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The Decomposition of Figures Into Smaller Parts – Boltyanskii and Gohberg

In this post, we will see the book The Decomposition of Figures Into Smaller Parts by V. G. Boltyanskii and I. T. Gohberg. The book is part of the Popular Lectures in Mathematics Series.

About the book:

This book is devoted to some interrelated problems of a new, rapidly developing branch of mathematics called combinatorial geometry. Common to all the problems examined here is the notion of “ cutting” a geometric figure into several “smaller pieces.” There are several different criteria for what constitutes a “ smaller piece” ; hence this book necessarily treats several different problems. All the theorems proved here are very recent; the oldest of them was proved by the Polish mathematician Karol Borsuk about forty years ago. This theorem of Borsuk is the core around which all of the subsequent exposition unfolds. The most recent theorem is barely a year old.


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New top story on Hacker News: William Stein on the struggle for open source funding in pure mathematics [pdf]

William Stein on the struggle for open source funding in pure mathematics [pdf]
36 by adenadel | 7 comments on Hacker News.

The Evanston Colloquium Lectures On Mathematics PDF

These women leaders in science, technology, engineering, and math utilized their talent and hard work to become role models for STEM-inclined younger women and men. The Evanston colloquium: lectures on mathematics delivered from Aug. 28 to Sept. 9, 1893 before members of the Congress of Mathematics held in connection with the World’s Fair in Chicago at Northwestern University, Evanston, Ill., by Felix Klein. Get this from a library! The Evanston colloquium: lectures on mathematics delivered from Aug. 28 to Sept. 9, 1893 before members of the Congress of Mathematics held The Project Gutenberg EBook of The Evanston Colloquium Lectures on Mathematics, by Felix Klein This eBook is for the use of anyone anywhere at no cost and with Zaalberg, Louise. See: Bertrand, H. Zabeltitz, Georg Büchner Zobel von. See: Büchner, Georg,. Zaccagnini, Guido, 1868-¶ Rimatori siculo-toscani del dugento. The Evanston colloquium: lectures on mathematics delivered from Aug. 28 to Sept.

9, 1893 before members of the Congress of mathematics held in connection with the World’s fair in Chicago at Northwestern university, Evanston, Ill. Did you know that you can help us produce ebooks by proof-reading just one page a day? Go to: Distributed Proofreaders The English Babylon comes from Greek Babylṓn (Βαβυλών), a transliteration of the Akkadian Bābilim. [not in citation given] Archibald Sayce, writing in the The Evanston Colloquium Lectures on Mathematics Delivered from Aug. 28 to Sept. 9, 1893, before members of the Congress of Mathematics held in connection with the Learn more about the Department of Materials Science and Engineering at the McCormick School of Engineering. 1894] KLEIN’S EVANSTON LECTURES, 119 KLEIN’S EVANSTON LECTURES. The Evanston Colloquium : Lectures on mathematics, deliv­ ered from Aug. 28 to Sept.

9,1893, before members of the Congress of Mai hematics held in connection with the World’s Fair in Chicago, at Northwestern University, Evanston, 111., by FELIX KLEIN. Reported by Alexander Ziwet. Publications: The Evanston Colloquium Lectures on Mathematics. Bull. Amer. Math. Soc. 18 (1912), 8.//projecteuclid/euclid.bams/1183421391 List of the new elected members to the European Academy of Sciences Buy The Evanston Colloquium: Lectures on Mathematics Delivered From Aug. 28 to Sept. 9, 1893 Before Members of the Congress of Mathematics Held in at Northwestern 論文リスト. 408) Accuracy of Td-DFT in the Ultraviolet and Circular Dichroism Spectra of Deoxyguanosine and Uridine, Tomoo Miyahara and Hiroshi Nakatsuji , J Existentialism (/ ɛ ɡ z ɪ ˈ s t ɛ n ʃ ə l ɪ z əm /) is a tradition of philosophical enquiry associated mainly with certain 19th and 20th-century European Mathematics Calendar. Submit an entry to the Mathematics Calendar. Questions about the Mathematics Calendar? Email us.

An Introduction To Multivariable Mathematics PDF

An Introduction to Multivariable Mathematics Full Text There is also an appendix which provides a nine-lecture introduction t real analysis. This wikibook aims to be a high quality calculus textbook through which users can master the discipline. Standard topics such as limits, differentiation and Our goal is to bring our own open courseware as well as high-quality ones that are freely available online. We want to help college students everywhere master Find helpful customer reviews and review ratings for An Introduction to Multivariable Mathematics (Synthesis Lectures on Mathematics and Statistics) at Amazon Multivariable Calculus with Engineering and Science Applications , Mathematics, 577 pages, 1996, Aimed at students seeking a career in science, engineering or mathematics, this text on multivariable calculus emphasizes that calculus is best understood via geometry and, Philip M. MIT Mathematics courses available online and for free.

Learn and research science, biology, chemistry, electronics, mathematics, space, terminology and much more. This free online textbook (e-book in webspeak) is a course in basic analysis. This book started its life as my lecture notes for Math 444 at the University of Mathematics [ undergraduate program | graduate program | faculty] All courses, faculty listings, and curricular and degree requirements described herein are 1 CHAPTER 1 LinearAlgebra 1 VECTORSINRn Rn will denote real Euclidean space of dimension n—that is, Rn is the set of all ordered n-tuples of real numbers,referred UW TACOMA DIVISION OF SCIENCES AND MATHEMATICS MATHEMATICS – TACOMA Detailed course offerings (Time Schedule) are available for.

Winter Quarter 2018 Buy An Introduction to Partial Differential Equations with MATLAB, Second Edition (Chapman & Hall/CRC Applied Mathematics & Nonlinear Science) on College Textbooks Offline, Online, Print, Digital, Affordable | Worldeide Center of Mathematics An introduction to multivariable mathematics. [L Simon] — The text is designed for use in a 40 lecture introductory course covering linear algebra, multivariable differential calculus, and an introduction to real analysis. COLLEGE OF ARTS & SCIENCES MATHEMATICS Detailed course offerings (Time Schedule) are available for. Winter Quarter 2018; The text is designed for use in a forty-lecture introductory course covering linear algebra, multivariable differential calculus, and an introduction to real analysis. Description: A short introduction to key problems and concepts regarding multivariable process control. View More A short introduction to key problems and concepts regarding multivariable process control.

The dearth of women in STEM fields: a new take

The dearth of women in STEM (science, technology, engineering, and mathematics) in the U.S. and U.K. is well known, and it turns out it’s also an issue in other Western countries. It’s usually attributed to sexism that bars women from entering these fields. Other explanations are a difference in interests and preferences: perhaps women prefer to enter fields other than STEM for reasons other than the presumption that they’ll be discriminated against or criticized in the field. That idea—that there are inherent differences in the preferences of males and females (and we don’t know whether these are acculturated, genetically based, or a mixture of these)—was the subject of James Damore’s infamous Google memo, for which he was demonized and, at least in part, fired. (I’m told that Damore had a history of bad interactions at Google.) Finally, one can claim that women have lower abilities in STEM fields than do men, so even if they preferred such studies, the meritocracy would weed them out.

A new paper in Psychological Science (free Unpaywall access; pdf here, reference at bottom) by Gijsbert Stoet and David C. Geary points to the second explanation: consistent differences in preference, and dispels the third, finding no consistent sex differences in abilities. This doesn’t rule out sexism, as they didn’t test for that, but the important factor seems to be preference. That’s because the authors find a strong and counterintuitive correlation between the gender gap in stem degrees and the index of gender equality in countries. In those countries with more gender equality, the gap between men and women in getting STEM degrees is larger. The authors explain that as resulting from a combination of sex-based preferences and the standard of living in different countries.

Let me say first that I think there’s plenty of evidence that men and women differ in their preferences for what kind of work they want to do. I suspect, but don’t know, that part of that difference is based on evolution. After all, men and women have evolved separately for some six million years since we split from our common ancestor with the chimps, and it’s not unreasonable to think that different sex roles over that period led to the evolution of different preferences. I hasten to add that even if this be true, it is no reason to treat men and women unequally or give them different educational opportunities based on their sex. I’ve often emphasized that true equality between the sexes means that nobody be treated differently because of their gender, and that men and women be given the same opportunity from birth to realize their talents and ambitions. But if preferences be different, this may still lead to different outcomes.

In overall science literacy, women and men were pretty equal throughout the world. As they authors note, “We found that girls outperformed boys in 19 (28.4%) countries, boys outperformed girls in 22 (32.8%) countries, and no statistically significant difference was found in the remaining 26 (38.8%) countries.” That is, there’s no inherent trend for one sex to be better than the other, though there are statistically significant differences among countries. That militates against some inborn difference and suggest that those differences are cultural.

However, when the authors looked at intraindividual differences in ability, that is, relative ability, they found that women generally ranked higher in reading compared to their average ability, while men ranked higher in science and mathematics compared to their average ability. Combined with the data above, I interpret this to mean that, overall, men and women are equal in science literacy and math comprehension, but since women have higher reading ability than men, they are higher overall academically. Nevertheless, there’s a big and consistent difference in these areas. As the authors note:

When the authors looked at this “gender gap” in relative performance, they found out that it was larger in countries that were more gender equal. That is, the more equal the country in gender treatment, the greater the relative performance of women in reading over science and math, and the greater the relative performance of men in science and math over reading. Here’s a figure showing that, which also shows you the countries that are more gender equal (higher on the y axis) and those at the bottom (countries like Lebanon, Jordan, Turkey, Tunisia, and Algeria):

Not only was the intraindividual “gender gap” larger in more gender-equal countries, but the percentage of women getting STEM degrees was lower in more gender-equal countries. Places like Norway, Finland, Sweden, Ireland, and Switzerland, which rank high on gender equality, had a much lower percentage of women among college STEM graduates than less gender-equal countries like the UAR, Tunisia, Turkey, and Algeria. Would you have expected that? The negative correlation is striking (same Y axis: higher Y scores mean more gender equality):

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Objective mathematics by SK goyal pdf

Hey guys here i am providing objective mathematics by SK goyal book pdf

SK goyal

I hope guys that this pdf will help you in your preparation. Please share this post with your frnds and if you want pdf of any other book let me know in comments and to get updates of our latest post follow us.

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Download JAMB MATHEMATICS Past Questions And Answers By Akahi Tutors (PDF)

Download JAMB MATHEMATICS Past Questions And Answers By Akahi Tutors (PDF)

Download JAMB MATHEMATICS Past Questions And Answers By Akahi Tutors (PDF)

Episcopal Book Of Common Prayer Baptism

Episcopal Book Of Common Prayer Baptism

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New top story on Hacker News: How to write Mathematics [pdf]

How to write Mathematics [pdf]
6 by lainon | 0 comments on Hacker News.

Open Call for K-3 Nonfiction Submissions

By Carol Hinz, Editorial Director of Millbrook Press and Carolrhoda Books

UPDATE MAY 2, 2018: The submissions window for this open call is now closed. Thank you to all those who submitted manuscripts.

One of my favorite things about children is their sense of wonder. My own kids regularly ask me questions about things I take for granted (“Why does it get dark at night?”) and prompt me to think about familiar things in new ways (“My cheese looks like Minnesota!”)

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New top story on Hacker News: How to write Mathematics [pdf]

How to write Mathematics [pdf]
8 by lainon | 0 comments on Hacker News.

mathematics entrance exam pdf – Google Search

mathematics entrance exam pdf – Google Search — shared by UC Mini

Five Questions Atheists Cannot Plausibly Answer

Below I have presented five questions that I do not believe that atheists will be able to plausibly answer.

1. Despite the culture or era, sane humans have the innate sense of what’s right and what’s wrong and we prefer to do what’s right to help our fellow humans. No matter the major religion, we all are aware of the Golden Rule. We prefer the humble over the braggarts, the selfless over the selfish, and the truthful over the liars.

Cross-cultural sociologists and psychologists and leadership scholars like Hofstede, Trompenaars, House, and Schwartz have found that societies vary in ways inconsistent with our innate morality. For example, not all societies are considered “cooperative or collective.” Collective societies are in Asia, Northern Europe, the Arab region, Africa, and South America. Highly individualist societies are in Western Europe, the United States and Canada. Many societies are hedonistic, hierarchical, and have preferences against gender egalitarianism. So, what we know that we ought to do is often inconsistent with what we are actually doing. How do we know what we ought to do?

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A Glowing Geometric Proof that Root-2 is Irrational

It was a great shock to the Pythagoreans to discover that the diagonal of a unit square could not be expressed as a ratio of whole numbers. This discovery represented a fundamental fracture between the mathematical domains of Arithmetic and Geometry: since the Greeks recognized only whole numbers and ratios of whole numbers, the result meant that there was no number to describe the diagonal of a unit square.

Proving the Result

The usual way of proving the irrationality of √2 is to assume that it can be expressed as a ratio p/q and, by a simple arithmetical argument, show that this leads to a contradiction. Around 1950, the American mathematician Stanley Tennenbaum discovered an ingenious proof of the irrationality of √2. He never published this result, although he told many other people about it.

My Data Science/Machine Learning Job Interview Experience : List of DS/ML/DL Questions

Beginning this year, I had been taking interviews for a job change in Data Science (DS)/Machine Learning (ML)/Deep Learning (DL) field in India. In the process of 30-40 days of job hunt, I took interviews in about 8-10 companies inclusive of start-ups, services based and product based in nature. I believe, It would help job seekers; hence I decided to blog post my experience and what I learned along the way.

A bit of introduction first, I have 4+ years of experience in machine learning and its applications in field of speech analytics, text analytics and image analytics. Somehow, in general I felt that most of the job positions in this area revolve around text analytics (Natural language processing) followed by image analytics (Computer vision). There are very few companies pursuing speech/audio analytics. Having 5 years of experience, I was looking for a mid-level senior position where I can lead a team of DS/ML enthusiasts to do some interesting work/projects. I will be listing down the kind of questions that were asked in various technical interviews of recruitment process.

# Company 1 (20-25 minutes) – Global service based company

As in your CV, what have you done in building document exploration system ? I have implemented document clustering through topic modeling with LDA technique?
Let’s say, you are given a scenario where you have terabytes of data files consisting of pdfs, text files, images, scanned pdfs etc. What approach will you take in understanding or classifying them ?
How will you read the content of scanned pdfs or written documents in image formats ?
Why is naive bayes called “naive” ?
Tell me about naive bayes classifier ?
What is deep learning ? Difference between machine learning & Deep learning ?

Experience: There were few more questions like this but it went terrible for me. I really could not get what his expectation was as he was not going technical at all where as I was trying to dig deep into technical stuff. I tried discussing about training a tesseract or language models but he does not seem to be convinced. May be he wanted to hear something out of box or may be just good explanations or may be some better approach. I did not get the difference between getting interviewed as fresher and experienced professional as I was taking it for the first time in last 5 years.

# Company 2 (40-45 minutes) – Global service based company

How can you cluster documents in unsupervised way ?
How do you find the similar documents related to some query sentence/search ?
Explain TF-IDF ?
So As per my experience, Tf-Idf fails in document classification/clustering ? How can you improve further ?
What is LSTM neural network ? Explain me !! How does it work ?
What are word2vec vectors?
What do you mean by mutable and immutable objects in python ?
What are the data structures you have used in python ?

# Company 3 – (40 minutes) Global product & service based

How do you handle multi-class classification with unbalanced dataset ?
How did you perform language identification from text sentence ? (As in my CV)
How does you represent the symbolic chinese or japanese alphabets here ?
How can I design a chatbot ? (I had little idea but I tried answering it with intent and response tf-idf based similarity)
Can I develop a chatbot with RNN providing a intent and response pair in input ?
Suppose I developed a chatbot with RNN/LSTMs on Reddit dataset. It gives me 10 probable responses ? How can I choose the best reply Or how can I eliminate others replies ?
How does SVM learns non-linear boundaries ? Explain.

# Company 4 – (50 minutes) – 1 year old Heath care start-up

What is precision and recall ? Which one of this do you think is important in medical diagnosis ?
Define precision and recall ?
How do you draw ROC curve ? What does area under ROC curve signify ?
How will you draw ROC for multi class classification problem ?
Tell me any other metric to measure multi-class classification result ?
What is sensitivity and specificity ?
What is random about Random Forest ?
How do you perform text classification ?
How can you make sure to learn a context !! Well its not possible with TF-IDF ? (I told him about taking n-grams say n = 1, 2, 3, 4 and concatenating tf-idf of them to make a long count vector ?
Okay that is the baseline people start with ? What can you do more with machine learning ? (I tried suggesting LSTM with word2vec or 1D-CNN with word2vec for classification but he wanted improvements in machine learning based methods :-|)
How does neural networks learns non-linear shapes when it is made of linear nodes ? What makes it learn non-linear boundaries ?

# Company 5 – (50-55 minutes) – Amazon Inc.

What are the parameters in training a decision tree ?
What are the criteria for splitting at a node in decision trees ?
What is the formula of Gini index criteria?
What is the formula for Entropy criteria?
How is it decided that on which features it has to split ?
How do you calculate information gain mathematically ? Are you sure of formula!!
What is the advantage with random forest ?
Tell me about boosting algorithms ?
Okay !! So how does gradient boosting works ?
Do you know about Adaboost algorithm ? How and why does it work ?
What are the kernels used in SVM ? What is the optimization technique of SVM ?
How does SVM learns the hyperplane ? Talk more about mathematical details ?
Talking about unsupervised learning ? What are the algorithms ?
How do you decide K in K-Means clustering algorithm ?
Tell me at least 3 ways of deciding K in clustering ?
What other clustering algorithms do you know ?
Okay !! Can you tell DB-SCAN algorithm ?
How does HAC (Hierarchical Agglomerative clustering) work ?
Explain PCA ? Tell me the mathematical steps to implement PCA ?
What is disadvantage of using PCA ?
How does CNN work ? Explain the implementation details ?
Explain the back propagation steps of Convolution Neural Network ?
How do you deploy Machine Learning models ?
Lot of times, we may have to write ML models from scratch in C++ ? Will you be able to do that ?

# Company 6 – (50-55 minutes) – Global service based giant

What is the range of sigmoid function ?
Name the package of scikit-learn that implements logistic regression ?
What is mean and variance of standard normal distribution ?
What are the data structures you have used in python ?
Text classification method. How will you do it ?
Explain Tf-Idf ? What is the drawback of Tf-Idf ? How do you overcome it ?
What are bigrams & Tri-grams ? Explain with example of Tf-Idf of bi-grams & trigrams with a text sentence.
What is an application of word2vec ? Example.
How will you design a neural network ? How about making it very deep ? Very basic questions on neural network.?
How does LSTM work ? How can it remember the context ?
What is naive bayes classifier ?
What is the probability of heads coming 4 times when a coin is tossed 10 number of times ?
How do you get an index of an element of a list in python ?
How do you merge two data-set with pandas ?
From user behavior, you need to model fraudulent activity. How are you going to solve this ? May be anomaly detection problem or a classification problem !!
What will you prefer a decision tree or a random forest ?
How is using a logistic regression different from using a random forest ?
Will you use decision tree or random forest for a classification problem ? What is advantage of using random forest ?

# Company 7 (25-30 minutes) – Global business process management company

Which model would you use in case of unbalanced dataset: Random Forest or Boosting ? Why ?
What are the boosting techniques you know ?
Which model would you like to choose if you have many classes in a supervised learning problem ? Say 40-50 classes !!
How do you perform ensemble technique?
How does SVM work ?
What is Kernel ? Explain a few.
How do you perform non-linear regression ?
What are Lasso and Ridge regression ?

# Company 8 (60 minutes) – 4 years old product & services company

What are MFCCs ?
What is Gaussian Mixture model ? How does it perform clustering ?
How is Expectation Maximization performed ? Explain both the steps ?
How is likelihood calculated in GMM ?
How did you perform MAP adaptation for GMM-UBM technique of speaker identification ?
Tell me about I-vector technique you implemented ?
Okay !! What is factor analysis in this context ?
What was the difference between JFA and I-vector ? Why choose I-vectors over JFA
Have you implemented PLDA I-vector technique ?
Have you read Deep Speaker paper from Baidu ?
How do you select between 2 models (Model Selection techniques)?
Okay great BIC & AIC !! How does it work mathematically ?
Explain the intuition behind BIC or AIC ?
How do you handle missing data or NANs in your MFCC feature vector matrix ?
How did you perform language identification ? What were the feature ?
How did you model classifiers like speech vs music and speech vs non-speech ?
How can deep neural network be applied in these speech analytics applications ?


Your CV is very important. I will thrust on this again. Start building your profile impressive with projects, Kaggle competitions, MOOC certifications, research papers (if possible). I got call from amazon without any reference. Your CV can impress HR’s and interviewer right away. It is certainly hard to get picked for interview in good companies without reference.
Your confidence and drive that you carry will do half of the job. It’s very important to take interview with confidence and show that you have that drive. Personally I felt it matters in interviews (specially in startups and services based ones).
While in interview do not rush into answers. Take your time in thinking about questions and then answer suitably. Ask questions if you do not understand the question properly. You may need to calm down in interviews (that’s an issue with me sometimes)
Express yourself while explaining concepts properly. Give examples from projects you may have implemented. You must be thorough with the skills and projects written in CV.
Mostly, Employer looks for experienced candidates in this field. If you are a beginner then try to build your profile by implementing applications on your own. Your Github account can say a lot. Do participate in lot of Kaggle competitions. Take online MOOC certifications.
Lastly try to be modest with interviewer and nod to their opinions sometimes otherwise it may land you in rejections. You may find people arrogant sometimes. For an example, R or Python enthusiasts are sentimental about respective languages. It is better not to fall in such debate. Personally I feel these are tools to accomplish your logic and concepts.

Best of Luck.

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Download Nigerian Air Force (NAF) Past Questions and Answers

Download Nigerian Air Force (NAF) Past Questions and Answers.

Download Nigerian Air Force (NAF) Past Questions… Nigerian Air Force, NAF Past Questions, Download NAF Complete Past Questions Online, How to Apply for Nigeria Air force Recruitment Past Questions Online. See more details below;

Download Nigerian Air Force (NAF) Past Questions

The Nigerian Air force Past Questions is a compilation of questions from previous examinations. It is one useful tool that can help candidates achieve their goal.

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Law Optional Strategy: UPSC CSE (Mains)

Hello all.

This post will be about preparing for the law optional for the UPSC Civil Service Examination. I received quite some help for my law optional preparation from my seniors in college, who are now in the IAS. I hope to help you readers just like they helped me. 🙂

But before I begin, here are a few basic points:

The syllabus for law optional is enormous. It will require a good amount of time for its completion, so keep that in mind. I started studying for the optional only after prelims exam in June 2017, but I believe that was possible only because I had comprehensive notes with me from my college time for bulky subjects such as IPC and Constitutional Law. I was also following legal news and developments while in college, and all of that definitely helped.
Your preparation for the Law-I paper will certainly help you with General Studies- II paper. However, you must keep in mind that you will have to mentally dissociate the two. Your GS-II will suffer if you write your answers like a lawyer. You have to keep your GS-II paper as general as possible. Do not let your legal knowledge of the GS-II issues overexcite you.
Understanding the concepts is very important. Please spend more time in understanding crucial topics than the time you spend in memorising case law names. Your knowledge of suitable case law names will not help if you are unable to demonstrate a deep understanding of the question asked.
Try joining a test series if possible. Every other candidate would have joined a test series for their optional subject, and you should not put yourself at a disadvantage by not having any prior answer writing practice. I had joined ambition law institute’s test series. I believe practising helped- as I could time myself better, and it also made me more decisive about choosing which questions to attempt in the exam. However, please do not rely exclusively on any test series or coaching center. You must supplement it with your own strategy and hard work.
I will give due credit to my education at NLU, Delhi for my law optional marks. However, I know of quite a few people who have aced at law optional without having a law degree! So if the subject interests you, don’t let your lack of a legal degree become a hindrance.

The Wire -it has a very good opinion-based coverage of legal issues. An article I had read from this website helped me in answering the question in 2017’s Law I paper on the Rajbala v. State case. However, be sure to have your own opinion on the articles you read about as well.
Livelaw- any recent legal developments that you ought to know about are covered here.
I had also subscribed to google alerts for the keyword ‘law’. I used to glance through the emails to see if there is any recent legal development that I have missed.

20 marker- about 3 pages, 250 words
15 marker- about 2.5 pages, 200 words
10 marker- about 1.5 pages, 150 words

Constitutional and Admin Law

Topic Nos. 1 to 3 (Distinctive features, Fundamental Rights and their relationship with DPSPs etc).- MP Jain
Topic Nos. 4 to 11- Constitutional Law Dukki (supplemented with MP Jain, DD Basu and Laxmikant wherever I needed more details)
Topic Nos. 12 to 15- Admin Law Dukki
Topic No. 16 (ombudsman)- Made self notes from the internet
In addition, I was following Gautam Bhatia’s blog

International Law

Topic No. 1- Shaw
Topic No. 2 Relationship between international law and municipal law- International Law Dukki, SK Kapoor
Topic No. 3 State Recognition etc.- SK Kapoor
Topic No. 4 Law of the Seas- Shaw
Topic Nos. 5-7- SK Kapoor
Topic No. 8 United Nations- the internet
Topic Nos. 9,10- SK Kapoor

Law of Crimes

For IPC, I referred to my college notes which were a mix of the bare act and some very important case laws for different offences. In addition to that, to fully cover the syllabus I referred to the bare Act, and the Criminal Law Dukki. Make sure to focus on the illustrations for important sections such as murder, theft etc.
Prevention of Corruption Act- the internet
Protection of Civil Rights Act- the internet, and also make sure to cover the Atrocities Act and the recent amendments made to it
Plea Bargaining- Read the sections from CrPC, and referred to an article on it online

Law of Torts

Law of Torts by Bangia will help you to sufficiently cover the syllabus. However, revising it will be a problem so make extremely short notes for quick revision.
Consumer Protection Act- I went through the sections of the bare Act. Additionally, do cover the recent developments regarding the new consumer protection Act.

Law of Contracts and Mercantile Law

Contract Law i.e. Topic 1-7 can be covered well from the Contract Law Dukki. However, do make it a point to read the important sections from the bare Act. You may also refer to Avtar Singh to read more on topics that the Dukki doesn’t properly cover.
Contract of Agency- Booklet on the topic, available in Rajinder Nagar market
Sale of Goods Act- Same as above
Formation and Dissolution of Partnership- Bare Act and Dukki
Negotiable Instruments Act- Booklet available in Rajinder Nagar market, along with Dashrath Roopsingh case and associated developments
Arbitration and Conciliation- I referred to my college notes, and the new Act. Primers on the difference between the 1996 and 2015 Acts are helpful too.
Standard form contracts- Contract law dukki
Contemporary Legal Developments- The wire, livelaw, spicyIP, any new reports of the Law Commission. This is one topic for which you really cannot know what to study. Keep an eye on any recent legal developments you read about in the newspapers, or anything legal which is being talked about by op-ed writers.
PIL- MP Jain, articles from the internet
IPR- primer by Nishith Desai Associates on the IPR regime in India. It is sufficiently detailed and covers the topic well.
IT Law- referred briefly to the IT Act, 2000. Covered important sections such as the ones on penalties and offences.
Competition Law- read the PDF files available on the website of the Competition Commission of India on abuse of dominant position, anti-competitive practices
ADR- for this, I read section 89 of the Civil Procedure Code and related jurisprudence (it is a short topic).
Major statutes concerning environment law- There is a document available on a government of India website, which I unfortunately am unable to find again. I’m trying to look for it.
Right to Information Act- studied this from Admin Law Dukki
Trial by Media- 200th report of the Law Commission of India

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Emergence of Benford’s Law in Classical Music

Azar Khosravani, Constantin Rasinariu

We analyzed a large selection of classical musical pieces composed by Bach, Beethoven, Mozart, Schubert and Tchaikovsky, and found a surprising connection with mathematics. For each composer, we extracted the time intervals each note was played in each piece and found that the corresponding data sets are Benford distributed. Remarkably, the logarithmic distribution is not only present for the leading digits, but for all digits.

Maya Numerals for Beginners

Shadow of the Tomb Raider is coming our way later this year and while we don’t know much about the upcoming game at the time of writing, it’s no secret that the game will be touching on Maya civilisation and mythology.

The first piece of official artwork features a Maya temple towering over dense jungle foliage and the official site used a series of Maya-themed puzzles throughout March and April to promote Lara’s next adventure. In a couple of these puzzles, numerical values were assigned to each of the glyphs and fans were then instructed to line up the glyphs correctly in order to unlock the signs for a significant date.

The glyphs used in these puzzles may not have been accurate representations of the glyph forms of Maya numerals but let’s take a quick look at the numerals used in the example below. The symbol in the centre of the three rings of glyphs is the Maya equivalent of the number “8”, which is represented by three dots and a bar. The dots each have a numerical value of 1, while the bar has a numerical value of 5 (i.e. 1+1+1+5 = 8).

Maya Numbers and the Maya Calendar: A Non-Technical Introduction to Maya Glyphs (FAMSI)

Maya Numberals and Mathematics (Maya Archaeologist)

Maya Math Game (Smithsonian National Museum of the American Indian)

Official ‘Tomb Raider’ Site Launches Maya-Themed Puzzle
Lara Croft Will Cast Her ‘Shadow’ On Gaming This September
5 Fantastic Free Resources for Learning Maya Glyphs

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My Maths Strategy

Disclaimer : All the things mentioned below is based on my experience. It is not the only strategy. I humbly believe in principle of Anekantavada.

Dear all,

I have written 4 mains with maths and secured variety of marks in them. I got 238(122+116) in 2014, 195 (122+73) in 2015, 288 (145+143) in 2016 and 310 (147+163) in 2017. I have interacted with numerous aspirants who took mathematics in these 4 years. I would like share various aspects that I have observed in these years. I did no coaching for maths. Neither did I join any test series.

Linear Alegbra : this is the one of the easiest portion in paper 1. The key lies in finding the correct answer in minimum time. Linear Algebra book and Matrices Book by Krishna series is sufficient. One can read schaum series as well. Please do last 15 years UPSC question from this chapter for improvisation.
Calculus : Questions from this chapter are also straightforward. Books needed are : Shanti Narayan – Course on Mathematical Analysis (S. Chand), mathematical analysis by S.C. Malik and Savita Arora. For covering asymptotes and curve tracing, differential calculus by shanti Narayan needs to be studied. For practicing definite integral question (which is coming as 10 marker), Series Integral Calculus by A.R. Vashishtha (Krishna Series) can be studied.
Analytical Geometry : Analytical geometry by shanti Narayan (S Chand) or Series Analytical Geometry by A R Vasishtha(Krishna Series). Krishna series book contains more solved examples so I personally prefer it. Questions pertaining to conicoid are not easy, so for some selective good questions, how to start the question needs to be remembered.
Ordinary Differential Equation: M.D. Raisinghania (S. Chand). For Laplace, selective chapter from advance differential equation by M D raisinghania needs to be studied. Focus should be on solving question without doing ZERO calculation mistakes.
Vector Analysis: Vector Analysis by Krishna series. Solve at least last 15 year question from UPSC paper.
Statics : Krishna Series
Dynamics : Krishna Series

Solve relevant chapters from Krishna series for statics and dynamics. Mostly question is coming from these books only. If a new question comes in exam which is not easy, it becomes difficult to solve in that pressure situation.
For friction: Read Golden Statics By N.P Bali. It is there on google books.

Modern Alegbra : Group theory by R Kumar and Ring theory by R Kumar( Vardhaman Publications). Question in past 2 years have become very tricky. They are asking proof of theorems. So approach should be to cover basics first and get comfortable level in it and then go for learning higher stuff. This portion creates a lot of challenge for majority of students as they read modern alebra for first time in their student life. Therefore ample time and lot of revisions are needed.
Real Analysis : Raisinghania – Elements of Real Analysis (S. Chand) and Mathematical Analysis by S.C. Malik and Savita Arora. Since past 2 years, there has been some very unconventional questions from this portion. Some question in my opinion are meant to be bouncer, so nothing much can be done on that front. Therefore the best approach is to ensure that one should be able to solve easy and moderate level questions. Please do past 15 year papers from this portion.
Complex Analysis : complex analysis by Krishna series. This portion is quite straight forward.
Linear Programming : Linear Programming by R.K Gupta. One of easiest topic. But ensure by adequate practice and diligence that there is no mistake in finding answer.
Partial Differential Equations– M.D. Raisinghania + internet searching for practicing boundary value problem. I will also upload some material on this.
Numerical analysis : Jain & Iyengar book or any book which is there in state engineering college mathematics course. I will upload a pdf also soon.
Fluid Mechanics : M D Raisinghania. This portion is very challenging. Best bet is to memorise and practice examples form this book. If some tough question comes in exam which is not from this book, it becomes quite unapproachable.
Mechanics: Rigid Dynamics (Volume I & Volume II). It has similar case as that of Fluid mechanics.

Try to solve past 20 years question papers. If time doesn’t permits, atleast solve papers for the portion that I have mentioned.
Revision is the must thing. Even if you cover some tough topic and don’t revise it enough. Touch will be lost, and all the hard done earlier will go in vain. So revise, revise and revise. My typical revision schedule after prelims was like that

Fluid mechanics, mechanics : 4 times
Statics, dynamics, modern algebra : 3 times
Rest topics : 2 times

Focus and practice a lot on finding the correct answer. Silly mistakes can cost you dearly. As it did in my case.
Revise all formulas once in every 2 weeks
Paper 2 in 2016 and 2017 came very tough. I think this will become a norm. Please practice more for this paper.

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School Transformation Without School Improvement in Atlanta’s all Charter District

Since the 2015 all charter district reforms in Atlanta, the so called “education gap” has grown significantly. This is reflected in both state and federal testing data.

I recently wrote about Superintendent Castarphen and her history of bullying staff and working to privatize public education. That post was motivated by an email from Ed Johnson providing his initial review of the just released TUDA (Trial Urban District Assessment) data from the 2017 testing cycle.

Mr. Johnson is a longtime advocate for public education. He is a native Georgian, a former NSA analyst and an expert in Deming inspired quality management. His writings have been published in many places including the Atlanta Journal-Constitution and he has been a candidate for the Atlanta Public Schools (APS) board. With his permission, I am posting his more deepened analysis of recent testing data from Atlanta.

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What I’ve Been Reading, Mid-March 2018

So here’s some of the stuff I’ve noticed while being on the Internet and sometimes noticing interesting mathematical stuff.

Here from the end of January is a bit of oddball news. A story problem for 11-year-olds in one district of China set up a problem that couldn’t be solved. Not exactly, anyway. The question — “if a ship had 26 sheep and 10 goats onboard, how old is the ship’s captain?” — squares nicely with that Gil comic strip I discussed the other day. After seeing 26 (something) and 10 (something else) it’s easy to think of what answers might be wanted: 36 (total animals) or 16 (how many more sheep there are than goats) or maybe 104 (how many hooves there are, if they all have the standard four hooves). That the question doesn’t ask anything that the given numbers matter for barely registers unless you read the question again. I like the principle of reminding people not to calculate until you know what you want to do and why that. And it’s possible to give partial answers: the BBC News report linked above includes a mention from one commenter that allowed a reasonable lower bound to be set on the ship’s captain’s age.

In something for my mathematics majors, here’s A Regiment of Monstrous Functions as assembled by Rob J Low. This is about functions with a domain and a range that are both real numbers. There’s many kinds of these functions. They match nicely to the kinds of curves you can draw on a sheet of paper. So take a sheet of paper and draw a curve. You’ve probably drawn a continuous curve, one that can be drawn without lifting your pencil off the paper. Good chance you drew a differentiable one, one without corners. But most functions aren’t continuous. And aren’t differentiable. Of those few exceptions that are, many of them are continuous or differentiable only in weird cases. Low reviews some of the many kinds of functions out there. Functions discontinuous at a point. Functions continuous only on one point, and why that’s not a crazy thing to say. Functions continuous on irrational numbers but discontinuous on rational numbers. This is where mathematics majors taking real analysis feel overwhelmed. And then there’s stranger stuff out there.

A (work in progress) translation of Joyal’s original paper on species

tl;dr: I’m working on an English translation, with additional commentary, of Joyal’s 1981 paper introducing the concept of combinatorial species. Collaboration and feedback welcome!

Back when I was writing my PhD thesis on combinatorial species, I was aware that André Joyal’s original papers introducing combinatorial species are written in French, which I don’t read. I figured this was no big deal, since there is plenty of secondary literature on species in English (most notably Bergeron et al., which, though originally written in French, has been translated into English by Margaret Readdy). But at some point I asked a question on MathOverflow to which I hadn’t been able to find an answer, and was told that the answer was already in one of Joyal’s original papers!

So I set out to try to read Joyal’s original papers in French (there are two in particular: Une théorie combinatoire des séries formelles, and Foncteurs analytiques et espèces de structures), and found out that it was actually possible since (a) they are mathematics papers, not high literature; (b) I already understand a lot of the mathematics; and (c) these days, there are many easily accessible digital tools to help with the task of translation.

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Crash Course in Maths for JEE Advanced 2018.

Good day everyone!

Welcome to the best crash course in Mathematics for JEE Advanced 2018.

So, now let’s buckle up for the toughest examination in India. And what makes it the toughest? Good question set in Mathematics.

96/124 marks in Mathematics in JEE Advanced 2016.
115/120 marks in Mathematics in JEE Mains 2016.
A verified educator on India’s largest educational platform Unacademy.
Secured International Rank 34 in International English Olympiad.
Ranked 52 in National Interactive Maths Olympiad (NIMO).
11 gold medals in various olympiads at state (Rajasthan) and national level.
Qualified NSEA(National Standard Examination in Astronomy)-2015.

LIVE SESSIONS: The course consists of 25 sessions of 1 hour duration each(It can be extended on some days). Session recording will be provided for all the sessions.
‘25 Live Sessions + 5 Live Doubt Sessions + 10 Full length JEE Advanced practice Mathematics papers’ will be given as pdfs’ and the doubts shall be discussed Live.
DISCUSSION FORUMS: The enrolled students will have an access to a closed WhatsApp group and FB group promoting interaction with the educator and other students.
PERSONALISED LEARNING: All enrolled students will have access to doubt clearing sessions, learning materials, test papers and discussion with peers.
STUDY MATERIAL: The enrolled students will receive Practice Problems sheet after each live class. They can discuss the doubts with me personally on WhatsApp group or the closed FB group.

5 Live Doubt Sessions will be held along with the Live Classes so that the concepts become crystal clear.
10 full length Mathematics question papers will be provided for the best preparation for JEE Advanced 2018.
25 Practice sheets (One after each live class) will be provided for the revision of the topics taught.
Moreover, the video recording for the live sessions will also be available to the students so that they can watch it later.
The class timings will be the same as discussed above for the scheduled dates. More or less, we can extend the class too according to the requirement of the chapter.

Now the question arises, what happens if you miss a class?
Though I actively encourage you to try and attend all the live sessions part of the course, if in case you’re unable to attend a session due to any reason, the recordings of the live sessions will be made available to the batch.

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Pythagorean Crimes

Pythagorean Crimes, by Tefcros Michaelides

Synopsis: Athens, 1929. Stefanos Kantartzis is found murdered, and Michael Igerinos, his best friend of 30 years, is being questioned by the police as the last person to see him alive.

While looking at his dead friend’s body, Michael is immediately taken back to the late summer of 1900 when he and Stefanos first met in the crammed Sorbonne University lecture hall. The story of their friendship begins during the Second International Congress of Mathematics—an event that was to become a landmark for 20th century mathematical research.

Ruth Davidson’s chaotic attack on school standards is ignorant


The Scotsman today allows Ruth to emerge from the shadows with an ill-informed anecdotal rant attacking the Curriculum for Excellence in Scottish Schools. It’s an almost entirely evidence-free critique other than a single reference to unreliable international comparisons:

‘Time to end the chaos in the classroom. And, no-one has the faintest idea whether the curriculum has actually boosted standards. All we do know, 13 years on, is that Scotland has slipped down the international Organisation for Economic Co-operation and Development’s league table for attainment and that those nationwide Scottish surveys which the SNP has not yet abolished show a fall in literacy and numeracy standards among children in both primary and early secondary school. ‘

Wales: 18.6/1
Northern Ireland: 17.6/1
England: 17.4/1
Scotland: 13.7/1

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