Thomas W. Judson
Open-Source Textbooks, Software, and Resources
- SFA A-Z
- CoCalc, a collaborative environment for doing mathematics by W. Stein.
- My open source textbooks Abstract Algebra: Theory and Applications and The Ordinary Differential Equations Project have a new home at judsonbooks.org.
- Open Textbook Initiative. The The American Institute of Mathematics (AIM) has developed evaluation criteria to identify the open source textbooks that are suitable for use in traditional university courses. The Editorial Board maintains a list of approved textbooks which have been judged to meet these criteria.
- UTMOST: Undergraduate Teaching in Mathematics with Open Software and Textbooks. The UTMOST project is an NSF IUSE grant focusing how students understand and faculty actually use textbooks in undergraduate mathematics courses. UTMOST will use this understanding to produce textbooks that are more effective in promoting student learning. The major components of the project involve education research, resource development, dissemination, and evaluation.
- UTMOST Sage Cell Repository. The Sage cell repository is a highly structured catalog of reusable Sage cells that can be easily embedded into online documents. Each Sage cell is tagged with important attributes to make it easy for instructors, authors, and anyone using Sage to find examples of Sage code appropriate for their needs. Below is an example of a Sage cell that plots a sine curve.
- PreTeXt is a lightweight XML application for authors of scientific articles, textbooks and monographs that incorporates the best of DocBook, LaTeX, and HTML. When a document is written in PreTeXt, it is possible to quickly produce print, PDF, web, HTML, Sage Notebooks, Jupyter Notebooks, and even Braille from a single source.
- Logic and Proof for Teachers, an open source textbook by Lesa L. Beverly, K.M. Childs, T. W. Judson, and D. A. Pace available in PDF format and online.
- A First Course in linear Algebra, an open source textbook by R. Beezer.
- Sage, open source mathematics software founded by W. Stein.
- ODE Reviews. Reviews of articles relating to the teaching and learning of ODEs.
- The CODEE Journal. The CODEE Journal is a peer-reviewed, open-access publication, distributed by the CODEE (Community of Ordinary Differential Equations Educators) and published by the Claremont Colleges Library, for original materials that promote the teaching and learning of ordinary differential equations.
- SIMIODE (Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations). SIMIODE is a resource for faculty members and students who want to focus on compelling applications, modeling, motivation for studying differential equations, and instructional technologies and make investigation of realistic scenarios possible. SIMIODE provides a comprehensive and cohesive community approach to studying differential equations.


by Scott Foresman - Addison Wesley .
Written in English
|The Physical Object|
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Competency Determine and interpret the linear correlation coefficient, and use linear regression to find a best fit line for a scatter plot of the data and make predictions. Scenario According to the U.S. Geological Survey (USGS), the probability of a magnitude 6.7 or greater earthquake in the Greater Bay Area is 63%, about 2 out of 3, in the next 30 years. In April 2008, scientists and engineers released a new earthquake forecast for the State of California called the Uniform California Earthquake Rupture Forecast (UCERF).As a junior analyst at the USGS, you are tasked to determine whether there is sufficient evidence to support the claim of a linear correlation between the magnitudes and depths from the earthquakes. Your deliverables will be a PowerPoint presentation you will create summarizing your findings and an excel document to show your work.
Concepts Being Studied
Correlation and regression Creating scatterplots Constructing and interpreting a Hypothesis Test for Correlation using r as the test statistic You are given a spreadsheet that contains the following information: Magnitude measured on the Richter scale Depth in km Using the spreadsheet, you will answer the problems below in a PowerPoint presentation.
What to Submit
The PowerPoint presentation should answer and explain the following questions based on the spreadsheet provided above. Slide 1: Title slide Slide 2: Introduce your scenario and data set including the variables provided. Slide 3: Construct a scatterplot of the two variables provided in the spreadsheet. Include a description of what you see in the scatterplot. Slide 4: Find the value of the linear correlation coefficient r and the critical value of r using α = 0.05. Include an explanation on how you found those values. Slide 5: Determine whether there is sufficient evidence to support the claim of a linear correlation between the magnitudes and the depths from the earthquakes. Explain. Slide 6: Find the regression equation. Let the predictor (x) variable be the magnitude. Identify the slope and the y-intercept within your regression equation. Slide 7: Is the equation a good model? Explain. What would be the best predicted depth of an earthquake with a magnitude of 2.0? Include the correct units. Slide 8: Conclude by recapping your ideas by summarizing the information presented in context of the scenario. Along with your PowerPoint presentation, you should include your Excel document which shows all calculations.


The diesel O&M cost is a critical factor in HOMER Pro analyses, and we know frustratingly little about it. For diesel generators, I typically assume an O&M cost of about 2 US cents per kWh at rated output. That would be $1/hr for a 50 kW diesel. HOMER assumes that the O&M cost per hour is independent of the power output, so that 50 kW diesel would cost $1 per hour of operation whether idling or running full blast.
HOMER Pro calculates the annual O&M cost of the diesel by multiplying the hourly O&M cost by the operating hours per year. In a diesel-only system, that 50 kW generator would run full time and the O&M cost would be $8,760/yr. In a wind-diesel-battery system if it ran only 3,000 hours per year, its O&M cost would drop to $3,000/yr.


A random walk is the path traveled by taking a step, then randomly turning either left or right, then repeating: a step, a random turn, a step, a random turn, and so on. Although a random walk sounds simple and is easy to code, it is an enormously important subject in many branches of science, such as physics, biology, economics and mathematics. Google Scholar lists 2,380,000 academic research papers on the subject.
The science of random walks is not the subject of this blog. Rather, our aims are to improve our coding skills in MakeCode for Minecraft and to explore random walk patterns as art.
Demo and How It Works
- steps — the number of steps in the walk, maximum 3000, default 100.
- stepSize — the number of blocks in a single step, maximum of 10, default 3.
- blockGroup — is the group of blocks that can be used to create a random walk. The values can be 0, 1 or 2, default 0.
- blockGroup 0 is LapisLazuliBlock or TNT depending or the random direction (left or right).
- blockGroup 1 choses a block randomly from a colorful array of choices.
- blockGroup 2 choses a block randomly from a variations of black choices.
A simple random walk program called Agent Wanderer is found on Microsoft MakeCode for Minecraft site. The code below provides more flexibility by providing three arguments (see above) and using the Builder, which is faster than the Agent. the code below is shared at https://makecode.com/_AF0cdjKVu4zq, where it can be downloaded and run in MakeCode for Minecraft.
The code also includes a few utility Chats or function, which I plan to document in other posts. The utilities are:
- Move Me — moves the player to the east and/or south the specified number of blocks. Good for moving to a clean spot in the world.
- Handy Compass– prints directions on the sky asynchronously. Handy for knowing the direction a random walk moves.
- Go to Ground — moves the player to be “on the ground,” which is Y=4 in a flat world.
- Canvas — replaces grass over a large area to create a white background for a random walk.
- Add code to determine the percentage of the time does a random walk wander to the north, to the south, and so on?
- Add a counter for the number of right turns as opposed to left turns.
- Add a counter for the number of blocks that are south of the origin, east of the origin, and so on.
- How often does a walk return to land on the origin block during its path?
- Instead of replacing blocks that have already been replaced, stack them; thus, counting the number of times each block has been traversed.
A particularly intriguing activity is to try replacing


|EffeLou 28 octobre 2014|
- You know, I don't think math is a science, I think it's a religion.
- A religion?
- Yeah, all these equations are like miracles. You take two numbers, and when you add them, they magically become one NEW number! No one can say how it happens. You either believe it or you don't. This whole book is full of things that have to be accepted on faith: it's a religion!
- And in the public schools, no less: call a lawyer.
- As a math atheist, I should be excused from this.


Confident Numeracy - Online Course
*COURSE DELIVERED ONLINE*
This course is designed to enable you to increase your confidence in using maths… whether you are returning to study after a period away, just about to start at university or thinking about taking a professional or part-time course, this course will enable you to:
- Prepare for subjects with mathematical content
- Build confidence in using mathematics to solve problems
- Development understanding in key mathematical skills
- Understand and develop applied problem solving
- Build your confidence so you can achieve your potential
What you will study
The indicative syllabus outline for this course includes:
- Basic arithmetic operations
- Calculators (How to use)
- Factors and prime numbers
- Exponentials and Logarithms
- Ratios and percentages
Who is this course for?
This course is for anyone who:
- Wants to develop their confidence in handling mathematical skills
- Is starting University in September (regardless of University)
- Is transitioning between level 3 and 4 of university study
- Is thinking about starting a part-time or professional course but is not 100% sure due to current low qualifications
- Anyone who has already applied to University but needs to increase their entry grades
There are two points of assessment;
- Assessment one: Online Quiz (10% weighting)
- Assessment two: Portfolio (90% Weighting)
Course start dates
Course 1: This course will start on the 25th January 2021 and will run for 6 weeks.
Course 2: This course will start on the 12th April 2021 and will run for 6 weeks.
Course 3: This course will start on the 28th June 2021 and will run for 6 weeks.
You will need to log in weekly to access the course content and undergo your studies.
*Please Note* Individuals only need to book the course once, the different courses refer to different start dates and they all have the same content.
Visit the online store to book the online shop.
Bookings for the course will close a week prior to the course start date.


Did you think being one of the top 1% of enthusiasts for optical illusions was impressive?
Only 0.1 percent of people can apparently answer this numerical eye exam, so puzzle fans are going crazy trying to figure it out.
The frustrating video jigsaw was posted to TikTok for the first time in April, but it's currently exploding up as users try to solve it.
The eye-catching picture appears to simply display the numerals 6, 8, 4, and 1 on the surface.
The "literal image," which is defined as combining tiny images to make a larger one, however, on closer study, it becomes evident that there are far more numbers hiding within.
Unfortunately, even the most observant TikTok users had trouble finding all 10 integers, and many of them came up with wildly dissimilar solutions.
The number five, which, according to some puzzlers, is made "by the gorilla as he starts swinging his right arm," is said to have been the one that viewers had the most difficulty spotting.
One even made the joke that there are far more than 10 numbers after spotting the "infinite" symbol.


Welcome to the official website of the International Conference on Applied Mathematics and Analysis (ICAMA2016)
The main purpose of this conference is to bring together leading experts and young researchers to share new ideas, trends and methods of applied mathematics and analysis. The developments in the field of applied mathematics open new research areas in analysis and vice versa. Therefore, the conference will provide a forum for exchanging ideas and discussing the recent progress in both fields. A special emphasis will be put on Difference, Differential and Dynamic Equations, Fractional calculus, Fixed point theory and and their applications.
The conference is dedicated to the memory of Prof. Gusein Sh. Guseinov (Hüseyin Şirin Hüseyin) 1951-2015.
There will be a bus from Baskent Ogretmenevi at 8:30 and from Dafne Hotel at 08:45 to Atilim University every morning on July 11,12,13, 2016 for those who stay there. The bus will drive you back at the end of the daily program. Participants staying in other hotels in Ankara can use service busses of Atilim University. For more information please click here.
A Thematic Issue in the Journal of Inequalities and Applications entitled Thematic Issue in the Memory of Gusein Sh. Guseinov is offered for the proceedings of the conference. Full paper submissions will be peer reviewed and evaluated based on originality, technical and research content/depth, correctness, contributions, and readability.
Deadline for submissios is January 1, 2017.
Gusein Sh. Guseinov
Registration: June 20,2016
Abstract submission: June 20, 2016
Faculty: 150 USD (or 450 TL)
Student: 50 USD (or 150 TL)
Registration fee should be paid via bank transfer. There is no possibility of payment at the registration desk. You can find bank account numbers on the registration page.


Saturday, October 26, 2013
Saturday Night Fun Days Old?
Your mission, should you decide to accept it (cue the Mission Impossible! music) is to:
1) Do you know how many days you have lived? How many hours? How many minutes? How many seconds?
2) For this challenge - do some calculating. Figure out how many days you've lived, how many hours, how many minutes, how many seconds (you can round off to account for the time you were born on your birth date - do you know it?). Tell us your birth date, birth time (if you know it), and then calculate your time alive up until your birth time today.
NOTE: If math befuddles you, use the Age Calculator at http://www-users.med.cornell.edu/~spon/picu/calc/agecalc.htm
3) What does all of this mean to you? Think about that marvelous "machine" inside your chest beating in rhythm. Share your thoughts!
Well since I turned 65 June 14, 2013 I am 23,876 days old, or 573,024 hours old, or 34,381,440 minutes old. The Seconds overran my little calculator so I rounded off to 206,280,000 seconds. So I guess my heart has beat about 206 million times, and if I live as long as my dad I have another 35 years to go or another 100+ million heart beats. Glad I got his genes as all the tests for my heart health say my heart is still young.


Everybody Hates Math was the 21st episode of the second season of Everybody Hates Chris. It was the 43rd episode overall. It premired on May 7, 2007.
SHORT SUMMARY: Rochelle decides to help tutor Chris for a math competition in algebra, when Chris doesn't think she's helping he turns to his grandmother Maxine for help. Tonya blackmails Drew when she takes the blame for breaking Julius' favorite chair for Drew.
Rochelle: Chris, what kinda answer is that?
Narrator: The kind you'd come up with was a crazy woman screamin' at you.
Narrator: Going behind my mother's back to get help from my grandmother made me feel guiltier than Janet Jackson at a half-time show.
To watch the full episode click HERE


Aryabhata is the author of several treatises on mathematics and astronomy, some of which are lost.
His major work, Aryabhatiya, a compendium of mathematics and astronomy, was extensively referred to in the Indian mathematical literature and has survived to modern times.
If he continues to spend his time in New Mexico, he could easily complete the book by year’s end and start the final editing and promotional process for a fall release.
Summary: sixth book is going to be called The Winds of Winter, taking the title of the originally last book of the trilogy and the later planned fifth of six books.
Q: When will A Dance with Dragons be released on paperback? However, Amazon lists it as available on October, 29 2013. Q: Is there any way to read The Winds of Winter now?


Congratulations to our Y11 pupils on the excellent GCSE results they received today. Their success and achievement is the culmination of five years of hard work and their reward for studying and revising so well.
90% of pupils gained A*-C in English, 82% in Maths and 78% in both Maths and English. 74% of pupils gained five A*-C including English and Maths and 39% of pupils achieved the English Baccalaureate. 27% of all grades were at A*/A .


Many of our students start Dove House with a lower level of mathematical ability than their mainstream peers, but we are committed to help every pupil reach their full potential in the subject. At Dove House we deliver maths through a range of interactive activities, age appropriate resources and diverse teaching styles to best suit the learning needs of our students. We wish to develop the independence and resilience of our learners and ultimately help them develop confidence in their abilities.
Every year group is set according to ability and Maths lessons are delivered by Maths specialist teachers from Year 7 through to Year 11. Our goal is to make Maths fun, relevant and exciting, whilst helping students to achieve an appropriate Maths qualification.


Asymmetric encryption is about choosing a function that is very easy to calculate, but whose inverse is very costly. The discrete logarithm is such a one-way function. However, there are functions for which the inversion can be abbreviated with additional information. In such a case one speaks of a trapdoor function.
- Newly published: Atos whitepaper on post-quantum cryptography
- Newly published: cryptovision special issue of “The Vault” magazine
- US standards body NIST announces four winners in post-quantum competition
- Mindshare 2022 video: Two great days in 70 seconds
- New GreenShield version receives BSI approval


Main / Arcade / Applied mathematics book
Applied mathematics book
Name: Applied mathematics book
File size: 428mb
Your book, The Princeton Companion to Applied Mathematics (), seems to have got some very high praise: a 'tour de force,' 'The treasures [in this book] go. Online shopping for Books from a great selection of Probability & Statistics, Statistics, Differential Equations, Game Theory, Linear Programming, Graph Theory. Dover offers foundational works, problem books, applied mathematics books, and more for engineers, physicists, and others. All are the lowest-priced editions .
research universities have applied mathematics for scientists and engineers. such a the syllabus is quite different than given in this venerable pair of books. PDF Drive is your search engine for PDF files. As of today we have ,, eBooks for you to download for free. No annoying ads, no download limits. Applied Mathematics is the branch of mathematics which deals with applications of mathematics to the real world problems, often from problems stemming from.
This elegantly edited landmark edition of Gert Kjærgård Pedersen's C*-Algebras and their Automorphism Groups () carefully and sensitively extends the. 24 Jan Introduction to Methods of Applied Mathematics or. Advanced Mathematical Methods for Scientists and Engineers. Sean Mauch. Results 1 - 30 of Discover Book Depository's huge selection of Applied Mathematics Books online. Free delivery worldwide on over 18 million titles. Try the Math Association of America's Basic Library List. It's searchable by subject (including applied mathematics), has reviews, and are put up by a single. Looking for books on Applied Mathematics? Check our section of free e-books and guides on Applied Mathematics now! This page contains list of freely.


— "There are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – there are things we do not know we don't know." (Donald Rumsfeld) — In this class, we learn to deal with the "known unknowns", a field called Uncertainty Quantification (UQ). More specifically, we focus on methods to propagate uncertain input parameters through differential equation models. Given uncertain input, how uncertain is the output? The first part of the course ("how to do it") gives an overview on techniques that are used. Among these are: ● Sensitivity analysis ● Monte-Carlo methods ● Spectral expansions ● Stochastic Galerkin method ● Collocation methods, sparse grids — The second part of the course ("why to do it like this") deals with the theoretical foundations of these methods. The so-called "curse of dimensionality" leads us to questions from approximation theory. We look back at the very standard numerical algorithms of interpolation and quadrature, and ask how they perform in many dimensions.


In this article, we will show you how to upgrade to Rank Math PRO. We have a full video of the process here as well:
1 First, you need to purchase a license of Rank Math PRO.
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Select the zip file that you downloaded by clicking on Choose file button. Then click on Install Now.
5 Once the plugin is installed, you need to enable the Rank Math SEO PRO plugin. Once enabled, you can check the plugin in the Installed Plugins as both the Free and PRO versions of Rank Math have to be installed and activated on the site.
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Note: In case, your Free version is already connected to Rank Math, you need to disconnect and reconnect with your Rank Math account for the PRO license and updates to become available.
To disconnect Rank Math, click the Disconnect Account button.
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A Software Engineer, and Math enthusiast.
A Fullstack software engineer from Venezuela 🇻🇪 who enjoys to blog about my experiences with the aim to help others and my future self. I’m currently pursuing a Msc. in applied mathematics at the University of Carabobo. Throughout my career, I’ve gained valuable experience in developing distributed high-load systems, cloud computing, and web applications. You can check more about my profesional profile here: CV
I have fundamental math skills in probability theory, random process, and statistics. I also have in-depth knowledge and understanding of the following languages:


Fermats last theorem was an enigma until 1995 when Andrew Wiles proved it. But his proof is a little long and complicated. Fermat said that his proof was just a little to long to fit on the side of a page he wrote the theorem on. So the hunt for Fermats proof I think it still on, assuming that his proof was correct.
Fermats last theorem states that for any a,b,c there is no n larger then 2 that satisfies the equation
a^n + b^n = c^n
This only has to be proved for cases of a and b where they are coprime.


WHAT IS BILUR
bilur is an cryptoCommodity, based on a consensus peer-to-peer network that enables a new money system and completely decentralized. Bilur, by definition, will be backed by units of stored energy.
1 bilur = 1 Ton Oil Equivalent (TOE) = 11.6 MWh of energy
1 TOE Brent crude = 6.481 barrels x Brent assessment price*
*This value is variable and calculated daily with Brent assessment. As an example, with the average Brent Barrel price Feb 2017, 1 BILUR = $ 356.45


Posted on 02 Aug 2021 by Steve Markham
Math with Straingers
On the train ride to Provo from Salt Lake City, Kyle struck up a conversation with a stranger about the YouTube videos of Magic he was watching. Once he found out how nerdy we are, he asked us a math puzzle that had stumped him for 6 months: Find a number where if you swap the first and last digit, you get twice the value.
My immediate intuition was “provably impossible” and after a minute of thought I said that out loud. Kyle had it proved within a few minutes. The strainger sent me a link to the original source, and it turns out he misremembered it. I hope the guy hadn’t been losing sleep for six months, because the real puzzle is hard, but doable: Find the smallest positive integer where if you move the last digit to the front, you get twice the value.
There are two approaches, one algebraic, and one intuitive. Let a be an n-digit integer, and b be a single digit integer. Then we seek an (a,b) such that 2*(10*a+b)=10^n*b+a, or equivalently, 19*a = (10^n-2)*b. That implies that a = b*(10^n-2)/19, and since b is a single digit and a is an integer, 10^n-2 must have a factor of 19 in it.
Kyle discovered his own method for finding such a n, but I used what I call “short division” which looks like long division, except you don’t write out the products below, you just right the difference after subtraction as a tiny superscript. What are we dividing? Well, divide 19 into a bunch of 9s until you get a remainder one. Then, instead of adding another 9, you change that last 9 into an 8, and that means 19 goes in evenly. So, 19 goes into 99 five times, remainder 4; it goes into 49 twice, remainder 11, it goes into 119 6 times, remainder 5, etc. The punchline is that 19*5,263,157,894,736,842=99,999,999,999,999,998. Yeah, I know, that number is much larger than I expected. It seems like we’re almost done, with b=1 and a=5,263,157,894,736,842, but 99,999,999,999,999,998=10^17, and that a is only 16 digits. Recall that we stipulated a must be n-digits. But, we can easily add digits by using b>1. The smallest value that works will be when b=2, but any value of b will work.
The intuitive method works faster, but it’s harder to know for sure that it’s the smallest value. In this method, we simply assume that the last digit is a 1, and then see what that implies. Suppose our number is XYZ1; then twice the value is 1XYZ. Thats means Z=2, since when we double the 1 in the ones place, we’ll get 2 for sure. By similar logic, doubling a 2 in the tens place gives Y=4, and X=8. Moving leftward through our number, 8 will double into 16, but we only write the 6 and carry the 1. Double 6 gives 12, but we carried a 1, so we write 3 and carry a 1 again. Then 7, then 4, then 9, then 8, then 7, then 5, then 1, then 3, then 6, then 2, then 5, then 0, then 1. At this point the sequence repeats itself, and that is a clue. So we have 1052631578947368421. If we drop the leading 1, then we are left with a number that, when you move the 1 from the back to the front, it doubles in value. BUT, dropping the 1 in front requires leaving a leading 0 in front, which is weird. However, the double value will be the b=2 value from our original method, namely 105,263,157,894,736,842. And that does indeed look like something that, when doubled, will start with a 2, and in particular will be 210,526,315,789,473,684 (which is b=4).
We can find b=4, or 8 by doubling. But we can also find b=3 by simply cycling hrough the numbers until it ends with a 3. And there are 2 of those, but the smaller one is the 3 followed by the one, 157,894,736,842,105,263; the other one starts with a 6, and will have a carried 1 in front instead of a 3, when it is doubled.
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Test retest of overall barriers score. a. Bland Altman Line of Equality showing overall barriers score calculated from responses at time a (first administration) plotted against overall barriers score calculated at time b (two weeks later) (N = 17). b. Bland Altman plot showing mean overall barriers score against differences between the overall barriers score at time a (first administration) and b (two weeks later). The centre line represents zero (i.e., perfect agreement). The top and bottom lines represent 95% limits of agreement (mean ± 1.96SD) so that in a randomly selected respondent from the general population the difference between the two responses would be expected to lie between these limits of agreement with approximately 95% probability (N = 17).


General Equilibrium Theory An Introduction Pdf Download > bit.ly/2eHteA7
General Equilibrium Theory An Introduction Pdf Download
Concept and history of general equilibrium theory 2. A market economy: the unbounded technology case; 18. Self-contained mathematical chapters and exercises at the end of each chapter make this an ideal textbook for advanced-level courses.' Paolo Siconolfi, Columbia UniversitySee more reviews Customer reviews Not yet reviewedBe the first to review Log in to review Review was not posted due to profanity , create a review (If you're not , sign out) Please enter the right captcha value Please enter a star rating. It offers a revised and extended treatment of core convergence, including the case of non-convex preferences, and introduces the investigation of approximate equilibrium with U-shaped curves and non-convex preferences. Product details Edition: 2nd Edition Date Published: June 2011format: Hardbackisbn: 9780521826457length: 380 pages dimensions: 254 x 178 x 22 mmweight: 0.88kgcontains: 42 b/w illus. An Economy with Supply and Demand Correspondences:23. Your review must be a minimum of 12 words. The new edition updates discussion throughout and expands the number and variety of exercises. Informationen Ausland: klicken Sie bitte hier.
This volume is slim, yet fully self-contained and rigorous; it should be useful to advanced undergraduates and graduate students, as well as to researchers in economic theory and mathematical economics.' Jean-Michel Grandmont, Universit Ca' Foscari di Venezia, Italy, and Centre de Recherche en Economie et Statistiques, France'A comprehensive treatment of classical general equilibrium theory from its most elementary to its most abstract formulation. Logic and set theory 7. Welfare Economics and the Scope of Markets: 19. .. It offers a revised and extended treatment of core convergence, including the case of non-convex…mehrGerte: PCmit KopierschutzeBook HilfeInhaltsangabe Andere Kunden interessierten sich auch frAlle ProdukteFrank AckermanFlawed Foundations of General Equilibrium Theory (eBook, PDF)Frank AckermanFlawed Foundations of General Equilibrium Theory (eBook, PDF)C. Concept and history of general equilibrium theory; 2. The core of a market economy; 22. MwSt. Ross Starr's book is the best attempt so far at combining economic intuition with rigor in dealing with those staples of general equilibrium theory that are the existence and the two welfare theorems.
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Student Decline in Maths and Science Subjects to be Examined
It has been revealed that a high number of high school seniors are abandoning the traditional subjects of mathematics and science, as they are becoming less of a requirement for many courses of further education at university. The head of a NSW curriculum authority has stated that over the past ten years the majority of NSW universities have completely dropped such subject requirements for many of their degree courses. The president of the NSW’s Board of Studies, Tom Alegounarias, understands the problem and sees that if students do not have to struggle to maintain high marks in these difficult subject to gain a university place then they simply won’t. The trend begins in year 12, where the number of students studying science and maths has decreased drastically on the last twenty years.
A recent study by Trends in International Mathematics and Science concluded that 14% of Australian year 4 pupils said that they did not enjoy science, and that the figure grew to 33% by year 8. Mr Alegounarias argues that these telling figures are linked to the growing number of new subjects that are on offer in schools, with students preferring to write custom essays over more calculated, correct/incorrect answer based subjects. John Kennedy, a science teacher from Sydney, however, believes that this shift in subject preference occurs much earlier, with many children turning away from maths and science in their very early school days. After seeing notable changes of attitude in students from their time in year 7 to their time in year 10, Mr Kennedy plans to undertake a longitudinal study to gain a better understanding of exactly, why, when, and how school students become less likely to choose science and maths subjects in favour of others in their final school years.Read all posts


Dr. Mohamad Saad
Dr. Mohamad Saad
Dr. Mohamad Saad’s research encompasses topics including statistical genetics, biostatistics, bioinformatics, systems biology and genetics. He is interested in developing statistical methods, approaches and computational tools to help understanding the genetic etiology of complex human diseases such as Parkinson’s disease, Alzheimer’s disease and cancer. These approaches aim to discover new genetic and environmental causes for those diseases in order to find cures, prevention measures and better therapies.
His research expertise includes many analytical approaches that are being used and proposed for Genome Wide Association Studies (GWAS) such as: association analysis for common and rare variants in population- and family-based designs, linear mixed models, clustering methods, mutli-dimension reduction techniques, linkage analysis, imputation of missing genotypes, MCMC and LASSO.
Dr. Mohamad Saad is a scientist in the Data Analytics group at Qatar Computing Research Institute. He joined QCRI in February 2017 and works on topics in statistical genetics, biostatistics, bioinformatics, and systems biology.
Dr. Saad has a background in applied mathematics and statistics. He obtained his Bachelor's degree in Applied Mathematics (Majoring in Statistics) at Lebanese University in 2006, before he moved to France where he obtained his Masters degree in Statistics/Biostatistics from the University of Montpellier II, Monpellier in 2007, and his Ph.D. in Statistical Genetics/Biostatistics/Bioinformatics from University of Paul Sabatier III, Toulouse, in 2012.
In Summer 2012, he moved to the United States for a postdoctoral position and joined the Department of Biostatistics at the University of Washington, Seattle, as a Postdoctoral Senior Fellow and stayed until Fall 2016.
2012: Ph.D. in Statistical Genetics / Biostatistics, University of Paul Sabatier 111 & National Institute of Health and Medical Research, Toulouse, France
2007: M.Sc. in Statistics/Biostatistics, Montpellier University, France
2006: B.Sc. in Applied Mathematics (Majoring in Statistics), Beirut, Lebanon
For other research see his Google Scholar page
2014: James V. Neel Young Investigator Award for the Best Presentation by a Young Investigator at the International Genetic Epidemiology Society, Vienna, Austria, August 2014.


Mathematicians Come To Aid Of ODU Football
By ODU Athletics
March 31, 2008
The fledgling Old Dominion University NCAA football program may have found a secret weapon in the university's highly ranked Department of Mathematics and Statistics.
When the Monarch coaching staff wanted to design a complicated workout regime for their 100 tryout players earlier this year, they turned to ODU mathematicians for help.
The coaches' problem was this: They had divided their tryout candidates into eight groups and they had developed four different workout stations. To increase the effectiveness of the workout sessions, they wanted two groups to compete against each other at each workout station during each of four workout rounds. Furthermore, they wanted each group to compete at each station during the workout without ever competing against the same group twice.
Andy Rondeau, the defensive coordinator and linebackers coach, admitted that the coaches were flummoxed. "We always end up with a conflict or with groups that compete against each other more than once," he wrote in an e-mail that began, "Dear Math Department, I am sorry to bother you, but we have a math problem."
As Rondeau's luck would have it, the note fell into the hands of Mark Dorrepaal, chair of the math department. He is internationally known for figuring out math puzzles without using a computer, and his true love is tackling Major League Baseball scheduling puzzles.
In 2006, Dorrepaal won media attention by holding the lead for a few weeks in an Internet contest that challenged mathematicians to come up with the most efficient round-robin schedule for 14 National League baseball teams. Although there are billions of possibilities, Dorrepaal came up with a schedule that required fewer travel miles than any of the previous submissions-most of which were the products of specially designed computer software.
So the challenge presented by the football coaches did not seem difficult at all to Dorrepaal. His solution was to divide the eight groups into two categories (X consisting of groups A, B, C, D and Y consisting of groups E, F, G, H). "Then in each of the four rounds, a group from category X is paired off with a group from category Y," he wrote to Rondeau.
He also attached a grid to show the complete solution. "You have my full permission to use it," he mused. "I am honored to be able to help the team."
"Well, sir, you have our gratitude and great respect," Rondeau responded. He said the coaches employed the solution, and it worked. Some of the coaches wanted to know more about the "formula" that Dorrepaal uses, and all of them "are wondering why we were not able to figure it out," Rondeau added.
For head coach Bobby Wilder, Dorrepaal's assist was more evidence of support on campus for the team, which is composed currently of walk-ons who are trying out. ODU, which last fielded a football team in 1940, will start intercollegiate competition in 2009. "So many people have done so much to help since we have been here," Wilder said. "The professor's solution worked perfectly and allowed us to run our workout in a timely manner."
Dorrepaal noted in an interview that another member of the department, Professor Dayanand Naik, saw the same request for help from the coaches and worked independently on a solution. "His solution was identical to mine, but he submitted it a few hours after I did, so he didn't get credit. He deserves credit, too."
Among math departments at the nation's public universities, ODU's department consistently ranks among the top 100 in research and development expenditures.


Geometry comes to life in these amazing origami paper sculptures! Geometric Origami: Easy to Follow Instructions For 10 Geometric and Modular Folds, by world renowned origami artist Nick Robinson released January 19, 2016 by Rock Point Gift & Stationery. Includes a 63 page book with step-by-step instructions for 10 origami models and 70 sheets of colorful 6" x 6" folding paper with graphic patterns and solids, and matte silver reverses. Modular origami refers to models that are folded with multiple pieces of paper. Enjoy the thrill of discovery that comes from folding your own 2 and 3 dimensional geometric works of art! Designed for novices. Would make a unique gift. Get your copy below.
Origami Step-By-Step Fold Instructions


Students, in Chapter 14 of the NCERT Class 10 Maths book, you have been told about Statistics Statistics. In this chapter, you have been given information about the formulas related to the grouped data of the table, mean, median, mode, etc. You will also learn about how to plot a graphical representation of data (curves or ellipses) in this chapter.
Summary of Statistics
- What is statistics:- The systematic grouping of data grouped in any table is called statistics.
- The following methods and formulas are used to find the mean of grouped data which are as follows
According to the above formula, it is assumed that the frequency of each class is centered at its mid-point, that is, the class sign.
- The formula for finding the mode of grouped data
- The cumulative frequency of a class in a frequency distribution is the sum of the frequencies of all the classes preceding that class.
- The following formula to find the median of grouped data
- Graphically Representing Cumulative Frequency Distributions Graphically by Cumulative Frequency Curves.
- The median of the grouped data can be found by putting the perpendicular on the horizontal axis from the point of intersection of the ellipses of both types of curves to the corresponding value of the intersection of the perpendicular and the horizontal axis.
- The empirical relationship between the three measures of central tendency
3 median = mode + 2 mean
- If the frequency of more than one value is occurring in a table, then in such a situation the data is called multi-modal data.
examples of statistics
Students, if you want to see more examples related to Chapter 14, then you can see in the pdf file given in the article. Click here
Solutions of EXERCISE 14.1 (Mean of Grouped Data)
Solutions of EXERCISE 14.2 (Mode of Classified Data)
Solutions of EXERCISE 14.3 (Mean of Classified Data)
Solutions of EXERCISE 14.4 (Cumulative Frequency)
Students, if you want to get solutions related to other questions of Chapter 14 questionnaire, then you can get the solutions from the pdf file given in the article. Below we have provided the PDF file for you.
Frequently Asked Questions (FAQs)
What is the frequency?
When an event occurs repeatedly in an experiment or study or there is a repetition of the data taken in the survey, it is called frequency.
What is the difference between mean and median?
Mean:- Whenever the total sum of the data given in a table is divided by the total observed values of the data, it is called the mean.Median: In statistics, the median is that which divides any series into two equal parts.
What is the mode in statistics?
If a term occurs more than once in any series, then that term will be called the mode of that series.
What is the formula for the direct method of statistics?
The formula for the direct method mean of statistics is as follows Direct Mean Method = Sum of Total Posts / Total Posts
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Statement of Purpose
Growing up in a family that loved numbers and calculations was not only inspiring but also thought provoking. I did not endear to learn mathematics but my parents encouraged me to excel in the subject. I could think of anything in terms of numbers, and that said, I became a mathematics guru from junior school to the university. My family has been the source of motivation even when applying for advanced studies in mathematics or related fields.
I plan to study PhD in statistics from your graduate school. Having had a strong background in mathematics, I have a strong foundation to handle statistical models and problems at advanced levels. My deep understanding of mathematics has honed me with the numerical, critical thinking, and abstract skills to identify problems and provide solutions. Basically, statistics is founded on probability and uncertainty that is largely mathematical in nature. I choose your institution to pursue this program because it offers the best in terms of theory and practice.


Two Player Bluetooth Math Game! You can now use two devices and play competitively or cooperatively with your classmates or parents.
4 Dice: Fraction Games hones the many concepts of fractions that include adding, subtracting, multiplying and dividing through a series of game mode options. The game also enhances analytical thinking by providing the answer and requiring students to determine the appropriate equation.
- Two Player Bluetooth Math Game!
- High order thinking game to challenge students in a fun way
- Progress reports sent to teachers to assess progress and target individual weaknesses
- A built-in whiteboard to give students a place to work through problems
4 Dice: Fraction Games is a math app for middle school and upper elementary students.
For teachers, one major benefit of using this game is that it provides immediate feedback of their students' progress via email.
Engaging Students Beyond the App
The 4 Dice App comes with a printable game sheet that makes it easy to prepare lessons and involve the whole class.
Common Core Mathematical Standard
4.NF Extend understanding of fractional equivalence and ordering.
5.NF Use equivalent fractions as a strategy to add and subtract fractions.
6 NF Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
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As in the first edition the purpose of this book is to present an extensive range and depth of topics in discrete mathematics and also work in a theme on how to do proofs proofs are introduced in the first chapter and continue throughout the book most students taking discrete mathematics are mathematics and computer science majors. New expanded coverage throughout on writing mathematical proof supplies students with a more comprehensive and in depth presentation of discrete mathematics topics new extensive increase in problems in chapters 1 8 includes an increase in the number that involve proofs helps students to think logically and understand the basic concepts before moving on to more advanced material. Experimenting with combinatorica a widely used software package for teaching and research in discrete mathematics provides an exciting new way to learn combinatorics and graph theory with examples of all 450 functions in action plus tutorial text on the mathematics this book is the definitive guide to combinatorica. Discrete mathematics second edition in progress january 13 2020 springer to my family especially anne and mia for in this second edition i tried to make the exposition simpler and clearer i added complexity will need some discrete mathematics such as combinatorics and graph. Introduction to enumerative and analytic combinatorics fills the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics the book first deals with basic counting principles compositions and partitions and generating functions
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Let the solution be.3643 units and.2812 units and find the third side using equation (3) a 2 b 2 c 2 - 2 b c cos (A) a sqrt.3643*18.2812 cos (56).3543 units As an example check that the. More references to geometry problems. Geometry tutorials, Problems and Interactive applets. You're reading a free preview, pages 4 to 11 are not shown in this preview. Buy the full Version, you're reading a free preview, pages 15 to 27 are not shown in this preview. Buy the full Version, you're reading a free preview, pages 31 to 100 are not shown in this preview. Buy the full Version.
Two-step equation word problem: computers (video) Khan Academy
2 p z thesis 2 (1 cos (A) y - p 2 h z sin (A) y. We now substitute p, h and angle a by their values. 200 z y (2 2 cos (56) z y sin (56) 1800. Solve the above system to obtain. Z.6456 and y 811.035, we now substitute z by b c and Y by b c to obtain two equations in b and c as follows. B.6456 and b c 811.035. We now combine the above equations to obtain an equation in one unknown as follows.
B 811.035 /.6456, multiply all terms to obtain a quadratic equation. B 2 811.035.6456 b, solve to obtain. B.3643 and.2812. We now use the equation b c 811.035 to find. For.3643,.2812 and for.2812,.3643. It is in fact one solution since c and b are interchangeable.
The area of the triangle may be calculated using sides c and b as follows area (1 / 2) b c sin (A). But the area of the triangle may also be calculated using the altitude h and corresponding base a as follows area (1 / 2). We now combine the two expressions for the area to obtain an equation as follows b c sin (A) h a (equation 2). A third equation is obtained using the law of cosine as follows a 2 b 2 c 2 - 2 b c cos (A) (equation 3). We now have 3 equations with 3 unknowns which we have to solve. Equation (1) gives a p - (b c substitute the above into equation (3) to obtain (p - (b c) 2 b 2 c 2 - 2 b c cos (A).
Expand the left hand side of the above equation and simplify p 2 (b c) 2 - 2 p (b c) b 2 c 2 - 2 b c cos (A) p 2 b 2 c 2 2 b c - 2 p (b c). We now use a p - (b c) in equation (2) and write b c sin (A) h (p - (b c) which may be written as follows b c sin (A) h p - h (b c) (equation 5). We now define two variables as follows. Z b c and y b c and rewrite equations 4 and 5 as follows. P 2 2 y - 2 p z - 2 Y cos (A). Y sin (A) h p -. The above equations make a system of linear equations with unknowns z and.
How do you write and Solve an Equation From a word Problem
However, the two bases that are most widely used are l0 and. A logarithm with base 10 is called a common logarithm. Its value at dissertation x is denoted by log x, that is, a logarithm with base e is called a natural logarithm, and its value at x is denoted by In x, that is, consequently: Sometimes we can use the definition of logarithms to evaluate common. Problem : In the figure below, abc is a triangle whose perimeter has a length of 100 units and the length of the altitude h is equal to 18 units. The size of the internal angle a is equal to 560. Find all sides of the triangle. Solution to Problem : The given perimeter p 100 gives an help equation as follows a b c p (equation 1).
The following table lists the equivalency of each logarithmic form. At times, we can find the numerical value of a logarithm by converting to exponential form and then using the one-to-one property of exponents, as the next example illustrates. Evaluating Logarithms evaluate each logarithm. In each case we let u equal the given expression, and write the logarithmic equation in its equivalent exponential form and then solve the resulting equation for u as shown in the following table. We use the equivalency between the logarithmic and exponential forms to solve certain equations involving logarithms, as the next example shows. Solving Logarithmic Equations Solve each logarithmic equation for. First we rewrite the given equation in exponential form and then solve the resulting equation. Evaluating Logarithms - statement base 10 and Base e the base of a logarithmic function can be any positive number except.
have the following logarithm definition: Let b 0 and. The logarithm of x with base b, which is represented by y, is defined by y logb x if and only if x by for every x 0 and for every real number. In words, this definition says that the logarithm y is the exponent to which b is raised to get x The two equations in the above definition are equivalent and as such can be used interchangeably. The first equation is in logarithmic form and the second is in exponential form. The diagram below is helpful when changing from one form to the other: Base of logarithm is the same as exponent base It is important to observe that logb x is an exponent. For instance, the numbers in the right column of Table 1 are the logarithms (base 2) of the numbers in the left column. Converting Exponentials to logarithmic Convert each exponential form equation to logarithmic form, The equivalencies are listed in the following table. Converting Logarithmic to Exponentials Convert each logarithmic form to an equivalent exponential form.
Solve applied Problems, in the previous section we essay learned that the graph of the inverse function f-1 1 is a reflection of the graph of f across the line. Exponential functions are one-to-one, so they have inverses. Consequently, if we graph the function. F (x) bx and reflect its graph across the line y x, the result is the graph of f-1. This new function is given the name logarithmic function with base b, and it is written. For example, as Figure 1 shows, the graph of f-1 (x) log2, is the reflection of the graph of f (x) 2x across the line. Since logarithms, in a sense, evolve as inversesof exponential functions, algebra of logarithms is derived from the algebra of exponents, as we shall see. Converting Exponentials to logarithmic Forms and Vice versa. A logarithm is actually an exponent.
How do you write an Equation from a word Problem?
Help : Logarithmic and exponential functions, here is a complete list of logarithmic and exponential functions accepted by quickMath. The tables show the usual form in which the functions appear in textbooks, along with the form accepted by quickMath. In most cases, the quickMath version is identical to the textbook version. If there is a function missing best which you would like see added to those supported by quickMath, just send your suggestion. Convert Exponentials to logarithmic Forms and Vice versa. Evaluate logarithms Base 10 and Base. Use the Properties of Logarithms. Use the Change-of-Base formula.


How many triangles are there in this picture? 94.7% of Americans miss the answer. Try it first, then see the answer below.
6 small red triangles
3 small white triangles
3 medium red triangles with a small white triangle center
1 large triangle with 3 small triangles in the center
total = 13
Triangles within a Triangle
Date: 11/10/96 at 07:38:57 From: Cato H. Jensen Subject: Geometry, Math Project (GCSE) 1996 This is an English project called "Triangles in Triangles" for I and H level. We are doing this in 10th grade. The question is: Investigate equilateral triangles of other sizes in order to examine the relationship between the size of a triangle and the total number of triangles it contains. The numbers (where n = total number of triangles and b = number of triangles in the base) given are : b n 1 1 2 5 3 13 4 27 5 48 6 78 7 118 8 170 I need to find a formula for the total number of triangles when there are X base triangles. I have done the rest of the project, but this part has gotten me really stuck.
Date: 01/04/97 at 15:58:04 From: Doctor Chaos Subject: Re: Geometry, Math Project (GCSE) 1996 I think the best way to approach your problem is to examine the pattern you were given in order to calculate the total number of triangles. Look at these pictures: This triangle has 3 little triangles in the base so b=3. / In this triangle, there are nine (9) little /__ triangles or b^2. Then there are three (3) / / triangles which are larger (containing 4 little ones) /__/__ and one (1) largest (containing all 9). / / / /__/__/__ 9+3+1 = 13 triangles. This triangle has 4 little triangles in the base so b = 4. / The total of little triangles is b^2 or 16. /__ The number of bigger triangles (containing 4 little / / ones) is 7. The number of still bigger triangles /__/__ (containing 9 little ones) is 3. The number of / / / largest triangles contains all 16 and is 1. /__/__/__ / / / / 16+7+3+1 = 27 triangles /__/__/__/__ If we examine the numbers of triangles at every level, we may see a pattern which may then suggest a formula. b = Number of triangles in the base l = Number of little triangles f = Next largest triangle (contains 4) n = Next largest triangle (contains 9) s = Next largest triangle (contains 16) T = Total number of triangles b l f n s T 1 1 0 0 0 1 2 4 1 0 0 5 3 9 3 1 0 13 4 16 7 3 1 27 5 25 ? ? ? 48 6 36 ? ? ? 78 7 49 ? ? ? 118 8 64 ? ? ? 170 Organize the data you have already collected and see if there is a formula that will help you add up the various sizes of triangles to arrive at the total. You might even need 2 different formulas; one for an odd number on the base and one for even numbers. You never know until you try. Good luck. -Doctor Chaos, The Math Forum Check out our web site! http://mathforum.org/dr.math/


The Robust re-scaling transformation (RR) is a transformation the help reveal latent structure in data. It uses three steps to transform the data:
The sequence of these transformations helps focus analyses on consequential variance in the data rather than having it be focused on variation resulting from the feature’s measurement scale or outliers.
This is the github page for our R package ‘rrscale’ to perform the transformation.
Our R package is available on CRAN: https://cran.r-project.org/package=rrscale
Our docker image for reproducing the analysis in paper can be found here.


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Personal Reflection about My Learning Profile - Essay Example
Mathematics, as they say, has always been a sore point in my life. If I remember correctly, as a little child I cried a river of tears more than I care to count, especially since I used to experience problems in counting and counting being part of mathematics made it even harder. The moment anyone, be it the teacher or a student, begins to spout numbers at me then it was rapidly becoming my habit to shut down. I used to experience a difficult time in completing basic addition and subtraction sums as my perception were that math was difficult. As my memoryâ€™s ability to store information was also not that good, I used to count my fingers and toes to get the answers to the simplest of the arithmetic questions posed at me and it was becoming embarrassing and tedious. Moreover, this was further worsened by the fact that I did not train as I was expected to both inside and outside my math classroom mainly because I hated the subject with a zeal. When my parents realized this, there was nothing they could do to make me do better at math rather they decided to push me to learn multiplication and division by drilling me over and over again.
As a freshman in Binghamton University, my earlier experiences have made the understanding and application of threshold concept a bit easy. To start with is my newly developed interest in mathematics which came to light and boomed exponentially during my junior high school immediately after taking the Calculus AB class. For example, my teacher Luba Goldenberg taught us to visualize instead of memorizing during the first day of the class. This proved to be my eye-opener. Later on, she said that she would like to give us the trig quiz which asked about the answer to Sin 11Ï€ over 6. She also mentioned to us to try to answer each question in three seconds.Â Â
Write something about yourself. No need to be fancy, just an overview.


In this paper, I will examine Kant’s claim that our representation of space is an inutition. Having established that space is a priori, Kant claims that its representation is not a “discursive or, as is said, general concept of relations of things in general, but a pure intuition” (Kant 175). Beginning with his conception of total space, I will elaborate on its implications regarding all other representations of space. After showing that our representation of total space is necessarily prior to all other representations of it, I will examine Kant’s deduction of space as an intuition. I will conclude with two potential objections.
Kant’s argument begins with the claim that we can only represent a single space: total space. He argues that when we refer to many spaces, we are only speak of things contained in this total space. Consider a house and its comprising rooms. While each room occupies a specific individual space, all of these spaces are still contained in the space taken by the full house. If this is true, then it must follow that all non-total spaces are contained in total space.
Now, if one could prove that the representations of non total spaces are prior to the representation of total space, then one could object to Kant’s argumentative thesis. One could claim that total space is a concept derived from the composition of non-total spaces, and thus must not be an intuition. Anticipating this, Kant adds that the representation of total space is necessarily prior to a representation of its contained parts, because its contained parts are “only thought in it” (Kant 175).
Only total space is boundless; all non-total spaces are bounded. If a space is bounded, then it must have circumscribed limits that dictate the spatial locations that fall within that region of space. Because any bounded space is not total, there must then be spatial locations that do not fall within that region. Hence, by condition of being bounded, all non-total spaces must exclude some spatial locations.
Yet, if something is not represented, it cannot be excluded. Thus, these excluded spatial locations must be represented. Hence, we must represent another spatial region that contains both the circumscribed region and the excluded spatial points. Now, we know that non-total spaces can be arbitrarily large – that is, anything but boundless – so, we must conclude that we represent total space.
There must first be a container before anything can be contained in it. I believe this is self-evident; it is also nonsensical to suppose otherwise. Tea cannot be contained in a cup without there first being a cup which could contain the tea. If this is the case, then it follows that the representation of total space is necessarily prior to all other spatial representations. By all other representations of space, I mean all concepts that regard non-total spaces and the concept of total space.
This is what Kant intends when he subsequently states that total space “is essentially single; the manifold in it, thus also the general concept of spaces in general, rests merely on limitations” (Kant 175) In reference to the earlier potential objection, Kant has shown that the representation of total space is not the composition of non-total spaces. Thus, by proving that the representation of total space – that is, the representation that is not the concept predicated on it – is necessarily prior to all other spatial representations, Kant concludes that all concepts of space must be grounded on an a priori intution of total space.
In the introduction to the Transcendental Aesthetic, Kant writes, “in whatever way and through whatever means a cognition may relate to objects, that through which it relates immediately to them, and at which all thought as a means is directed as an end is an intuition” (Kant 172). Thus, for Kant to have demonstrated that our representation of total space is an intuition, he has to have shown us that our representation of space fulfills 2 conditions: (1) singularity and (2) immediacy.
To fulfill (1), Kant must have shown that the representation of total space presents particular object(s). As referenced by the earlier objection, Kant proved that the representation of total space cannot be derived from a group of things i.e. non-total spaces. Hence, the representation of total space does not bear a general feature that holds over a set of objects. If this is the case, then the representation of total space must not be general, and thus, is singular.
To fulfill (2), Kant must have shown that the representation of total space is not related via another representation. He has proven that all other spatial representations must be mediate to the representation of total space. Yet, an objector can accept this, but still argue that this does not rule out the possibility that our representation of total space is still mediate to another representation. For such a claim to hold, (s)he must prove that the representation of total space derives from a representation that does not regard space. However, this is inconcievable. It is nonsensical to hold that one could derive a representation of total space from another representation that is independent of it. Hence, the representation of total space must be immediate.
Not only does his argument meet the conditions of an inutition, but also I find his consideration of all non-total spaces as being thought in total space to be quite keen. Recall that the representation of any non-total spatial region necessitates the representation of a spatial region that contains it and its excluded points. I argued that since non-total spaces can be arbitrarily large, it must follow that the representation of total space contains any representation of a non-total space.
An objector may claim that regardless of how arbitrarily large a non-total space W is, it is not represented in total space, but rather in a non-total space X that contains W and some spatial locations that W excludes. If this is so, then the representation of X can be thought in the representation of W. It would follow that the representation of total space is not necessarily prior to the representation of all non-total spaces. Rather, only the representation of a non-total space that contains the the non-total space we are considering as well as some of its excluded spatial locations is necessarily prior.
Yet, we can turn the table and ask that if X is bounded – as it must be since it is non-total – then what circumscribes its limits? Dogmatic in his/her ways, (s)he will claim that it is only some non-total space Y that contains X and some of its excluded spatial locations. But then we can again ask: If Y is bounded – as it must be since it is non-total – then what circumscribes its limits? Like a true dogmatist, (s)he will claim – this time, hopefully a bit more hesitantly – that it is only some non-total space Z that contains Y and some of its excluded spatial locations. But then we can again ask that if Z is bounded…
This will repeat ad infinitum until the dogmatic objector realizes that (s)he cannot legitimately circumscribe a non-total space unless it is represented in total space. Hence, we still arrive at Kant’s conclusion.
Another objecter might model an argument off of the Cartesian plane. In the paradigmatic (x,y) coordinate system, we represent both axes with perpendicular lines and have a grid that corresponds to each pair of coordinates. At the poles of each axis, we draw arrows to illustrate that each axis extends infinitely. Both the dashes on the page and the area the coodinate plane takes up is all finite. Yet, the what is drawn on the page models infinite 2D space.
This objector will agree that non-total spaces can only be represented within boundless space. Yet, (s)he will argue that this does not entail that our prior representation – the representation in which non-total spaces are thought in – must itself be boundless. Instead, this prior representation can model boundless in the same sense that the Cartesian plane models infinite 2D space, while also being bounded in the same sense the Cartesian plane is created in finitie space with finite scratches on the page. In this sense, we are not representing total space, but rather, a non-total space that can be extended.
While an interesting effort, Kant would object to this for two reasons. First, in the way that we have been considering it, space cannot be extended. In our implicit definition, all spaces either contain a smaller space or are contained in a larger space. They cannot stretch; they cannot shrink. Also, Kant would argue that this mimics the earliest objector’s claim that total space is a concept derived from non-total spaces. Even though the Cartesian plane finitely models infinite 2D space, it is still predicated on the representation of the totality of 2D space. Therefore, regardless of whatever way one can think of mapping the coordinate plane to the representation of non-total spaces, it will still entail that total space is represented prior.
In conclusion, I have elaborated on Kant’s argument that our representation of space is an intuition. After considering what he meant by total space, I have shown that it cannot be constructed through composition of non-total spaces. In doing so, I have shown that the representation of total space is necessarily prior to all other representations of space. To substantiate this claim, I considered singularity and immediacy, and showed that Kant’s argument does indeed satisfy these conditions. Already finding Kant’s argument to be sufficient, I then considered two possible objections and showed that Kant’s arguments still hold in light of their concerns.
Kant, Immanuel. Critique of Pure Reason. Ed. Paul Guyer and Allen W. Wood. Cambridge: Cambridge UP, 1998. Print.


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Dynamic Time Warping (DTW) is a way to compare two -usually temporal- sequences that do not sync up perfectly. It is a method to calculate the optimal matching between two sequences. DTW is useful in many domains such as speech recognition, data mining, financial markets, etc. It’s commonly used in data mining to measure the distance between two time-series.
In this post, we will go over the mathematics behind DTW. Then, two illustrative examples are provided to better understand the concept. If you are not interested in the math behind it, please jump to examples.
Let’s assume we have two sequences like the following:
The sequences and can be arranged to form an grid, where each point is the alignment between and .
A warping path maps the elements of and to minimize the distance between them. is a sequence of grid points . We will see an example of the warping path later.
Warping Path and DTW distance
The Optimal path to can be computed by:
where is the Euclidean distance
Overall path cost:
Restrictions on the Warping function
The warping path is found using a dynamic programming approach to align two sequences. Going through all possible paths is “combinatorically explosive”. Therefore, for efficiency purposes, it’s important to limit the number of possible warping paths, and hence the following constraints are outlined:
- Boundary Condition: This constraint ensures that the warping path begins with the start points of both signals and terminates with their endpoints.
- Monotonicity condition: This constraint preserves the time-order of points (not going back in time).
- Continuity (step size) condition: This constraint limits the path transitions to adjacent points in time (not jumping in time).
In addition to the above three constraints, there are other less frequent conditions for an allowable warping path:
- Warping window condition: Allowable points can be restricted to fall within a given warping window of width (a positive integer).
- Slope condition: The warping path can be constrained by restricting the slope, and consequently avoiding extreme movements in one direction.
An acceptable warping path has combinations of chess king moves that are:
- Horizontal moves:
- Vertical moves:
- Diagonal moves:
Let’s import all python packages we need.
import pandas as pd import numpy as np # Plotting Packages import matplotlib.pyplot as plt import seaborn as sbn import matplotlib as mpl mpl.rcParams['figure.dpi'] = 300 savefig_options = dict(format="png", dpi=300, bbox_inches="tight") # Computation packages from scipy.spatial.distance import euclidean from fastdtw import fastdtw
Let’s define a method to compute the accumulated cost matrix for the warp path. The cost matrix uses the Euclidean distance to calculate the distance between every two points. The methods to compute the Euclidean distance matrix and accumulated cost matrix are defined below:
def compute_euclidean_distance_matrix(x, y) -> np.array: """Calculate distance matrix This method calcualtes the pairwise Euclidean distance between two sequences. The sequences can have different lengths. """ dist = np.zeros((len(y), len(x))) for i in range(len(y)): for j in range(len(x)): dist[i,j] = (x[j]-y[i])**2 return dist
def compute_accumulated_cost_matrix(x, y) -> np.array: """Compute accumulated cost matrix for warp path using Euclidean distance """ distances = compute_euclidean_distance_matrix(x, y) # Initialization cost = np.zeros((len(y), len(x))) cost[0,0] = distances[0,0] for i in range(1, len(y)): cost[i, 0] = distances[i, 0] + cost[i-1, 0] for j in range(1, len(x)): cost[0, j] = distances[0, j] + cost[0, j-1] # Accumulated warp path cost for i in range(1, len(y)): for j in range(1, len(x)): cost[i, j] = min( cost[i-1, j], # insertion cost[i, j-1], # deletion cost[i-1, j-1] # match ) + distances[i, j] return cost
In this example, we have two sequences and with different lengths.
# Create two sequences x = [3, 1, 2, 2, 1] y = [2, 0, 0, 3, 3, 1, 0]
We cannot calculate the distance between and since they don’t have equal lengths (the code follows).
fig, ax = plt.subplots(figsize=(14, 10)) # Remove the border and axes ticks fig.patch.set_visible(False) ax.axis('off') xx = [(i, x[i]) for i in np.arange(0, len(x))] yy = [(j, y[j]) for j in np.arange(0, len(y))] for i, j in zip(xx, yy[:-2]): ax.plot([i, j], [i, j], '--k', linewidth=4) ax.plot(x, '-ro', label='x', linewidth=4, markersize=20, markerfacecolor='lightcoral', markeredgecolor='lightcoral') ax.plot(y, '-bo', label='y', linewidth=4, markersize=20, markerfacecolor='skyblue', markeredgecolor='skyblue') ax.set_title("Euclidean Distance!??", fontsize=28, fontweight="bold") fig.savefig("ex1_euclidean_distance.png", **savefig_options)
Compute DTW distance and warp path
Many Python packages calculate the DTW by just providing the sequences and the type of distance (usually Euclidean by default). Here, we use a popular Python implementation of DTW that is FastDTW which is an approximate DTW algorithm with lower time and memory complexities.
dtw_distance, warp_path = fastdtw(x, y, dist=euclidean)
Note that we are using SciPy‘s distance function Euclidean that we imported earlier. For a better understanding of the warp path, let’s first compute the accumulated cost matrix and then visualize the path on a grid. The following code will plot a heatmap of the accumulated cost matrix.
cost_matrix = compute_accumulated_cost_matrix(x, y)
fig, ax = plt.subplots(figsize=(12, 8)) ax = sbn.heatmap(cost_matrix, annot=True, square=True, linewidths=0.1, cmap="YlGnBu", ax=ax) ax.invert_yaxis() # Get the warp path in x and y directions path_x = [p for p in warp_path] path_y = [p for p in warp_path] # Align the path from the center of each cell path_xx = [x+0.5 for x in path_x] path_yy = [y+0.5 for y in path_y] ax.plot(path_xx, path_yy, color='blue', linewidth=3, alpha=0.2) fig.savefig("ex1_heatmap.png", **savefig_options)
The color bar shows the cost of each point in the grid. As can be seen, the warp path (blue line) is going through the lowest cost on the grid. Let’s see the DTW distance and the warping path by printing these two variables.
print("DTW distance: ", dtw_distance) print("Warp path: ", warp_path) >>> DTW distance: 6.0 >>> Warp path: [(0, 0), (1, 1), (1, 2), (2, 3), (3, 4), (4, 5), (4, 6)]
The warping path starts at point (0, 0) and ends at (4, 6) by 6 moves. Let’s also calculate the accumulated cost most using the functions we defined earlier and compare the values with the heatmap.
cost_matrix = compute_accumulated_cost_matrix(x, y) print(np.flipud(cost_matrix)) # Flipping the cost matrix for easier comparison with heatmap values! >>> [[32. 12. 10. 10. 6.] [23. 11. 6. 6. 5.] [19. 11. 5. 5. 9.] [19. 7. 4. 5. 8.] [19. 3. 6. 10. 4.] [10. 2. 6. 6. 3.] [ 1. 2. 2. 2. 3.]]
The cost matrix is printed above has similar values to the heatmap.
Now let’s plot the two sequences and connect the mapping points. The code to plot the DTW distance between and is given below.
fig, ax = plt.subplots(figsize=(14, 10)) # Remove the border and axes ticks fig.patch.set_visible(False) ax.axis('off') for [map_x, map_y] in warp_path: ax.plot([map_x, map_y], [x[map_x], y[map_y]], '--k', linewidth=4) ax.plot(x, '-ro', label='x', linewidth=4, markersize=20, markerfacecolor='lightcoral', markeredgecolor='lightcoral') ax.plot(y, '-bo', label='y', linewidth=4, markersize=20, markerfacecolor='skyblue', markeredgecolor='skyblue') ax.set_title("DTW Distance", fontsize=28, fontweight="bold") fig.savefig("ex1_dtw_distance.png", **savefig_options)
In this example, we will use two sinusoidal signals and see how they will be matched by calculating the DTW distance between them.
time1 = np.linspace(start=0, stop=1, num=50) time2 = time1[0:40] x1 = 3 * np.sin(np.pi * time1) + 1.5 * np.sin(4*np.pi * time1) x2 = 3 * np.sin(np.pi * time2 + 0.5) + 1.5 * np.sin(4*np.pi * time2 + 0.5)
Just like Example 1, let’s calculate the DTW distance and the warp path for x1 and x2 signals using FastDTW package.
distance, warp_path = fastdtw(x1, x2, dist=euclidean)
fig, ax = plt.subplots(figsize=(16, 12)) # Remove the border and axes ticks fig.patch.set_visible(False) ax.axis('off') for [map_x, map_y] in warp_path: ax.plot([map_x, map_y], [x1[map_x], x2[map_y]], '-k') ax.plot(x1, color='blue', marker='o', markersize=10, linewidth=5) ax.plot(x2, color='red', marker='o', markersize=10, linewidth=5) ax.tick_params(axis="both", which="major", labelsize=18) fig.savefig("ex2_dtw_distance.png", **savefig_options)
As can be seen in above figure, the DTW distance between the two signals is particularly powerful when the signals have similar patterns. The extrema (maximum and minimum points) between the two signals are correctly mapped. Moreover, unlike Euclidean distance, we may see many-to-one mapping when DTW distance is used, particularly if the two signals have different lengths.
You may spot an issue with dynamic time warping from the figure above. Can you guess what it is?
The issue is around the head and tail of time-series that do not properly match. This is because the DTW algorithm cannot afford the warping invariance for at the endpoints. In short, the effect of this is that a small difference at the sequence endpoints will tend to contribute disproportionately to the estimated similarity.
DTW is an algorithm to find an optimal alignment between two sequences and a useful distance metric to have in our toolbox. This technique is useful when we are working with two non-linear sequences, particularly if one sequence is a non-linear stretched/shrunk version of the other. The warping path is a combination of “chess king” moves that starts from the head of two sequences and ends with their tails.
Thanks for reading 🙏
And finally, you can find my knowledge forest 🌲 (raw digital notes) at notes.ealizadeh.com.
📩 Join my mailing list
 Donald J. Berndt and James Clifford, Using Dynamic Time Warping to Find Patterns in Time Series, 3rd International Conference on Knowledge Discovery and Data Mining
 Salvador, S. and P. Chan, FastDTW: Toward accurate dynamic time warping in linear time and space (2007), Intelligent Data Analysis
 Diego Furtado Silva, et al. On the effect of endpoints on dynamic time warping (2016), SIGKDD Workshop on Mining and Learning from Time Series
Programatically understanding dynamic time warping (DTW)
In order to create a mapping between the two signals, we need to create a path in the above plot. The path should start at (0,0) and want to reach (M,N) where (M, N) are the lengths of the two signals. Our aim is to find the path of minimum distance.
Understanding Dynamic Time Warping - The Databricks Blog
Try this notebook in Databricks This blog is part 1 of our two-part series . To go to part 2, go to Using Dynamic Time Warping and MLflow to Detect Sales Trends. The phrase "dynamic time warping," at first read, might evoke images of Marty McFly driving his DeLorean at 88 MPH in the Back to the Future series.
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Dear children and parents... WELCOME TO YEAR 6!!
You've now had a chance to meet your new teachers and we can't wait to start our journey together.
In the meantime, have a restful 6 weeks off.
Remember to keep checking this class page for regular updates in September.
Miss Hill and Miss O'Neil
Take a look at our class reads from this half term. Follow the links to find out more about each book!
In 6M, we have been reading Boy 87 by Ele Fountain and The Boy at the back of the class by Onjali Q Rauf.
In 6D, we have been reading Holes by Louis Sachar.
In guided reading, we have been looking at a range of texts including non fiction, poetry and classical fiction. In class, we have been using VIPERS questioning to help develop our understanding each text type.
In maths this half term, year six have been working on reading and writing numbers up to ten million and using the four operations on whole numbers. Take a look below at some of the problems we have solved and methods we have been using.
In design technology, year six have been developing their sewing skills. The children designed and made a geometric design using a variety of stitches. We have looked at why and when we would use different stitches including running stitch, overstitch, blanket stitch and back stitch. Take a look at the tutorials below to see each type of stitch to practice at home!


Includes bibliographical references and index.
|Statement||[edited by] Antonio Giambruno, César Polcino Milies, S.K. Sehgal.|
|Series||Lecture notes in pure and applied mathematics ;, 247, Lecture notes in pure and applied mathematics ;, v. 247.|
|Contributions||Giambruno, A., Milies, César Polcino., Sehgal, Sudarshan K., 1936-|
|LC Classifications||QA174 .G768 2006|
|The Physical Object|
|LC Control Number||2005053799|
Wallace defines a ring and explains the importance of the axioms used in its definition. While Wallace gives some examples of rings and introduces some basic definitions, he defers the discussion of ring theory until after he has discussed groups, which have a simpler, if less familiar, by: This Book offers an introduction to the foundations of mathematics together with the fundamental algebraic structures, namely groups, rings, fields, and arithmetic. Intended as a text for undergraduate and graduate students of mathematics. This is the first in a series of three : Springer Singapore. Basic Algebra is the first volume of a new and revised edition of P.M. Cohn's classic three-volume text Algebra which is widely regarded as one of the most outstanding introductory algebra textbooks. For this edition, the text has been reworked and updated into two self-contained, companion volumes, covering advanced topics in algebra for second- and third-year undergraduate and postgraduate. to Group Rings by Cesar Polcino Milies Instituto de Matematica e Estatistica, Universidade de sao Paulo, sao Paulo, Brasil and Sudarshan K. Sehgal Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton. Canada SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. A c.I.P. Catalogue record for this book is available from the Library of Congress.
The book covers groups, rings, and fields. In group theory, group actions are the unifying theme and are introduced early. Ring theory is motivated by what is needed for solving Diophantine equations, and, in field theory, Galois theory and . Get this from a library! Groups, rings, and group rings: International Conference: Groups, Rings, and Group Rings, July August 2, , Ubatuba, Brazil. [A Giambruno; César Polcino Milies; Sudarshan K Sehgal;] -- "This volume represents the proceedings of the conference on Groups, Rings and Group Rings, held July August 2, , in Ubatuba, Brazil. The Galois group of the polynomial f(x) is a subset Gal(f) ˆS(N(f)) closed with respect to the composition and inversion of maps, hence it forms a group in the sense of Def And from the properties of Gal(f) as a group we can read o whether the equation f(x) = 0 is solvable by radicals or not. Groups,RingsandFields 9 Examples of rings. Number systems (1) All of Z, Q, Rand Care commutative rings with identity (with the number 1 as the identity). (2) Nis NOT a ring for the usual addition and multiplication. These are binary operations and we do have a zero element, namely 0, so axiom (A2) Size: KB.
The general algebraic object is the tensor ring of a bimodule. Importance subclass are pass algebras or quiver algebras1. Its elements are formal linear combinations of passes in a directed graph (quiver). The product of two passes is its concatenation if one pass ends where the other one starts or zero if Size: KB. Abstract Algebra Theory and Applications. This text is intended for a one- or two-semester undergraduate course in abstract algebra. Topics covered includes: The Integers, Groups, Cyclic Groups, Permutation Groups, Cosets and Lagrange’s Theorem, Algebraic Coding Theory, Isomorphisms, Normal Subgroups and Factor Groups, Matrix Groups and Symmetry, The Sylow Theorems, Rings, Polynomials. EXERCISES AND SOLUTIONS IN GROUPS RINGS AND FIELDS 5 that (y(a)a)y(a)t= ethen (y(a)a)e= e Hence y(a)a= e:So every right inverse is also a left inverse. Now for any a2Gwe have ea= (ay(a))a= a(y(a)a) = ae= aas eis a right identity. Hence eis a left identity. If Gis a group of even order, prove that it has an element a6=esatisfying a2 = e:File Size: KB. A Principal Ideal is an Ideal that contains all multiples of one Ring element. A Principal Ideal Ring is a Ring in which every Ideal is a principal ideal. Example: The set of Integers is a Principal Ideal ring. link to more Galois Field GF(p) for any prime, p, this Galois Field has p elements which are the residue classes of integers modulo p.


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