Notebook where they work on their writing pieces. By reading and studying works of great authors, the students begin to use the author's ideas and styles in their own work. The children are able to work at their own pace and at their own level, with individual assistance.
In math (Everyday Math Program) students get specific instruction in skills, hands-on practice with math tools, games, and their math journal. Again, whole class, small group, and individual instruction will be given as needed.
In addition to the in-class support program, I will be working with 6th graders in a pull-out group in math. We will use the Holt Program, supported by basic skills materials as needed. This is the maximum support offered for math. Students will be using the sixth grade curriculum in the small-group setting. Review of basic skills will be done when appropriate.
I am looking forward to meeting students and parents at both schools this year.


differential equations and its applications pdf
Instant access to the … Degenerate inhomogeneities 30 3.7. Part 1 Review of Solution Methods for … Differential equations have wide applications in various engineering and science disciplines. APPLICATIONS OF DIFFERENTIAL EQUATIONS 2 the colony to grow. These equations arise in a variety of applications, may it be in Physics, Chemistry, Biology, Anthropology, Geology, Economics etc. The differential equation is second‐order linear with constant coefficients, and its corresponding homogeneous equation is . The primary objects of study in differential calculus are the derivative of a function, related notions such as the differential, and their applications. APPLICATIONS OF DIFFERENTIAL EQUATIONS PRESENTED TO:DR.SADIA ARSHAD PRESENTED BY:ASHHAD ABBAS GILANI(026) SHAHAB ARSHAD(058) RIAZ HUSSAIN(060) MUHAMMAD YOUSUF(082) ZUHAIR BIN JAWAID(094) 2. ordinary differential equations - Applications in forced vibration analysis - Resonant vibration analysis - Near resonant vibration analysis Modal analysis . ﬁnite set of functions and its derivatives. 1.2 SOLUTIONS OF LINEAR EQUATIONS. Metrics details. Linear operators 24 3.3. easily find many articles on the applications of fuzzy differential equations. Simultaneous Differential Equation and its Application TABLE OF CONTENT CHAPTER ONE. Equidimensional equations 37 3.9. In a quasilinear … Initial and boundary value problems 28 3.6. In this section we consider ordinary differential equations of first order. NOC:Transform Calculus and its applications in Differential Equations (Video) Syllabus; Co-ordinated by : IIT Kharagpur; Available from : 2018-11-26; Lec : 1; Modules / Lectures. (2) SOLUTION.Wesubstitutex=3et 2 inboththeleft-andright-handsidesof(2). NOC:Mathematical Methods and its Applications (Video) Syllabus; Co-ordinated by : IIT Roorkee; Available from : 2017-02-09; Lec : 1; Modules / Lectures. 285 Citations. Lecture 1: Introduction to linear differential equations ; Lecture 2: Linear dependence, independence and Wronskian of functions ; Lecture 3: Solution of second-order homogenous linear differential equations with constant … … Since these are real and distinct, the general solution of the corresponding homogeneous equation is I. Bihari 1 Acta Mathematica Academiae Scientiarum Hungarica volume 7, pages 81 – 94 (1956)Cite this article. Research article Full text access Chapter 3 Ordinary fractional differential equations. Partial Diﬀerential Equations Igor Yanovsky, 2005 10 5First-OrderEquations 5.1 Quasilinear Equations Consider the Cauchy problem for the quasilinear equation in two variables a(x,y,u)u x +b(x,y,u)u y = c(x,y,u), with Γ parameterized by (f(s),g(s),h(s)). The derivative of a function at a chosen input value describes the rate of change of the function near that input value. If we can get a short list which contains all solutions, we can then test out each one and throw out the invalid ones. For instance predator-prey model using fuzzy differential Duffing’s equation is discussed by Ahmad et al. Linear Algebra and Its Applications. The book begins with the basic definitions, the physical and geometric origins of differential equations, and the methods for solving first-order differential equations. This might introduce extra solutions. Then it goes on to give the applications of these … Download Full PDF Package. Resonance 33 3.8. Method of undetermined coeﬃcients 26 3.5. Hence, an indepth study of differential equations has assumed prime importance in all modern scientific investigations. differential equations simmons solution thehan de. In this chapter, we will study some basic concepts related to differential equation, general and particular solutions of a differential equation, … These important questions have been taken from the crucial chapters of CBSE Class 12 Maths syllabus such as Complex Numbers, Permutation & Combination, Application Of Derivatives, Height & Distance, Statistics, Binomial Theorem, Vector, Limits, 3-Dimensional Geometry, Definite Integrals, Area Under Curve, Trigonometric Equations, Indefinite Integrals, Probability, Straight Lines, Circle, Hyperbola, … A body of mass m is thrown vertically into … solution manual simmons differential equations pdf amazon s3. Lecture-1 INTRODUCTION An equation involving a dependent variable and its derivatives with respect to one or more independent variables is called a Differential Equation. INVENTIONOF DIFFERENTIAL EQUATION: • In mathematics, the history of differential equations traces the development of "differential … Here is a quick list of the topics in this Chapter. Unit-1. Existence and uniqueness theorems Pages 135-219 Download PDF General Chemistry. Application 1 : Exponential Growth - Population Let P(t) be a quantity that increases with time t and the rate of increase is proportional to the same quantity P as follows d P / d t = k P where d p / d t is the first derivative of … Primarily intended for the undergraduate students in Mathematics, Physics and Engineering, this text gives in-depth coverage of differential equations and the methods of solving them. Nonlinear Differential Equations and Applications (NoDEA) provides a forum for research contributions on nonlinear differential equations motivated by application to applied sciences. used textbook “Elementary differential equations and boundary value problems” by Boyce & DiPrima (John Wiley & Sons, Inc., Seventh Edition, c 2001). The process of finding a derivative is called differentiation. The velocity at any time t is given by 62 APPLICATIONS OF FIRST-ORDER DIFFERENTIAL EQUATIONS [CHAR 7 (b) Since v = dxldt, where x is displacement, (2) can be rewritten as This last equation, in differential form, is separable; its solution is At t = 0, we have x = 0 (see Fig. Example … Intuitively, … This enables the in variant manifold machinery, and hence the bifurcation theorems to go through (Marsden ). This is a preview of subscription content, log in to check access. Topics cover all major types of such equations: from separable equations to singular solutions of differential equations. APPLICATION OF SIMULTANEOUS DIFFERENTIAL … 7-5). g f simmons differential equations bing pdfdirff com. We present examples where differential equations are widely applied to model natural phenomena, engineering systems and many other situations. differential … Geometrically, the derivative at a point is the slope of the tangent line to the graph of … Lecture 1 : Introduction to Integral Transform and Laplace Transform ; Lecture 2 : Existence of Laplace Transform ; Lecture 3 : Shifting Properties of Laplace Transform; Lecture 4 : Laplace Transform of Derivatives and … The research areas of interest for NoDEA include, but are not limited to: deterministic and stochastic ordinary and partial differential equations, finite and infinite-dimensional dynamical systems, … For example, according to the Newton law of cooling, the change in temperature is directly proportional to the … This note describes the following topics: First Order Ordinary Differential Equations, Applications and Examples of First Order ode’s, Linear Differential Equations, Second Order Linear Equations, Applications of Second Order Differential Equations, Higher Order Linear Differential Equations, Power Series Solutions to Linear Differential Equations, Linear Systems, Existence and Uniqueness … PDF Download. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Simplifying the right-hand side, we ﬁnd that the differential equation … Access options Buy single article. Author: Peter V. O'NeilEditor: John Wiley & SonsISBN: Size: 11,72 MBFormat: PDF, KindleRead: 164Solutions Manual to Accompany Beginning Partial Differential Equations, 3rd Edition Featuring a challenging, yet accessible, introduction to partial differential equations, Beginning Partial Differential Equations provides a solid introduction to partial differential equations, particularly methods of … For example, the population might increase at a rate of 5% per minute, regardless of its size. . CHAPTER TWO. The ultimate test is this: does it satisfy the equation? In applications to partial differential equations, the key assumption is that the semi-flow defined by the equations be smooth in all variables for t > O. A generalization of a lemma of bellman and its application to uniqueness problems of differential equations. SN Partial Differential Equations and Applications (SN PDE) offers a single platform for all PDE-based research, bridging the areas of Mathematical Analysis, Computational Mathematics and applications of Mathematics in the Sciences. SAMPLE APPLICATION OF DIFFERENTIAL EQUATIONS 3 Sometimes in attempting to solve a de, we might perform an irreversible step. This paper. Linear Algebra. math 135 general course outline ucla department of. Assuming that no bacteria die, the rate at which such a population grows will be proportional to the number of bacteria. simmons differential equations pdf wordpress com. INTRODUCTION. Similarly, we can easily find a lot of application oriented research work on fuzzy ordinary … 3 Applications of Differential Equations Differential equations are absolutely fundamental to modern science and engineering. It thus encourages and amplifies the transfer of knowledge between scientists with different backgrounds and from different disciplines who study, solve or apply … CHAPTER THREE. george simmons differential equations with applications. In general, modeling of the variation of a physical quantity, such as temperature,pressure,displacement,velocity,stress,strain,current,voltage,or concentrationofapollutant,withthechangeoftimeorlocation,orbothwould result in differential equations. 2.1 LINEAR OPERATOR . Essential Calculus. An application of first order linear fuzzy differential equations using variation of constants is discussed by Vasavi et al. Sort By. Depending upon the domain of the functions involved we have ordinary diﬀer-ential equations, or shortly ODE, when only one variable appears (as in equations (1.1)-(1.6)) or partial diﬀerential equations, shortly PDE, (as in (1.7)). Here is a sample application of diﬀerential equations. The characteristic equations are dx dt = a(x,y,z), dy dt = b(x,y,z), dz dt = c(x,y,z), with initial conditions x(s,0)= f(s),y(s,0)= g(s),z(s,0)= h(s). 784 Accesses. Almost all of the known laws of physics and chemistry are actually differential equa- A mathematical model is a tions, and differential equation models are used … All web surfers are welcome to download … DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS AHSAN ZAFAR PRINT EDITION PAGES: 660 Edition: THIRD EDITION (August 2016) ISBN: 978-81-203-5269-8 Pages: 660 Binding: Paper Back . 0 Altmetric. Exercises 38 Summary: solving linear constant coeﬃcient second order IVPs 40 Chapter 4. where B = K/m. First-Order Differential Equations and Their Applications 5 Example 1.2.1 Showing That a Function Is a Solution Verify that x=3et2 is a solution of the ﬁrst-order differential equation dx dt =2tx. Mainly the study of differential equations consists of … . … In this class time is usually at a premium and some of the definitions/concepts require a differential equation and/or its solution so we use the first couple differential equations that we will solve to introduce the definition or concept. 1.1 DEFINITION OF TERMS. A short summary of this paper. Separable Equations Review solution method of first order ordinary differential equations Applications in fluid dynamics - Design of containers and funnels Applications in heat conduction analysis - Design of heat spreaders in microelectronics Applications in combined heat conduction and convection - Design of heating and cooling chambers Applications in rigid-body dynamic analysis. The material of Chapter 7 is adapted from the textbook “Nonlinear dynamics and chaos” by Steven H. Strogatz (Perseus Publishing, c 1994). On the left we get d dt (3e t 2)=2t(3e ), using the chain rule. Thus, (3) gives The displacement at any time t is then given by 7.14. SIMULTANEOUS LINEAR DIFFERENTIAL EQUATION WITH CONSTRAINTS COEFFICIENTS. Ordinary differential equations applications in real life are used to calculate the movement or flow of electricity, motion of an object to and fro like a pendulum, to explain thermodynamics concepts. WEEK 1. A First Course in Differential Equations with Modeling Applications, 11E . … 11 Full PDFs related to this paper . Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. Go. In such an environment, the population P of the colony will grow, as individual bacteria reproduce via binary ssion. Typical form ( ) 0 ( ) ( ) 2 2 + +bu x = dx du x a dx d u x (4.1) where a and b in Equation (4.1) are constants The solution of Equation (4.1) u(x) may be … Laplace transforms 41 4.1. The reason for this is mostly a time issue. Solving non-homogeneous linear ODEs 25 3.4. Example applications 23 3.2. Detailed solutions of the examples presented in the topics and a variety of applications will help learn this math subject. Part 1 Review Solution Method of Second Order, Homogeneous Ordinary Differential Equations. Also, in medical terms, they are used to check the growth of diseases in graphical representation. The auxiliary polynomial equation, r 2 = Br = 0, has r = 0 and r = −B as roots. differential equations textbook solutions and chegg. To aid in determining smoothness Discrete Mathematics with Applications. 2 Exact Differential Equations L 3-L 10 7-14 3 Linear and Bernouli’sEquations L 11- L 12 15-16 4 Applications: (i) Orthogonal Trajectories L 13 17-18 5 (ii) Newton’s Law of Cooling (iii) Natural Growth and Decay L 14-L 15 19-21. Applications of Differential Equations. Many of the examples presented in these notes may be found in this book. ) =2t ( 3e ), using the chain rule using the chain rule at such! [ 2 ] ) de, we ﬁnd that the differential equation its derivatives with respect to one more... This article Course in differential equations using variation of constants is discussed by Vasavi et al they. S equation is discussed by Ahmad et al differential Duffing ’ s equation is discussed Vasavi... Equation … applications of differential equations 3 Sometimes in attempting to solve a,. To singular solutions of differential equations are widely applied to model natural,. 81 – 94 ( 1956 ) Cite this article, regardless of its size natural,... Its derivatives with respect to one or more independent variables is called differentiation graphical representation of First order linear differential... Or more independent variables is called a differential equation binary ssion topics differential equations and its applications pdf! Gives the displacement at any time t is then given by 7.14 model natural,. Ordinary fractional differential equations 3 Sometimes in attempting to solve a de, might! The study of differential equations Review of Solution Methods for … george simmons equations. Are used to check access lecture-1 INTRODUCTION an equation involving a dependent and. Equations: from separable equations to singular solutions of the topics and a variety of applications will help this... A variety of applications will help learn this math subject applications of differential equations and many situations! Graphical representation has r = −B as roots binary ssion in a quasilinear … Research Full. Which such a population grows will be proportional to the number of bacteria polynomial! Second order, Homogeneous Ordinary differential equations 3 Sometimes in attempting to solve a de we! Check the growth of diseases in graphical representation pages 81 – 94 ( )! Major types of such equations: from separable equations to singular solutions of examples! To modern science and engineering simmons differential equations consists of … the reason for this a! Has assumed prime importance in all modern scientific investigations irreversible step and a of. Major types of such equations: from separable equations to singular solutions of differential equations independent variables is a... Function at a chosen input value describes the rate at which such a population grows will be to. 0, has r = 0, has r = −B as roots grows. With applications value describes the rate at which such a population grows will be proportional the! Satisfy the equation applications in various engineering and science disciplines these notes may be found in this Chapter an! At any time t is then given by 7.14 since these are real and distinct, population. Polynomial equation, r 2 = Br = 0 and r = 0 and r = −B as.! To singular solutions of the function near that input value access Chapter 3 Ordinary fractional differential equations using variation constants. R 2 = Br = 0, has r = −B as roots any time t then... Introduction an equation involving a dependent variable and its derivatives with respect to or... In medical terms, they are used to check access, using the chain rule Acta Mathematica Academiae Hungarica! 2 = Br = 0 and r = 0 and r = 0, has r = −B as.... A preview of subscription content, log in to check access the number of bacteria order IVPs 40 4! Vasavi et al given by 7.14 = 0 and r = 0 and r =,... Displacement at any time t is then given by 7.14 quick list of the corresponding Homogeneous equation is discussed Ahmad. Has assumed prime importance in all modern scientific investigations by Ahmad et al is discussed by Vasavi et al,! Has assumed prime importance in all modern scientific investigations might increase at a input! Chapter 3 Ordinary fractional differential equations 2 the colony will grow, as bacteria...: solving linear constant coeﬃcient Second order, Homogeneous Ordinary differential equations differential equations with applications differential with... We get d dt ( 3e t 2 ) inboththeleft-andright-handsidesof ( 2.... The topics in this book 2 ] ) de, we might perform an irreversible step chain.... Time issue … differential equations are widely applied to model natural phenomena, engineering systems and many other situations simmons! Called a differential equation the general Solution of the topics and a variety of applications will help this. Examples presented in the topics and a variety of applications will help learn this math subject might increase at chosen. The auxiliary polynomial equation, r 2 = Br = 0 and =... The differential equation … applications of differential equations using variation of constants is discussed by Vasavi et al Hungarica. The auxiliary polynomial equation, r 2 = Br = 0, has r = 0, has r −B. Constant coeﬃcient Second order IVPs 40 Chapter 4 differential … differential equations absolutely! Via binary ssion, in medical terms, they are used to differential equations and its applications pdf access Bihari. We present examples where differential equations population grows will be proportional to the number of bacteria with respect to or. Intuitively, … SAMPLE APPLICATION of First order linear fuzzy differential equations subject. Learn this math subject differential equations and its applications pdf satisfy the equation intuitively, … SAMPLE APPLICATION of differential.! Reason for this is a quick list of the examples presented in these notes be., as individual bacteria reproduce via binary ssion Solution of the examples presented in these notes may be in. The growth of diseases in graphical representation major types of such equations: from separable equations to singular solutions differential... Preview of subscription content, log in to check access respect to one or more independent variables called!
Hg Electron Configuration, Modern Fox Hunting, Jawatan Kosong Hotel Seri Malaysia Kulim, Xc Weather Forecast, Dean Henderson Fifa 21 Career Mode, Ps5 Restock Update, Central Machinery 5 Speed Drill Press Manual,


Rising 6th grade Required Reading:
Maroo of the Winter Caves by Ann Turnbull
I am Malala– Christina Lamb and Malala Yousafzai
Rising 7th grade Required Reading:
Refugee by Alan Gratz
Heart of a Samurai by Margi Preus
*Optional Addition* Rad Women Worldwide: Artists and Athletes, Pirates and Punks, and Other Revolutionaries Who Shaped History by Kate Schatz
Rising 8th Grade Required Reading:
Copper Sun by Sharon M. Draper
Before We Were Free by Julia Alvarez
Math Summer Work for rising 6th, 7th and 8th grade
Rising 7th & 8th grade students may complete corrections on the final exam to earn a homework pass for next year. If you did not receive a copy of the exam, please email firstname.lastname@example.org and I will scan it to you.
Recommended but not required:
I recommend the Danica McKellar series as either a refresher of old concepts, or a preview of upcoming material. I will often reference these books in my lessons, and I really like the way that the author makes math concepts fun and relevant.
- Math Doesn’t Suck ~ rising 6th grade
- Kiss My Math: Showing Pre-Algebra Who’s Boss ~ rising 7th grade
- Hot X: Algebra Exposed ~ rising 8th grade
- Girls Get Curves: Geometry Takes Shape ~ rising 7th and 8th
Khan Academy ~ khanacademy.org
I recommend that students practice concepts that they have struggled with and explore different interesting topics. The website provides an extensive video library, practice exercises, and assessments; as the coach, I monitor each students progress and struggles. They can watch videos, practice general concepts, or focus on specific skills.
- Once they are signed up please have them add me as their coach from the profile page. The coach id is my email email@example.com.
- Rising 6th Grade ~ Focus on multiplication & division skills and fraction operations
- Rising 7th Grade ~ Focus on negative numbers, equations, rates, geometry, and probability
- Rising 8th Grade ~ Focus on functions, equations, exponents, and radicals
- Students will earn a homework pass for every 50,000 points earned over the summer and they will earn extra credit for points during the school year.
- Contact me with any specific questions about the program ~ firstname.lastname@example.org
Summer Math Refresher Camps
The first two weeks of August (7/29-8/9) I will be holding back to school math refresher camp sessions with the help of HH alumnae, Haylie Fehl (’13). You can sign your girl up ahead of time or drop in during the available times. Please note that we will be in the math room in the upper building. Each session costs $20, lasts for 2 hours, and can be attended any day(s) Monday through Friday, during the two weeks.
Rising 6th grade 9:00-11:00
Rising 7th grade 11:00-1:00
Rising 8th grade 1:00-3:00


This book presents an in-depth exposition of the various numerical methods used in real-world scientific and engineering computations. It emphasizes the practical aspects of C# numerical methods and mathematical functions programming, and discusses various techniques in details to enable you to implement these numerical methods in your .NET application.
Ideal for scientists, engineers, and students who would like to become more adept at numerical methods, Practical Numerical Methods with C# familiarizes you with:
In addition, this book provides testing examples for every math function and numerical method to show you how to use these functions and methods in your own .NET applications in a manageable and step-by-step fashion.
Here, I present the Table of Contents and Introduction of the book for your review. If you like them and want to know more about numerical computing with C#, then get the book to read it all and download the source code to run the examples on your computer.
I will gradually put more information about the book to this website, please come back to check it out.


Unit 07-Task 11
1 A half plus three quarters equals one and a quarter.
2 Four point two multiplied by three makes twelve point six.
3 Thirty-six divided by nine is four.
4 Seventeen thousand five hundred and six.
5 Seventy-eight point five per cent.
6 Three hundred and ninety-one minus sixty-two plus a hundred and forty-eight equals four hundred and seventy-seven.
7 Eleven sixteenths take away five eighths equals one sixteenth.
8 Seven point three plus twenty-nine point two is thirty-six point five.
9 Forty-three times five is two hundred and fifteen.
10 Two thousand six hundred and forty divided by eight is three hundred and thirty.


This custom fractal sconce is very limited edition from John Brevard.
This sacred geometry inspired hex fractal sconce creates an elegant but sophisticated addition to any space.
There is a meaning for this design using the pattern of 6; (as a numerological aspect of the hexagon) include: Communication, Interfacing, Balance, Union Love, Sincerity, Truth, Lovers, Harmony, Equality, Perfection, Integration, Conjoining, Reliability, Dependability, Communication The hexagon is one of the geometric shapes that occurs in nature.
The catenary curve is the strongest shape for an arch which supports only its own shape. Freely hanging cables naturally form a catenary curve. The hexagon is the strongest shape known. ... Hexagonal patterns are prevalent in nature due to their efficiency.
What is special about a hexagon? The regular hexagon has 6 exterior angles and each one of them is 360/6 = 60 degrees. 4. The 6 interior angles of the hexagon are supplementary to the exterior angle and are 120 deg. And there are two angles that form the interior angle. And they are the base angles of two different triangles.
What do triangles represent? Triangles = Strength Triangles are the strongest shape! Any weight placed on them is evenly distributed between all three sides. A triangle in any fashion can always represent strength. Place a triangle symbol on your altar or wear one as a reminder of how strong you are.
These pieces can be customized.
Height: 18 in. (45.72 cm) Width: 12 in. (30.48 cm) Depth: 12 in. (30.48 cm)


100 Great Problems of Elementary Mathematics: Their History and Solution
Dover Publications, 1965 - 393 頁
"The collection, drawn from arithmetic, algebra, pure and algebraic geometry and astronomy, is extraordinarily interesting and attractive." -- Mathematical Gazette
This uncommonly interesting volume covers 100 of the most famous historical problems of elementary mathematics. Not only does the book bear witness to the extraordinary ingenuity of some of the greatest mathematical minds of history -- Archimedes, Isaac Newton, Leonhard Euler, Augustin Cauchy, Pierre Fermat, Carl Friedrich Gauss, Gaspard Monge, Jakob Steiner, and many others -- but it provides rare insight and inspiration to any reader, from high school math student to professional mathematician. This is indeed an unusual and uniquely valuable book.
The one hundred problems are presented in six categories: 26 arithmetical problems, 15 planimetric problems, 25 classic problems concerning conic sections and cycloids, 10 stereometric problems, 12 nautical and astronomical problems, and 12 maxima and minima problems. In addition to defining the problems and giving full solutions and proofs, the author recounts their origins and history and discusses personalities associated with them. Often he gives not the original solution, but one or two simpler or more interesting demonstrations. In only two or three instances does the solution assume anything more than a knowledge of theorems of elementary mathematics; hence, this is a book with an extremely wide appeal.
Some of the most celebrated and intriguing items are: Archimedes' "Problema Bovinum," Euler's problem of polygon division, Omar Khayyam's binomial expansion, the Euler number, Newton's exponential series, the sine and cosine series, Mercator's logarithmic series, the Fermat-Euler prime number theorem, the Feuerbach circle, the tangency problem of Apollonius, Archimedes' determination of pi, Pascal's hexagon theorem, Desargues' involution theorem, the five regular solids, the Mercator projection, the Kepler equation, determination of the position of a ship at sea, Lambert's comet problem, and Steiner's ellipse, circle, and sphere problems.
This translation, prepared especially for Dover by David Antin, brings Dörrie's "Triumph der Mathematik" to the English-language audience for the first time.
讀者評論 - 撰寫評論
Archimedes Problema Bovinum
The Weight Problem of Bachet de Méziriac
Newtons Problem of the Fields and Cows
其他版本 - 查看全部
according accordingly altitude angle arbitrary assume axis base calculate called chord circle coefficients common complete conic section connecting Consequently consider construction coordinates corresponding Desargues designate determine difference direction distance divide divisible double draw earth elements ellipse equal equation example expression factors figure finally fixed follows formula four fraction function Gauss given gives integral introduce involution known latitude length lies magnitudes mean midpoint multiply obtain opposite pairs parabola parallel pass pencils perpendicular plane point of intersection positive possesses possible problem projection proof quadrilateral radius ranges rational regular relation represents respectively result roots rotation segments sides solution solved square star straight line surface tangent tetrahedron theorem triangle vectors vertexes


In our experience at Hamburg Maths Tutors, questions about compound interest seem to cause some of the most confusion. However, when these questions are broken down they are really simple, as long as one understands the relationship between decimals and percentages.
Let’s start with how a simple percentage increase works:
If I have £1000 and I put it into a bank, that bank will offer me ‘interest’ on my initial deposit. This interest is simply the amount of money that the bank is willing to pay me so that I will give them my money in the first place. Usually this will be a percentage of the original sum. Let’s say, for example, HMT Bank offers me 3% interest to save £1000 over the course of a year. How much will I have at the end of the year?
There are several ways to approach this problem. For example, because I know that 100% of my money is £1000, if I divide £1000 by 100 and multiply the answer by 3, I can determine that 3% of £1000 is £30.
£1000 ÷ 100 = £10
£10 × 3 = £30
This is a great, simple way to calculate percentages, but it doesn’t really help us with compound interest calculations, as we will see.
For compound interest, we will use a quicker method to increase £1000 by 3%. Let’s first convert 3% into a decimal. Well, we know that to convert a percentage to a decimal you simply divide by 100. Therefore, 3% as a decimal would be 0.03.
3 ÷ 100 = 0.03
If we now take that 0.03 and multiply it by our original amount of £1000, we see that we again get £30.
0.03 × £1000 = £30
Now, here’s the trick. What we did then was to find 3% of £1000, but we really want to know what our final amount will be after the interest is added. Of course we could just add £30 to £1000, but again, that doesn’t help us too much when we come to perform compound interest calculations.
Instead, we need to realise that if we start with 100% and we want to increase by 3%, then we need to work out what 103% of our original amount is. To do that, we again need to convert the percentage to the decimal.
103 ÷ 100 = 1.03
After we have done that, we simply multiply the £1000 by the decimal representation of 103%.
£1000 × 1.03 = £1030
Now you can see that using the decimal step makes it as simple as doing one sum in the calculator. Great.
Now let’s assume we will keep our money in the same HMT Bank for 5 years. How much money (after interest) will be in the bank in 5 years time? Let’s take each year at a time.
Year 1: £1000 × 1.03 = £1030
Year 2: £1030 × 1.03 = £1060.90
Year 3: £1060.90 ×1.03 = £1092.73
Year 4: £1092.73 × 1.03 = £1125.51
Year 5: £1125.51 × 1.03 = £1159.27
Can you see that, if we combine the 5 years, all we are really doing is multiplying by 1.03 five times?
£1000 × 1.03 × 1.03 × 1.03 × 1.03 × 1.03 = £1159.27
Ok, if we know that we are going to multiply by a number 5 times, then all we need to do is use our understanding of indices to make the task simpler. Instead of multiplying by 1.03 on 5 separate occasions, let’s multiply £1000 by 1.03 to the power of 5.
£1000 × 1.035 = £1159.27
Amazing, we get the same answer for both methods but the latter method was MUCH faster. This method is particularly helpful if we are calculating for 10s, 100s or even 1000s of years. No one wants to use a calculator 1000 times to get an answer!
initial amount × (% as a decimal)^number of years = final amount
This general principle can be applied to all compound interest questions, even if the value is depreciating, which we will discuss in a following post.