Welcome,you are looking at books for reading, the calculus combined, you will able to read or download in pdf or epub books and notice some of author may have lock the live reading for some of country. It is best to study it before studying any of the calculus lectures to understand where it is on the map. This text book on differential calculus has been specially written according to the latest syllabus of ugc unified syllabus as per choice based credit system for b. Piskunov this text is designed as a course of mathematics for higher technical schools. Differential and integral calculus n free ebook download as pdf file. Remark the above equalities are called identities because they are valid for all real. Differential calculus by gorakh prasad pdf download. Check our section of free ebooks and guides on differential calculus now. Ncert book class 12 maths pdf free download part 1. Calculus i or needing a refresher in some of the early topics in calculus. Continuity of a function have been made as short as possible. Accompanying the pdf file of this book is a set of mathematica.
This book is based on an honors course in advanced calculus that we gave in the. Is book ka naam hai rd sharma objective mathematics pdf. This leads us into the study of relationships and change, the starting point for mathematical analysis and the calculus which are needed in all. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. The more you see of the big picture the better you learn. Arihant differential calculus book differential calculus by. Vertical shift and amplitude, frequency and period, phase shift, examples, phase shift of half a period, equivalent sine and cosine models. Click download or read online button to get exercises from the calculus for beginners book now. The definite integral as a function of its integration bounds. Exercises from the calculus for beginners download ebook. Calculus ii trigonometric formulas basic identities the functions cos. Consider a mapping n from a neighborhood of zero in v to a neighborhood of zero in v if n0 0 and if n is continuous at 0, then we can say, intuitively, that nv approaches 0 in v.
Download calculus by james stewart free download pdf. The positive response to the publication of blantons english translations of eulers introduction to analysis of the infinite confirmed the relevance of this 240 year old work and encouraged blanton to translate eulers foundations of differential calculus as well. Books in the series are available free of chargefrom the websites. An accessible introduction to the fundamentals of calculus needed to solve current problems in engineering and the physical sciences. This book is a revised and expanded version of the lecture notes for basic calculus and other similar courses o ered by the department of mathematics, university of hong kong, from the. Differential equations department of mathematics, hkust. Differential calculus by shanti narayan pdf free download. Key angle formulas 37 angle addition, double angle, half angle formulas 38 examples 41 power reducing formulas 41 product. Trigonometric functions integral d c pandey optics and modern physics 0. To proceed with this booklet you will need to be familiar with the concept of the slope also called the gradient of a straight line. Using newtons law, we model a mass m free falling under gravity but with air.
Free differential calculus books download ebooks online. Number and symbols and in book 2 space and deals with the mathematics we need in describing the relationshipsamong the quantities we measure in physics and the physical sciences in general. Limits, continuity and differentiation of real functions of one real variable, differentiation and sketching graphs using analysis. This book on precalculus with geometry and trigonometry should be treated as simply an enhanced version of our book on college algebra. For help with downloading a wikipedia page as a pdf, see help. This book was compiled by dr john shakeshaft and typeset originally by fergus gallagher, and currently by. Introduction to hyperbolic functions pdf 20 download 85e802781a the, book,includes,some,exercises,and,examples,from,elementary, calculus. The derivative, rules for finding derivatives, transcendental functions, curve sketching, applications of the derivative, integration, techniques of integration, applications of integration, sequences and series. Differential calculus, an outgrowth of the problems concerned with slope of curved lines and the areas enclosed by them has developed so much that texts are required which may lead the students directly to the heart of the subject and prepare them for challenges of the field. That is integration, and it is the goal of integral calculus. See more ideas about precalculus, trigonometry and calculus. A copy of the license is included in the section entitled gnu free documentation license. Annual temperature cycles, trigonometric functions, trigonometric models. Which book is better, amit m agarwal or objective sharma.
Friends aaj ham aap sabhi ke liye bahut hi important book lekar aaye hain. Foundations of differential calculus book download pdf edition. Download introduction to integral calculus pdf book free from introduction to integral calculus pdf. It has two major branches, differential calculus and integral calculus.
Pdf produced by some word processors for output purposes only. Basic topological, metric and banach space notions, the riemann integral and ordinary differential equations, lebesbgue integration theory, fubinis theorem, approximation theorems and convolutions, hilbert spaces and spectral theory of compact operators, synthesis of integral and differential calculus, miracle properties of banach spaces. Differentiation and integration of these functions is covered in chapters 35. Textbook instructors manual study guide download resource materials. Ifyoursyllabus includes chapter 10 linear systems of differential equations, your students should have some preparation inlinear algebra. Ye book dhanpat rai publication ke dwara publish ki gayi hai aur rd sharma sir.
A text book of differential calculus with numerous worked out examples. Trigonometric identities and equations 43 verifying identities. Rahul guptas answer to which book is the best for calculus from beginner to advanced ov. Click on cengage maths pdf buttons to download pdf in a single click. Pdf calculus by james stewart book pdf free download. Each book in this series provides explanations of the various topics in the course and a substantial number of problems for the student to try. Trigonometry handbook table of contents page description chapter 4. If youre looking for a free download links of matlab differential and integral calculus pdf, epub, docx and torrent then this site is not for you. You may need to revise this concept before continuing. Download matlab differential and integral calculus pdf ebook. Ive tried to make these notes as self contained as possible and so all the information needed to read through them is either from an algebra or trig class or contained in other sections of the. Most of the topics that appear here have already been discussed in the algebra book and often the text here is a verbatim copy of the text in the other book.
One of the goals of this book is to prepare you for a course in calculus by directing your attention away from particular values of a function to a study of the function as an object in itself. The identity function 10,1 of 0,1 is a local inverse of f, and. Calculus handbook table of contents schaums outlines other useful books an important student resource for any high school math student is a schaums outline. This book emphasis on systematic presentation and explanation of basic abstract concepts of differential calculus. Textbook calculus online textbook mit opencourseware. Published in 1991 by wellesleycambridge press, the book is a useful resource for educators and selflearners alike. The book is intended for anyone who, having passed through an ordinary course of school mathematics, wishes to apply himself to the study of mathematics or its applications to science and engineering, no matter whether he is a student of a university or technical college, a teacher, or an engineer. Jan 30, 2020 download introduction to integral calculus pdf book free from introduction to integral calculus pdf.
Trigonometry is an important introduction to calculus, where one stud ies what mathematicians call analytic properties of functions. All web surfers are welcome to download these notes, watch the youtube videos. Understanding basic calculus graduate school of mathematics. Calculus for the life sciences ii lecture notes trigonometric functions pdf 271p this note explains the following topics. Fundamental rules for differentiation, tangents and normals, asymptotes, curvature, envelopes, curve tracing, properties of special curves, successive differentiation, rolles theorem and taylors theorem, maxima and minima, indeterminate forms. We need your support, kindly share this web page with other friends. The material of chapter 7 is adapted from the textbook nonlinear dynamics and chaos by steven h. Elementary differential equations with boundary value problems is written for students in science, engineering,and mathematics whohave completed calculus throughpartialdifferentiation. Therefore it need a free signup process to obtain the book. Before starting our discussion of calculus and differential equations, it is. The right way to begin a calculus book is with calculus. Cengage maths concepts have been explained from scratch believing that students have no prior knowledge of the same. Differential and integral calculus lecture notes pdf 143p. This site is like a library, use search box in the widget to get ebook that you want.
We use the equals sign in mathematics to mean logical identity. This is a wikipedia book, a collection of wikipedia articles that can be easily saved, imported by an external electronic rendering service, and ordered as a printed book. Calculus, originally called infinitesimal calculus or the calculus of infinitesimals, is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. All web surfers are welcome to download these notes, watch the youtube videos, and to use the notes and videos freely for teaching and. Introduction to integral calculus pdf download free ebooks. These books contain exercises and tutorials to improve your practical skills, at all levels. Get chapterwise cbse class 12 maths ncert books pdf online. It contains many worked examples that illustrate the theoretical material and serve as models for solving problems. A trigonometric identity is an equation involving trigonometric functions that is. With calculus, eighth edition, stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. This book has been designed to meet the requirements of undergraduate students of ba and bsc courses. James stewarts calculus texts are worldwide bestsellers for a reason. Download our amit m agarwal differential calculus pdf ebooks for free and learn more about amit m agarwal differential calculus pdf.35 1479 1020 348 715 93 1487 78 1177 105 480 830 179 118 1372 935 1168 504 1498 676 535 302 575 1176 1084 900 332 1368 144 289 428 3 283 234 752 1190 877 328 762 1426


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GMAT Algebra: Things to Remember
If you’re just beginning your GMAT prep and it’s been a while since you’ve studied math at a high school level or above, you’re likely very intimidated. Just reading a practice algebra problem is overwhelming and makes your head spin. The good news is, you’ll probably catch on in no time. But it’s important to approach your studies in a way that gets you to your goal: competence and GMAT success. Here are some things to remember as you prepare for the GMAT algebra questions.
The Difference Between Memorizing and Knowing
There are certain formulas you should know to help you move quickly and easily through the Quant section of the GMAT. However, simply memorizing the formulas without fully grasping their applications won’t help you at all. In fact, that approach will probably hinder you, since you will be cluttering up your mental space with less-than-useful information. Your first step in acing GMAT algebra is to really know algebra. In this sense, there isn’t a shortcut. Now, you need to know what sorts of questions are on the exam and study specifically to those concepts. But be sure you know the material, including both how and when to use it, instead of just knowing it for recitation.
Practice Problems Come After Drilling Concepts, Not Before
If your knees buckle when you see a GMAT algebra practice problem, you're not alone. Algebra often seems complicated and confusing when it’s not a regular part of your life. Instead of beginning with practice problems and trying to work them out without full understanding, it’s better to prepare by learning the concepts in another context first. Why not tackle the practice problems right away? Well, while there are many different algebra problems on the GMAT, they all fit pretty neatly into categories. Once you learn the categories and how to solve them, you will be to able to read the practice questions without even a hint of mystery. Instead, you will simply categorize the problem by what formulas or functions you need, and then get to work.
Begin at the End
If you face a GMAT algebra problem that threatens to get the best of you, try taking what you know of the answer and working backward. For instance, if the problem wants you to find a decimal but you are given fractions, conversion is a good first step. Or if you are working with squared numbers, establish first whether you are finding the difference or the sum, write your final formula, and then begin plugging in your numbers. Remember also not to be tripped up by language. “Positive number” does not necessarily mean a positive integer. You may not always need all of the information you are given, so stick to what you know and don’t doubt yourself if you end up not using all you have.
In the end, GMAT algebra is straightforward and conquerable. Unlike the verbal section, there isn’t much room for interpretation. Math is math. However, if you are unfamiliar with the concepts it can feel impossible to master. Take it one concept at a time, and don’t anticipate tackling practice questions until the concepts make sense to you and come to you easily. Also, work the problems backward when you get stuck the other way. If you are looking for the best and most successful way to learn GMAT algebra concepts, check out EMPOWERgmat’s online GMAT course. We guarantee that you will see results.


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Milos Stehlik is Facets’ creative director and a renowned film expert. Here he discusses the many appearances of mathematicians in cinema, and explores how their struggles and genius is shown.
Years ago, I had a friend who thought the magic number was six. If he saw a house number for example, and if it was 2049, he would do some figures. “Two and four is six, six and nine is 15, one and five is six, this house is a lucky number.” I am not sure if this was something he invented or learned, or if it really makes any logical sense under any circumstances, but hey, whatever. It made him happy.
Recently, on NPR, I learned that Czechs believed that the magic number is eight. Being Czech, ironically, it was the first time I heard this. Nevertheless, I guess it’s parenthetically supported by Czech history.
For example it was 1618 when the Czechs threw out Hapsburg emissaries from the windows of Prague castle. The Hapsburg emissaries survived by landing on a heap of garbage and thus started the Thirty Years War which ended in 300 years of Hapsburg domination. Please, don’t ask me why throwing the bad guys out the window is always referred to as “defenestration.”
There are other eights in Czech history of course. In 1918 Czechoslovakia became an independent republic. 1948, the Communists took over Czechoslovakia. 1968, the Prague Spring and Soviet invasion. And, slightly off, 1989, there’s an eight still in there, the Velvet Revolution, lead to the fall of Communist rule.
So Much for History
In an interesting article in The Guardian, writers and mathematicians argued that mathematicians are too serious to be depicted accurately on film . A mathematician’s endless hours scribbling formulas on a sheet of paper is just too boring or undramatic. Today we have many typical ways of showing mathematical brilliance like the white marker on a window. But it’s just not true.
Peter Greenaway is certainly a filmmaker who is always fascinated by numbers. Not only does Greenaway express his fascination in the aptly titled Drowning By Numbers which came out in the very lucky year 1988, but even in his films like The Pillow Book (1996). The Pillow Book is a really brilliant film based on the famous 10th century diaries of a Japanese courtesan, where language barriers are crossed by complex patterns of cryptic symbols.
Many films have been able to give life to mathematicians. The elation of mathematical discovery is well rendered on screen. Take The Imitation Game (2014), even with all its inaccuracies and shameful handling of Alan Turing’s sexuality, when the genius who broke the Nazi codes and helped win World War II finally cracks it, it’s certainly exciting.
The transcendental character of mathematics was taken up by Darren Aronofsky. His bold, debut feature, Pi (1998) is the bizarre story of a lonely mathematician who might have unlocked the formula which represents a key to the universe. And there are other films which give life to previously unknown number wizards. But more recently films have taken up the personal struggles of real mathematicians.
Hidden Figures (2016) proved a really honest film which deserved much greater exposure. The film told the story of the human computers at NASA, the African American women who faced segregation and racism, even as they provided the calculations to help U.S. be competitive in the space race.
The Man Who Knew Infinity (2016) similarly, follows the huge obstacles which faced Indian mathematics protégé Srinivasa Ramanujan. He made his way through the over-privileged, patronizing, racist, and dismissive world of British academia at Oxford.
Then there are what are today becoming classics such as Good Will Hunting (1997), A Beautiful Mind (2001), Moneyball (2011), Fermat’s Room (2007), and A Brief History of Time (1991), Errol Morris’s cerebral documentary about Stephen Hawking are all well known around different circles of film lovers.
In their own right, Enigma (2001), The Theory of Everything (2014) a fictionalized Hawking’s life, and Stand and Deliver (1988), depict a real love of mathematics in people of all backgrounds. In the Marleen Gorris film Antonia’s Line (1995) one of the five generations of women in the film is a child prodigy who grows up to be a mathematician.
This is just scratching the surface, but it’s obvious that math is in everything. A Pixar scientist, Tony DeRose, believes that film could not exist without math from the numbers that create a pixel that forms the digital image, to understanding how light bounces around in an environment. DeRose advanced this view in a 2013 TED Talk .
And of course, math is also present in so-called Hollywood accounting. That’s where the real creativity kicks in.


Bio: My current research subject is memory-augmented recurrent neural networks. I am generally interested in the statistical learning theory and the math behind various learning algorithms. Before this, I did a master's in computer science at the university of Montreal and Mila under the supervision of Prof. Guillaume Rabusseau . My master's research was focused on the application of tensor network methods in machine learning and the study of the complexity of the corresponding models. Here you can find my thesis.
Website template adopted from Michael Niemeyer.


In fact, reading a tape measure has little to do with mathematical calculations. It's more about combining your basic understanding of fractions (which you did learn in fifth grade, right?) with an understanding of how the hash-marks work on today's tape measures.
Begin: Learn How to Read a Tape Measure in 9 Steps
Common Tape Measure Features
- Designated "Foot" Markers: Most tape measures tell you where each foot mark is. This way, you don't need to calculate 36 inches as equaling 3 feet. It simply tells you.
- The Hook End: Ever wondered why the metal hook at the end of your tape measure slides around? Could it be a bad riveting job in the factory? The hook slides back and forth so that you can measure either by butting the tape against an object or by hooking it on the edge of the object. The sliding motion ensures that you get an accurate measurement in either direction.
- Hash Marks For Studs/Joists: This tape measure has red hash-marks at every sixteen inches. It's a convenient way to mark off wall studs or joists, which typically are sixteen inches apart.
- Feet vs. Inch Designations: At the one foot mark, the numbering splits off in two directions. On the top, it gives you measurements in feet (as in, 3 feet, 2 inches). On the bottom, it gives you measurements purely in inches (38 inches). Either way, it's the same measurement, just a different way of expressing it.


JackpotGraphs.com began tracking the Jackpotjoy progressives on January 5, 2007. Jackpotjoy has 0 progressive games to choose from.
In the table below, green numbers appear when the current jackpot is higher than the average hit size. Purple numbers appear when the time since the last hit is greater than the average hit interval. Games with green or purple numbers have higher scores, and games with higher scores may be more likely to pay out sooner than games with lower scores. Tip: The table below is sortable. Click the column headings to sort the information.
Notes about the detailed jackpot data in the table above:
1. The Hits figure in the table above refers to the number of times the jackpot has been hit in the last 365 days.
2. The Total Paid Out figure shows the total amount that the jackpot has paid out in the last 365 days.
3. The Average Hit Size is the average size of the jackpot when hit, based on hits in the last 365 days. If a jackpot has been hit less than 5 times in the last 365 days, the average hit size is calculated using the previous 5 hits, regardless of when they occurred.
4. The Average Hit Interval is the average time between hits in the last 365 days. If a jackpot has been hit less than 5 times in the last 365 days, the average hit interval is calculated using the previous 5 hits, regardless of when they occurred. If less than 3 hits have been recorded, "n/a" appears.
5. The Score is calculated as follows: [ ( Current Jackpot / Average Hit Size ) + ( Last Hit / Avg. Hit Interval ) ] x 100.


A n n o u n c e m e n t
Manitoba K-12 Website Updates: Curriculum Development and Implementation
•The new My Learning at Home website is now available.
This website allows grade 5 to 8 students to find videos, animations and interactive
websites to help them understand or deepen their understanding of many concepts
in mathematics and science.
•The new My Child in School website is now available.
This website provided information for parents of students from
Kindergarten to Grade 12.


It’s finals time this week, but the blog rolls on! I was rather happy with how this lecture came out. In these slides and this audio, I talk about how to decide which statistical test you might run based on your data. This mostly deals with methods in which you are comparing some number of averages.
Then, we discuss a task many students are tackling this week: How to fill out the formula sheet your professor gives you for a PsychStats 2 final exam. How to remember which is the repeated measures t-test vs the independent groups ANOVA? My advice: Don’t memorize, learn to differentiate. Listen for more.


Finding a technical co-founder for a new startup is notoriously hard. After struggling with it for a while, I decided to figure out exactly how hard it is.
To do that I simply estimated how many needles there are in the co-founder haystack. The answer is discouraging but intuitively accurate: there are only about two thousand potential co-founders in the entire United States.
How hard? Let’s use Fermi Estimation
In Fermi estimation, we wave our hands and spin minimal knowledge into approximate truth. The goal is to quicky get an estimate that’s close enough to correct for our purposes. For a link-bait blog post, “close enough” is not very close at all. And that’s close enough®.
We do Fermi estimation by breaking down our final quantity (number of viable co-founders) into a chain of constituent quantities. I model the problem like this:
Viable co-founders =
(% of programmers who are 2 standard deviations above the mean)
* (total number of programmers in the world)
* (% of world population living in the USA)
* (% of Americans in a startup approriate age-range)
* (% of programmers who know a given technology)
Now we basically just guess each of those quantities (with a Google sense check if possible)
% of programmers who are 2 standard deviations above the mean = 2.5% (by math)
total number of programmers = 25 million (number of StackOverflow accounts)
% of world programmers in the USA = 5% (US pop as % of world pop)
% of Americans in a startup approriate age-range = 20%
% of programmers who know a given technology = 30% (guess)
Now run the numbers:
Okay, so that all adds up to:
2.5% * 25,000,000 * 5% * 20% * 30% = drum roll 1875
So that’s it! Out of a US population of 319 million, a mere ~2000 people are viable co-founders. That’s just 1 in 1.5 million people.
Dang that’s hard.
Then factor in the fact that the vast majority of great programmers are already employed (or 3 years into starting their own succesful company), and that only a small % will have your same interests and a compatible personality. It becomes easy to see why so many startups deliver bad technology or are torn apart by co-founder conflicts.
P.S. If you’re looking for an opportunity and love music, metadata, and HCIR, shoot me an email at george j london on gmail. Or if you just like Fermi estimations, follow me on Twitter


We also have a whole school approach to developing the numeracy skills of all of the students at BHNPS. We focus on developing mathematical understanding, fluency, logical reasoning, analytical thought and problem solving skills.
We aim to equip students with the mathematical strategies necessary for their school life and real world contexts and appreciate that mathematics is an essential and relevant part of life. In each level, in some form we covers aspects of number, space, measurement, chance and data, working mathematically and structure.
We believe learning numeracy is more effective when it is interesting, enjoyable and challenging. Our approach to numeracy aims to further develop a student’s confidence, knowledge, understanding, appreciation, curiosity and most of all a love of mathematics.
We use digital technologies and tools to support mathematical exploration and consolidation of skills; A vast array of concrete resources to assist with hands on learning for Prep to Grade 6 and access to online mathematics programs and resources e.g. Mathletics and Big Brainz.


A group of 10 students from year 11 visited Balliol College, one of the 38 colleges that make up Oxford University on Tuesday 13th November. For once the M42 was kind (on the way there at least!) so after many games of “Uno” on the way, we arrived at the college bang on time. The morning was spent touring the college and having an introductory talk about Oxford and what it can offer. We then had lunch in the hall – with Miss Jordan very excited that she finally got to sit at the top table!
In the afternoon, a tutor from the college ran a Maths problem solving session with the students. The students were fantastic, getting straight down to trying to solve the problems, working collaboratively to do so. The tutor commented herself on how impressed she was by this and the willingness of the students to try and seek solutions themselves without asking for guidance on how to. One problem involved trying to predict how a computer would arrange a visual diagram of different numbers, based round knowledge of Prime factors. Having be shown what the computer did with numbers 1-59, the students were then challenged to predict the diagrams for 60, 101 and 1001. A second problem involved trying to organise the numbers 1 to 17 in a line so that each pair of adjacent numbers added up to a square number. From this the students were then challenged to think whether they could come up with a system for doing this if the initial numbers were extended.
Having exercised our brains, we then visited University college (the college linked to Staffordshire) so that students could compare the similarities and differences between different colleges, before having free time to get a drink/snack before the longer than expected (a less co-operative M42) journey home.
Mr Farrell (Head of Humanities)


Ms. LePree - Math 7 and Pre-Algebra
Hello! I'm Ms. Allison LePree and I am very excited to be here at ASK Academy with you this year! I have been teaching for 18 years, 16 of those in middle school math. I love teaching math and hope that you will love learning math this year with me! I'm a mom of one daughter, Brittany, and I also have two four-legged fur babies. I like to travel all around New Mexico and dream of going to Spain some day! I'm here to help you succeed, so PLEASE let me know what you need!


This article continues from the previous article, by continuing the trend into even larger numbers. These are Numbers that are rarely mentioned outside of tables of large figures cited in physics and astronomy ...
Next up ...
At this point it's getting difficult to keep track of all of those zeroes. One sextillion is rarely heard of, and not well known, but it is officially recognized and the legitimate continuation after quintillion. One Sextillion is 1 followed by 21 zeroes ( 7 groups of 3 ).
The earth has a mass of about 5.98 Sextillion metric tons ( 1 Metric Ton = 1000 kilograms ).
There are about 6 sextillion cups of water in all the oceans of the world
The volume of the earth is about 1.085 Sextillion cubic meters.
The distance between one end of the universe and the other may be about 87.9 sextillion miles !
Now another order of a thousand ...
One Septillion is 1 followed by 24 zeroes ( 8 groups of 3 zeroes ). A Septillion is a Trillion Trillions !
One liter of water contains about 33.4 Septillion water molecules.
The earth has a mass of about 5.98 Septillion kilograms.
One Octillion is 1 followed by 27 zeroes ( 9 groups of 3 zeroes ) . An octillion is a billion billion billions !! It's almost impossible to even comprehend that.
The earth has a mass of about 5.98 Octillion grams.
The mass of the sun is about 1.989 Octillion metric tons.
The volume of the sun is about 1.412 Octillion cubic meters
One Nonillion is 1 followed by 30 zeroes ( 10 groups of 3 zeroes ). A nonillion is a quadrillion quadrillions !? Or a million trillion trillions.
The mass of the sun is about 1.989 nonillion ( 1.989x10^30 ) kg
One Decillion is 1 followed by 33 zeroes ( 11 groups of 3 zeroes ).
The Area of the Milky Way galaxy is approximately 702 Decillion square kilometers.
The mass of the sun is about 1.989 decillion ( 1.989x10^33 ) grams
One Undecillion is 1 followed by 36 zeroes ( 12 groups of 3 zeroes ).
The volume of the M Supergiant Star , Betelguese , is roughly 1.21 undecillion cubic meters.
One Duodecillion is 1 followed by 39 zeroes ( 13 groups of 3 zeroes ).
The great lakes contain roughly 52.92 duodecillion water molecules !!
One tredecillion is 1 followed by 42 zeroes ( 14 groups of 3 zeroes ).
There are about 200 Tredecillion atoms contained in the entire atmosphere of earth
There is about 100 tredecillion grams of matter contained in the grand total of all the stars in the milky way galaxy.
One quattuordecillion is 1 followed by 45 zeroes ( 15 groups of 3 zeroes ), and yes that is the official name. quattuor means "four" in latin, and deci means "ten".
There are about 41.75 quattuordecillion water molecules in all the water on the earth.
One quindecillion is 1 followed by 48 zeroes ( 16 groups of 3 zeroes ). A quindecillion is equal to a trillion trillion trillion trillions !
The earth is composed of about 89 quindecillion molecules
One Sexdecillion is 1 followed by 51 zeroes ( 17 groups of 3 zeroes ).
The volume of the milky way galaxy is about a sexdecillion cubic miles
One Septendecillion is 1 followed by 54 zeroes ( 18 groups of 3 zeroes ).
The Volume of the Pleiades star cluster ( a near by star cluster within the milky way galaxy ) is roughly 226 Septendecillion cubic centimeters
One Octodecillion is 1 followed by 57 zeroes ( 19 groups of 3 zeroes ).
The Pleiades star cluster may contain roughly 800 Octodecillion hydrogen atoms
One Novemdecillion is 1 followed by 60 zeroes ( 20 groups of 3 zeroes ).
The Volume of the milky way galaxy is about 147 Novemdecillion cubic feet.
One Vigintillion is 1 followed by 63 zeroes ( 21 groups of 3 zeroes ). Currently it is the largest "official illion" that is part of a continuous nomenclature starting from million , billion , trillion , etc.
The volume of the sphere approximating the Virgo Super Cluster ( The super cluster in which we reside ) is roughly 3.54 Vigintillion cubic kilometers
ONE THOUSAND VIGINTILLION
A Thousand Vigintillion does not have a proper number name, there is no "illion name" for it. Scientists are perfectly comfortable using "scientific notation" and calling it simply "ten to the sixty sixth". The most common proposal for this number is naturally enough "unvigintillion", based on the trend established with decillion, undecillion, duodecillion, etc.
There are about a thousand vigintillion atoms in our galaxy
ONE MILLION VIGINTILLION
One million vigintillion is also known by number ethusiasts as "duovigintillion".
Note that by the time we reach numbers this big, it becomes very difficult to think of any example at all, not because numbers this big don't have physical representers, but simply because it is difficult to find an example that falls exactly in this range.
The Volume of the observable universe may be roughly a million vigintillion cubic miles
The Virgo Super cluster may contain close to 200 million vigintillion hydrogen atoms in it's 200 trillion stars
ONE BILLION VIGINTILLION
One Billion vigintillion, better known simply as "trevigintillion".
The volume of the virgo super cluster is roughly 3.54 billion vigintillion cubic meters.
The volume of the great wall Super structure ( a giant "filament" composed of galaxy clusters ) is roughly 1.9 billion vigintillion cubic meters
ONE TRILLION VIGINTILLION
One Trillion vigintillion, also called "quattuorvigintillion".
Unfortunately I was not able to come up with an example for this tremendous number, although there must certainly be a trillion vigintillion of something because this number is smaller than the lower bound for the number of sub-atomic particles in the observable universe. Let's just say that there is about a trillion vigintillion sub-atomic particles in 1/1000 of the volume of the observable universe.
ONE QUADRILLION VIGINTILLION
One Quadrillion vigintillion , also called "quinvigintillion".
It is estimated that the observable universe may contain roughly a quadrillion vigintillion sub-atomic particles
ONE QUINTILLION VIGINTILLION
One Quintillion vigintillion, also called "sexvigintillion".
The volume of the universe is roughly a quintillion vigintillion cubic feet
ONE SEXTILLION VIGINTILLION
One Sextillion vigintillion, also called "septenvigintillion".
The volume of the universe is roughly a sextillion vigintillion cubic inches
ONE SEPTILLION VIGINTILLION
One Septillion vigintillion, also called "octovigintillion".
The Volume of the universe is about 47 septillion vigintillion cubic millimeters.
ONE OCTILLION VIGINTILLION
Also called "novemvigintillion".
ONE NONILLION VIGINTILLION
Also called "trigintillion", from the latin word "triginta" for 30.
ONE DECILLION VIGINTILLION
Because of the tremendous scale of these numbers, it is no longer practical to make jumps of a 1000 fold. Instead I will now be making jumps of a billion fold ! Because of this certain "illions" here will have no entries.
One decillion vigintillion is also called "untrigintillion".
The Volume of the universe is 47 decillion vigintillion cubic micrometers.
A micrometer = 10^-6 meters. Microbes can be measured in micrometers.
ONE UNDECILLION VIGINTILLION
Also called "duotrigintillion".
ONE DUODECILLION VIGINTILLION
Also called "tretrigintillion".
ONE TREDECILLION VIGINTILLION
One tredecillion vigintillion is also called "quattuortrigintillion".
The volume of the universe is 47 tredecillion vigintillion cubic nanometers.
A nanometer = 10^-9 meters.
Note: Recall that a Googol = 10^100 . This means that the volume of the universe is
4,700,000 googol cubic nanometers. The Googol is often regarded as impractically large, an not representative of anything in reality. However when we consider the entirety of the known universe divided by the some of the smallest known units of space, we easily exceed the googol. This proves that numbers as big as a "googol" are not as impratical and meaningless as once thought.
ONE QUATTUORDECILLION VIGINTILLION
Also called "quintrigintillion".
ONE QUINDECILLION VIGINTILLION
Also called "sextrigintillion".
ONE SEXDECILLION VIGINTILLION
One sexdecillion vigintillion is also called "septentrigintillion".
The volume of the universe is 47 sexdecillion vigintillion cubic picometers.
A picometer = 10^-12 meters.
ONE SEPTENDECILLION VIGINTILLION
Also called "octotrigintillion".
ONE OCTODECILLION VIGINTILLION
Also called "novemtrigintillion".
ONE NOVEMDECILLION VIGINTILLION
Also called "quadragintillion" from the latin word "quadraginta" for 40.
The volume of the universe is 47 novemdecillion vigintillion cubic femtometers.
A femtometer = 10^-15 meters. It is said that the diameter of protons and neutrons is about 1 femtometer, and that this is also the range of the strong nuclear force.
ONE VIGINTILLION VIGINTILLION
Also called "unquadragintillion".
ONE THOUSAND VIGINTILLION VIGINTILLION
Also called "duoquadragintillion".
ONE MILLION VIGINTILLION VIGINTILLION
Also called "trequadragintillion".
The volume of the universe is 47 million vigintillion vigintillion cubic attometers.
An attometer = 10^-18 meters. It is said that the diameter of electrons and quarks is about 1 attometer.
ONE BILLION VIGINTILLION VIGINTILLION
Also called "quattuorquadragintillion".
ONE TRILLION VIGINTILLION VIGINTILLION
Also called "quinquadragintillion".
ONE QUADRILLION VIGINTILLION VIGINTILLION
Also called "sexquadragintillion".
The volume of the universe is 47 quadrillion vigintillion vigintillion cubic zeptometers.
A zepto meter = 10^-21 meters.
ONE QUINTILLION VIGINTILLION VIGINTILLION
Also called "septenquadragintillion".
ONE SEXTILLION VIGINTILLION VIGINTILLION
Also called "octoquadragintillion".
ONE SEPTILLION VIGINTILLION VIGINTILLION
Also called "novemquadragintillion".
The volume of the universe is 47 septillion vigintillion vigintillion cubic yoctometers.
A yoctometer = 10^-24 meters.
ONE OCTILLION VIGINTILLION VIGINTILLION
Also called "quinquagintillion" from the latin word "quinquaginta" meaning 50.
ONE NONILLION VIGINTILLION VIGINTILLION
Also called "unquinquagintillion".
ONE DECILLION VIGINTILLION VIGINTILLION
Also called "duoquinquagintillion".
The volume of the universe is 47 decillion vigintillion vigintillion cubic milli-yoctometers.
A milli-yoctometer = 10^-27 meters. Normally one is not allowed to combine prefixes, but in this case there is no prefix for 10^-27. We will learn more about this in the next chapter when we discuss SI prefixes.
ONE UNDECILLION VIGINTILLION VIGINTILLION
Also called "trequinquagintillion".
ONE DUODECILLION VIGINTILLION VIGINTILLION
Also called "quattuorquinquagintillion".
ONE TREDECILLION VIGINTILLION VIGINTILLION
Also called "quinquinquagintillion".
The volume of the universe is 47 tredecillion vigintillion vigintillion cubic micro-yoctometers.
A micro-yoctometer = 10^-30 meters.
ONE QUATTUORDECILLION VIGINTILLION VIGINTILLION
Also called "sexquinquagintillion".
ONE QUINDECILLION VIGINTILLION VIGINTILLION
Also called "septenquinquagintillion".
ONE SEXDECILLION VIGINTILLION VIGINTILLION
Also called "octoquinquagintillion".
The volume of the universe is 47 sexdecillion vigintillion vigintillion cubic nano-yoctometers.
A nano-yoctometer = 10^-33 meters.
ONE SEPTENDECILLION VIGINTILLION VIGINTILLION
Also called "novemquinquagintillion".
ONE OCTODECILLION VIGINTILLION VIGINTILLION
Also called "sexagintillion" from the latin word "sexaginta" meaning 60.
There is a theoretical "smallest unit of distance" that arrises in modern physics. It is the result of combining quantum mechanics with general relativity. In general relativity deals with the large scale features of our universe, while quantum mechanics deals with the small scale features.
In general relativity, gravity is reinterpreted as a force which distorts the fabric of space-time, and by doing so, effects the motion of neighboring objects. In otherwords, the theory says that the presense of matter distorts the local space-time.
In Quantum mechanics, what we can't observe is ultimately unknowable. It postulates that at the smallest scale the universe is random and chaotic, and is only governed by laws of statistics. As a by-product of this, it is said that on small scales, "virtual particle pairs" can spontanteously pop in and out of existence. Because these virtual particles are created and destroyed so rapidly, it is argued, that the conversation law of mass-energy is not broken. Another even weirder consequence of the theory is that as the scale gets smaller and smaller, more energy will pop in and out of existence in shorter time frames.
When we combine the 2 theories there is an interesting result. As we go down into smaller and smaller scales, eventually we encounter a scale where highly massive virtual pairs are created. Because of the huge amount of mass, general relativity says there will be a very huge local distruption in the space-time fabric. Eventually these distortions become so severe that the equations literally explode. This "bubbly space-time" is sometimes refered to as "quantum foam".
The result is that the continuity and consistency of space and time ceases to be meaningful. It is said that concepts such as "here" or "there", "past" and "future", get scrambled, so that there is no concept of sequence.
It is therefore impossible to measure distances smaller than this threshold. Hence, it becomes meaningful to talk of a "smallest possible distance that can be meaningfully measured". This minimum distance is called the "Planck Length", and it is approximately 10^-35 meters. So Now what if we take the entirety of the known universe and divide it by the smallest possible spatial unit ? ...
In this case we can say that the volume of the universe is 47 octodecillion vigintillion vigintillion cubic Plank lengths, that's 4.7 x 10^184 Pl^3 .
Note that this volume is computed by treating the universe as if it were the hyper-surface of a 4-dimensional sphere ( sometimes called the "glome" among the polychorists ). One can think of this "glome" as starting out as an infintesimal point at the big bang, and then expanding like a 4 dimensional balloon 4-space. In other words, this volume is only the volume of the universe 'now'. At an earlier time the volume would have been smaller, and in the far future it may be much larger still ! And notice the exponent, 184. Most people think numbers these large have no physical meaning, but what these estimates show is that they may very well represent tangable and measurable things !!
So that's it right ? We have reached the end of physical numbers ... not quite. Assuming the universe will continue to exist and expand the volume will increase with time. Cosmologists usually say the big bang occured somewhere around 15,000,000,000 years ago. What if we were to consider the universe a long long time from now ? ...
This page is now getting too large, so I will continue this discussion in a third part. Now we will consider the very limits of numbers that can have meaning in physics !!


Millennium Puzzle Model Kits are the perfect way for you to get your kids involved with math. This Millennium Puzzle Model Kit includes all the pieces needed to build a puzzle model of the famous Millennium from Yu Gi Oh!
Your children will love creating their Real Millennium puzzle.
There is no doubt that old anime used to help children develop their arithmetic and math skills. Who among us has not played Yu-Gi-Oh, but instead participated in national and international competitions
Yu Gi Oh Millennium puzzle will revive adults’ memory and strengthen children’s logic. Best gift for your kids when you make them watch anime.
You can also choose the Gold Sarcophagus to add to your collection


Engineering Roundabout in Jeddah
Al Handasa Square I sone of the distinguished landmarks in Jeddah City and is one of the largest road junctions. In the middle of this square there are giant geometrical tools like a compass, a protractor, a triangle and a ruler. These are among the largest geometrical tools in the world.
=> AL Handasa Square was constructed in 1986 A.D.
=> Its total land area is about 4.000 square meters.
=> The height of the compass is 35 meters.
=> It was recorded in the Guinness record for 1989-1990.
=> The total weight of AL Handasa Square is 66 tons.
=> The total cost is 1.5 million S.R.
=> Written on it the Qur’anic verse “He has taught man that which he knew not” was chosen to be written on the model ruler. (1) Surat AL-Alaq (v) (source)


That there is the Klein Bottle, first conceived of in 1882 by German mathematician Felix Klein. Klein’s “non-orientable surface,” as it’s called in the math community, is like a Möbius strip in that you cannot distinguish inside from outside; follow it with your eyes and you’ll see one turns into the other, which makes me very, very uncomfortable.
I’m told that the Klein Bottle is, in essence, two Möbius strips connected together. I’d like to start sketching that to work out how it goes together, but I can’t because I’m too stupid.
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Thanks for visiting Geometry for Beginners. This write-up goes back to the principle of finding an area, yet this moment the figure will certainly be a circle rather than a polygon. Terms we have utilized previously for discovering area - like base and also height - do not relate to circles, so brand-new terminology becomes necessary. Additionally, we need to recognize some concepts we have never run into before to understand the derivation of the formula.
Note: Some mathematicians do, in fact, take into consideration a circle to be a polygon - a polygon with a boundless variety of sides. The principle of "boundless variety of sides" originates from Calculus; however, a couple of psychological photos can aid Geometry students to recognize the basic idea. Obtain a paper if your capability to envision photos in your mind is as weak as mine. Currently, draw (either on paper or your psychological whiteboards) a triangle. With the triangular and also all the other numbers, try to make all the sides equal in size. Currently, relocate to the right of the triangular as well as draw a square of similar dimension. Move right once more, and attract a Pentagon. Then draw a hexagon and an octagon. This is usually sufficient figures to see the pattern that as the variety of sides boosts, the polygon becomes a growing number of circular.
In Calculus, we consider what the "result" would be if we can continue to enhance the variety of sides of a polygon for life. We call this result the from "restriction." For our circumstance, a polygon with a limitless number of sides would certainly have a circle as its limitation.
Along with comprehending this limitation idea, we likewise have to examine the significance of pi before we can recognize the formula for the area of a circle. Keep in mind that the unreasonable number pi is the proportion of the circumference of a circle (distance around) to its diameter (distance across with the facility). Additionally, keep in mind that area amounts the border of polygons as well as has two possible formulas: C = (pi) d or C = 2( pi) r. Currently, we prepare to find the area of circles.
We currently know that area is determined with squares; and, for rectangular shapes, those squares are easy to see as well as count. Unfortunately, squares do not match circles perfectly. To understand the area formula for circles, we need excellent mental picture abilities as well as a mutual understanding of the "limitation" concept discussed earlier in this write-up.
On your "paper" draw a circle with a diameter of 1 to 2 inches. Currently, split this circle into 4 equivalent parts by attracting an additional size vertical to the original size. You should currently be able to see 4 forms like items of pizza. Now, take those 4 pieces and fit them side-by-side however alternating punctuate and after that aim down. We now have a parallelogram-type number having two bumps or curves on both the top and lower as well as a rather high lean to the side.
Currently, we are posting likely to do the same type of limitation procedure we reviewed previously. Look back at your circle with 4 parts. Draw 2 even more sizes to divide each component in half. You ought to currently see 8 pie-shaped items that coincide "elevation" as before, but are a lot more narrow. Take these 8 pieces and fit them side-by-side, once more rotating point up and also point down. Once more, we have that parallelogram-type form, and now the lean to the side is decreased. Said in a different way, the sides are becoming more upright. On top of that, the top, as well as bottom currently, have four bumps or contours each. However the curves are flatter.
As we remain to split the circle into increasingly more pie items and continue suitable the assemble side by side as previously, the resulting number comes to be a rectangular shape because the sides come to be upright and also the contours on the leading and also bottom squash completely. The elevation of this resulting rectangular shape is the distance of the circle, r. The leading and bottom of the rectangle originated from the circumference. This indicates the base is one-half of the area, C.
The area of the circle is the same as the area of the rectangle. The rectangular shape area formula can. Thus, an adjustment from A = bh to A = (1/2C)( r). Keeping in mind the formula for circumference, we could change the area formula also further. A = (1/2C)( r) comes to be A = 1/2( 2( pi) r)( r). By simplifying the multiplication, the outcome is A = (pi) r ^ 2.
This circle area formula, A = (pi) r ^ 2, could be made use of to find the area if we know either the span or size of the circle; or we could find what the span or diameter should be for an offered area.
As an example: If the distance of a circle is five cm., find the area of the circle.
Option: A = (pi) r ^ 2 ends up being A = (pi) 5 ^ 2 or A = 25pi. The last type of the response will rely on the instructor, the circumstance, or the topic. Sometimes, we desire the response in regards to pi since this is the SPECIFIC response. However, we psychologically estimate for implying using 3 as the worth of pi. Thus, the circle has an exact area of 25pi sq. cm. Which is about 75 sq. centimeters. Other situations need a much more precise decimal value for the area, so we use the pi key on the calculator.
3 Final Cautions Concerning Circles:
1. Responses with pi are EXACT, while decimals are ESTIMATIONS.
2. Distance and also diameter are frequently confused. Making use of the wrong worth is very simple. THINK!
3. The circumference, as well as area solutions, are similar and also easy to puzzle. THINK before you begin servicing with a formula!
Write something about yourself. No need to be fancy, just an overview.


Douglas L. Corey
Dr. Corey's research compares mathematical instruction practices in the United States with those abroad. He also examines the relationship between a teachers mathematics knowledge and teaching effectiveness. Dr. Corey hopes to develop ways math teachers can improve their teaching.
Dr. Peterson researches ways that student teachers can optimize learning through teaching and student thinking instead of classroom management. Partially based on his observations of student teaching in Japan, Dr. Peterson and his colleagues have developed the concept of MOSTs (Mathematical Opportunities in Student Thinking). Dr. Peterson is currently chair of BYUs Mathematics Education Department.


Computes a weighted average of inputs. Used in the context of computing weighted averages of predictions.
Predictions are averaged using
weights (in order of appearance in the data) which are optimized using
nonlinear optimization from the package "nloptr" for a measure provided in
measure (defaults to
Learned weights can be obtained from
Using non-linear optimization is implemented in the SuperLearner R package.
For a more detailed analysis the reader is referred to LeDell (2015).
Note, that weights always sum to 1 by dividing through sum(weights) before weighting incoming features.
The parameters are the parameters inherited from
LearnerClassif, as well as:
Measure to optimize for.
Will be converted to a
Measure in case it is
"classif.ce", i.e. misclassification error for classification
"regr.mse", i.e. mean squared error for regression.
Optimizer used to find optimal thresholds.
character, converts to
opt. Initialized to
Nloptr hyperparameters are initialized to
xtol_rel = 1e-8,
algorithm = "NLOPT_LN_COBYLA"
and equal initial weights for each learner.
For more fine-grained control, it is recommended to supply a instantiated
LearnerClassifAvg$new(), id = "classif.avg")
LearnerRegrAvg$new(), id = "regr.avg")
LeDell, Erin (2015). Scalable Ensemble Learning and Computationally Efficient Variance Estimation. Ph.D. thesis, UC Berkeley.


The Definition, Formula, and Problem Example of the Slope-Intercept Form
That Passes Through (3 – One of the numerous forms used to represent a linear equation the one most frequently used is the slope intercept form. The formula for the slope-intercept in order to identify a line equation when that you have the straight line’s slope as well as the y-intercept, which is the coordinate of the point’s y-axis where the y-axis crosses the line. Learn more about this particular linear equation form below.
What Is The Slope Intercept Form?
There are three fundamental forms of linear equations, namely the standard slope-intercept, the point-slope, and the standard. Even though they can provide the same results , when used, you can extract the information line generated quicker by using the slope intercept form. As the name implies, this form makes use of the sloped line and the “steepness” of the line determines its significance.
This formula can be utilized to discover a straight line’s slope, the y-intercept or x-intercept in which case you can use a variety of formulas available. The line equation of this specific formula is y = mx + b. The slope of the straight line is signified with “m”, while its intersection with the y is symbolized by “b”. Every point on the straight line is represented by an (x, y). Note that in the y = mx + b equation formula, the “x” and the “y” need to remain variables.
An Example of Applied Slope Intercept Form in Problems
The real-world in the real world, the slope-intercept form is commonly used to represent how an item or problem evolves over the course of time. The value of the vertical axis is a representation of how the equation deals with the intensity of changes over the amount of time indicated through the horizontal axis (typically the time).
A basic example of the application of this formula is to discover how many people live in a certain area as the years go by. If the population of the area increases each year by a predetermined amount, the value of the horizontal axis will grow by one point as each year passes, and the value of the vertical axis is increased to represent the growing population according to the fixed amount.
You may also notice the beginning value of a particular problem. The starting point is the y’s value within the y’intercept. The Y-intercept represents the point where x is zero. In the case of a problem above the beginning value will be when the population reading begins or when time tracking starts along with the related changes.
This is the point in the population at which the population begins to be recorded for research. Let’s say that the researcher began to calculate or the measurement in the year 1995. The year 1995 would become”the “base” year, and the x=0 points will be observed in 1995. This means that the population in 1995 will be the “y-intercept.
Linear equations that use straight-line formulas are almost always solved this way. The beginning value is represented by the y-intercept, and the change rate is expressed through the slope. The primary complication of this form generally lies in the horizontal interpretation of the variable in particular when the variable is attributed to an exact year (or any type of unit). The first step to solve them is to ensure that you know the meaning of the variables.


You should learn algebra, and master it, if you want to be successful; algebra is essential. WeБve all heard the mythologies for not having to learn algebra from bored high school students and the New York Times. However, here is a look at a different set of myths concerning why you should learn algebra. You should study algebra because. math is inherently beautiful
You should study algebra because. it will help you develop critical thinking skills You should study algebra because. youБll use it directly on the job It doesnБt take long to figure out that these myths arenБt fully satisfying. Most students will inquire as to the purpose of learning algebra and the vast majority of them will be given an answer that does not provide purpose and context but rather underscores to the student that even БweБ (the parents, the educators, etc. ) donБt know why we teach algebra. Math is beautiful said few high school students ever.
IБm going to guess that the only people who say that math is beautiful are high school or college math teachers. Seriously, telling students that they should study algebra because itБs beautiful will only serve to further disillusion them with the very thing we want them to learn. Yes, math is beautiful but that isnБt why we should learn algebra. Critical thinking skills are a basic skillset that is developed in a variety of ways. Learning to read develops critical thinking skills. Reading challenging books develops critical thinking skills. Learning to БreadБ music and play an instrument develops critical thinking skills. Learning logic and rhetoric develops critical thinking skills. I think you are starting to get the picture. Learning algebra does have limited value in sharpening critical thinking skills but that is hardly a good enough answer to the studentБs question of Бwhy must I learn this?
Б For the final myth, letБs be honest; how many of us actually use algebra directly on the job? IБve spoken with carpenters who regularly use trigonometry and many who only use basic arithmetic and are successful carpenters. Most students who have even a vague idea of what industry they want to work in will already know if advanced algebra will be required in that line of work. There are some careers out there that rely on algebra everyday and if a student is interested in those careers, focusing on algebra is a must. But for everyone else, saying БyouБll use it at workБ, while occasionally true, is an easily spotted myth. 1. Speed: We can directly use algebra to solve problems more quickly and easily than we could do otherwise. For example, a simple algebraic equation can help you make a recipe smaller or when youБre doing home repairs. 2. A Building Block: Algebra can serve as a building block that we can use to learn more advanced math like statistics, calculus, etc. and learn more advanced subjects, like physics, chemistry, etc.
Experts say that members of the next generation could change jobs 30-40 times throughout their career, so you donБt know if you will need some of the algebra you learn or not. Learning algebra is a life skill beneficial for upward mobility. 3. So that we can understand and critically evaluate the math done by others such as reporters, political candidates, insurance salesmen, bank loan officers, etc. People will always use the skills they have to succeed and while you could succeed in some careers without understanding algebra, understanding algebra will make it easier to succeed. Algebra is an important life skill to have if you want to do things quicker, be able to transition easier from career to career, and avoid being taken advantage of by people who can БtwistБ the numbers in their favor.
Part three of a four part series on math. Part 1 Бб Part 2 Бб Part 3 Бб Part 4 Бб I highly recommend the book \”The Brain That Changes Itself\” by Dr. Norman Doidge. As with any skill, there are multiple ways to meet your goal. You don\’t have to lift weights to be strong, but it is one way to get there. Math is a very good way to grow your brain and your mental discipline. My intent was to make a case for why it is important and give a potentially new perspective to make it more appealing to learn; not necessarily looking to convince or coerce. Algebra becomes fun once you get the hang of it, like solving puzzles. It clearly has multiple purposes and is a step toward so many other skills in life. It wasn\’t my best subject in school, but I have since learned to really enjoy teaching it and appreciate how it has translated into other ares of my life. Hope you will give it a chance to do the same for you.


For most tool post grinding operations, the material removal rate is dependent upon three factors: work diameter, depth of cut, and traverse rate. The removal is expressed in cubic in./min. and can be found using the following equation:
Removal Rate = Traverse (in./min.) x Depth (in.) x work diameter (in.) x 3.14
Example: Find the metal removal rate for an external grinding operation of 6" diameter shaft with a .001" depth of cut and a 12 in./min. traverse.
Removal Rate = 12 x .001 x 6 x 3.14 = .023 in3 / min.
Traverse feed depends upon the width of the wheel being used and the grinding operation being performed. For roughing, 3/4 the width of the wheel should be fed per work revolution. To find the traverse rates, the following formulas can be used.
- Traverse (ipr) = 0.75 x wheel width
Example: Find the traverse rate for a roughing operation using a 6 x 1/2 x 1/2 wheel
Traverse = 0.75 x ( 1/2 ) = .375 ipr
- Traverse (ft/min) = 0.75 x wheel width x SFM (work)
Example: Same as above with 50 SFM (work)
Traverse = .75 x 1/2 (50)
= 1.56 ft./min.
For finishing operations, a finer feed of 1/8 or less the width of the wheel per work revolution is used.
The depth cut used for roughing should be as much as the wheel can stand without breaking down. For finishing, the depth of cut is always light - .001" or less.


2015-2016 Chamblee Middle School Math Team
8th Grade Math Team practices will be held each Tuesday from 4:05 until 5:10 PM.
7th Grade Math Team practices will be held each Thursday from 4:05 until 5:10 PM.
We are able to carry a maximum of 25 students on each of the teams. If more than 25 attend the first meeting for each team, we use the results of the tryout test to select the 25.
To cover the cost of the buses and registration fees, we are asking that each mathlete pay $100. You can pay by cash or check (check made payable to Chamblee Middle School). A receipt will be provided. It is very important that you submit your payment by September 24.


How to Start With Machine Learning?
Machine learning is about using sample data to build mathematical models that enable computer systems to perform tasks without obtaining explicit instructions. Image recognition, self-driving vehicles, Internet search engines, computer vision, spam email filtering, and many other systems use machine learning. It’s also applied in financial forecasts, medical diagnostics, fraud detection, and so on.
Machine learning is a vast and promising area. It offers exciting solutions to real-world problems as well as a variety of well-paid jobs.
This article is about learning and starting a career in this field.
First, you should learn the fundamentals:
- Learn mathematics
- Learn the theory and intuition behind data science and machine learning
- Learn programming
- Learn libraries for data science and machine learning
- Practice by playing with data
Once you’ve got the foundations, you should always learn more and keep yourself up-to-date by following the progress in the area:
Read data science, machine learning, and artificial intelligence blogs and papers Follow interesting people, groups, companies, and organizations on Twitter and other social networks Include yourself in discussions, ask questions, give the answers to other people’s questions The rest of the article is about the first part: building the fundaments of your knowledge.
The knowledge of mathematics is very important for people into data science and machine learning. It allows them to understand in-depth how and why the machine learning methods function. It also allows one to correctly design experiments, test hypotheses, combine methods, optimize hyperparameters, an so on.
Three main branches of mathematics required for machine learning are:
Calculus Linear algebra Probability and statistics Calculus is important because everything else relies on it, especially probability theory, statistical methods, and convex optimization. There are many potentially useful calculus books like:
Calculus by J. Stewart Thomas’ Calculus by G.B. Thomas, M.D. Weir, and J.R. Hass; please note that the latest edition of this book is authored by J.R. Hass, C.E. Heil, and M.D. Weir If you’re a complete beginner, you can try the tutorial Calculus for Beginners and Artists from the Massachusetts Institute of Technology.
Linear algebra is the basis of many machine learning methods and approaches such as linear regression and linear discriminant analysis. It’ll teach you how to handle multi-dimensional data and how to find relations between them. Some recommended books in linear algebra are:
Linear Algebra and Its Applications by D.C. Lay, S.R. Lay, and J.J. McDonald Introduction to Linear Algebra by G. Strang Linear Algebra and Its Applications by G. Strang Linear Algebra and Learning from Data by G. Strang You might also find beneficial the YouTube lectures of prof. G. Strang from the Massachusetts Institute of Technology available on YouTube.
The theory of probability and statistics have many concepts used in machine learning. Conditional probability, the Bayes theorem, the central limit theorem, hypothesis testing, regression techniques, and the entropy of information are just several examples of such concepts. Some convenient books about probability and statistics are:
Introduction to Probability and Statistics for Engineers and Scientists by S.M. Ross Probability and Statistics for Engineering and the Sciences by J.L. Devore You don’t need a high knowledge level in mathematics to start with machine learning, but once you want to understand and perform some serious stuff, you’ll feel the need for it.
Learn the Theory and Intuition behind Data Science and Machine Learning
You’ll also need to get insight in the applied aspect of mathematical concepts, that is to understand precisely how machine learning methods are designed. Some good books about these concepts are:
An Introduction to Statistical Learning by P. Forrest An Introduction to Statistical Learning with Applications in R by G. James, D. Witten, T. Hastie, and R. Tibshriani The Elements of Statistical Learning: Data Mining, Inference, and Prediction by T. Hastie, R. Tibshirani, and J. Friedman There are also two fantastic, free, online books:
Deep Learning by I. Goodfellow, Y. Bengio, and A. Courville Neural Networks and Deep Learning by M. Nielsen You’ll find many good explanations and visual representations there. The notes from the machine learning courses are freely available from the Web sites of the Stanford University and Massachusetts Institute of Technology. The lectures of these courses are also freely available on YouTube. Duomly offers a comprehensive course on machine learning, as well as several articles you might find useful:
How to create a chatbot in Python?
How to create image recognition with Python?
Differences between Artificial Intelligence and Machine Learning and why it’s important for us
How to pass the machine learning interview?
They explain the intuition behind the machine learning methods and provide their step-by-step implementations.
Learn Libraries for Data Science and Machine Learning
One of the most important things is to master programming libraries for data science and machine learning. The leading Python libraries for this purpose are:
- NumPy is a fundamental and high-performance Python library for manipulating arrays and numerical computing
- SciPy is a comprehensive library for numerical computing based on and extending NumPy Pandas is a library for easy and intuitive manipulation of one- and two-dimensional labeled data, also related to NumPy
- Scikit-learn is a comprehensive and widely-used machine learning library built on top NumPy and SciPy for data preprocessing, regression, classification, cluster analysis, model selection, and dimensionality reduction
- TensorFlow is a deep learning library focused primarily on neural networks by Google
- Keras is a library for creating and training neural networks that can be used with the TensorFlow, CNTK, or Theano backends
- Matplotlib is a powerful and widely-used library for data visualization
- Bokeh is a library for interactive data visualization and presentation in the Web browsers
The official Web sites usually provide good and free documentation and tutorials for each of these libraries. One additional especially good tutorial is the Anatomy of Matplotlib. It’s freely available on GitHub.
Practice by Playing with Data
If you want to become an expert in any area, you have to practice a lot.
You should get an interesting dataset. It may be related to sports, medicine, weather, finances, government, just anything you’re passionate about. Then, you can use it to do some data cleaning, data standardization, regression, classification, cluster analysis, pattern recognition, association rule learning, dimensionality reduction, and more.
You can download free datasets from many websites like Kaggle, FiveThirtyEight, Socrata OpenData, Wikipedia, UCI Machine Learning Repository, data.world, data.gov, Google Trends, Google’s BigQuery public datasets, the British government’s official data portal, Reddit, Nord Pool electricity market, and many more.
In addition, the libraries such as scikit-learn, TensorFlow, and Keras provide the datasets suitable for practice.
One more interesting resource is the TensorFlow Neural Network Playground that allows you to create and use neural networks visually from your browser.
For more information on the datasets, check Duomly’s article:
15 Best Machine Learning Datasets For Free.
Learning machine learning is a challenging and interesting task. It requires knowledge in many areas. Once you master it, it offers huge possibilities to apply it and finds interesting and well-paid jobs.
This article presents some resources for learning data science and machine learning, get data to practice with, as well as a few general advises.
There are many more fascinating books, courses, tutorials, blog posts, videos, and so on. Maybe more than one could read or watch during an average human lifetime. There are many average or low-quality stuff, as well. There are some new resources appearing every day.
Machine learning is just at its beginning. It grows and develops. If you want to be involved with it, you should too.
Thank you for reading!
This article was provided by our teammate Mirko.


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Write a method named negativeSum that accepts a Scanner as a parameter reading input from a file containing a series of integers, and determine whether the sum starting from the first number is ever negative. The method should print a message indicating whether a negative sum is possible and should return true if a negative sum can be reached and false if not. For example, if the file contains the following text, your method will consider the sum of just one number (38), the sum of the first two numbers (38 + 4), the sum of the first three numbers (38 + 4 + 19), and so on up to the sum of all of the numbers:
38 4 19 -27 -15 -3 4 19 38
None of these sums is negative, so the method would produce the following message and return false:
no negative sum
If the file instead contains the following numbers, the method finds that a negative sum of -8 is reached after adding 6 numbers together (14 + 7 + -10 + 9 + -18 + -10):
14 7 -10 9 -18 -10 17 42 98
It should output the following and return true, indicating that a negative sum can be reached:


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The HP-35 was the first handheld calculator to perform transcendental functions (such as trigonometric, logarithmic and exponential functions). Most contemporary calculators could only perform the four basic operations – addition, subtraction, multiplication, and division. The HP-35 and subsequent models have replaced the slide rule, used by generations of engineers and scientists.
Society: IEEEMain Category: ElectricDateCreated: 1972Hewlett-Packard CompanyPalo AltoState: CAZip: 94304Country: USAWebsite: http://www.ieeeghn.org/wiki/index.php/Milestones:Development_of_the_HP-35,_the_First_Handheld_Scientific_Calculator,_1972Creator: Hewlett-Packard Company
YearAdded:Image Credit: Courtesy WikipediaEra_date_from: 1972


Both parameters which are related to the network topology and. The distinction that we make between networks comes from the. A common property of many large networks is that the vertex connectivities follow a scalefree powerlaw distribution. These networks present a rich set of scaling properties that can be characterized by the usual techniques of statistical physics. Emergence of scaling in random networks barabasi al1, albert r. A common property of many large networks is that the. Oct 15, 1999 emergence of scaling in random networks barabasi al1, albert r. Emergence of scaling in random networks unm computer science. The probability of an edge uv between any vertices u and v is some function of the dot product u v of their respective vectors. However, driven by the computerization of data acquisition.
Random networks and percolation percolation, cascades, pandemics properties, metrics of random networks basic theory of random networks and cascades. Emergence of scaling in random networks barabasi and albert 286 5439. The core layer is a high speed backbone between distruibution blocks, that is networks that are geographically dispersed. Complete the reflection questions that accompany the pdf file for this activity. This feature is found to be a consequence of the two generic mechanisms that networks. Traditionally, networks of complex topol ogy have been described with the random graph theory of erdo.
It is meant to be used within this program of study. This lecture will introduce the concepts of random and scale free networks. Transcription factors controlling really many genes. While some real networks still display an exponential tail, often the functional form of pk still deviates from poisson distribution expected for a random graph. The reported scaling law for might help to better understand criticality in multilayer.
And in particular, were going to start looking at growing random networks. The above discussion indicates that there are a number of endstates or absorbing states for random networks, that include the scalefree state, when powerlaw scaling prevails at all times, the fully connected state, which will be the absorbing state of the er model for large connection probability p, and the ripened state. Pdf albert, r emergence of scaling in random networks. They are called scalefree, because zooming in on any part of the distribution doesnt change its shape. Okay, hi folks, were back again, and well be talking a little bit more about random networks. In social networks this effect is known as the smallworld effect.
Citeseerx document details isaac councill, lee giles, pradeep teregowda. A random dotproduct graph associates with each vertex a real vector. In this approach, we start from a onedimensional regular network with periodic. Most of the networks seen in nature as well as those generated by humans are of the scalefree type and present striking resilience properties against random attacks and damage, but they are vulnerable in the case of. This method is a random means of selecting the root bridge. Network scaling needs as they grow and expand, all enterprise networks must. Theory of random networks and their role in communications.
Emergence of scaling in random networks albertlaszlo barabasi. Biological networks contain more nodes with very many links than you expect by random. Emergence of scaling in random networks leonid zhukov. Scaling networks lab manual contains all the labs and class activities from the cisco networking academy course of the same name. Abstract as cancer is a complex disease, the representa tion of a malignant cell as a proteinprotein interaction network ppin and its subsequent analysis can provide insight into the behaviour of cancer cells and lead to the discovery. The only compulsory option is the input network file net. Traditionally, networks of complex topology have been described with the random graph theory of erdos and renyi er 7, but in the absence of data on large networks, the predictions of the er theory were rarely tested in the real world. A common property of many large networks is that the vertex connectivities follow a scale free powerlaw distribution. This shortening of path length tends to increase connectivity. The pioneering article of watts and strogatz led to an explosion of results on the beta model and a variant due to newman and watts in which edges are added but none are taken away.
Routes to chaos in neural networks with random weights 1465 our class mimic any dynamical system, and whether our method of sampling is representive of that class of dynamical systems. Lecture 6 growing random networks so far, we have focused onstaticrandom graph models in which edges among \ xed n nodes are formed via random rules in a static manner. The theory of random graphs lies at the intersection between graph theory and probability theory. To introduce on option you must introduce first its option key preceded by a dash, one white space and then the argument value. Scaling properties of multilayer random networks j. About this lab manual scaling networks lab manual contains all the labs and class activities from the cisco networking academy course of the same name. A common feature of percolation models is that the undrelying graph is constrained by an underlying euclidean embeddeing, or a lattice. Unlike real world networks, there is low clustering in random networks. Traditionally, networks of complex topology have been described with the random graph theory of erdo. More practice if you would like more practice activities, combine your lab manual with the new ccna routing and switching practice and study guide isbn.
Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. Networks on discrete points continuum spatial random networks z 1 z 2 z 0 32 4447 16 20 21201621162830. The answer to the former is the uniform approximation put forth by hornik et al. These networks turned out to have rather di erent properties than classical random graph models, for example in the number of connections that the elements in the network make. This work has deepened my understanding of the basic properties of random graphs, and many of the proofs presented here have been inspired by our work in 58, 59, 60. To random networks model with single or double preferential attachments, we have proved that the two models are of scalefree networks if the parameters are chosen properly and got the scaling exponent. Barabasi, 1999 typical values for problem barabasi, 1999 price, 1976 www 2. Department of physics, university of notredame, notredame, in 46556.
Traditionally, networks of complex topology have been described using the random graph theory of erd. Random networks and percolation mit opencourseware. Cisco networking academy is a comprehensive program that delivers information technology skills to students around the world. The distribution layer forwards traffic fromto different local networks. And, so this fits into our study of network formation.
Another model, which generalizes gilberts random graph model, is the random dotproduct model. So, situations where there are new nodes entering over time. Therefore, the resulting network very rarely contains highly connected nodes. Bibsonomy is offered by the kde group of the university of kassel. Emergence of scaling in random networks penn state. If pntn then there will not be any component of size. Finally, we will move to a new model, closer to that used in wireless ad hocsensor networks. Compared to an unclustered network of the same degree correlations, clustered networks result in. Science 286, 509512 article pdf available in science 2865439. A scaling law for random walks on networks theodore j. This feature is found to be a consequence of the two generic mechanisms that networks expand continuously by the addition of new vertices.
Support critical applications support converged network traffic support diverse business needs provide centralized administrative control. Organizers hoping to create networks for other purposes e. In this paper, we describe rangen, a random network generator for generating activityonthenode networks and accompanying data for different classes of project scheduling problems. These slides and a draft paper writeup \models for connected networks over random points and a routelength statistic with julian shun are on my web page. One of the phenomena of real networks is that the average distance through the network from one node to another is small compared to the network size. True for almost all social and biological networks. Random networks patterns in nature, an online book. Erd osrenyi model has small distances, but low clustering and a rapidly falling degree distribution. Network design i random networks degree distribution. Properties of random networks department of computer. Volume 1 describes the preliminary topics of random graphs as models for realworld networks. Emergence of scaling in random networks albertlaszlo.1455 677 57 1490 1464 141 1500 96 310 1053 900 921 303 991 609 1398 232 1020 810 652 1517 1169 1170 1151 517 364 996 1276 304 487 964 94 165


Expanding Your Horizons 2016
Expanding Your Horizons (EYH) is an annual conference designed to interest middle and high school age girls in STEM careers; early enough to impact their math and science course selection in high school. EYH believes that "having an interest in science, technology, engineering and mathematics, collectively known as STEM, can be an important catalyst for career development for current and future generations".
This year's EYH event was held on March 5 at the University of San Diego's Shiley Center for Science and Technology. CER volunteers led workshops focused on energy, electricity, motors, dynamos, and plasma science; the pictures below are from the workshop hosted by CER members.


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Hey there!! You're probably busy right now just cause everything always seems to be busy. But while it's busy I hope that it's also worthwhile. One of the reasons I've been posting less is cause I have my Grade 8 piano coming up in less than a month and a girl has to practice and keep her nails short. But short nails can still have sweet designs.
Triangles are my favourite shape, they're just edgier than circles and squares. I think about shapes more than most cause I do A level maths. It's hard, I'm sure you guys who've done it know that. Anyway getting away from maths I love the bright colours and just how cool the triangle pattern looks. It's just mega fun.
I used toothpicks to freehand this as usual, as you can tell the triangles are not all the same size but that doesn't bother me. It's just so uniform and I like that sometimes.
Yellow: Rimmel - Sunshine
Red: OPI - Jinx
Orange: Essie - Fear Or Desire
Green: Barry M - Kiwi
Blue: Barry M - Malibu
Thank you so much for reading and I hope you have a wonderful day!! :)


Statsoft electronic statistics textbook is free and provided as a service to the public. The consumer price index for december 2017 was launching by general director of statistics timor-leste directorate general of statistics (gds. Homepage of the federal statistical office of germany. Mr ning jizhe attended the 50th anniversary of the unido and visited the unido mr ning jizhe, commissioner of the national bureau of statistics (nbs) of china.
Twitter cards help you richly represent your content on twitter now use analytics to measure their effectiveness learn more. The united nations statistics division is committed to the advancement of the global statistical system we compile and disseminate global statistical information. [email protected] introdução à estatística e estatística descritiva 0 [email protected] estatÍstica um conjunto de procedimentos e princípios para. Memoria estatística do brasil na biblioteca do estatistica das estradas de memoria estatística do brasil na biblioteca do ministerio da fazenda no.
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Khan academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere if you're seeing this message. Isi 2019 - 62nd isi world statistics congress, malaysia, 18-23 august 2019 isi 2019 website is now live please check the website regularly for new announcements and. Mz:2005:2 documentação do curso de amostragem 17-23 february 2005 ta for the scandinavian support program to strengthen the institutional capacity of the national.
“the asa-sas usa partnership on stats has set its sights squarely on the target of developing a statistical literate citizenry, and is quite likely the most. Our free elementary statistics books will help you acquire a better understanding of the core concepts of statistics the textbooks in this section cover subjects. Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data in applying statistics to, eg. Category:statistics from wikimedia commons, the free media repository jump to: navigation, search this is a main category requiring frequent diffusion and maybe. Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution inferential statistical analysis infers. A wikipedia for schools article about statistics content checked by sos children's villages.


A 3D shape or an object is made up of a combination of certain parts. Most of the solid figures consist of polygonal regions. These regions are- faces, edges, and vertices. Solid geometric shapes which have faces, edges and vertices are known as polyhedrons.
A cylinder is a three-dimensional solid figure which consists of two circular bases connected with a curved surface made by folding a rectangle. The top and bottom faces of a cylinder are congruent. It has a total of 3 faces, 2 edges, and no vertices. 2b1af7f3a8