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Viewing: Blog Posts Tagged with: Mathematics, Most Recent at Top [Help]
Results 1 - 25 of 72
1. Does the ‘Chinese room’ argument preclude a robot uprising?

There has been much recent talk about a possible robot apocalypse. One person who is highly skeptical about this possibility is philosopher John Searle. In a 2014 essay, he argues that "the prospect of superintelligent computers rising up and killing us, all by themselves, is not a real danger".

The post Does the ‘Chinese room’ argument preclude a robot uprising? appeared first on OUPblog.

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2. Conversations in computing: Q&A with Editor-in-Chief, Professor Steve Furber

Oxford University Press is excited to be welcoming Professor Steve Furber as the new Editor-in-Chief of The Computer Journal. In an interview between Justin Richards of BCS, The Chartered Institute of IT and Steve, we get to know more about the SpiNNaker project, ethical issues around Artificial Intelligence (AI), and the future of the IT industry.

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3. Can a robot be conscious?

Can a robot be conscious? I will try to discuss this without getting bogged down in the rather thorny issue of what consciousness –– really is. Instead, let me first address whether robot consciousness is an important topic to think about. At first sight, it may seem unimportant. Robots will affect us only through their outward behavior, which may be more or less along the lines of what we tend to think of as coming along with consciousness, but given this behavior, its consequences to us are not affected by whether or not it really is accompanied by consciousness.

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4. Can one hear the corners of a drum?

Why is the head of a drum usually shaped like a circle? How would it sound if it were shaped like a square instead? Or a triangle? If you closed your eyes and listened, could you tell the difference? The mathematics used to prove that “one can hear the corners of a drum” are founded on […]

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5. Very Short Resolutions: filling the gaps in our knowledge in 2016

Why make New Year's Resolutions you don't want to keep? This year the Very Short Introductions team have decided to fill the gaps in their knowledge by picking a VSI to read in 2016. Which VSIs will you be reading in 2016? Let us know in the comment section below or via the Very Short Introductions Facebook page.

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6. How do people read mathematics?

At first glance this might seem like a non-question. How do people read anything? All suitably educated people read at least somewhat fluently in their first language – why would reading mathematics be different? Indeed, why would mathematics involve reading at all? For many people, mathematics is something you do, not something you read.

But it turns out that there are interesting questions here. There are, for instance, thousands of mathematics textbooks–many students own one and use it regularly. They might not use it in the way intended by the author: research indicates that some students–perhaps most–typically use their textbooks only as a source of problems, and essentially ignore the expository sections. That is a shame for textbook authors, whose months spent crafting those sections do not influence learning in the ways they intend. It is also a shame for students, especially for those who go on to more advanced, demanding study of upper-level university mathematics. In proof-based courses it is difficult to avoid learning by reading. Even successful students are unlikely to understand everything in lectures – the material is too challenging and the pace is too fast – and reading to learn is expected.

Because students are not typically experienced or trained in mathematical reading, this returns us to the opening questions. Does this lack of training matter? Undergraduate students can read, so can they not simply apply this skill to mathematical material? But it turns out that this is not as simple as it sounds, because mathematical reading is not like ordinary reading. Mathematicians have long known this (“you should read with a pencil in hand”), but the skills needed have recently been empirically documented in research studies conducted in the Mathematics Education Centre at Loughborough University. Matthew Inglis and I began with an expert/novice study contrasting the reading behaviours of professional mathematicians with those of undergraduate students. By using eye-movement analyses we found that, when reading purported mathematical proofs, undergraduates’ attention is drawn to the mathematical symbols. To the uninitiated that might sound fine, but it is not consistent with expert behaviour: the professional mathematicians attended proportionately more to the words, reflecting their knowledge that these capture much of the logical reasoning in any written mathematical argument.

Another difference appeared in patterns of behaviour, which can best be seen by watching the behaviour of one mathematician when reading a purported proof to decide upon its validity (see below). Ordinary reading, as you might expect, is fairly linear. But mathematical reading is not. When studying the purported proof, the mathematician makes a great many back-and-forth eye movements, and this is characteristic of professional reading: the mathematicians in our study did this significantly more than the undergraduate students, particularly when justifications for deductions were left implicit.

This work is captured in detail in our article Expert and Novice Approaches to Reading Mathematical Proofs. Since completing it, Matthew and I have worked with PhD and project students Mark Hodds, Somali Roy and Tom Kilbey to further investigate undergraduate mathematical reading. We have discovered that research-based Self-Explanation Training can render students’ reading more like that of mathematicians and can consequently improve their proof comprehension (see our paper Self-Explanation Training Improves Proof Comprehension); that multimedia resources designed to support effective reading can help too much, leading to poorer retention of the resulting knowledge; and that there is minimal link between reading time and consequent learning. Readers interested in this work might like to begin by reading our AMS Notices article, which summarises much of this work.

In the meantime, my own teaching has changed – I am now much more aware of the need to help students learn to read mathematics and to provide them with time to practice. And this research has influenced my own writing for students: there is no option to skip the expository text, because expository text is all there is. But this text is as much about the thinking as it is about the mathematics. It is necessary for mathematics textbooks to contain accessible text, explicit guidance on engaging with abstract mathematical information, and encouragement to recognise that mathematical reading is challenging but eminently possible for those who are willing to learn.

Feature Image: Open book by Image Catalog. CC0 1.0 via Flickr.

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7. Is an engineering mind-set linked to violent terrorism?

In a British Council report Martin Rose argues that the way STEM subjects are taught reinforces the development of a mind-set receptive to violent extremism. Well taught social sciences, on the other hand, are a potentially powerful intellectual defence against it. Whilst his primary focus was MENA (Middle East and North Africa) he draws implications for education in the West.

The post Is an engineering mind-set linked to violent terrorism? appeared first on OUPblog.

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8. Addressing anxiety in the teaching room: techniques to enhance mathematics and statistics education

In June 2015, I co-chaired the organising committee of the first international mathematics education conference of the Institute of Mathematics and its Applications (IMA) titled ‘Barriers and Enablers to Learning Maths’ with the University of Glasgow, who also hosted it. The two and a half day conference explored approaches to teaching and learning mathematics and was structured around ten parallel sessions that delegates could choose from, including ‘Addressing mathematics & statistics anxiety’ and ‘Enhancing engagement with mathematics & statistics.’

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9. Let us not run blindfolded into the minefield of future technologies

There is a widely held conception that progress in science and technology is our salvation, and the more of it, the better. This is the default assumption not only among the general public, but also in the research community including university administration and research funding agencies, all the way up to government ministries. I believe the assumption to be wrong, and very dangerous.

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10. The Erdős number

The idea of six degrees of separation is now quite well known and posits the appealing idea that any two humans on earth are connected by a chain of at most six common acquaintances. In the movie world this idea has become known as the “Bacon number”; for example Elvis Presley has a Bacon number […]

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11. Making sense of mathematics

Mathematics is used in increasingly sophisticated ways in modern society, explicitly by experts who develop applications and implicitly by the general public who use technological devices. As each of us is taught a broad curriculum in school and then focuses on particular specialisms in our adult life, it is useful to ask the question ‘what does it mean to make sense of mathematics?’.

The post Making sense of mathematics appeared first on OUPblog.

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12. The Fragility of Grand Discoveries

When I was in graduate school at Berkeley I was offered a prestigious fellowship to study for a year in Germany, but I decided it would be a disruption, so I wrote a short note declining the offer. As, letter in hand, I stepped to the mailbox, I bumped into a woman from the scholarship [...]

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13. The role of logic in philosophy: A Q&A with Elijah Millgram

Elijah Millgram, author of The Great Endarkenment, Svantje Guinebert, of the University of Bremen, to answer his questions and discuss the role of logic in philosophy. On other occasions, you’ve said that logic, at least the logic that most philosophers are taught, is stale science, and that it’s getting in the way of philosophers learning about newer developments. But surely logic is important for philosophers. Would you like to speak to the role of logic in philosophy?

The post The role of logic in philosophy: A Q&A with Elijah Millgram appeared first on OUPblog.

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14. Will we ever need maths after school?

What is the purpose of mathematics? Or, as many a pupil would ask the teacher on a daily basis: “When are we going to need this?” There is a considerably ruder version of a question posed by Billy Connolly on the internet, but let’s not go there.

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15. Yes, maths can be for the amateur too

A friend of mine picked an argument with me the other day about how people go on about the beauty of mathematics, but this is not only not obvious to non-mathematicians, it cannot be accessed by those outside the field. Unlike, for example, the modern art, which is also not always obvious, mathematical beauty is elusive to all but the mathematicians. Or so he said.

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16. Diamonds are forever, and so are mathematical truths?

Try googling 'mathematical gem'. I just got 465,000 results. Quite a lot. Indeed, the metaphor of mathematical ideas as precious little gems is an old one, and it is well known to anyone with a zest for mathematics. A diamond is a little, fully transparent structure all of whose parts can be observed with awe from any angle.

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17. The real charm of imaginary numbers

Few elementary mathematical ideas arouse the kind of curiosity and astonishment among the uninitiated as does the idea of the “imaginary numbers”, an idea embodied in the somewhat mysterious number i. This symbol is used to denote the idea of , namely, a number that when multiplied by itself yields -1. How come?

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18. World Statistics Day: a reading list

On 20 October 2015, the global mathematical community is celebrating World Statistics Day. In honour of this, we present here a reading list of OUP books and journal articles that have helped to advance the understanding of these mathematical concepts.

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19. Better medical research for longer, healthier lives

When I started my career as a medical statistician in September 1972, medical research was very different from now. In that month, the Lancet and the British Medical Journal published 61 research reports which used individual participant data, excluding case reports and animal studies. The median sample size was 36 people. In July 2010, I had another look.

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20. From number theory to e-commerce

The American Mathematical Society held on October 1903 its regular meeting in New York City. The program announced a talk by Frank Nelson Cole (1861-1921), with the unpretending title of 'On the factorization of large numbers'. In due course, Cole approached the board and started to multiply the number 2 by itself, step after step and without saying a word, sixty seven times.

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21. Why know any algebra?

A recent meme circulating on the internet mocked a US government programme (ObamaCare) saying that its introduction cost $360 million when there were only 317 million people in the entire country. It then posed the rhetorical question: "Why not just give everyone a million dollars instead?"

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22. Why Literacy Teachers Should Care About Math

I’ll be the first to admit it: I didn’t pay much attention to math. I specialized in literacy and focused on reading, speaking, listening, writing, social studies, and science instruction. Math? My third graders went down the hall each day to the “math classroom.” My co-teacher and I collaborated over best teaching practices, family relationships, and classroom management, but I didn’t spend time delving into the third-grade mathematics standards.

It wasn’t until I entered into our first parent-teachers-student conferences in September that I realized I couldn’t afford to compartmentalize my students’ learning.

In those conferences, we had students who loved math and had excelled in math every year leading up, but were now struggling to advance. They seemed to have hit an invisible wall. What happened?

Two words: Word problems.

Why Literacy Teachers Should Care About Math (1)Some of our students who were English Language Learners, reluctant readers, or who struggled to read at grade level for other reasons all of a sudden “couldn’t do” math anymore because the vocabulary, text length, and sentence structure were increasing in complexity. Even though they knew what 9 x 5 was, they couldn’t read and decipher the sentence:

Rene enjoys wearing a new outfit every day. His father bought him nine pairs of shorts and five shirts. Rene doesn’t want to wear any outfit twice. How many different outfit combinations does he have?

Now several of my students weren’t only struggling to read in my literacy class, but also struggling to read in math class. This was disheartening and confusing for them because math was a subject they loved, excelled at, and didn’t feel “below their grade level” because of language abilities or background schema. Yet reading challenges were following them down the hall and across instruction periods.

Guess what: Reading teachers are ALSO math teachers.

What?

Let me explain.

  • A text is a text no matter the form. Those ELA standards about determining the central idea and unknown or multiple-meaning words apply to word problems along with poems, plays, and biographies. Word problems can be lengthy, involve two or more steps, and contain new and unknown vocabulary that require examining context clues to solve.
  • Great English teachers improve students’ math scores. According to The Hechinger Report, researchers from Stanford and University of Virginia looked at 700,000 students in New York City in third through eighth grade over the course of eight school years. Results: Students of good English language arts teachers had higher than expected math scores in subsequent years.
  • Starting in second-grade mathematics, students are reading, interpreting, and solving two-step and multi-step word problems. Even as early as kindergarten and first grade, students are encountering one-step word problems. Bottom line: If they can’t read, they will get left behind in math, too.

So, how can literacy teachers embrace math?

1. Nice to meet you, Math. I’m ELA. The Common Core website also falls victim to sequestering the ELA and math standards. Whether you teach both math and literacy or only one, compare the math standards to the ELA standards of your grade. Open two windows on your computer setting the Reading or Language standards of your grade side by side with the Operations & Algebraic Thinking standards for your grade. What do they have in common?

(Hint, hint: determining central idea of a text, interpreting unknown words or phrases, using context clues, and learning general academic and domain-specific words)

2. Share what read aloud or model text you are reading for the week or unit if you have a separate teacher for math instruction. In word problems, you or the math instructor can write a few of the problems about the characters. Reading In Her Hands: The Story of Sculptor Augusta Savage? Make Augusta the main character in the word problems.

This book has several money references because Augusta earned money from her teaching and from competitions she entered. Use some of the scenes in the book to review the values of currency. For example, Augusta earned a dollar every day from the principal of her school. How many different ways can you make $1.00 using combinations of quarters, dimes, nickels, and pennies?

3. Reward students with a math problem during the reading instruction block. (I’m telling you—students LOVE seeing you break out math during a literacy block). This gives students a break, uses a different part of their brains/thinking, and allows them to display their abilities in another subject (which is especially important if English makes a student feel doubtful or shy). Students can do this if they finish their required assignment early or you are transitioning between periods.

4. Allow students to create a word problem using the setting and characters of a book they are reading as an incentive, extension opportunity, or way to engage reluctant readers. Students can submit problems for you to review at the end of the day and the next day you can post one with the student author’s name. Students will have a chance to model (and observe) high quality writing and thinking, as well as delight in their peers’ recognition.

5. Word problems ARE story problems. Treat a word problem like any other fiction story. Have students identify the main character(s) and the problem. Give the word problem a setting. Encourage students to expand the math problem into a fiction story through writing or drawing.

6. Make a math bin in the classroom library. Whatever gets a student excited to read and pick up a book, right? Just as we will scour web deals and dig through yard sales for books on tiger sharks and poison dart frogs, don’t forget to hunt for math-themed books to add to your classroom library if math is your students’ passion.

from Ice Cream Money

7. Pick math-themed books to align with units students are covering in the grade level’s math standards. Great read alouds and leveled readers exist to help teach concepts around counting, money, time, geometry, and mixed operations, such as:

8. Even books without explicit math themes can inspire math conversations.

From Baby Flo: Florence Mills Lights Up the Stage:

  • Florence was promised twenty-five cents a night to perform at the Empire Theater. If she performed every night for one week, how much money did she earn? How much money would she earn in two weeks?
  • After her performance in the butchers’ shop, Florence earned $3.85. How many nickels would you need to make $3.85? How many pennies would you need to make $3.85?

From Silent Star: The Story of Deaf Major Leaguer William Hoy:

  • If Hoy was born in 1862 and died in 1961, how old was he when he passed away? If Hoy started playing in the major leagues in 1888 and retired from baseball in 1902, how many years did he play in the major leagues? How many years ago did Hoy last play baseball? If Hoy were alive today, how old would he be?

From Love Twelve Miles Long:

  • Frederick’s mother walks twelve miles. How many yards does she walk? How many kilometers and meters does she walk?

If students can’t read, they will struggle to succeed in math (and science and social studies). These challenges will compound with each year affecting self-confidence and commitment. Bridging math and literacy for students is a powerful way for students to see that learning how to derive meaning from text has real world applications and that you are invested in their entire education.

img_1587Jill Eisenberg, our Senior Literacy Expert, began her career teaching English as a Foreign Language to second through sixth graders in Yilan, Taiwan as a Fulbright Fellow. She went on to become a literacy teacher for third grade in San Jose, CA as a Teach for America corps member. She is certified in Project Glad instruction to promote English language acquisition and academic achievement. In her column she offers teaching and literacy tips for educators. 

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23. How do we protect ourselves from cybercrime?

Modern society requires a reliable and trustworthy Internet infrastructure. To achieve this goal, cybersecurity research has previously drawn from a multitude of disciplines, including engineering, mathematics, and social sciences, as well as the humanities. Cybersecurity is concerned with the study of the protection of information – stored and processed by computer-based systems – that might be vulnerable to unintended exposure and misuse.

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24. 10 Ways to Use Instagram in the Classroom

Think there’s no need for sepia-toned filters and hashtags in your classroom? Don’t write off the world of #selfies just yet.

Instagram is one of the most popular social media channels among generation Z, or those born after 1995 and don’t know a world without the Internet. It shouldn’t come as much of a surprise that this is a generation of visual learners and communicators, where sharing your life-from the food you’re about to eat to your thoughts about anything and everything-is a part of your everyday routine. So, why allow Instagram in your classroom?

For starters, preparing students to be college and career ready involves helping them build their digital literacy skills on a professional level, and Instagram is a technological tool that offers educators innovative ways to motivate and engage students, opening up a new platform for collaboration, research, and discussion. Secondly, we all know the importance of interest and ownership for getting students excited about learning, and since your students probably already love Instagram you’ve already won half the battle.

Teacher/Classroom Instagram Accounts

Create a private classroom Instagram account that you control and instagramcan use to connect with your students, their parents and guardians, and other grade team members. Invite them to follow your account and catch a glimpse of your everyday classroom moments and adventures.

  1. Student of the Week: Each week, feature a different student on the class Instagram account, posting photos-with their permission- of their favorite classroom projects and other examples of their hard work and achievement. This is a fun opportunity to highlight your students’ individual strengths, positively reinforcing their behavior and progress.
  2. Daily/Weekly Classroom Update: Similar to student of the week, you can instagram your students’ classroom projects and activities on a daily or weekly basis. From photos of new classroom reads to capturing field trip memories, this is an excellent way to build a sense of community while allowing parents to see what lessons, topics, and exciting activities are happening in your classroom. This is also a great way to easily and quickly share your classroom ideas with other grade team teachers.
  3. Student takeover: If you’re not able to encourage students to create their own individual Instagram accounts, invite each student to “take over” the classroom account for a day or week by sharing photos from his or her everyday life. This is a great opportunity for students to learn more about their peers by instagramming their interests, hobbies, routines, and even cultural traditions.
  4. Photo Inspiration: Finding inspiration to write can be one of the most difficult parts of the writing process. Spark your students’ imaginations and help them discover new ideas through instagramming writing prompts by playing with different angles, perspectives, and filters to capture random moments and objects that you encounter throughout your day-to-day.
  5. Caption That! For a variation of the writing prompt, post an interesting photo and ask your students to write a descriptive caption in the comments. Differentiate how challenging this task is by asking students to write their caption using specific sentence types, different parts of speech, clauses, prepositional phrases, and their current vocabulary words.
  6. Daily challenges: If your students are able to follow the classroom Instagram account on a regular basis, you can use it to post daily challenges in the form of visual word problems, review questions, and bonus questions. Instagram photos of important learned concepts and pose questions to your students in the caption, asking them to write their answers in the comments. For example, this fifth-grade teacher used Instagram to review who Henry Ford was and other important events in history.

Student Instagram Accounts

Asking your students to follow the classroom Instagram account with their personal accounts is one, highly unlikely, and two, probably not the best idea. What you can do is ask your students to create additional Instagram accounts that would only be used for school or classroom purposes. You know how LinkedIn is your professional Facebook? A similar idea applies here.

  1. A Day in the Life: Challenge students to assume the role of a classroom longfictional literary character and share images that he or she believes the specific character would post, highlighting the character’s interests, personality traits, and development throughout the story. The 15-second video option is a great way to really let students get into character through recorded role-playing and even performance reenactments. These activities can also be applied to important figures in history, such as the creator of Honda, Soichiro Honda, or jazz musician, Melba Liston.
  2. What the Kids are Reading: Students can snap photos of their favorite reads and write a brief 1-5 sentence review in the caption. To take it a step further, ask them to record 15-second long persuasive book trailers to hook their peers. Boost further discussion among your students by asking them to comment on other book reviews and book trailer videos to share their opinions. Tip: Encourage your students to use a unique #hashtag (ex.: #SMSGrade4Reads) for each book review posted, and by the end of the year you will have a visual library of all of the books your class has read.
  3. Math Hunt: “Why do we have to learn this?” “I won’t need this in my everyday life.” Sound familiar? Help your students see the real-world math applications all around them by sending them on a hunt to document or illustrate their knowledge of different math concepts:
  • Geometry: lines (parallel, perpendicular, and intersecting), angles (right, acute, obtuse, etc.) symmetry, and three-dimensional shapes (prisms, cubes, cylinders, etc.)
  • Everyday fractions and arrays
  • Concepts of money
  • Examples of volume vs. mass, area vs. perimeter
  1. STEM Research: Students can watch, observe, and record science experiment data and results over time by documenting any step-by-step process with photo and video narration of learned science concepts. Outside of the lab, students can use their Instagram accounts for observing science in nature or sharing their own scientific findings. What makes this special is how quickly and easily students can share and revisit their visual references and recorded data.
  • Physical & chemical changes
  • Weather patterns and phases of the moon
  • Animal adaptations
  • Habitats in nature

Note: Instagram, as well as Facebook, Twitter, Pinterest, Tumblr, and Snapchat, has a minimum age limit of 13 to open an account, but according to Instagram’s parents’ guide, there are many younger users on Instagram with their parents’ permission since you don’t have to specify your age. Always check with your school’s administrator and obtain parental permission before sharing photos of students or their work.

Know of any other interesting ways to use Instagram or other social media sites in the classroom? Already using Instagram in the classroom? Let us know in the comments!

veronicabioVeronica has a degree from Mount Saint Mary College and joined LEE & LOW in the fall of 2014. She has a background in education and holds a New York State childhood education (1-6) and students with disabilities (1-6) certification. When she’s not wandering around New York City, you can find her hiking with her dog Milo in her hometown in the Hudson Valley, NY.

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25. Putting two and two together

As somebody who loves words and English literature, I have often been assumed to be a natural enemy of the mathematical mind. If we’re being honest, my days of calculus and the hypotenuse are behind me, but with those qualifications under my belt, I did learn that the worlds of words and numbers are not necessarily as separate as they seem. Quite a few expressions use numbers (sixes and sevens, six of one and half a dozen of the other, one of a kind, etc.) but a few are more closely related to mathematics than you’d expect.

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