Engineering Mathematics and Computational Science. Programme aim Nowadays, one can without hesitation, state that there is mathematics in virtually everything. There is mathematics behind mobile phones, cars and oil tankers. Welcome to Pearson SuccessNet! We have made some important updates to Pearson SuccessNet! Please see the Feature Summary for more details. As always, please contact us if you have any questions. Phone: 1-800-234-5832 (Monday. Common Core State Standards Initiative. Home; About the Standards. Development Process; Frequently Asked Questions; Myths vs. Key Shifts in Mathematics; Statements of Support; Preparing America's students. 44 thoughts on “ Am I a constructive mathematician. Nor does it mean they are rejecting platonism. There may be one true world of mathematics; but it does not contain a distinguished “true” model of. Graphing Calculators in the Mathematics Classroom. Does it mean to bridge the many content strands within. Education Outreach Program; Rules, Forms and Resources. Rules For All Projects; Roles and Responsibilities of Students and Adults; Hazardous Chemicals, Activities or Devices; Potentially Hazardous Biological Agents. What does 'Ubuntu' mean. Ubuntu does not mean that people should not enrich themselves. The freedom to run the program. What Does It Mean To Enrich A Mathematics Program Of StudyInternet is built on mathematics and Google is based on probability theory. Cryptology and secure data transfer are based on classical number theory. New mathematical methods are necessary for understanding modern physics and chemistry, e. Bioinformatics has quickly grown to become one of the big areas of applied mathematics. A continuing development of mathematical methods is necessary in order to deal with the huge amounts of information generated by e. Who should apply. Engineering Mathematics and Computational Science turns to you who wants to sharpen your engineering studies with state- of- the- art mathematical competence as well as to you who with a keen curiosity- driven mathematical interest. Passing the LET would mean a passport to being a professional teacher. Mathematics, according to. An effective mathematics program is based on a carefully designed set of content standards that. A templeton conversation. Does science make belief in God obsolete? This is the third in a series of conversations among leading scientists and scholars about the 'Big Questions.' For the other Big Questions in this series. Site and author information for Interactive Mathematics. IntMath aims to interest and educate people in the joys of mathematics. I mean Math is a beautiful subject which is in sync with. What Does It Mean To Enrich A Mathematics Program For GradeOf course, it also turns to you who have realised that deep mathematical knowledge is on demand in an ever increasing number of areas. Why apply. The Master's program provides a solid base in mathematics and/or mathematical statistics or computational science. It is also possible to choose a direction towards bioinformatics. We also offer a number of courses in financial mathematics. On completion of the Master's program, you will be able to not only master a given area of engineering, but also take part in the development of mathematical models and algorithms. Other Programmes that might interest you. Applied Mechanics. Applied Physics. Complex Adaptive Systems. Computer Science - Algorithms, Languages, and Logic. Innovative and Sustainable Chemical Engineering. General entry requirements in detail. Chalmers Bachelor’s degree. Are you enrolled in a Bachelor’s degree programme at Chalmers now or do you already have a Bachelor’s degree from Chalmers? If so, different application dates and application instructions apply. Specific entry requirements. Bachelor. Others have become employed in industry, for example in the automotive industry and the pharmaceutical industry or as consultants for industry. Research connections. Research in mathematical sciences, in Sweden and elsewhere, is very intense. Mathematical research in on demand from an increasing number of sectors and at the same time mathematics continues to flourish as a research are in its own right. These directions of research are not in opposition to each other. On the contrary, they enrich and inspire each other. It is a fact that many of the mathematical results that are of very concrete use today, were developed by pure mathematical curiosity, sometimes decades or even centuries ago. Swedish mathematical research is by tradition strong. In particular this is true also for the Department of Mathematical Sciences at Chalmers and Gothenburg University. The Department is joint for the two universities, which helps to give it the size needed to create a stimulating environment, socially and scientifically. A number of Master's students have continued their studies at the department towards a Ph. D. Department of Mathematical Sciences.
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Before taking the examination, you will need to fulfill the organization's requirements, including the completion of 6. The Indiana Department of Health's Indoor and Radiologic Health can provide you with a radiology license that will allow you to work legally in the state. Registering with the The American Registry of Radiologic Technologists will increase your chances of being hired on at a hospital or other health care facility, and you will need to re- certify every couple of years by taking 2. Outlook for Ultrasound/Sonography Careers in Indiana. With a projected employment increase of 3. Bureau of Labor Statisticsreports that this sector of the health care industry will provide an additional 4. United States. Presently, health care facilities across Indiana employ about 1,0. Umar bin al- Khattab, the Second Khalifa of the Muslims . Shibli, his biographer, says that in his youth he grazed camels. Before accepting Islam, Umar was one of the most rabid enemies of Muhammad, the Messenger of God. When Muhammad proclaimed his mission, many people acknowledged him as the Messenger of God. Umar acknowledged him as Messenger of God after six years. Some historians claim that Umar was a most awe- inspiring man, and when he accepted Islam, the idolaters were gripped with fear for their lives. But this is only a case of a dominant myth being in conflict with ugly facts. Umar was born in Mecca to the Banu Adi clan, which was responsible for arbitration among the tribes. His father was Khattab ibn Nufayl and his mother was. The Rightly Guided Caliphs: Umar ibn. A short biography of Prophet Muhammad’s companion. The Rightly Guided Caliphs: Umar ibn Al-Khattab (p. Omar Ibn Khattab (RA) MBC TV Series Discussion Guide https://www.facebook.com/OmarMBCStudyGuide TABLE OF CONTENTS I. Umar Ibn Al-khattab (A Biography 2 Vol Set). This book describes, among other things, the principles based upon which `Umar ibn al-Khattaab (Radi Allah Anh). Umar was from the Ban. His mother, Hantama, was the daughter of H This particular Umar Ibn Al Khattab Download PDF start with Introduction, Brief Session till theIndex/Glossary page. Umar was born in Mecca around 581 to the Adi clan of the Quraish tribe. This biography of Khattab covers different stages of his life. When Umar accepted Islam, the idolaters remained where they were, and nothing changed for them; but it was Muhammad who was compelled to leave his home, and had to find sanctuary in a desolate ravine. He spent three years in that ravine, and during those years of exile, his life was exposed to deadly perils every day and every night. During this entire period of more than 1. Umar, like many other Muslims in Makkah, was the silent spectator of the ordeals of his master. He made no attempt to bring those ordeals to an end. Muhammad Mustafa established brotherhood among Muslims both in Makkah and in Medina. In Makkah, he made Umar the “brother” of Abu Bakr, and in Medina, he made him the “brother” of Utban bin Malik. Khalifa Umar bin al-Khattab. Khalifa Umar bin al-Khattab Khalifa Umar bin al-Khattab - Death of Umar. Khalifa Umar bin al-Khattab - Death of Umar.For his own brother, Muhammad chose Ali ibn Abi Talib in both cities. In 3 A. H., Umar's daughter, Hafsa, was married to the Apostle. Umar was one of the fugitives of the battle of Uhud (Baladhuri). He himself said later: “When Muslim were defeated in Uhud, I ran toward the mountain.” (Suyuti in al- Durr al- Manthoor). At the siege of Khyber, Umar made an attempt to capture the fortress but failed. Umar was one of the fugitives of the battle of Hunayn. Abu Qatada, a companion of the Prophet, says: “In Hunayn when the Muslims were fleeing, I also fled, and I saw Umar with others.” (Bukhari and Kitabul- Maghazi). In 8 A. H. He ordered Umar to serve as a ranker in the expedition. Though Umar spent eighteen years in the company of Muhammad Mustafa, the Messenger of God, the latter never appointed him to any position of authority – civil or military. When the Apostle of God was on his deathbed, he asked the companions to bring pen, paper and ink so he might dictate his will but Umar defied him. He did not let the Apostle dictate his will and testament. Umar was not present at the funeral of the Prophet of Islam. He was brawling with the Ansar in the outhouse of Saqifa when the body of the Prophet was being buried. Umar was the khalifa- maker of Abu Bakr. During Abu Bakr's khilafat, Umar was his principal adviser. The Banu Umayya were the traditional champions of idolatry and the arch- enemies of Muhammad and his clan, the Banu Hashim. Muhammad had broken their power but Umar revived them. The central component of his policy, as head of the government of Saqifa, was the restoration of the Umayyads. He turned over Syria to them as their “fief,” and he made them the first family in the empire. A modern student of history might find claims made on behalf of some companions of the Prophet rather extravagant and baffling. He might notice in them the clash of popular imagination with historical reality. But if he wishes to make a realistic evaluation of the roles they played in the lifetime of the Prophet, there is no better way of doing so than to turn away from rhapsody and rhetoric, and to focus attention on facts and facts alone. When Umar took charge of the caliphate, the Muslim armies were fighting against the Persians in Iraq and the Romans in Syria. The army in Syria was under the command of Khalid bin al- Walid, the favorite general of Abu Bakr. Umar's first act as khalifa was to dismiss him from all his commands, and to appoint Abu Obaida bin al- Jarrah as the supreme commander of the Muslim forces in Syria. Shibli says that Umar had, for a long time, nursed a secret hatred of Khalid because of the latter's excesses. Umar had indeed dismissed Khalid because of his excesses but it appears that personal rancor was also at work. He was jealous of Khalid's fame and popularity. If he disliked Khalid's transgressions, he ought to have formally indicted him, and should have ordered full investigation of his crimes in murdering Malik ibn Nuweira and in appropriating his widow. If Khalid had been proven guilty, then Umar ought to have passed sentence on him according to the Islamic law. But there was no indictment and no investigation. Khalid was summarily dismissed and he died in poverty and obscurity in 2. A. H. Umar's caliphate is notable for its many conquests. His generals conquered Iraq, Iran, Azerbaijan, Kirman, Seistan, Khurasan, Syria, Jordan, Palestine and Egypt, and incorporated them into the empire of the Muslims. All of these were permanent conquests. The Romans lost Syria, Palestine and Egypt for ever; and in Persia, the Sassani empire ceased to exist. Among other events of the caliphate of Umar, were the first outbreak of plague in Syria in 1. A. H., and a famine in Hijaz in the same year. Between them, the plague and the famine killed more than 2. Suyuti and Abul Fida). Since the empire had grown enormously in all directions, Umar had to establish an administrative system. But the Arabs did not have any experience in administration. Umar, therefore, left the Persian and the Roman framework of administration in the conquered provinces undisturbed. The Persian and the Roman staff carried on the day- to- day work as before. Umar founded numerous military cantonments in Iraq, Syria and Egypt. Since he wanted the Arabs to be a purely fighting and ruling class, he did not allow them to buy land and to settle down or to become farmers in the conquered territories. To assess land revenue, Umar again had to retain the Persian and the Romans systems. But in Iraq it was found necessary to survey the arable lands and to assess tax on them. Arabs knew less than nothing about assessing land revenue. There was, however, one exception in Uthman bin Hunaif of Medina. He was a man of outstanding ability as a revenue expert. Though it was Umar's policy not to appoint the citizens of Medina (Ansar) to any important positions, in this particular case he had no choice, and he appointed Uthman bin Hunaif as the commissioner of land development in Iraq. Qadi Yusuf says that Uthman bin Hunaif was an authority in all Arabia on taxation, assessment of land revenue and land reclamation (Kitabul- Kharaj and Siyar- ul- Ansar). Within less than a year, Uthman bin Hunaif had completed the job of taking measurements of the whole new province, and of making assessments for the collection of land revenue. He was, thus, the first Financial Commissioner of Iraq, and incidentally, one of the few Ansaris to hold any position of authority in the caliphates of Abu Bakr, Umar and Uthman bin Affan. When Syria, Jordan and Palestine were conquered, Umar appointed Yazid bin Abu Sufyan the governor of Syria; Shurahbil bin Hasana governor of Jordan, and Amr bin Aas the governor of Palestine. Abu Obaida bin al- Jarrah was appointed governor of the city of Damascus. When Amr bin Aas conquered Egypt, Umar made him its governor. Yazid bin Abu Sufyan, the governor of Syria, died in the plague of 1. A. H. When Umar heard the news of his death, he went to see Abu Sufyan to offer condolences to him. But Abu Sufyan interrupted Umar's commiseration, and asked him, “Whom are you going to appoint governor of Syria in place of my late son, Yazid?” Umar said: “Of course, his brother, Muawiya.” Abu Sufyan immediately forgot his sorrow at his son's death, and rejoiced in the elevation of Muawiya, his second son, as governor. Umar appointed Muawiya the new governor of Syria. When Abu Obaida died, Umar placed Damascus also under Muawiya's jurisdiction. He fixed his salary at 6. Isti'ab, Volume I). After dismissing Khalid bin al- Walid as supreme commander of the forces in Syria, Umar had appointed him, for a time, governor of the district of Kinnisirin but dismissed him again for his alleged “pomposity.”Saad bin Abi Waqqas, the victor of the battle of Qadsiyya fought against the Persians, was Umar's governor of Iraq. He too was dismissed in 2. A. H. Amr bin Aas was Umar's governor in Egypt. Umar did not dismiss him but curtailed his powers by appointing Abdullah bin Saad bin Abi Sarah as a “watchdog” over him in fiscal matters. Umar was a most exacting taskmaster for all his generals and governors. He was quick to lend his ears to any complaint against them, and he was even quicker to dismiss them –with one exception – Muawiya! He was forever indulgent to the sons of Abu Sufyan and the clan of Banu Umayya. Muawiya, the son of Abu Sufyan and Hinda, the governor of Syria, lived in Damascus in imperial splendor, surrounded by a glittering retinue. It was a lifestyle that Umar did not tolerate in any other governor. But Muawiya, for him, was a “special,” and the rules which applied to others, did not apply to him. Tabari has recorded the following incident in Volume VI of his History. Umar was in Damascus and Muawiya came to see him every day – mornings and evenings – bedecked in regal outfit, with splendidly caparisoned mounts and escorts. When Umar commented, rather acidly, upon his pageantry, he said that Syria was swarming with Roman spies, and it was necessary to impress them with the “glory” of Islam. His pageantry, he said, was only the outward emblem of that glory - the glory of Islam. But Umar was not convinced, and remarked: “This is a trap laid by the slick and guileful man.”Muawiya answered: “Then I will do whatever you say, O Commander of the Faithful.”Umar said: “If I raise an objection to anything, you baffle and bewilder me with words. I am at a loss to know what to do.”Here Umar can be seen utterly “helpless” before his own prot. He could condone Muawiya anything and everything. He, in fact, appeared to be ostentatiously courting Abu Sufyan and his sons. Livingsoft Northwest - Custom Fit / Custom Design Sewing Patterns Hat Shop. Create just the. perfect hat or purse to match any garment, mood, or. Fashion hats, fun hats, costume hats, berets. Sewing is the craft of. 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Most DUI diversion programs involve rehabilitation or educational programs focusing on alcohol abuse awareness. DUI diversion can also involve other requirements like community service, letters of apology to victims, blood alcohol monitoring, and the payment of fees. The eligibility requirements for DUI diversion programs will of course vary by state, since each state has different DUI laws. In general, eligibility requirements for DUI diversion will usually require that the defendant: Doesn’t have any current DUI charges besides the present charges. Did not have any DUI convictions prior to the present charge (sometimes up to 1. Was not enrolled in a DUI diversion program at the time of the arrest, (and sometimes, not enrolled up to 1. DUI Diversion is a specific type of diversionary program. Legal Topics > Criminal Law and Police > Automobile > Drunk Driving DUI/DWI. Was not enrolled in a DUI diversion program at the time. Back on Track Program. Diversion/Back on Track Program; Drug-Impaired DUI; DUI License. Contesting a Drunk-Driving Charge, by Our Miami DUI Defense Attorney March 21, 2016; Fighting Test Results in Miami. Doesn’t have any previous convictions for felonies or vehicular assault. Did not cause death or serious bodily injury to the plaintiff. Also, some jurisdictions don’t allow the defendant to participate in DUI diversion if they had previously been adjudicated as a youthful offender in the past five years. Oregon DUII Diversion Program, Class, and Rules. Oregon law cuts a DUII driver a break if it is their first drunk driving offense by allowing them to enter into the diversion program. Learn About Avoiding a DUI Conviction With a DUI Diversion Program. If you have been arrested for a first time DUI offense you might be eligible to enter into a diversion program to allow your DUI charge to get dismissed after. DUII Diversion Program Classes Portland – Oregon Drunk Driving Attorneys. If the DUI occurred while the defendant’s license was expired or suspended, it may also disqualify them from diversion. DUI Diversion programs usually involve an enrollment fee, though this can sometimes be waived with proof of hardship. What If I Don’t Complete the DUI Diversion Program? DUI diversion programs usually last up to two years. This can result in the re- imposition of the original sentence that was avoided through the diversion program (i. For example, if the offender refuses to attend rehabilitation classes, or refuses to submit to blood alcohol monitoring, they will likely be disqualified from the diversion program. Thus, diversion is much like probation in a criminal case- the DUI offender must complete the entire diversion program in order to avoid a jail sentence and keep the charges off their record. The person participating in the diversion program may often be required to check in with a probationary officer who will oversee their progress. 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CORRELATION AND REGRESSION / 47 CHAPTER EIGHT CORRELATION AND REGRESSION Correlation and regression are statistical methods that are commonly used in the medical literature to compare two or more variables. Rank correlation coefficients, such as Spearman's rank correlation coefficient and Kendall's rank correlation coefficient ( Beamer-tu-logo Variance CovarianceCorrelation coef With big data, one sometimes has to compute correlations involving thousands of buckets of paired observations or time series. For instance a data bucket corresponds to a node in a decision tree, a customer segment, or a. We now show how to perform hypothesis testing to determine whether the population correlation coefficient is statistically different from zero or some other value. Note that for normally distributed populations a correlation. Specific contexts of interest include multivariate feature selection (a combinatorial problem) or identification of best predictive set of metrics. In large data sets, some buckets will contain outliers or meaningless data, and buckets might have different sizes. We need something better than the tools offered by traditional statistics. In particular, we want a correlation metric that satisfies the following. Five conditions: Independent of sample size to allow comparisons across buckets of different sizes: a correlation of (say) 0. X, Y) of size n, regardless of n. Same bounds as old- fashioned correlation for back- compatibility : it must be between - 1 and +1, with - 1 and +1 attained by extreme, singular data sets, and 0 meaning no correlation. More general than traditional correlation: it measures the degree of monotonicity between two variables X and Y (does X grow when Y grows?) rather than linearity (Y = a + b*X + noise, with a, b chosen to minimize noise). Yet not as general as the distance correlation (equal to zero if and only if X and Y are independent) or my structuredness coefficient. Not sensitive to outliers, robust. More intuitive, more compatible with the way the human brain perceives correlations. Note that R- Squared, a goodness- of- fit measure used to compare model efficiency across multiple models, is typically the square of the correlation coefficient between observations and predicted values, measured on a training set via sound cross- validation techniques. It suffers the same drawbacks, and benefits from the same cures as traditional correlation. So we will focus here on the correlation. To illustrate the first condition (dependence on n), let's consider the following made- up data set with two paired variables or time series X, Y: X Y0 0. Here n=8 and r (the traditional correlation) is equal to r=0. If n=7 (delete the last observation), then r=0. Clearly we observe high correlations when n is even, although they slowly decrease to converge to 0, for large values of n. If you shift Y one cell down (assuming both X and Y are infinite time series), then correlations for n even are now negative! However, this (X, Y) process is supposed to simulate a perfect 0 correlation. The traditional correlation coefficient fails to capture this pattern, for small n. This is a problem with big data, where you might have tons of observations (monthly home prices and square feet for 3. In particular, comparisons between buckets of different sizes become meaningless. Our starting point to improve the standard correlation will be Spearman's rank correlation. It is the traditional correlation, but measured on ranked variables. All correlations from the new family that I will introduce in the next section, are also based on rank statistics. By working on ranked variables, you satisfy conditions #3 and #4 (though #4 will be further improved with my new correlation). Let's denote Spearman's coefficient as s. It is easy to prove (see Wikipedia article) that: s = 1 - S(X, Y)/q(n)where. S(X, Y) = SUM. A very interesting and important fact, and a source of concerns, is that q(n) = O(n^3). In short, q(n) grows too fast. A new family of rank correlations. Without loss of generality, from now on we can now assume that X is ordered and thus x(j) = j. Our new correlation will be denoted as t, or t(c) to emphasize the fact that it is a family of correlations governed by the parameter c. Bayesian statisticians might view c as a prior. The new correlation is computed as follows: Step ACompute u =SUM. Also, if you reverse Y order, then only the sign of the correlation changes (but this was already true for s, prove it as an exercise). It always satisfies condition #2 when c> 0. Also, when c> 0, t=+1 if and only if s=+1, t=- 1 if and only if s=- 1. It is identical to s (Spearman's) when c=2. However c=2 makes t too sensitive to outliers. Also c=2 is an artificial value that makes old- style computations and modeling easy. But it is not built with practical purposes in mind, unlike c=1. In short, it is built based on theoretical and historic considerations, and suffers drawbacks and criticism similar to old- fashioned R Squared. I conjecture that q(n) = O(n^. When c is large, it creates a very long, artificial tail for the distribution of T(c). A small c is preferred, otherwise, very rare, extremely high values of T(c) artificially boost q(n) and create a t that is not well balanced. We will focus here on the case c=1. We compute the rank distances between X and Y (in u) as well as between X and Z, (in v), where Z is Y in reversed order, and then pick up the smallest between u and v. This steps also determines the sign of the correlation. I provide look- up tables for small values, approximations are used for large values. Distribution of correlation vector (s, t), for n=9 . Which one makes sense, s or t? Both are not statistically different from 0. Asymptotic behavior and normalization. Again, we assume that t is defined using c=1. Simulations where X = (0, 1, .., n- 1) and Y is a random permutation of n elements (obtained by first creating n random numbers then extracting their rank) show thatt converges faster than s to 0: in one experiment, the observed t averaged over 3. Average . This is critical when you compute correlations across thousands of data buckets of various sizes: you are bound to find outliers in some buckets. And if you look for extreme correlations, your conclusions might be severely biased: read the curse of big data for explanations. Below is the distribution for T, when n=1. When n=1. 0, 9. 7. When n=7, 9. 2. 0% of t values are between - 0. So the distribution of t depends on n. Theoretically, when c gets very close to 0, what happens? Histogram for T (n=1. Interesting fact: t and s agree most of the time. The classic correlation r between s and t, computed on all n! All we know so far is that q(n)=O(n^2). Also, when n is a multiple of 3, then q(n)=(n- 6)+(n^2)/3. Is there an exact formula if n is not a multiple of 3? We are going to ask this question on Kaggle. If no exact formula is known, a simple solution would consist in using an approximate t, based on q(n)=(n- 6)+(n^2)/3 and T truncated to (n- 6)+(n^2)/3. Normalization. Because the correlation is in the range . There are various ways to accomplish this, but it always involves transforming t. Some research still needs to be done. For r or s, one typically uses the Fisher transformation. But it will not work on t, plus it transforms a bounded metric in a non- bounded one, making interpretation difficult. Permutations. Finally, most of this research and these simulations involve the generation of a large number of permutations for small and large n. Here I discuss how to generate these permutations. One way is to produce all permutations: click here to download the source code. However, it becomes very slow when n is larger than 2. Map Reduce to split the task on multiple virtual machines, in parallel. Another strategy is to sample enough random permutations to get a good approximation of t's distribution, as well as q(n). There is a one- to- one mapping between permutations of n elements, and integer numbers between 1 and n! Each of these numbers can be uniquely represented by a n- permutation, and the other way around. See questions 7. 9 and 8. Check the numbering permutations section in the Wikipedia article on permutations, for details. I will write a simple, easier to read version of this algorithms. In short, it is very slow: O(n^2) to transform a number into a permutation or the other way around. So instead, I used a rudimentary approach (click here to download my source code), which is just as fast: Algorithm to generate a random permutation (p(0), p(1), .. Generate p(k) as a random number on . Repeat Step 1 until p(k) is different from p(0), p(1), .. Answer: read here. Final comments. If you are interested in using correlations to assess how good your predicted values are likely to be, I recommend dividing your data set into two sets, for cross- validation: test and control. Fine- tune your model on the test data (also calledtraining set) usingt to measure its predictive power. But the real predictive power is measured by computington the control data. Read this article about a leaving- one- out strategy to accomplish a similar goal. Note that t, unlike s, has a bi- modal distribution, with a dip around 0. This makes sense, since a correlation of 0 means no pattern found (a rare event), while different from 0 (but far from - 1 or +1) means pattern found - any kind of pattern however slight - a more frequent event. Indeed, we view this bi- modal distribution as an advantage that t has over s. This is a new trend in data science - using algorithms to define stuff. The fact that s uses square distances, rather than distances (like t) makes it less robust, as outliers heavily weights on s. While both s and t are based on rank statistics to smooth out the impact of outliers, s is still very sensitive to outliers when n is large. And with big data, we see more cases of large n. This is particularly true for data with small relative variance (defined e. You could spend years of research on this whole topic oftand random permutations, and write a book or Ph. D. Here I did the minimum amount of research to get to a good understanding and solution to the problem. This way of doing data science research is in contrast with slow- paced, comprehensive academic research. Related articles. |
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