In the vast realm of mathematics, certain constants hold a mystique that captivates the minds of scholars and enthusiasts alike. One such intriguing element is the enigmatic “pi123.” In this article, we embark on a journey to unravel the mysteries surrounding pi,123, exploring its mathematical significance and the role it plays in various mathematical contexts.
The Significance of Pi123:
Pi, represented by the symbol π, is a fundamental mathematical constant that represents the ratio of a circle circumference to its diameter. However, the addition of “123” to the term introduces an element of mystery and curiosity. Pi123 remains a less-explored concept, often leaving mathematicians and researchers intrigued by its potential applications and implications.
Exploring the Mathematical Landscape:
Pi,123 has garnered attention for its potential role in specific mathematical sequences and patterns. Researchers delve into the depths of mathematical equations, seeking connections that involve pi,123 and examining its potential significance in various mathematical frameworks.
Applications in Number Theory:
Number of theory, a branch of pure mathematics, is known for its exploration of integers and their properties. Pi123 may hold significance in number theory, leading to investigations into its potential relationships with prime numbers, sequences, and other mathematical phenomena.
Computational Mathematics and Pi,123:
In the realm of computational mathematics, researchers are keen on uncovering the computational aspects of pi,123. Whether it reveals patterns in algorithms, aids in numerical computations, or plays a role in mathematical modeling, the exploration of pi,123’s computational applications remains an area of ongoing research.
Pi,123 in Mathematical Education:
Understanding pi,123 also extends to its potential role in mathematical education. Educators and curriculum developers explore innovative ways to incorporate unique mathematical concepts into teaching materials, aiming to inspire curiosity and critical thinking among students.
Challenges and Future Directions:
While pi,123 holds promise in various mathematical domains, challenges persist in fully understanding its implications. Researchers continue to grapple with complex mathematical questions, pushing the boundaries of current knowledge to unlock the secrets hidden within pi,123.
Frequently Asked Questions (FAQs) about Pi,123:
What is Pi,123, and how does it differ from regular pi (π)?
Pi,123 is a term that adds the sequence “123” to the well-known mathematical constant pi (π). While π represents the ratio of a circle’s circumference to its diameter, the addition of “123” introduces a unique element that has garnered attention for its potential significance in mathematical contexts.
Is Pi,123 commonly used in mathematical equations and formulas?
Pi,123 is not as commonly used as the standard pi (π) in mathematical equations and formulas. However, researchers are exploring its potential applications in specific mathematical sequences, computational mathematics, and number theory.
What role does Pi,123 play in computational mathematics?
The role of Pi,123 in computational mathematics is an area of ongoing research. Researchers are investigating whether Pi,123 reveals patterns in algorithms, aids in numerical computations, or plays a role in mathematical modeling.
Are there any known connections between Pi,123 and number theory?
Pi,123 has piqued the interest of mathematicians in the field of number theory. Investigations are underway to explore potential connections between Pi,123 and prime numbers, sequences, and other aspects of number theory.
How might Pi,123 be incorporated into mathematical education?
Pi,123 could be incorporated into mathematical education as an engaging concept to inspire curiosity and critical thinking among students. Educators and curriculum developers may explore innovative ways to introduce Pi,123 and its unique mathematical properties.
What challenges exist in understanding the implications of Pi,123?
Challenges in understanding the implications of Pi,123 include its less-explored nature and the complexity of mathematical questions surrounding it. Researchers continue to face challenges in fully unraveling the mysteries and implications of Pi,123.
Are there practical applications of Pi,123 in real-world scenarios?
While Pi,123’s practical applications in real-world scenarios are not well-established, ongoing research may reveal unexpected connections or uses. Currently, the focus is on understanding its role in theoretical and computational aspects of mathematics.
How can enthusiasts contribute to the exploration of Pi,123?
Enthusiasts can contribute to the exploration of Pi,123 by staying informed about ongoing research, engaging in discussions within mathematical communities, and supporting initiatives that promote mathematical curiosity and discovery.
In conclusion, pi123 stands as a captivating addition to the realm of mathematical constants, sparking curiosity and exploration among mathematicians and researchers. As ongoing investigations delve into its significance across diverse mathematical disciplines, the mystery surrounding pi,123 continues to unfold, enriching our understanding of the intricate world of mathematics. Pi,123 remains a fascinating topic with much to be discovered, and these FAQs provide a glimpse into the current understanding and ongoing inquiries surrounding this intriguing mathematical concept.


Tools are designed to help their users do their tasks more efficiently and crunching numbers is no exception. I’ve been humming along with Excel and my trusty scientific calculator just fine, but as I’m getting more involved with calculations such as discounting I’ve decided it may be worth the time to pick up a financial calculator that has many of these formulas built-in.
I ended up buying the HP 10BII, which is among the most popular financial calculators out there. It’s very reasonably priced, has training modules on the HP web site, contains advanced functions such as IRR and NPV, and has a user-friendly keypad. For $30-40, this is a must have for anyone in finance or real estate.


What are the disadvantages of two-way ANOVA?
- It becomes difficult to maintain homogeneity of the blocks if the number of treatments is large enough.
- The technique can be challenging and time-consuming.
- In order to get accurate results, a missing value cannot be ignored.
ANOVA, or its non-parametric counterparts, allow you to determine if differences in mean values between three or more groups are by chance or if they are indeed significantly different. ANOVA is particularly useful when analyzing the multi-item scales common in market research.
The disadvantage of the ANOVA F-test is that if we reject the null hypothesis, we do not know which treatments can be said to be significantly different from the others, nor, if the F-test is performed at level α, can we state that the treatment pair with the greatest mean difference is significantly different at level ...
ANOVA assumes that the data is normally distributed. The ANOVA also assumes homogeneity of variance, which means that the variance among the groups should be approximately equal. ANOVA also assumes that the observations are independent of each other.
One of the biggest problems with traditional repeated measures ANOVA is missing data on the response variable. The problem is that repeated measures ANOVA treats each measurement as a separate variable. Because it uses listwise deletion, if one measurement is missing, the entire case gets dropped.
A two-way ANOVA is used to estimate how the mean of a quantitative variable changes according to the levels of two categorical variables. Use a two-way ANOVA when you want to know how two independent variables, in combination, affect a dependent variable.
The results of a one-way ANOVA can be considered reliable as long as the following assumptions are met: Response variable residuals are normally distributed (or approximately normally distributed). Variances of populations are equal.
Answer and Explanation: ANOVA's main advantage over t-tests is in comparing multiple predictor variables at the same time. This can make it easier to use, and faster.
The advantage of variance is that it treats all deviations from the mean as the same regardless of their direction. The squared deviations cannot sum to zero and give the appearance of no variability at all in the data. One drawback to variance, though, is that it gives added weight to outliers.
There are three primary assumptions in ANOVA: The responses for each factor level have a normal population distribution. These distributions have the same variance. The data are independent.
Why is the F-test not recommended?
Why is the F-test not recommended? Special problems with small sample sizes: Even if none of the test assumptions are violated, an F test with small sample sizes may not have sufficient power to detect a significant difference between the two samples, even if the variances are in fact different.
The F-test compares the population variances while the t-test compares the population means. 1.3 Select all samples using random or stratified random procedures. Perform all testing and measuring in accordance with standard acceptable practices.
An ANOVA can only be conducted if there is no relationship between the subjects in each sample. This means that subjects in the first group cannot also be in the second group (e.g. independent samples/between-groups). The different groups/levels must have equal sample sizes.
An ANOVA is quite robust against violations of the normality assumption, which means the Type 1 error rate remains close to the alpha level specified in the test. Violations of the homogeneity of variances assumption can be more impactful, especially when sample sizes are unequal between conditions.
At this point, it is important to realize that the one-way ANOVA is an omnibus test statistic and cannot tell you which specific groups were statistically significantly different from each other, only that at least two groups were.
The biggest drawbacks are known as order effects, and they are caused by exposing the subjects to multiple treatments. Order effects are related to the order that treatments are given but not due to the treatment itself. For example, scores can decrease over time due to fatigue, or increase due to learning.
Repeated measures designs have some great benefits, but there are a few drawbacks that you should consider. The largest downside is the problem of order effects, which can happen when you expose subjects to multiple treatments. These effects are associated with the treatment order but are not caused by the treatment.
- Pro: As the same participants are used in each condition, participant variables (i.e., individual differences) are reduced.
- Con: There may be order effects. ...
- Pro: Fewer people are needed as they take part in all conditions (i.e. saves time).
The only difference between one-way and two-way ANOVA is the number of independent variables. A one-way ANOVA has one independent variable, while a two-way ANOVA has two.
There is only one factor or independent variable in one way ANOVA whereas in the case of two-way ANOVA there are two independent variables. One-way ANOVA compares three or more levels (conditions) of one factor. On the other hand, two-way ANOVA compares the effect of multiple levels of two factors.
Why is ANOVA more preferable to t-test?
The key difference between ANOVA and T-test is that ANOVA is applied to test the means of more than two groups. In contrast, a t-test is only used when the researcher compares or analyzes two data groups or population samples.
Allen Wallis), or one-way ANOVA on ranks is a non-parametric method for testing whether samples originate from the same distribution. It is used for comparing two or more independent samples of equal or different sample sizes.
One-way ANOVA is used when the researcher is comparing multiple groups (more than two) because it can control the overall Type I error rate. Advantages: It provides the overall test of equality of group means. It can control the overall type I error rate (i.e. false positive finding)
So, if two t-tests are being conducted, there is a 10% chance of conducting a Type I error. Using ANOVA in this scenario (that is comparing means of three or more groups) restricts the chance of Type I error to 5% and therefore results are more statistically significant.
Why not compare groups with multiple t-tests? Every time you conduct a t-test there is a chance that you will make a Type I error. This error is usually 5%. By running two t-tests on the same data you will have increased your chance of "making a mistake" to 10%.
Advantages:Due to Variation, organism can be developed to survive in adverse conditions, more resistant to diseases, also it creates diversity. Disadvantages: It can also cause some undesired effects like genetic disorder, diseases, etc.
One problem with the variance is that it does not have the same unit of measure as the original data. For example, original data containing lengths measured in feet has a variance measured in square feet.
- It doesn't give you the full range of the data.
- It can be hard to calculate.
If you conduct an ANOVA test, you should always try to keep the same sample sizes for each factor level. A general rule of thumb for equal variances is to compare the smallest and largest sample standard deviations. This is much like the rule of thumb for equal variances for the test for independent means.
As regards the normality of group data, the one-way ANOVA can tolerate data that is non-normal (skewed or kurtotic distributions) with only a small effect on the Type I error rate.
What is the conclusion for ANOVA test?
Since the test statistic is much larger than the critical value, we reject the null hypothesis of equal population means and conclude that there is a (statistically) significant difference among the population means.
ANOVA separates the within group variance from the between group variance and the F-test is the ratio of the mean squared error between these two groups.
So, the P-value is the probability of obtaining an F-ratio as large or larger than the one observed, assuming that the null hypothesis of no difference amongst group means is true.
The F value is used in analysis of variance (ANOVA). It is calculated by dividing two mean squares. This calculation determines the ratio of explained variance to unexplained variance.
t-test is statistical hypothesis test used to compare the means of two population groups. ANOVA is an observable technique used to compare the means of more than two population groups. t-test compares two sample sizes (n) both below 30. ANOVA equates three or more such groups.
Verifying the Requirements
The k samples must be independent of each other; that is, the subjects in one group cannot be related in any way to subjects in a second group. The populations must be normally distributed. The populations must have the same variance; that is, each treatment group has population variance σ2.
Regression is a statistical method to establish the relationship between sets of variables to make predictions of the dependent variable with the help of independent variables. On the other hand, ANOVA is a statistical tool applied to unrelated groups to determine whether they have a common meaning.
- An important advantage of this design is it is more efficient than its one-way counterpart. ...
- Unlike One-Way ANOVA, it enables us to test the effect of two factors at the same time.
- One can also test for independence of the factors provided there are more than one observation in each cell.
With the two-way ANOVA, there are two main effects (i.e., one for each of the independent variables or factors). Recall that we refer to the first independent variable as the J row and the second independent variable as the K column. For the J (row) main effect… the row means are averaged across the K columns.
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What 3 effects are produced in a two factor Anova?
The 2-factor ANOVA quantifies the statistical significance of these three observations: the main main effect for rows, the main effect for columns, and the interaction.
The factorial ANOVA has a several assumptions that need to be fulfilled – (1) interval data of the dependent variable, (2) normality, (3) homoscedasticity, and (4) no multicollinearity.
ANOVA's main advantage over t-tests is in comparing multiple predictor variables at the same time. This can make it easier to use, and faster. For example, if one wants to compare different recipes for a medication, then one can use either ANOVA or a t-test.


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Goodreads helps you keep track of books you want to read. Want to Read saving…. Want to Read Currently Reading Read. Other editions. Enlarge cover. Error rating book. Refresh and try again. Open Preview See a Problem? Details if other :. Thanks for telling us about the problem. Return to Book Page. Presenting an introduction to the mathematics of modern physics for advanced undergraduate and graduate students, this textbook introduces the reader to modern mathematical thinking within a physics context.
Topics covered include tensor algebra, differential geometry, topology, Lie groups and Lie algebras, distribution theory, fundamental analysis and Hilbert spaces. The Presenting an introduction to the mathematics of modern physics for advanced undergraduate and graduate students, this textbook introduces the reader to modern mathematical thinking within a physics context.
The book also includes exercises and proofed examples to test the students' understanding of the various concepts, as well as to extend the text's themes. Get A Copy. Hardcover , pages. More Details Original Title. Other Editions 5. Friend Reviews. To see what your friends thought of this book, please sign up. Lists with This Book. This book is not yet featured on Listopia. Community Reviews. Showing Average rating 4. Rating details. More filters.
Sort order. Apr 21, Jason "jcreed" rated it really liked it. Excellent, from-the-ground-up summary of the basic mathematics behind a lot of physics; group theory, topology, linear algebra, measure theory, differential geometry. In particular I think it's highly suitable to someone knows a decent amount of pure mathematics, but not much about how physicists tend to make use of it.
The explanation of Hilbert spaces is neither dumbed down nor unclear. Eduardo rated it liked it Feb 15, Ruud rated it liked it Feb 21, Dimitrios rated it really liked it Mar 29, Rebcabin rated it liked it Sep 09, Kaiser rated it it was amazing Jul 10, Yuri Popov rated it really liked it Apr 04, Utensil rated it really liked it Jun 18, Dudley Grant rated it it was amazing Nov 30, Donny Martamin rated it really liked it Apr 19, Tim rated it it was amazing Nov 22, Fadi rated it it was amazing Jul 23, Brendan McAuliffe rated it really liked it May 09, Stefano Ivo rated it really liked it Aug 09, Hollis rated it it was amazing Jul 05, Jaime Olmos rated it it was amazing Jul 19, Rob is currently reading it Nov 24, Odo is currently reading it Jan 26, Rubaiya marked it as to-read Nov 23, Zheng Ma added it Jan 08, Yunus marked it as to-read Mar 20, Xoanon93 added it May 03, Ben added it Aug 25, James Tauber added it Sep 03, Lyubomir marked it as to-read Dec 01, Nitin Rughoonauth added it Dec 03, Winkhorst marked it as to-read Jun 26, Kinan Bab marked it as to-read Aug 25, Hamdi Ahmed marked it as to-read Sep 05, Daniel marked it as to-read Dec 06, Tom added it Feb 05, Andrew marked it as to-read Apr 01, Ben marked it as to-read Jun 30, Adil Gambarov is currently reading it Aug 19, Jacob Lovatt marked it as to-read Aug 31, About Peter Szekeres.
Peter Szekeres. Books by Peter Szekeres. As dedicated readers already know, some of the best and most innovative stories on the shelves come from the constantly evolving realm of young ad Read more Trivia About A Course in Moder No trivia or quizzes yet. Quotes from A Course in Moder Welcome back. Just a moment while we sign you in to your Goodreads account.
A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry
A Course in Modern Mathematical Physics : Groups, Hilbert Space and Differential Geometry


EE 525X: Spring 2018
Data Analytics in Electrical and Computer Engineering
Course SummaryIntroduction to a variety of data analysis techniques -- particularly those relevant to electrical and computer engineers. Topics include techniques for classification, visualization, and parameter estimation, with applications to signals, images, matrices, and graphs.
This is a graduate-level course focusing on data analysis foundations. Particular emphasis will be placed on the principles of state-of-the-art data processing techniques; on methods to analyze correctness and efficiency of such techniques; and on the evaluation of these techniques on real-world test datasets.
Course InformationLectures: MW 4:10pm-5:30pm, Science 0277.
Grading: Six (6) homework problem sets (60%); final course project (40%).
Problem sets will be posted roughly once every fortnight on Blackboard. Problem sets will involve a mix of theory and practical implementation.
The final course project can be carried out either individually or teams of two (2). The project will involve either conducting research on a specific topic, or implementing and evaluating modern data analysis techniques on a real-world dataset.
Pre-reqs: Knowledge of undergraduate probability (EE 322 or equivalent); familiarity with linear algebra and optimization.
- Review of mathematical basics.
- Classification: Nearest neighbors, kernel methods, SVMs.
- Matrix analysis: Singular value decomposition, matrix factorization.
- Graph analysis: Connectivity, trees, random walks.
- Data visualization: Clustering, nonlinear dimensionality reduction.
- Streaming algorithms: Distinct elements, frequency moments, heavy hitters.
- Sampling: Sparse recovery, compressive sensing, matrix completion.
BookA. Blum, J. Hopcroft, and R. Kannan, Foundations of Data Science.
NotesHere is a single monograph containing all lecture notes from the Spring '17 edition. Notes were made using (pandoc-flavored) Markdown, which is a real lifesaver if one wants to quickly typeset math-heavy lecture resources. (Thanks, Boaz Barak, for the idea.)
Lecture Schedule (tentative)
- Introduction, course overview, logistics.
- Basics of probability.
- Modeling data in high dimensions.
- Introduction to supervised learning.
- Nearest neighbors.
- The perceptron algorithm.
- Support vector machines, the kernel trick.
- Multi-layer networks.
- Linear regression.
- Singular value decomposition (SVD).
- Applications of the SVD.
- Principal components analysis.
- Non-negative matrix factorization.
- Introduction to graphs.
- Random walks on graphs.
- Graphs, electrical networks, and resistances.
- Applications of random walks.
- Spectral clustering.
- k-means, hierarchical clustering.
- Graphical models.
- Dimensionality reduction.
- Introduction to streaming algorithms.
- Frequent elements, heavy hitters.
- Compressive sensing and matrix completion.


Original Posting At http://pastor-patrick.blogspot.com/2017/10/mathematics-truth.html
Mathematics the Truth
An interesting book that begins with an error on its cover makes this reader doubt the usefulness of the book. First of all, the error – the author’s name, as best I can tell, is spelled wrong. Now, this does not define the entire book, but does make one want to read it carefully.
I did find the book of interest. It is written to a beginning master’s level mathematician. It might be handled by a well-equipped calculus student with a bit of exposure to differential equations, ultimately the focus seems to be helping the student jumping into his final years of training to see the parallels between mathematics and the physical world. The author firmly that this connection to the physical world should become the real motivation for studying mathematics:
Currently mathematics is taught like Latin, without motivation, restricted to the period from Euclid in the BC to the Renaissance. Those few proceeding to university mathematics and mathematical physics are re-educated without the benefit of previous orientation while the rest are abandoned to popularisations. This is not right …
The author attempts to weave mathematics with these physical concepts that either underlay or that are supported by the mathematical truths. The book, obviously, does not a cover entire field of math or physics, but enough parallels are drawn to aid the student or teacher to take these initial thoughts further.
I do wish the book included a bit more documentation, allowing the student to continue his or own self-study of the topics presented. Too much material is presented as “common knowledge” that might be so to the fully trained mathematician, but not to the student making progress through the field. That being said, the book is readable – provided the student has a basic understanding of the mathematics. However, once the reader reaches the point where his mathematics training has progressed, a set of good math texts will be needed to fill in some of the gaps.
Physicists and mathematicians would do well to find ways to add this book to their courses as a supplementary text. Those already in the field will find the book to be of help understanding the contribution each has made to their respective fields.
This review is based on a free electronic copy provided by the publisher for the purpose of creating this review. The opinions are mine alone.


By Bibhutibhushan Datta
Read or Download Ancient Hindu Geometry: The Science Of The Sulba PDF
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Additional resources for Ancient Hindu Geometry: The Science Of The Sulba
This exercise can be taken as the basis for a nonstandard construction which trisects an angle: simply reconstruct Figure t49 with the given angle in place of AOE. It is known that the trisection of an arbitrary angle is not possible using classical Euclidean methods. The construction suggested here is also not possible. If we take the vertex of the given angle as O and draw any circle centered at O, we will determine point E and diameter AB. We must now ﬁnd point C along line AB so that CD = OA.
SOLUTIONS FOR BOOK I to AA and BB , respectively (as shown in the diagram). Line OF , perpendicular to DE, will pass through the intersection point of AA and BB since OF is the third altitude of the triangle formed by EA , DB , and DE. This construction works only if we assume that points A and B, as well as segment DE, lie within the limits of the diagram. Students can draw for themselves the situation in which O lies outside the angle formed by lines AA , BB . The construction remains valid in this case.
The length 1. SOLUTIONS FOR BOOK I 23 B B' X M' M p Y N' N q A Figure t32 of the path AN M B is equal to AN + N B plus the length of XY , while the length of path AN M B is equal to AN + N B = AB plus the length of XY . But the triangle inequality tells us that AN + N B > AB , so the path AM N B is shorter. Notes. As further exercise, students may be asked to show that one obtains just the same solution if we translate A (by Y X) rather than B. Students may also be asked to prove the analogous statement for two pairs of parallel lines and two given directions.


LAMINARY FLUID FLOW IN A PIPE AND DIMENSIONAL NUMBER OF REYNOLDS. Sh.A. Mengliev Termez State University Kh.F. Kholturaev Tashkent Institute of Irrigation and Agricultural Mechanization Engineers
LAMINARY FLUID FLOW IN A PIPE AND DIMENSIONAL NUMBER OF REYNOLDS
Termez State University
Tashkent Institute of Irrigation and Agricultural Mechanization Engineers
The article provides information on the mathematical modeling of the incompressible viscous fluid in the pipe. The study shows laminar and turbulent regimes of fluid motion, as well as the physical meaning of these regimes. Consider a straight round pipe with a diameter constant along the entire length. The flow rate on the walls of the pipe due to adhesion is zero, in the middle of the pipe, it has the greatest value. A cylinder with a characteristic length and a characteristic radius inside the liquid whose axis coincides with the axis of the pipe is considered and the flow of the liquid through the cylinder is studied. The calculation formulas for calculating the maximum flow velocity in the cylinder, the volume of liquid passing through the cross-section of the pipe, the coefficient of resistance to friction in the pipe along the flow length, and the maximum value of the tangential stress are derived. The results of comparison of empirical and semi-empirical formulas for calculating the coefficient of resistance to friction are presented -.
Key words: Reynolds number, laminar flow, turbulent flow, parabolic flow, the friction force is the integral coordinate of the pipe, viscosity, density, bulk flow velocity, average speed, maximum speed, radius, Gegen, Poisal, Darcy-Weisbach, the volume of fluid resistance coefficient.


Through colorful illustrations, Scripture references, and interactive exercises, Kindness Counts! helps children learn basic math skills while teaching them the importance of kindness. They will learn that God loves them and wants them to spread his kindness and love to others, and they will see that even the smallest acts of kindness matter.
Parents and teachers will appreciate the practical ideas that children can apply in sharing kindness with others, such as collecting coins for the needy or helping their parents at home. At the same time, children are introduced to basic mathematical skills like counting, addition, subtraction, and measuring. Each colorful illustration includes an interactive math problem for children to solve. This book makes it fun to learn math-and to share God's kindness with the world.
- Page Count: 32
- June 30, 2007


Written in English
|The Physical Object|
|Pagination||iii, 196 leaves|
|Number of Pages||196|
Page 3 - BOOK I* THE LANGUAGE OF ALGEBRA 5. The language of algebra has its alphabet, vocabulary, and grammar. 6. The symbols of algebra are of two kinds: one class represent its fundamental conceptions and may be called its letters, and the other represent the relations or modes of combination of the letters and are called the signs. 7. Learn algebra relations functions with free interactive flashcards. Choose from different sets of algebra relations functions flashcards on Quizlet. Overview: What Are Relations and Functions? A relation in algebra is a set of ordered pairs. The first element of the ordered pair is the domain, and the second element in the ordered pair is the range. If every first element is paired with only one second element, or every domain has a . Learn functions algebra 2 relations with free interactive flashcards. Choose from different sets of functions algebra 2 relations flashcards on Quizlet.
Peirce would consider this to be an inadequate analysis. Reality, he held, is more than a matter of discrete events occurring at given points in space-time. Reality is also a matter of the relations between events, and here is where his category of thirdness enters. Thirdness is the category of law, of habit, of continuity, of relatedness. algebra of unary relations on X is any subalgebra of this. Such algebras are also known as ﬁelds of sets. These algebras are boolean algebras (exercise). Conversely, any boolean algebra is isomorphic to an algebra of unary relations on some set (Stone, ). So boolean algebra axioms are sound and complete for unary relations:File Size: 1MB. After a preliminary review of set theory, the treatment presents the basic definitions of the theory of abstract algebras. Each of the next four chapters focuses on a major theme of universal algebra: subdirect decompositions, direct decompositions, free algebras, and varieties of algebras. Problems and a Bibliography supplement the by: A relation from a set A to set B is nothing but a subset of the cartesian product of A and B which is denoted by AXB. The types of relations are nothing but their properties. There are different types of relations namely reflexive, symmetric, transitive and anti symmetric which are defined and explained as follows through real life examples.
The only formal prerequisite is a background in abstract algebra and some mathematical maturity, though the reader will also benefit from familiarity with Boolean algebra and naïve set theory. The measured pace and outstanding clarity are particularly suited to independent study, and provide an unparalleled opportunity to learn from one of the Format: Hardcover. Welcome folks to the discussion of The Metaphysical Club. Message One - on each non spoiler thread - will help you find all of the information that you need for each week's reading. For Week Seven - for example, we are reading and discussing the following: Week Seven - August 5th - August 11th Part Three - Chapter Seven The Peirces ( - ) Please only discuss Chapter Seven through . The PEIRCE EDITION contains large sections of previously unpublished material in addition to selected published works. Each volume includes a brief historical and biographical introduction, extensive editorial and textual notes, and a full chronological list of all of Peirce's writings, published and unpublished, during the period covered.3/5(1). Relations and Functions. Each relation or function has a domain and a range. Functions may be one to one, and may be discrete or continuous. Functions satisfy the vertical line test: any vertical line crosses the graph at most once.


It's my 601st post already? Wow.
Today I again went through my yearly ritual of making promises to myself to not procrastinate and make higher grades in school.
I don't know why, but I just do it. I always feel like I have to hype myself up to assure myself that I will indeed be ready for the school year.
The only thing I'm really worried about, as I've stated before, is Math. Math and I have a rocky relationship. This year I know that I'm going to need extra help, so I plan on talking to my parents about a tutor. My grandparent's have a friend who is a Maths professor at UT (a super awesome university in Texas) and he's offered to tutor me if I need any extra help understanding things.
I don't see why Math is so hard for me. All of my classes are honor classes EXCEPT for math. I excel in everything EXCEPT math.
Oh well. As long as my grade is a B or higher, I'm good. I was lucky enough to get a B average last year in math.
Also, I just recently found out that I had to read A Tale of Two Cities for AcaDec over the summer. Oops. I bought the book, and I'm confident that I'll be able to finish it before the 24th. Wish me luck!


We’ve all heard it mentioned in the news in the briefings by the government and their scientific advisors, but what actually is the reproduction (R) number? Well, quite simply, it’s the average number of secondary infections produced by a single infected person.
An R number of 1 means that on average, every person who is infected will infect 1 other person, meaning the total number of infections is stable. If R is 2, on average, each infected person infects 2 more people. If R is 0.5 then on average for each 2 infected people, there will be only 1 new infection. If R is greater than 1 the epidemic is growing, if R is less than 1 the epidemic is shrinking. The higher R is above 1, the more people 1 infected person infects and so the faster the epidemic grows.
Quite a simple equation to understand even for those of us without great maths results!
R can change over time. For example, it falls when there is a reduction in the number of contacts between people, which reduces transmission, hence the drop in infection rates during lockdown. The third lockdown we’re in at the moment has seen the R number fall too; however, due to the highly infectious nature of the new variant, the decline is much slower than previous lockdowns. R increases when the numbers of contacts between people rise, leading to a rise in viral transmission.
Measles has one of the highest numbers with an R number of 15 in populations without immunity. That means, on average, one person will spread measles to 15 others.
If the R Numner is higher than 1, then the number of cases increases exponentially- It snowballs like debt on an unpaid credit card!. But if the number is lower the disease will eventually stop spreading, as not enough new people are being infected to sustain the outbreak.
The R number is one of the big three. Another is severity - some people have a very mild disease that does not cause many problems. But coronavirus and the disease it causes, Covid-19, can be severe and deadly.
The last is the number of cases, which is important for deciding when the authorities need to act. If you have a high number, but ease restrictions so the reproduction number is about 1, then you will continue to have a high number of cases.
R can vary in different parts of the country, communities, and subsections of the population. It cannot be measured directly so there is always uncertainty around its exact value.
This can be an issue when trying to calculate R when using a small number of cases linked to the lower infection rate or a smaller geographical area.
The growth rate reflects how quickly the number of infections are changing day by day. It is an approximation of the percentage change in the number infections each day. If the growth rate is greater than 0 (+ positive), then the epidemic is growing. If the growth rate is less than 0 (- negative) then the epidemic is shrinking.
The growth rate provides us with information on the size and speed of change, whereas the R value only gives us information on the direction of change.
To calculate R, information on the time taken between each generation of infections is needed. That is how long it takes for one set of people in an infected group to infect a new set of people in the next group. This can depend on several different biological, social, and behavioural factors. The growth rate does not depend on the ‘generation time’ and so requires fewer assumptions to estimate.
Neither one measure, R nor growth rate, is better than the other but each provide information that is useful in monitoring the spread of a disease and the actions required by the authorities to implement restrictions - or lift them.
The growth rate and R are estimated by several independent modelling groups based in universities and Public Health England (PHE). The modelling groups discuss their individual R estimates at the Science Pandemic Influenza Modelling group (SPI-M) - a subgroup of SAGE.
The growth rate is an average value that can also vary. A smaller number of cases means that variability in the underlying data makes it difficult to estimate the growth rate; there will be a wider range given for growth rate and frequent changes in the estimates. This will happen for both R and the growth rate; however, estimation of the growth rate requires fewer assumptions about the disease than R.
Estimates of growth rate for geographies smaller than regional level are less reliable and it is more appropriate to identify local hotspots through, for example, monitoring numbers of cases, hospitalisations, and deaths.
We hope you found this blog useful. Please share if you did and stay safe!
The Coda Team


New York, etc. Springer - Verlag, 1991. First edition. Hardcover. 9.25" x 6". 568pp. Yellow illustrated hardback. Fine condition. A very technical treatise on applied mathematics. With chapters on scalar autonomous equations, elementary bifurcations, scalar maps, dimension on and one half, higher dimensions, and more.
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Based on new UNC System guidelines related to Minimum Admission Requirements (MAR), UNCG is in the process of evaluating all applications submitted for consideration for the Fall 2020 cycle. This includes students who were previously denied admission based on prior guidelines. We will be contacting students who are now deemed admissible based on the new UNC System MAR criteria and our secondary review process.
The UNC system mandates the minimum high school courses required for admission to N.C. public universities. Incoming students must have completed:
- English: 4 units (emphasis on grammar, composition, and literature)
- Math: 4 units (including Algebra I, Geometry, Algebra II, and one approved course beyond Algebra II)
- Science: 3 units (including at least one unit in life or biological science, at least one unit in physical science, and at least one lab course)
- Social science: 2 units (must include one unit of U.S. history and one unit in history, economics, sociology, or civics)
- Foreign language: 2 consecutive units of the same language


Treasury Inflation Protection Securities or TIPS, are indexed bonds or bonds whose interest and principle payment are adjusted for changes in the price level. The interest rate on these bonds provides a direct measure of a real interest rate.
Using the Fisher equation:
i = ir + E(P)
i - nominal interest rate
ir - real interest rate
E(P) - expected inflation
We can re-arrange the terms to get:
Expected inflation rate for the next 10 years = ( (i) - Ten Year Treasury Constant Maturity Rate, monthly) - ((ir)- 10 Year TIPS, Monthly)
So the expected inflation rate for the next 10 years is around 3.2%.


The newest element of SimplyRead’s gradual rebranding over the past couple years has been the image of the shell, spiral, or ‘squiggly’ that appears here and above in our banner. I’m still playing with where to use it, since it first appeared in simplyread.ca’s site navigation buttons (and feedback is welcome).
I’ve been drawn to this shape forever, likely because it reminds me of seashells and ocean waves at the beach, snailshells and sunrays at home. I’m a tree-hugging Piscean from Nova Scotia, so I figure I come by this affinity naturally. It’s also pretty common to see similar designs included in home decor items aplenty.
But why would I want to associate it with my business?
Turns out, a very similar squiggly shape is also a much more revered and powerful symbol referred to as the Golden Ratio (as well as Golden Number, Golden Spiral or Fabonacci Number) You can search for any of these in Wikipedia and get a nice overview.
It’s explained on a terrific website I found during my research, called Making Sense of Maths. It describes how mathematicians view the Golden Ratio’s line pattern embodied in the spiral within the the nautilus shell. It continues, “When we see the wonders of nature through the eyes of pattern, Mathematics makes sense!”
Now, I’m definitely no mathematician. In fact, when I work with complex math or finances I have the greatest sense of what it’s like for a non-reader encountering print. So using a common element in nature to make a mathematical concept clear sure works for me.
I definitely get the concept of patterns, though. As my five-year-old is introduced to numbers, patterns is one of the first things she’s started learning.
People are naturally drawn to patterns in things around them, including information. Thus it’s a hugely useful tool for writers wanting to help readers navigate longer pieces. The more we can introduce verbal or visual patterns, the easier a reader can grasp relationships and ‘digest’ meaning.
And, I strongly relate to any concept that puts some logic to something as profound as the beauty of nature. To the left here is a royalty-free photo that shows an example, but a Google Images search for “Fibonacci spiral in nature” does much more justice to how far-reaching a concept it is.
Another idea inherent in the Golden Number is Infinity, through the infinite spiral and its mathematical equivalent, which are often related to the notion of pure, zenlike simplicity. (For more, read Chapter One of The Mystery of the Aleph: Mathematics, the Kaballah, and the Search for Infinity published on the Washington Post site.)
I’m thinking all of these ideas harmonize nicely with a brand that promotes clarity, ease-of-use, and a natural flow of things.
Hence the shell thingie.
(Credit is due to Clover, who created the original icon when she redesigned our website, and introduced me to the Golden Number concept.)


Stefano BistarelliUniversità degli Studi di Perugia
Stefano Bistarelli is Associate Professor of Computer Science at the Department of Mathematics and Computer Science at the University of Perugia and a Visiting Professor at Université Paris-Dauphine.
His research interests range from Artificial Intelligence to Programming Languages, with particular attention to constraint programming, constraint solution algorithms, and soft constraints. He also works on Computer Security and recently on Economics.
Currently active research topics are Computational Argumentation and Blockchain, Distributed Ledgers and Cryptocurrencies.


“Mama, I had a nice little treat today in Math class” the boy began to explain. “Oh yeah? What you figured out a new concept before anyone else?” I asked. “Oh no, not math related”. He replied. “But you said you had a….” I tried to say when he began to explain what he meant. “Oh no, I mean, since there was rain this morning, while I sat in math class, I looked out the window and saw a Cooper’s hawk, fly into the brush of trees on campus. The bird was so cool, I lifted my IPad and took a picture of it”. He finished triumphantly. “Wait, what?” I replied, confused by his initial statement that he was in math class when all this began. “Well you see while Mr. Urban was giving us our lesson during math, I noticed this hawk coming in for a respite out of the rain.” “So you weren’t paying attention to your math teacher?” I asked. “No, I was listening and paying attention and taking the picture of the hawk. So in fact, I was doing all three!I
Honestly when I opened my mouth to speak, I heard my mother’s voice say to him, “Surrrre”. “No mama its true, I always pay attention…” he said. “Now I know your lying…” I said with a smile. “Well, okay, maybe ‘paying attention’ are the wrong word choices, but I do always listen.” he tried. “Even when you’re taking a picture with your IPad of something happening outside?” I asked in a sarcastic tone. “Most definitely then.” He replied with a smile, before adding, “But I may have been wrong with my original designation of the hawk. It very well may have been a sharp shinned hawk, which, while sporting similar colors, is in fact smaller than the Cooper.”
Smiling back at him I said, “So which hawk are you?” Laughing he said “Size comparisons would make me a Cooper rather than the sharp shinned Mama. Though of course you do know I’m neither”. “Yes, you’re just interested…” I replied. “Exactly”.


SciPy 2016 Schedule
The 2016 conference will consist of two days of tutorials followed by three days of presentations, and conclude with two days of developer sprints on projects of interest to attendees.
See the sprints schedule here
To receive event and schedule updates please enter your email in the box below:
Announcing SciPy 2016 Keynote Speakers!
|Brian Granger - Cal Poly State University / Associate Professor of Physics|
Brian Granger is an Associate Professor of Physics at Cal Poly State University in San Luis Obispo, CA. He has a background in theoretical atomic, molecular and optical physics, with a Ph.D from the University of Colorado. His current research interests include quantum computing, parallel and distributed computing and interactive computing environments for scientific and technical computing. He is a core developer of the IPython project and is an active contributor to a number of other open source projects focused on scientific computing in Python.
Andreas Klöckner - University of Illinois at Urbana-Champaign
Andreas Klöckner is an Assistant Professor in the scientific computing group within the Department of Computer Science at the University of Illinois at Urbana-Champaign. He works on high-order numerical methods for the simulation of wave problems as well as issues in high-performance scientific computing that relate to bringing these methods to life on large-scale parallel computers. In support of his research, Dr. Klöckner has released numerous scientific software packages. He obtained his PhD degree at the Division of Applied Mathematics at Brown University with Jan Hesthaven, working on large-scale finite element simulations of wave problems in the time domain. From Brown, Klöckner moved to the Courant Institute of Mathematical Sciences at New York University as a Courant Instructor, where he worked on integral equation methods and fast algorithms within Leslie Greengard's group.
Hanna Wallach - Microsoft Research NYC / Adjunct Associate Professor, UMass Amherst
Hanna Wallach is a researcher at Microsoft Research in New York City and an assistant professor at the University of Massachusetts Amherst's School of Computer Science, where she is one of five core faculty members involved in UMass's recently formed Computational Social Science Initiative. Hanna develops new machine learning methods for analyzing the structure, content, and dynamics of complex social processes, such as the US political system, the US patent system, and software development communities. Her research contributes to machine learning, Bayesian statistics, and, in collaboration with social scientists, to the nascent field of computational social science. Her work on infinite belief networks won the best paper award at AISTATS 2010. Hanna has organized several workshops on Bayesian latent variable modeling and computational social science. She also co-founded the annual Women in Machine Learning Workshop. Hanna holds a B.A. in Computer Science from the University of Cambridge, an M.S. in Cognitive Science and Machine Learning from the University of Edinburgh, and a Ph.D. in Physics from the University of Cambridge.


Abstract: MATH/CHEM/COMP 2002, Dubrovnik, June 24-29, 2002
Recounting rationals, Knuth's problem and some conjectures
Dragutin Svrtan and Igor Urbiha
Department of Mathematics, Faculty of Science and Mathematics, University of Zagreb,
Bijenička c. 30, HR-10002 Zagreb, Croatia
We show that a sequence defined by q_0=0, q_2m= q_m/(1+q_m) (m>0), and q_(2m+1)=1+q_m generates all nonnegative rational numbers (without repetitions).
More generally we discover a ('new') bijective discontinuous
function h from nonnegative reals to positive ones which is defined by
We pose a (wide) Open Problem: Describe explicitly other orbits of h in various number field extensions of the field of rational numbers.
For quadratic extensions we state some results (including a solution of a recent problem of Knuth) and some intriguing conjectures.
1 I. Urbiha, Some properties of a function studied by De Rham, Carlitz and Dijkstra and its relation to the (Eisenstein-)Stern's diatomic sequence, Mathematical Communications 6 (2001) 181-198.
2 D. Svrtan, I. Urbiha, On explicit bijection between nonnegative integers and rationals and Knuth's problem, submitted.


Geometry and Surveying
This article provided by The Garden of Archimedes - A Museum for Mathematics.
Geometry becomes system
Euclidean geometry begins with the formalisation of surveyors' work, drawing straight lines and describing circles. Geometry shifts from the land to the table where the mathematician traces his diagrams, and from there to paper and books. Even the operating tools are different. What could be obtained on a large scale by pulling ropes, can now be drawn on a small scale with a ruler and compass, translated into mental objects and regulated by a complex system of definitions and axioms. The resulting reduction of scale takes the surveyor away from the land, and allows him to dominate, in all their complexity, many problems that the immensity of the horizon had excluded from his sight. Evidence for the use of geometry along the banks of the Nile dates to an extract from Herodotus, reported at the beginning, as well as a consistent tradition seeing the origins of Greek geometry in Egypt. To what extent this tradition is legendary is unclear, but it is reasonable to expect that evidence of the activity of the Egyptian land surveyors to be found in Greek mathematics and in particular in Euclid's Elements.
Faint evidence, since the Elements is a late work, where previous elaborations - now lost - converge, and one that is organised according to the axiomatic - deductive process, typical of Greek thinking and of all western mathematics. Evidence of early Egyptian geometry, then, won't be found in the general body of the work, nor in the demonstration of theorems. It is more likely that they appear in principles, definitions and postulates which are notable for having the function of translating natural phenomena into symbols and geometric shapes. In order that the abstract geometry of classical Greece describe the most profound properties of the real world, illuminate the most obscure relationships among the objects of the external world, what needs to be done is the following: First of all, it is necessary to precisely set the definitions of the objects taken in consideration to be totally sure of what is included or excluded in the dominion of geometry. Secondly, one must identify, through postulates, a system of primary properties and possible operations, starting from which the surveyors, aided only by logic, could extract the network of consistencies and interrelations that lie - often inaccessible to material investigation - in abstract concepts of geometry and, consequently, in ordinary objects.
If the definitions and postulates translate material objects from nature and the empiric procedures of the practice into the abstract figures and operations of geometry, it is in them that the evidence of a lost tradition can and must be found. They are conceptual evidences, since the main concepts echo the procedures and operations that were not formalised. These are linguistic clues, because the choice of terms is influenced by the operations on the defined objects.
Seen in this light, Euclid's Elements show a partial, but surprisingly clear correspondence, with the operations of the 'arpedonapti'. We have already discussed the right-angle. Early than that is the definition of the straight line -an always finite line, a segment- that recalls the operation of "pulling" a rope between two "points" ( literally "marks") that define its "limits". Its straightness is not dependent on it being the shortest distance between two points, but once again it brings us back to the uniformity of the tension, according to which "it lies uniformly in relation to its marks", a property that becomes even more evocative if read together with the definition preceding it: " the marks are the limits of the line".
Of the postulates, the first three reproduce exactly the land surveyors' operations:
to draw a line between two points:
one must draw a straight line from any mark to any other.
to prolong a given line:
and to make it straight, by rights, a finite line.
To describe a circumference:
with any centre and interval, describe a circle.
While the other two testify to, so to speak, the impossibility of demonstration. The fourth of them states that
all the right-angles are equal.
and the last is the famous "postulate of parallel lines":
If a line, falling on two other lines, forms internal angles smaller than right-angles on the same side, those two lines, if prolonged, will meet where the angles smaller than right-angles are.
The difference between these two postulates and the first three is evident. The first one, put into geometric terms, describes usual practical operations. What they ask is nothing but the translation into abstract form of the concrete process of land surveyors. The last two, on the contrary, have the nature of theorems. They do not express that which the surveyors can do, but the properties of the mathematic objects already introduced - essential, assumed properties in the demonstration of the theorems to follow.
In fact, these postulates are treated as theorems, and demonstrations attempted in different sources. Proclo, in his comment on the first book of the Elements, tried to prove the fourth postulate. The fifth was to be object of numerous attemps of demonstrations, which lead to the discovery of non Euclidean geometry at the beginning of the 19th century.


Co-Dept Chair-Math (K-6), Math (5)
Ms. Mendoza grew up in the East Bay and graduated from Mills College with a Bachelor of Arts degree in Economics. She received her elementary and secondary mathematics teaching credentials from San Francisco State University with special emphasis in middle school education. She has taught pre-algebra and algebra for over twenty-five years. Her career has included teaching in Richmond, California for the West Contra Costa School District, in the Mission District of San Francisco for San Francisco Unified School District, at Kennedy Middle School in the Cupertino Union School District, and at St. Martin School and Catholic Academy of Sunnyvale in the Catholic Diocese of San Jose. Ms. Mendoza is a graduate of the San Francisco Math Leadership Project, California League of Middle Schools Interdisciplinary Team Training, and the Silicon Valley Mathematics Initiative Mathematics Coaching Institute. She enjoys walking her dog Scooby, reading, trips to the farmer's market, and gardening.


Mathematics provides an effective way of building mental discipline and encourages logical reasoning
and mental rigor. Math helps with analytical thinking, with finances, is important in various fields such as engineering, food industry, medicine, computer science, cooking and architecture to name a few.
Our math curriculum is based on tried and trusted local and international best practices. It has been
customized for our students to easily assimilate the concepts starting from kindergarten through high
We evaluate each child using an age and level appropriate pre-assessment test so that we can develop a baseline of their current mastery of Math concepts. Based on the pre-assessment test results, we consult with the parents on the appropriate course level for their child. Our program delivery structure involves teaching concepts in a classroom setting and following that with homework that helps strengthen the material covered in the class. The homework is due before the next class and is graded by our instructors to measure the progress being made by the child. Depending on the student’s mastery of the subject, our instructors customize the next lesson plan.
All of our math classes (grades K-12) discuss the concepts that will be covered in their local schools as defined in the Common Core Standards and by the National Council of Teachers of Mathematics.
We understand that not all students learn the same way. Our philosophy is to provide students flexibility to learn at their pace, provide a nurturing environment where they can thrive.
What we Offer
We offer both small group and individual Math classes to cater to the unique learning needs of each child. We have an open enrollment process of students from grades K-12 throughout the year. Classes run throughout the year, including Summer.
We also offer coaching for competitive math tournaments. Please inquire for more details.
A personalized schedule will be provided upon completion of a pre-assessment to identify the right class for your child.
We will follow Ellington (CT) Public School closing schedules. No classes will occur on the days schools are closed.
Available Virtual and In-Person
Each child learns at their pace. Students are provided personalized, skill-based assignments, irrespective of their grade level.
We offer challenging and advanced learning opportunities to gifted children, and program our material to meet their skills.
Our lesson plans emphasize on developing a combination of analytical and problem solving skills along with strong mathematical foundation.
Success in Math is directly proportional to practice and successfully mastering the foundational concepts. Class and Home worksheets are provided to students to practice the assigned topics.
For group lessons, We maintain an instructor to student ratio of 1:5 so that each child gets the attention that they deserve.
Select one or more of the following:


Numeracy skills are vital in so many careers, as well as in everyday life. If you’d like to re-visit mathematics to boost your knowledge in key skills, then this step-by-step course is perfect.
Our approach aims to build confidence in a subject you may have previously found daunting or challenging. Using supportive, engaging materials, you’ll work at a pace that suits you, with plenty of scope to practise and revisit skills as you go.
Pre-GCSE Introduction to Maths includes three tutor-marked assignments, designed to track and confirm your progress. On completion, perhaps you’ll convert to our GCSE Mathematics online course to gain a formal qualification at a reduced cost?
You’ll be learning using accessible, engaging online resources, written by an expert team. With 12 months support from an NEC tutor included, you can also rest-assured that additional support is on-hand, should you need it.
Our Pre-GCSE Introduction to Maths course provides three units, which cover key mathematical concepts and techniques such as decimals, fractions, algebra and percentages, providing a direct pathway towards securing a GCSE in this vital subject.
This course is ideal if you:
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Meet Stefania who is just one of our first-class maths tutors:
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Abstract: We introduce a new model for cooperative agents that seek to optimize a common goal without communication or coordination. Given a universe of elements V, a set of agents, and a set function f, we ask each agent i to select a subset S_i ⊂ V such that the size of S_i is constrained (i.e., |S_i| < k). The goal is for the agents to cooperatively choose the sets Si to maximize the function evaluated at the union of these sets, U_i S_i; we seek max f(U_i S_i). We assume the agents can neither communicate nor coordinate how they choose their sets. This model arises naturally in many real-world settings such as swarms of surveillance robots and colonies of foraging insects. Even for simple classes of set functions, there are strong lower bounds on the achievable performance of coordinating deterministic agents. We show, surprisingly, that for the fundamental class of submodular set functions, there exists a near-optimal distributed algorithm for this problem that does not require communication. We demonstrate that our algorithm performs nearly as well as recently published algorithms that allow full coordination.
Story of Contribution: With my team, I developed two novel algorithms: Greedy-Sampling and Adaptive-Sampling and proved their approximation ratios. I implemented both algorithms in MATLAB and later parallelized them to reduce their runtime. To test these algorithms, I first selected seven large data sets from DBpedia, which represented subgraphs from Wikipedia, with varying graph properties. Then I ran both Greedy-Sampling and Adaptive-Sampling on these graphs alongside algorithms that either allowed communication between agents or allowed for a central planner to coordinate agents. The expected reward over multiple instances were computed and then compared.
Lessons Learned: Beyond the opportunity to explore new computing topics, such as optimization and mult-iagent systems, or to learn new tools such as MATLAB, this project allowed me to gain critical research skills. By collaborating with two professors and two graduate students, and by continuing to work on this project at my home institution for a semester, I learned to work as part of a team, even from a remote location. Simultaneously, I learned to work independently as I led the experimental portion of the project.
The project itself taught me to consider both the proven theoretical bounds as well as the real world performance of algorithms. And by leading the experiments portion of the project, I gained experience in choosing datasets that address the average case as well special cases in which the algorithms could perform in exceptional ways. When selecting previously published algorithms to test against, I gained experience in finding and analyzing literature.
Finally, by presenting my work at multiple venues, applying for travel grants, and drafting and revising a paper for publication, I learned to communicate my methods and results both to the scientific community and the general public.
Presenting at the Washington University in St. Louis NSF REU Poster Session.


Leads the reader from simple graphs through planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph. This shopping feature will continue to load items when the Enter key is pressed. Etwas ist schiefgegangen. The plane ℝ2 or the space ℝ3 are examples of normed spaces. Applied Functional Analysis, Second Edition (Textbooks in Mathematics), (Englisch) Gebundene Ausgabe – Illustriert, 2. Introductory Functional Analysis with Applications, Quantum Field Theory and the Standard Model, Functional Analysis: An Introduction to Metric Spaces, Hilbert Spaces, and Banach Algebras, Friendly Approach To Functional Analysis, A (Essential Textbooks in Mathematics), A Course in Functional Analysis (Graduate Texts in Mathematics (96)), Real Analysis: A Long-Form Mathematics Textbook, No-Nonsense Algebra: Part of the Mastering Essential Math Skills Series. There's a problem loading this menu right now. So when we study maps between normed spaces, it is natural to focus on maps which are well-behaved with these structures, and we’ll do this now. Dr. Oden is also a member of the US National Academy of Engineering and the recipient of the 2009 SIAM Distinguished Career Award. https://doi.org/10.1142/9781786343352_bmatter, "The book is written very clearly and notions are described via many illustrations and examples. These distributions will be “continuous linear functionals on the vector space of test functions D(ℝd)”: . This book is just amazing. Functional analysis is now a vast subject with many applications and this book gives an introduction to this branch of mathematics that can be understood by advanced undergraduates or beginning graduate students. Each chapter begins with an extensive introduction and concludes with a summary and historical comments that frequently refer to other sources. Zugelassene Drittanbieter verwenden diese Tools auch in Verbindung mit der Anzeige von Werbung durch uns. Edition (2. Find the top 100 most popular items in Amazon Books Best Sellers. Supporting material is introduced as appropriate, and only to the degree needed. https://doi.org/10.1142/9781786343352_0002. Dr. Demkowicz was one of the founding members of the Polish Association for Computational Mechanics (PACM), serving as its first president from 1991 to 1993. Find all the books, read about the author, and more. Gewöhnlich versandfertig in 3 bis 4 Tagen. This book constitutes a concise introductory course on Functional Analysis for students who have studied calculus and linear algebra. Leider ist ein Problem beim Speichern Ihrer Cookie-Einstellungen aufgetreten. In this last chapter of the book, we will see a generalisation of functions and their ordinary calculus to “distributions” or “generalised functions”. Through numerous illustrative examples and comments, Applied Functional Analysis, Second Edition demonstrates the rigor of logic and systematic, mathematical thinking. Instead, our system considers things like how recent a review is and if the reviewer bought the item on Amazon. This is a nicely written book of great value for stimulating active work by students. I consider the book very useful for (undergraduate) students in mathematics, physics and engineering, who have passed some courses on metric spaces and linear algebra. Please try your request again later. Previous page of related Sponsored Products. © 2020 World Scientific Publishing Co Pte Ltd, Nonlinear Science, Chaos & Dynamical Systems, Chapter 1: Normed and Banach spaces (599 KB), Chapter 4: Geometry of inner product spaces, Chapter 6: A glimpse of distribution theory. In particular, new material concerning Fredholm and semi-Fredholm operators is introduced, requiring minimal effort as the necessary machinery was already in place. It can be strongly recommended as an undergraduate or graduate text, or as a comprehensive book for self-study." Well done. Right now I am studying abstract algebra from I.N. Sie hören eine Hörprobe des Audible Hörbuch-Downloads. Areas in the book that demonstrate its unique character have been strengthened. The topics covered are Banach spaces, continuous linear transformations, Frechet derivative, geometry of Hilbert spaces, compact operators, and distributions. This book constitutes a concise introductory course on Functional Analysis for students who have studied calculus and linear algebra. Wir verwenden Cookies und ähnliche Tools, um Ihr Einkaufserlebnis zu verbessern, um unsere Dienste anzubieten, um zu verstehen, wie die Kunden unsere Dienste nutzen, damit wir Verbesserungen vornehmen können, und um Werbung anzuzeigen. The prerequisites are minimal, requiring little more than advanced calculus and no measure theory.
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Play online math games for kids. Try math fact practice game as a tool to practice skills and to measure proficiency. Play addition, subtraction, division, multiplication and time tests.
Math Games for Kids ( Fun Online Educational Game ) Free to Play | Kiloo. Smiles. Smiles ( Fun Online Kids Game ) Free to Play | Kiloo.com. Ballon Paradise.
Math Games – Free, Fun, Online Math Games for Kids ... Online math games for kids enable children to work with mathematical concepts in a context outside of the classroom. This makes math practice less of a task, and more of a challenging mission in a game. The Best Online Interactive Math Games for Every Grade Level Online math games for high school students are harder to find, but these games give students the chance to practice their skills in a unique way. Wrecks Factor How it works: Ships sail onto the board and wreck, displaying a quadratic equation. Cool Math Games for Kids - Play Free Online Games at ...


Deploy new algorithms for currently intractable problems in mathematical optimization, operations research, and mathematical modelling. Interface with customers to formulate real-world problems in precise mathematical terms and develop software to solve them efficiently. Engage with both internal and external customers to match their problems with cutting edge algorithmic tools. Research and develop the next generation of optimization algorithms exceeding present day state of the art.
The Microsoft Quantum team is collaborative and interdisciplinary. You will work closely with a team within Microsoft that brings together mathematicians, physicists, and software engineers, as well as interface directly with subject matter experts at customer organizations. By bringing together a unique combination of knowledge and skillsets, as well as cutting edge hardware, we build novel solutions to the world’s hardest and most impactful computational problems. This role will be ideal for candidates who continually learning about new computational problems and new algorithmic techniques.
For more information or to submit an application visit:
3+ years experience in mathematical optimization and the discovery, design, and implementation of advanced optimization algorithms.
Bachelor's degree in operations research, mathematics, physics, computer science, or a related technical field.
PhD/MS in operations research, mathematics, physics, computer science, or a related technical field.
Experience in engaging with customers and adapting problem formulations and solution methods to customer needs.
Experience working across organizational boundaries and in interdisciplinary teams.
Employer will assist with relocation costs.
About Microsoft Quantum
Be part of the next revolution in computing! Join Microsoft’s Azure Quantum team and solve customer problems using new algorithms and computing hardware. Our mandate is to develop computing systems to solve currently unsolvable problems.


St. James School celebrated International Pi Day with the inspired help of Math Teacher Annie Lerew. Students learn about pi (representing the ratio between a circle’s circumference and diameter) by memorizing as many digits as they can.
Pi goes on forever as a decimal beginning with 3.14, and some students really go far with the challenge. While some can remember up to 40, 50 and 60 digits, sixth grader Joseph can now recite over 100 digits of the irrational number. Participants earned a special t-shirt and induction into the exclusive St. James Pi Club in its 2nd year of celebration.
Even staff and teachers got in on International Pi Day in a friendly face off to see who could memorize the most digits.


In the majority of cases, the non-linear simulation of high-frequency systems requires at some point that a numerical solution be found for a system of perhaps highly non-linear differential equations. Usually these equations arise from non-linear equivalent-circuit models for microwave active devices. The central core of any direct time-domain transient circuit simulator, such as SPICE, is therefore a numerical integration algorithm. Of course direct time-domain simulators of this kind have difficulties accommodating general linear frequency-domain behaviour at high frequencies, but even in popular alternative simulation strategies such as Harmonic Balance, a time-domain differential equation solution continues to play a key role. The nature of the device equivalent-circuit models used is such that ‘stiff’ differential equations are often found, with very short time-constants arising from internal charge dynamics and efforts to describe non-quasistatic behaviour. However, it may be desired to perform an RF simulation of a circuit using digital modulation formats with long bit sequences, resulting in an extended solution period and excessively slow computation. Most existing circuit simulators use implicit numerical integration techniques with adaptive time stepping. These methods have good stability and accuracy control properties, but require the solution of non-linear algebraic equations at each time-step which can be computationally expensive.
Alternatively, predictor-corrector methods can be used. In the traditional predictor corrector, an explicit method uses polynomial extrapolation to provide an estimate of the solution at the next time step. The estimate is subsequently corrected using one iteration of an implicit formula. In relation to stiff problems, the maximum allowable time-step that can be used with the traditional predictor-corrector techniques such as the Adams-Moulton technique may be unacceptably small. We have developed algorithms which are based on a different form of predictor-corrector.
The new corrector stage in this work involves adjusting the output of the predictor stage to increase the accuracy of the local Padé approximation without requiring a higher-order derivative. While the advantages of the proposed method for explicit simulation are illustrated here, the same predictor technique could be used to improve the performance of any one of the standard implicit circuit simulation techniques.
The simple single-ended MESFET amplifier shown below is taken as a suitable test circuit for the technique. The amplifier is described by ten non-linear differential equations which are stiff in nature.
The figure below shows a short segment of the output voltage vo(t) obtained with the Adams-Moulton predictor-corrector method. A time-step of ~0.12ps was required to solve the given system of equations with this technique.
The figure below shows the corresponding result obtained with the new predictor-corrector method. The new technique permits the use of a step-size seven times larger, ie ~0.85ps, for a comparable level of accuracy. This constitutes a remarkable saving in computing time.


-Let this be the last post on this issue-
Your logic is impeccable but in practice it doesn't work because the floors are arbitrarily numbered.
The first 20 floors are actually more equal to 14 floors of 13'4" each, like most of the other floors.
I am not exactly sure of the math (Here is where Zen would step in and fill us all in) but trust me, 72 is the Octagon floor.
No, his logic was NOT impeccable. Don't make that assumption especially when it comes to this kind of issue. This really has nothing to do with floor height or building plans; it all boils down to the math:
Today I did a little mathematical exercise and was able to prove that the "octagon" is indeed on the 72nd floor. It took me some time to come up with, but in the end I figured out the height of the tower at which this "octagon" is found, which was 878 feet, and just about on the 72nd floor. To actually get the 878 figure, I used some pretty difficult triangle ratio methods and eventually mashed out this formula:
o=the height at which the octagon is found (the variable)
h=height of any one of 1WTC's triangular facades=1,183 feet
a=half of the base of any of the four larger triangle facades=100 feet
b=half of the base of any of the four smaller triangle facades=70.7107 feet
height of base=185 feet
Proving this formula would be impossible on this forum given that it is largely a geometrical proof and requires multiple diagrams to be drawn. The most important thing to know is that the facade triangles don't all have the same area (4 are larger, 4 are smaller) and therefore the octagon is a little higher up than just at the midpoint of the facade triangle height.
Also, does anyone know who first came up with the 72nd floor as the "octagon floor" that everyone keeps mentioning?


Prize Calculations and Discounts In addition to the several types of online lottery bets above, the Klik4D provider also includes prize and discount calculations that you can get, such as Prediksi Togel:
4D / 3D / 2D Lottery Prize
Prizes for 4D / 3D / 2D lottery are divided into 3 parts:
4D x 3000
If placing a 4D bet with a minimum bet of Rp. 1,000, the victory will be obtained in the amount of Rp. 3,000,000 (1,000 X 3,000)
3D x 400
When placing 3D bets with a minimum bet of Rp. 1,000, the victory that will be obtained is Rp. 400,000 (1,000 X 400)
2D x 60
When placing 2D bets with a minimum bet of Rp. 1,000, the victory will be obtained in the amount of Rp. 70,000 (1,000 X 70)
4D / 3D / 2D Togel Discount
Distribution of discounts for 4D / 3D / 2D lottery is also divided into 3 parts:
4D = 66%
If placing a 4D bet, Rp. 1,000, it will be deducted with a 66% discount. The calculation is (1,000 – 66% = 340) means the total payment to the city is Rp. 340 silver.
3D = 59%
If placing a 3D bet, Rp. 1,000, it will be deducted with a 59% discount. The calculation is (1,000 – 59% = 410) means that the total payment to the city is Rp. 410 silver.
2D = 29%
If placing a 2D bet Rp. 1,000, it will be deducted with a 29% discount. The calculation is (1,000 – 29% = 790) means the total payment to the city is Rp. 790 silver.
Free Plug in Gifts and Discounts
Plug in prizes free of 1.5%
7% discount means that if you place a bet of Rp. 10,000 – 7%, the payment to the city is Rp. 9,300. The total win that can be obtained is 10,000 X 1.5 = 15,000 + capital 9,300 = total winnings of 24,300.
Macau Plug-in Prizes and Discounts
Prize macau 6.50
15% discount means that if you place a bet of Rp. 10,000 – 15% discount, then the payment to the city is 8,500. The calculation of the total winnings to be obtained is 10,000 X 6.50 = 65,000 + capital 8,500 = then your overall win is equal to 73,500.
Gift and Discount Togel Jitu Jitu
Colok telling consists of As, Head, Head and Tail, each prize is As (X7), Head (X7), Head (X8) and Tail (X8).
6.5% discount means that if the bettor places a bet of 10,000 thousand with a 6.5% discount, the total payment to the dealer is 9,350. Calculation of total wins that can be obtained such as:
Ace (10,000 X 7 = 70,000 + capital 9,350 = overall win is 79,350)
Headers (10,000 X 7 = 70,000 + capital 9,350 = overall win is 79,350)
Head (10,000 X 8 = 80,000 + capital 9,350 = overall win is 89,350)
Tail (10,000 X 8 = 80,000 + capital 9,350 = overall win is 89,350)
Gift and Discount Shio Togel
Prizes for zodiac bets X 9
A discount of 10% means that if you place a bet of 10,000 – Prize Calculations and Discounts of 10%, then the total payment to the bookie is 9,000 and the total winnings that can be obtained are (10,000 X 9 = 90,000 + 9,000 capital = total winnings are 99,000).
Colok Naga Gifts and Discounts
Prize dragon (3D X 26) and (4D X 39).
A discount of 15% means that if you place a bet of 10,000 – a discount of 15%, then the payment to the dealer is 8,500. The total wins that can be obtained are:
(3D X 26 = 10,000 X 26,000 = 260,000 + 8,500 capital, the overall win is 268,500).
(4D X 39 = 10,000 X 39,000 = 390,000 + 8,500 capital, the overall win is 398,500).
Prize Calculations and Discounts That is an explanation of how to play online lottery, types of bets with. Understand it well before starting to play and now we will start to go into the discussion that has been eagerly awaited, namely tips on playing to easily win easily.
Tips to Play Online Togel Gambling Let Win
Togel is arguably one type of game that really requires feeling and also high fortune to be able to win and get huge profits, but here we will share some of the most powerful and proven online lottery winning tips as follows:
In the online lottery game the bet is in the form of real money, therefore before starting to play and place a bet the bettor must plan well in advance how much amount of capital you want to use in playing the lottery online.
Before starting to play, it is better to understand and learn well in advance, how to play all types of bets on online lottery games along with the calculation of prizes and discounts available.
Don’t just stick to one type of bet and numbers, try playing with different types of bets with different numbers.
Predict numbers well before placing bets on any online lottery market, prioritizing often discussing predictions or multiplying previous output numbers.
For example: On the 1st has a prediction number 00, 22, 56 and on the 2nd has a prediction number 11, 02, 88, then the method of calculating the prediction correctly is to reverse the numbers from the 1st and 2nd. For example: 0011, 2288, 5611.
Prize Calculations and Discounts Frequently look at dream books or natural codes that occur around you, most likely it can be a match for numbers that will come out of the market results later.
Try sharing or asking senior lottery gamblers, it is very likely that you can help you get JP whales or JP anchovies. For JP whales will get paid between 15-20 million and above, and JP anchovies will get paid between 1 and 14 million.
The way to play senior lottery on average is to look at the situation of the paito lottery reading, where you can share the lottery formula by releasing the results of the previous market. (The benchmark is 2D rear).
So many articles on how to play lotto online profitable with small capital along with tips to win the lottery, we hope all the explanations above can help facilitate the bettor in playing lottery and can get a big jackpot profit.
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This forum is now Defunct try our newer, quicker if a bit dull version HERE
Math is the subject that most students hate. Despite the development of several automated tools like Inverse function calculator, math problem solvers, etc., students find the subject too complicated and refrain from learning the lessons. It is essential to understand how the subject is vital in real-life and how it can help you solve major problems. The subject might have some complex issues, but once you know and understand the lessons, it will help you overcome the hurdles and sail through the problems easily. For students who are still wondering how the subject can be helpful in real-life, here are some reasons to learn math:
Math will make you work on a lot of problems. It is necessary to know the best ways to solve them. Most students give up citing several reasons, but once you start working on the problems, you will learn how to handle critical real-life problems. It is essential to confront them instead of running away from the problems. There are websites offering math homework help and business management assignment help to students, but it is equally important to understand the lessons and solve the problems yourself. The tasks will help you enhance your problem-solving skills and help you grab the right opportunities.
Understanding savings and expenditures
Once you start earning, it will be important for you to save money for the future. The Swinburne referencing style is an author-date citation style that has two parts: in-text citations that appear in the body of the paper and a reference list at the end. Math helps in keeping track of your income and expenditure. Knowing math will help you solve major calculation problems and let you save money for the future. You must seek the right help, learn the lessons well, and work on the problems yourself. It is impossible to handle savings and expenditures if you don’t know math well.
Daily grocery shopping
Visiting a shop to buy groceries involves math. Calculating the balance is important once you are done shopping. If you don't know math, you cannot understand if the shopkeeper returned the correct balance. dissertation writing Services cannot help you at that moment. It is necessary to know the basics of math to overcome these hurdles. Ensure to learn the subject well to sail through the problems easily.
Math has always made its presence felt, and you must know the subject well if you want to grab the right opportunities in the future. In addition, it is necessary to know the lessons well and implement the methods to overcome problems and sail through them easily. So, start learning math and enhance your skills for a better future.


I actually can't figure this one out. I mean, it's obvious from looking at it that they're equal, and probably you are going to use the Side-Angle-Side congruence property (er, postulate), but I can't figure out how to get that angle. There's probably a nice easy property about triangles inscribed in circles, but I can't remember it for the life of me.
Edit: Oh, got it. (looked up some properties)
In a circle, or congruent circles, congruent chords have congruent arcs. (and converse)
In a circle, or in congruent circles, two arcs are congruent if and only if the corresponding chords are congruent.
chord BC ≅ chord DC, so
arc BC ≅ arc DC, so
∠BAC ≅ ∠DAC


As my mother is equally afraid of small spaces as she is of large spaces, I will build my mother a geodesic dome, its outer wall comprised of two walls, essentially a dome over a dome, three feet of space between the two domes. The dome is then a very large space, but comprised of many small spaces. Because a geodesic dome is made up of many triangles and because—if the two domes are three feet apart—we may put narrow landings in every triangle, so that the inhabitant, or visitor, might sit, rest or hide in any one of the many triangles.
I am about six feet tall, but, bent in half, I fit in any triangle with three sides of three feet (area: 3.9 feet).
To make the geodesic dome, rows of slightly smaller triangles are arranged upon slightly larger triangles which are arranged below slightly smaller triangles, and on and on until the pattern forms a dome (this is oversimplified of course; in reality, the larger triangles form pentagons and the smaller triangles form hexagons and the dome is formed by rows of pentagons followed by rows of hexagons, and so on; but this does not change the fact that we’re looking at triangles).
If my mother is able to reach up to feel with her hands something up to seven feet tall, then my mother will be able to reach up and feel around from any bottommost triangle to any second bottommost triangle. If I provide her with a stick, three feet in length, she will be able to poke around in any third level triangle.
Now, if it took my mother ten seconds to, in total darkness, determine whether or not I was inside any given triangle, and, if my mother went about this systematically (not wildly running triangle to triangle wherever her fear compels her, screaming and calling for me) checking triangle after triangle, it would take her thirty seconds to check each column, bottom- most triangle to topmost triangle.
My mother could then, within reason–at ten seconds per triangle, three triangles per column–examine two columns per minute, or, one-hundred and twenty columns an hour. If, given that this is the Pacific Northwest and at this time of year we have roughly eight hours every night of total darkness, I believe my mother could (again if she is rational and efficient) examine nine-hundred and sixty triangles per night.
- I will never hide in any triangle which my mother cannot reach.
- I will never switch triangles at any point in the night. When darkness falls and I enter the dome, I pick one triangle and I stay in it.
- On any given night, I may enter the dome from any direction and climb into any triangle, so long as I don’t violate rules one or two.
On any given night then, my mother’s odds of finding me are dependent totally on the size of the dome. Given a dome with the diameter of one hundred feet and the height of fifty feet, and therefore with the dome surface area of 15,707.96 feet, we divide 15,707.96 feet by the area of one triangle, so 15,707.96 feet divided by 3.9 feet, equalling 4027.68, rounding up to 4028 total triangles.
Given that my mother is only capable of searching the first three triangles in any given column, and given the diminishing number of triangles (a loss of six per hexagon every row moving up–the largest number at the bottom of the dome and the smallest number, being the dome’s topmost point, one hexagon at the top), row-by-row, a dome with 4028 triangles, as my mother would only be capable of searching roughly ten percent (402 triangles) of the surface area of a dome fifty feet high (at 120 triangles examined per hour), it would take my mother less than half a night to examine every triangle in all three bottommost rows of the dome. Inevitably, she would find me.
Now, if we doubled the height and diameter of the dome (so, d=200 feet, h=100 feet) to get a dome surface area of 62,831.85, we then get 16,110.73 or, rounding up, 16,111 triangles. Searchability is diminished to seven percent because the dome is higher. My mother then is capable of searching 805 triangles. Again, piece of cake for my mother.
But if I design a dome one-thousand feet in diameter and five-hundred feet in height (dome surface area: 1,570,796.33 feet) then my mother must contend with 402,768 total triangles, five thousand searchable triangles, her chances of finding me in one night are reduced to roughly one night in five nights.
And a dome of one-hundred thousand feet in diameter and fifty-thousand feet in height (dome surface area: 15,707,963,267.95 feet)? My mother has an estimated 5,034,604 searchable triangles. A dome of 5,034,604 searchable triangles has a total volume of 261,799,387,799,149.4 cubic feet, the same volume as if Lake Michigan flooded Lake Huron.
In a dome of this size, my mother, on any given night, has a 1 in 5594 chance in finding me. If she spends every night systematically examining triangles (maintaining her rate of 960 triangles examined per night), feeling around in every triangle in the dark, and poking at the upper triangles with a stick, I will see my mother only once every fifteen years.
Dr. Maev Barba attended the Puget Sound Writer’s Conference in 2018. She is a PNW native and a great lover of books. She used to sell books door-todoor. A doctor of astronomy, Barba looks into space and considers neither the small as too little, nor the large as too great, for the lover of stars knows there is no limit to dimension.