FREE Math Book. "Counting Rocks! An Intro to Combinatorics" by Adams et al. Combinatorics is the mathematics of counting, arranging, and combining. It's the invisible engine powering our digital world, driving everything from cryptographic security to DNA sequencing. Studying it is FASCINATING because it allows us to solve massive, seemingly impossible puzzle problems using elegant, logical patterns. Machine learning models and neural networks rely on advanced combinatorial graph theory to map relationships and process complex data. “Combinatorics is the mathematical study of discrete mathematical objects and their combinations and arrangements. Other kinds of mathematics (like calculus and analysis) use continuous mathematical objects, which involve infinitesimally small increments. By contrast, discrete mathematics is the study of objects that come in larger chunks, such as whole numbers, polygons, and networks. If you have ever asked 'I wonder how many different ways I could... ?', then you have thought about combinatorics. The history of combinatorics began in ancient times, in places such as Egypt, India, China, and Iran. The computer revolution greatly amplified the importance of combinatorics and graph theory. There are also applications of this class and book to other fields, like linguistics, physics, chemistry, and biology. In general, from this class, you will gain experience solving problems about combinatorial structures and algorithms; we hope you will continue to use the experience and ideas you gain from this class for the benefit of many other people.” Contents What is Combinatorics? Counting Principles Counting Combinations Pascal’s Triangle and the Binomial Theorem Proof Techniques in Combinatorics Recurrence Relations Generating Functions Graph Theory Basics Trees Graph Optimization Planar Graphs Graph Coloring Link: mathematicalgemstones.com/ma…

◾️পশ্চিমবঙ্গ থেকে দুটো ঘটনা ভ্যানিস হয়ে গেল। ১| শুভেন্দু অধিকারীর PA এর রহস্য জনক মার্ডারের গল্প ২| দেশে ১৫.৫ লক্ষ কোটি টাকার যে দুর্নীতি হল । ◾️এই দুটো ঘটনার কোনও খবর নেই।

The SIR in West Bengal differed from the Bihar exercise in its procedural design, in the scale of deletions and in a new category of “logical discrepancies,” that swallowed 2.7 million Bengal voters. This category was invented specifically for Bengal, leading to patently absurd situations. The numbers defy easy comprehension. The ECI removed approximately 9 million voters from the state’s electoral roll ahead of the election. Of 3.4 million appeals filed, just 1,607 names were restored—fewer than 0.05 percent. Contrast this with Kerala, where over ninety-eight percent of flagged voters were reinstated through an efficient adjudication process. In Tamil Nadu, nearly 5 million voters were removed from just eight districts, accounting for more than half of all statewide deletions. Over a third of registered voters in the capital, Chennai, were erased from the rolls. The figures have no plausible administrative explanation. @GillesVerniers writes: caravanmagazine.in/politics/…

4000 EVMS destroyed!! Alipore Sadar strong room, in which 4000 EVMS were kept which were used in recent Bengal State Assembly elections, caught fire. Flames were first seen on 2nd & 3rd floors. But somehow Fire reached 7th & 8th floors without reaching 4th, 5th & 6th 😂😂

Good morning! Just got to know this! 1/2 A whole government Ministry is unleashed on me - because I speak against unscientific practices and primitive traditional healthcare that can harm, I communicate scientific information for public and patients alike. This was an official memo released during the Ministry of Ayush meeting on 12-6-2026 fully dedicated towards shutting down my social media presence. Imagine - the people in this meeting were eating biscuits and drinking tea, paid for by the citizens of the country - to decide how to gag and shutdown a citizen doctor who educates people on medical science via social media. Yesterday, my Instagram account was briefly hacked, but I got back control and removed unauthorized access within an hour. The Article 51A(h) of the Indian Constitution outlines the fundamental duty of every citizen to develop a "scientific temper, humanism, and the spirit of inquiry and reform". Added during the 42nd Amendment in 1976, this non-justiciable directive promotes logical reasoning, critical thinking, and rationality. The Ayush system is not scientific, it kills scientific temper, it does not promote the spirit of inquiry, it lacks logical reasoning, has the deadest version of critical thinking and none of its products and practices are rational. The only thing that needs to be shut down, is an unscientific body like Ayush that goes against the Indian Constitution and wastes public tax money... and not me. Also, please look closely at the person at the end, who is copied to, by the Ministry. His name is Vaidya K P Manikandan and he is the owner and founder of CNS Ayurveda Hospital, where children are treated for chronic conditions such as severe mental health disorders, autism and epilepsy (please see an official release from the hospital in the next post). One such victim of his was saved by my team (we reported it: pubmed.ncbi.nlm.nih.gov/3629…) and he put a criminal defamation case against me and the authors (for publishing a scientific peer reviewed paper!) which was later "stayed" by the High Court of Kerala. This has nothing to do with service to patients, but everything to do with protecting the business of alternative medicine (especially Ayurveda). These low life complaintants should be ashamed.

Who attacked the vessel? Pirates?

All three Indian sailors, who were reported missing after the US attack on a Palau-flagged ship off the Oman coast, have been confirmed dead, news agency Reuters reported. The US military said it attacked the oil tanker, MT Settebello, after  it tried to “violate” the blockade put up by the US outside the Strait of Hormuz, off the Oman coast.

"Who expanded India’s democratic imagination? Who strengthened its institutions? Who deepened its constitutional culture? ... [Also] who presided over the erosion of institutional autonomy, the weakening of democratic norms, and the decline of social harmony?" ~ @manojkjhadu

"Most people just want to live their lives, and they get caught up in shocking events not of their own making." ~ Joe Sacco on The Once and Future Riot newyorker.com/books/page-tur… @PenguinIndia

जनहित में जारी Ahmedabad Mirror, Pune Times Mirror, Ei Samay (Bengali), Navgujarat Samay (Gujarat) are not controlled, published or operated by The Times of India group any longer.

🇺🇸Trump has stated 55 times that he defeated Iran. 🇺🇸Trump has stated 35 times that Iran is destroyed. 🇺🇸Trump has stated 38 times that a deal is imminent. 🇺🇸Trump has stated 25 times that the Strait of Hormuz is open. Elect a clown, expect a circus.

> My name is Khan, > I am from India. > I am a Muslim. > I help 10 lakh poor children study online & ofline for just ₹200 and get them big government jobs. > I opened the world's lowest-cost hospital for the poor, and that is my crime, "Today, all the national media of India is after me. The people who should have spoken against the Indian government and raised the voice of the poor common people are instead after me. India's national media's biggest enemy right now is a teacher. India's famous teacher Khan Sir (Faizal Khan) is. The one who has produced the highest number of State Police and SI Police officers. Khan Sir teaches for only ₹200 and helps children from poor families get the highest number of government jobs. He teaches those poor families whose parents cannot even afford to buy clothes for their children and cannot properly feed them. Khan Sir opened a hospital for the poor by teaching in coaching institutes. Where poor people get a blood test for ₹7. An X-ray for ₹35. An ECG for ₹100. An MRI for ₹300. A CT scan examination for ₹900. As a teacher, Khan Sir is providing so many facilities to the poor from his own money, which the government should have done. Khan Sir is going to open a very big college for the poor, where children from poor families will study at the lowest cost in the world and receive excellent education. There, library, food, everything will be available to children for ₹10. Today, Khan Sir is being trolled the most in India. The Indian national media, which does not show the courage to ask even a single question to the Indian government Mr Modi, No matter how many problems there are in the country - corruption, pollution, exam paper leaks - they do not ask any questions, but today they are after Khan Sir. Is the government's crime so little that he is charging only ₹200 to provide education to the poor? He is providing expensive hospital tests to the poor at the lowest prices in the world. Is there any teacher in the world who teaches children for ₹200 and helps them get government jobs? Khan Sir should open his branches globally - America, Canada, UK, London - and teach children at the lowest fees in the world. At present, only his thousands of students are there to support Khan Sir, who are ready to give their lives for him. All the other people are busy trying to prove him anti-government. Everyone wants a teacher like Khan Sir to go to jail. Do you know Khan Sir...?

A booth in Bengal's New Town with 88% Muslim voters recorded 97% votes for BJP, handing BJP the seat. CPI(M) got 1 vote, TMC 5. 'This is an impossible result, where did our votes go?' ask locals. @shinjineemjmdr @Onkeyta_ & @Holytripper heard them. altnews.in/where-did-our-vot…

Science fiction authors in the order you want them to be right about AI: Iain Banks Becky Chambers Martha Wells Douglas Adams Charles Stross (Singularity Sky) Peter Watts Charles Stross (Laundry) Harlan Ellison

Extremely grateful that I get to do what I love doing and it reaches millions every month in a language that they best understand. Living my best life, fr! 🫶🏻

the reason barkatullah is being erased is that modi/rss want people to forget that there were people who did things other than apologise to the british raj. indianexpress.com/article/ex…

I freaking LOVE Terry Pratchett, sir. The reference alone is worth a follow. Thank you.

💔 "Nobody can take your freedom. I have lived in a dictatorship. There was a ban on everything! Was I less free in my mind? No, I wasn’t. Did I become a stupid person? No, I didn’t. Because no matter how much they looked at me, they could not get into my mind." ~ Marjane Satrapi

The Iranian navy, which has been destroyed eight times, has apparently closed the Strait of Hormuz again, because the United States, for the seventh time, won the war that wasn’t a war, so now the United States has to open the Strait of Hormuz that was already open before the not-war began. The not-war began because Iran had uranium that was totally, completely, beautifully obliterated, so they can’t build the nuclear bomb they weren’t building, which is why the United States had to start the not-war it definitely didn’t start. Now the United States, which has nuclear weapons, is threatening to use nuclear weapons to stop Iran from getting nuclear weapons, because nuclear weapons are far too dangerous for countries with nuclear weapons to allow other countries to have. If the United States saw the United States doing what the United States does in other countries, the United States would invade the United States to liberate the United States from the tyranny of the United States.

In West Bengal, those who have been excluded from the voter rolls—often for highly specious reasons, with an evident partisan bias—are especially vulnerable, since the expulsion of supposedly undocumented immigrants has been a salient part of the BJP agenda in the state for decades. After examining the SABAR Institute’s data, @marcopolar found some troubling patterns that raise questions about the ECI’s impartiality during the SIR process in West Bengal. Read the entire report in our June 2026 issue: caravanmagazine.in/politics/…