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lewelma

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Everything posted by lewelma

  1. Ok, I've been doing some more thinking. I think you need to work backwards. When you say a "few" AP courses are you talking 3 science APs? And when you apply for colleges aren't only the APs in 11th counting towards entrance? So your 12th grade AP would not be in your speciality. My ds will take AP Bio in 12th, because he is interested in Physics. Also, please note that APs are a second year of high school science. So given what you have told us, you need: 1st year bio, chem, and physics. and 2nd year (AP) for 2 or 3 of these. As you can see, this sets you up for more than one science class in each year of high school unless you start in middle school. And this really depends on your child's interests and abilities. So if you can, put 1 high school level science class in 8th - you suggested Conceptual Physics. Conceptual chemistry (or spectrum chemistry) or a bio class would also work. Me personally, I would not want to study for 2 science APs in a single year, although I know that many do. So just for example, if you want 3 AP without doubling up in science in highschool: 6th: earth science 7th: first year chemistry (spectrum chemistry or conceptual chemistry) 8th: first year physics (conceptual physics) 9th: first year bio 10th: AP chemistry 11th :AP bio 12th : AP physics If this schedule is too much for your student, shift it later by a year or 2. 6th: earth science 7th: physical science or environmental science etc 8th: first year chemistry (spectrum chemistry or conceptual chemistry) 9th: first year physics (conceptual physics) 10th: first year bio 11th: AP chemistry 12th :AP bio You can always double up on APs when they are older and more focused. You have also mentioned putting your kids back into school. Which sciences are offered at an AP or 2nd year level? That would also inform your choices for middle school I would also suggest that middle school be the time that you make sure that your student can read a textbook, answer written questions, and study on her own. Also, focus on Math. That will help with science as much as anything. HTH, Ruth in NZ
  2. My understanding is the following: Typically, between the ages of 13 and 15, kids take between 6 and 10 IGCSE exams. Then for 11th and 12th grade, kids take 4 AS level courses in 11th (1st year of A-level studies) and 3 A levels in 12th. So for all subjects (humanities, sciences, languages etc) the progression is IGCSE, AS, A levels. It was recommended to me to start ds earlier because he is advanced and so that there is not a big crunch. So our plan is: 7th: IGCSE Chemistry 8th: IGCSE Physics, IGCSE Math, 9th: AS chemistry, AS Math, ABRSM Music theory and practical 10th: AS physics, A chemistry,IGCSE English 11th: AS biology, A physics, A Math 12th: A Biology, AS English, Mandarin Exam from China I am pushing math and physics early so that applying for university entrance in Physics/engineering will be easier. We will skip IGCSE biology, because I think he already knows the material. Ruth in NZ
  3. I am in the same situation. I am beginning to think that *I* am going to have to go through the process a few times by myself and pay attention to what I do so that I can teach it. I need to make my implicit knowledge explicit. I too hope that WWS will fill in the gaps of my knowledge. However, I get the impression that it will be 1.5 years between each book, which is going to be a problem for my oldest. sigh. I do think that the more you do the easier it gets. So I plan to just get in there and do a few papers along side my ds. Either we will team write, or we will each work on our own paper but on the same topic, and compare notes/ideas as we are working. Personally, I don't think that I have EVER written a research paper on a historical topic. :001_huh: Probably for an essay test, but not for a research paper. For a research paper, you have to do research, document it, and extrapolate to the question. This is tough. I think, however, that my ds would prefer to research topics on cloning or genetic engineering. I completely agree. Where exactly do you get sources that are short and that a middle schooler can read that are on very specific topics? Seems to me that you need to read about a topic for a month before you sit down to write a research paper. Ruth in NZ
  4. My worms never smelled unless their bed needed a change. They need air, so we had them live in shredded newspaper. About 3 times a year, their castings would get too heavy and would smush all the newspaper down and the little worms had no air. So, at that point, you remove most of the castings, and give the worms a new bed of newspaper. Very easy.
  5. Course book: http://www.amazon.com/Cambridge-Physics-Coursebook-International-Examinations/dp/0521757738/ref=sr_1_2?ie=UTF8&qid=1336427026&sr=8-2 Workbook: http://www.amazon.com/Cambridge-Physics-Workbook-International-Examinations/dp/0521173582/ref=pd_bxgy_b_img_c This works kids through reading and interpreting graphs and data. Teacher's guide: (has answers, extra worksheets, and labs) I can't seem to find it on amazon, but I assume it exists as I have the one for chemistry from the same series. The previous exams are available and they will show you the depth and focus of the program. The exams require serious integration of the ideas studied during the course, so it is worth doing a few exams just for developing that thought process, even if your student would not actually take the exam. http://www.xtremepapers.com/ look at GCSE exams (slightly easier) or CIE. Both cover the material in the texts listed above. I cannot guarantee that these textbooks are the best out there, but the Cambridge International Exams (CIE) are well respected internationally. This physics course is a first year high school physics course. After this course, you then move on to a 2 year course of study for the A levels (equivalent of AP). In the European schools you study >1 science per year, so you study for the A levels over 2 years instead of 1 year like the AP exams. Hope that makes sense. If you are interested in physics, the person to ask is Regentrude as physics is her field. Ruth
  6. We kept our worms in the pantry! They lived in a cardboard box lined with a rubbish bag and covered with shredded newspaper to keep the fruit flies out. Our house is unairconditioned and stays at 60 to 65degrees year round.
  7. I only have a rising 7th grader, but here are my plans for his 8th grade year: Math: AoPS intermediate Algebra Science: High school physics preparing for the Cambridge International Exam in Physics + science fair project in physics Writing: Lost Tools of Writing Spelling: Spelling Wisdom (yes, we will continue with this, sigh) Vocab: MCT WWW1 Literature: working our way through the great books, with discussions with mom, and once per month essays (we might use Excellence in Literature) Mandarin: 3rd year with a tutor Violin: will take the level 5 ABRSM theory exam, and level 6 Practical Violin History: continue with read alouds and discussions with father at night PE: swimming, sailing, martial arts I think that is everything, Ruth in NZ
  8. Start slowly. Just find what you want for math and writing. Get these 2 down and then add your reading curriculum. Once reading is sorted then add spelling. Once spelling is sorted out, then add grammar, etc. While you are getting the core skill subjects organized, just go to the library and get readers and read alouds on lots of topics. Over the period of 6 months to a year, you will have your skill subjects (the 3 r's) and your content subjects (history and science) figured out. But don't expect to have it all up and going right away. You will also find that not all subjects need a curriculum for all kids. Your kid might be a natural speller or one that is already reading. So you don't need to add those in. You need to tailor your program for YOUR child. Also, I would recommend that you start a new thread with details about your student's likes and dislikes for math, how he learns, and what you as the teacher need, and then the hive will point you to a few curriculum that will meet your requirements. Then start another new thread for writing etc. This makes it easier for those of us with certain knowledge to find your questions and answer them. HTH, Ruth in NZ
  9. For anyone interested, I have updated the progress of our project. It is on the logic board. http://www.welltrainedmind.com/forums/showthread.php?t=361740&page=4 Yes. I studied population dynamics using nonlinear statistical modelling. Kind of interdisciplinary. Well, I am hoping to help a few people. I hear a lot of "I wouldn't even know where to start." By showing the process week by week, I hope to help people see that there will always be difficulties to overcome. And to never be surprised or upset by them. This sounds so interesting. Try to control all you can, but when there are variables that you can't control, you can increase your sample size to overcome that variability. Awesome project. I am glad I am keeping a diary of this process. It helps me to realize how much they learn through the process. There is a beach that has been "enriched" near us. They actually could not get sand to do it. So they went to a quarry and ground up rock to stick on the beach. :001_huh: This is the "sand" that ds is using to dump on the natural beach to evaluate longshore transport. The "sand" is a different color because it is ground up rock! Ruth in NZ
  10. Week 7. 6th grade This week was a disaster. He has 4 samples to go: high wind southerly and 3 low wind northerlies. And we got that high wind southerly this week, straight from Antarctica. Because of the tide table, we have to go out on the 2nd day of the storm. Problem #1: The wind speed is so high (40mph) that all the sediment has been stirred up. He can't see the bottom. Problem #2: He can't stand up in the breakers, and I am a bit nervous to send him out by himself past the breakers where the sediment might be less stirred up. Problem #3: His feet get completely tangled in all the sea weed that has been pushed into the surf. Problem #4: He comes in from the ocean and notices a sign reading "do not swim after a large storm due to pollution risk.":eek: He freaks. I tell him he will be ok because he has only put his head in once. Problem #5: We lose the meter stick! Problem #6: When we go out the next day for a low wind northerly, the sediment is still stirred up! And he can't see the bottom. He spent more than an hour each day working hard to get some sort of measurement. Could he see shells? Could he use wood instead of a meter stick? Could he shift down the beach to avoid the seaweed? Can he go out a bit further? Can he view from the dunes a place where the water is clearer? All the permutations take FOREVER to evaluate especially because it is blowing a GALE. And all for naught. Lesson learned, we need to be out on the first day of a southerly storm before it all gets mucky. Very frustrating. Data Collection: 3.5 hours Total time: 3.5 hours + 2 hours cleaning up the car, the wetsuits, and the children.
  11. We are in the middle of data collection and have run into some difficulties! I've just posted this week's efforts with my second grader. http://www.welltrainedmind.com/forums/showthread.php?t=361740&page=4 If you have never seen an investigation in action or if you have no idea how you would ever go about it in your own family, have a look. I am explaining our work step by step. Ruth in NZ
  12. Week 7. 2nd grade. The focus this week is data collection. The first thing we need to do is go to the 5 locations where we have already dug holes and check the slope of the land using his new invention. We have slope estimates, but they were really inconsistent because we didn't have a good tool. We build his invention with a meter stick, string, and a weight (2 magnets). We mark off 2 cm marks on the string that will hang down. The string slides through the hole in the meter stick so you can pull it up. Now all we need is a level, and we realize that we don't have one (I thought we did). So I suggest that we use a long flat container full of water, draw a line on it, and use it like a level. We try this and realize that we can't really see the water easily, so I decide to color the water with coffee. :lol: So we head out into the woods with a shovel and pitchfork (sort of concealed in a bag), the measuring device, the data notebook, and the container of coffee. We realize quite quickly that the coffee is leaking.:tongue_smilie: and that the magnets at the end of the string keeps falling off. We search multiple times in the leaf litter for the missing magnets:tongue_smilie:. Then the coffee spills on ds(11)'s shoe while we are climbing up a steep slope and he is NOT happy:tongue_smilie:. Believe it or not, we keep at it for more than 1.5 hours in 45 degree weather!!!! During our digging on a flat area in the woods, we come up with a great new idea. We notice that on a slope, there seems to be a lot of leaf litter collecting on the upward side of the plant. We decided to dig a hole there because we expect the soil to be quite deep. ds(8) and I dig down about 25 cm, think we hit the e-layer, measure, and fill the hole in. Now something VERY important happens from the point of view of understanding science. My older son tells us that he wants to re-evaluate the measurement. He re-digs the hole! :001_huh: At the time, I did not know that he had looked at the data sheet and found that the hole was not as deep as the previous hole. Once I realize what is going on we have a very LONG conversation about why scientists do "double-blind" studies. It is not that scientists would purposefully change data to fit their assumptions, it is more that your expectations subconsciously affect your data collection to sway it towards your expectations. Unfortunately, for this very important point, my ds(11) is correct and we had not hit the e-layer but rather just a big rock that started to crumble. So the topsoil is 5cm deeper than our first measurement. We decide that we need to look more carefully for rocks. And then we realize that the coffee has tipped over and completely leaked out. It is just one of those days! So a few days later, ds(8) and I go out by ourselves to do some reconnaissance. We won't be digging, just finding some good locations. The first thing he wants to do is show me a cliff in the woods. We get lost. When we finally find the cliff, I did not realize he was talking about the old quarry. As I look up a 10 story high cliff, I tell him we might have some trouble measuring the top soil. :D But then we notice some really interesting things, one side is lush with new growth, the other is barren. We hypothesize that it is due to one side being shaded from the sun year round. We discuss lichen, cracks in rocks, sliding soil from the top, slope, wind direction, and seed dispersal, and how all these factors interact to affect soil production and vegetation density. Next, he wants to go to a ridge line that he likes. We climb to the top and there is NO topsoil at all. But around the edge, there is grass holding some topsoil. Why? What has caused all the grass to leave the inner portion? I suggest herbicide, he suggests wind. We move to the next path he is interested in. The land near by is lumpy and undulating. We start to apply what we have learned from the cliff. Perhaps as the forest grew, certain areas were shaded, stayed moister, and developed more topsoil. As we wander through the woods for 1.5 hours we find more and more things to wonder about with soil, lay of the land, moisture, and vegetation. And then my darling little boy turns to me and says the most profound thing. "Mommy, you could study soil your whole life and still not answer all of these questions." Yes! YES! This is a point that most people NEVER come to. They have never spent 2 months of their life trying to answer a tiny question only to realize that there are so many questions. Each scientist works for a lifetime on one minuscule area of science; most non-scientists just don't ever get how or why you would get SO specialized. Then my ds says, "It makes me feel so small." And I just give him a big hug. Time to go home and have a cup of hot chocolate. Data collection: 1.5 hours Reconnaissance: 1.5 hours Total: 3 hours
  13. My friend's grandmother was 54 when her uncle was born! (and this was a very long time ago. :001_smile:) enjoy it! Ruth in NZ
  14. I got pg when older ds was 2.5. I wore him for the first 3 months as I had for the previous 2.5 years. But when I was 3 months pregnant, I pulled the ligaments that support the uterus (probably because of wearing him) and had to stop wearing him and go to bed for 3 weeks. not nice. I could not wear older ds after that. Ruth in NZ
  15. I really want to be a part of this conversation, but I am not sure that I will be of much help because I just don't like middle school science curriculum very much. What I do, is take high school curriculum and then only do 3/4ths of a year's material for a middle school program. Alternatively, I have used adult "coffee table" books (or high-school non-fiction) for middle school. Both of these options I pair with a 2-month long, science-fair type investigation at the end of the year (you knew I would say this. :D) 4th: Physics: 4 units: mechanics, electronics, astronomy, flight (we did middle school physics in 4th) Text: How things work Library books on electricity Scientific American's astronomy articles going back 10 years Electronics kit. Mechanical Kit Investigation: How does the angle of attack affect the flight time of a kite depending on the wind speed? 5th: Biology: 4 units: biochemistry, genetics, evolution, microbiology The Way Life Works The Cartoon Guide to genetics The stuff of life Biozone's Evolution Investigation: Which type of water supports the most diversity of micro-organisms, ocean, ditch, or river? 6th: Earth Science: 4 units: astronomy, oceanography, geology, meteorology. Text: Tarbuck's Earth Science Investigation: How does the wind direction and speed and the orientation of the bay affect longshore transport of sand? described in detail here http://www.welltrainedmind.com/forums/showthread.php?t=361740 I would really really recommend a year of earth science. As pp have mentioned this is often the last time it is studied. I never, ever studied earth science, and I will tell you that there was a LOT of material that I did not know. Earth science is and should be more than rock and cloud types. Although there is no math, there are a lot of really complex concepts. Meteorology, for example, is MUCH more difficult than watching the weather guy on TV. You could also use the earth science year to study environmental science. 7th chemistry. We will be starting the high school sequence next year. If I were in the US, we would use conceptual chemistry or Spectrum chemistry. But given that we live in NZ, my son will be studying first year high school chemistry to prepare for the Cambridge international exams (CIE). The text looks good. For labs, we will do some occasional easy-to-set-up "experiments", watch some demos on youtube, and do a science fair project. He will also attend a 3 day lab class run for homeschoolers here. 8th: Physics. We will use CIE's physics curriculum and go for the exam. HTH, Ruth in NZ
  16. This made me smile because I think you are the front runner! We are all looking forward to you blazing the trail for us. :001_smile: But I will put on my thinking cap over the weekend and see if I can come up with some ideas. Ruth in NZ
  17. I just posted my full list yesterday on the k-8 board. http://www.welltrainedmind.com/forums/showthread.php?t=376121 His favorites from that list were: Black Ships Before Troy, Sutcliff The Wanderings of Odysseus, Sutcliff Age of Fable Aeneid for children Ruth in NZ
  18. Here is next year's list for Early Modern in 7th grade Early modern: Europe Three Muskateers, Dumas Twenty Years After, Dumas Man in the Iron Mask, Dumas Rob Roy, Scott Mutiny on the Bounty, Nordhoff Count of Monte Cristo, Dumas The Scarlett Pimpernel, Orczy Tale of Two Cities, Dickens Coral Island, Ballantyne Early modern: America The House of the Seven Gables, Hawthorne Autobiography of Ben Franklin Autobiography of Fredrick Douglas Red Badge of Courage, Crane Gone with the Wind, Mitchell Huck Fin, Twain Pudd'nhead Wilson, Twain Innocents Abroad, Twain Late Modern Travels with Charley, Steinbeck Gift of the Magi (and others), O Henry To Kill a Mockingbird, Lee Distopian Iron Heel, London, 1908 Anthem by Ayn Rand, 1937 Walden 2, Skinner, 1948 Farenheit 451, Bradbury, 1953 Chrysalids, Windham, 1955 Do Androids Dream of Electric Sheep? PK Dick, 1968 Running Man, Bachman (King), 1982 House of Scorpian, N Farmer, 2002 Uglies, Westerfield, 2005 Hunger Games, Collins, 2011 Classic Sci Fi Invisible Man, Wells Mysterious Island, Verne The Moon is a Harsh Mistress, Heinlein Lost World, Doyle The Star Diaries, Lem A Perfect Vacuum, Lem
  19. First list is for my ds to read (he will not read all of these. He likes choice). Second list is for my dh to read to both boys (ages 11 and 8 at the time). History: Middle Ages and Early Renaissance (ds to read for 6th grade literature and history) 400-1000 Early Middle ages: Knights and Castles, Feudalism, Vikings Beowulf the Warrior , Sutcliff , The story of Rolf and the Viking Bow French , Sir Gawain and the Green Knight ,Tolkien Conn Yankee in King Arthur's Court , The Once and Future King, White, (trilogy) Tales from Arabian Nights Lang, 1000-1400 High Middle ages: Crusades, Holy Roman Empire Byzantium, Plague Ivanho Crispin: Cross of Lead, Avi Catherine Called Birdy, Cushman Mary, bloody Mary Meyer Sir Nigel, Doyle The White Company, Doyle Canturbury Tales, Original, just a few stories, Lord of the Rings, Tolkien, (trilogy) Eastern China, India, Japan, Africa (Mali), Khmer Empire A Single Shard, Park Lady of Ch'lao Kuo diary series South America Incas, Aztecs, Conquistadors Lady of Palenque diary series The Left-handed Spirit The captive O'Dell Early Rennaissance Apr, May, June Joan of Arc, Twain, Black Arrow, Stephenson Trumpeter of Krakow Dante's divine comedy Chwast (graphic novel), Optional by Sutcliff Outcast- Britain under roman rule, focus on celts and picts Sutcliff has a series on Arthur Mark of the horse lord – brtian under roman rul, N tribes Shining Company – britain, fuedal chiefs, saxons Blood Fued , Sutcliff , britain, constantinople Sword Song – vikings Read alouds 400-1000 Early Middle ages: Knights and Castles, Feudalism, Vikings British, White Stag (Attila the Hun) Vikings, Beowolf Castles, feudalism,Castle, City Macaulay King Arthur and His Knights, Pyle Arabian, Islam, One Thousand and One Nights, McCaughrean 1000-1400 High Middle ages: Crusades, Holy Roman Empire Byzentine empire, Plague High middle ages Adventures of Robin Hood, Pyle Midwife's apprentice Adam of the Road, Gray Shadow of a bull – Bull fighting Canturburly tales McCaughrean Eastern China, India, Japan, Africa, Khmer Empire Samurai's Tale, Haugaard South America Incas, Aztecs, Conquistadors Secret of the Andes Around the World's Rim Early Rennaissance Shakespeare Macbeth, Hamlet, A Midsummer Night’s Dream; Taming of the Shrew; Much Ado About Master Cronhhill – Plague in 1654, London fire Eyewitness: Vikings, Knights, Midevial Life, Castle, Arms and Armor,
  20. Here is my ds(11)'s version When Johannes Kepler studied at university he learned about Copernicus's new theory of heliocentricism which hypothesized that the sun is at the center of the solar system. However, most people still believed the earth was at the center of the solar system not the sun. After he finished university, Keplar became the assistant of the famous astronomer Tycho Brahe. During this time, his job was to track the orbit of Mars. They both believe that all orbits were circular. Thus, when they noticed that Mars was speeding up and slowing down, they were unable to understand why. Unexpectedly Tycho Brahe died. Keplar continued trying to find an explanation for the movements of Mars. He struggled with this problem for five years. He once wrote, "I was almost driven to madness considering and calculating this matter. I could not find out why the planet would rather go on an elliptical orbit." In 1605, Keplar solved the problem and formed his first law of planetary motion. "The planetary orbit is elliptical and the sun, the source of movement is at one of the foci of this ellipse." He published this work in 1609, but it was not accepted immediately.
  21. Here is my ds's 5th grade reading list. I like to give him some choice, so he did not read all of these. I read a lot of the ones that he read and then we discussed them. These discussions included literary elements like flashbacks or allusions, comparison between books, and societal context. My favourite discussion was about Henty's Victorian overlay on top of Egyptian history in the Cat of the Bubasties. HTH Ruth in NZ Ancients, Grade 5 Egypt Tales of Ancient Egypt, Green Golden Goblet Mara, Daughter of the Nile Cat of Bubastes, Henty Pyramid, McCaulay India Tales from India, Gray or Green? Myths and Legends Horowitz Greece Black Ships Before Troy, Sutcliff The Wanderings of Odysseus, Sutcliff Story of the Greeks (history, online) Tales of Greek Heroes, Green Heroes of Greece and Troy, Green, 1st ½ same as above, 2nd ½ on Troy) Rome Lantern Bearers series, Sutcliff Eagle of the Ninth The silver Branch Frontier Wolf Outcast For the Temple, Henty Young Carthaginian, Henty Age of Fable Story of the Romans The last Days of Socrates, Plato Aenid for children Aesop's Fables City, MacCaulay Myans Well of Sacrifice Secrets of the Stone Lady of Palenque (modern from diary series) Heart of Jaguar (modern, violent 1200's) Britian Warrior Scarlet , Sutcliff Beric the Briton, Henty China Lady of Ch'lao Kuo (modern from diary series) The left-handed Spirit Science and Religion Encyclopedia of ideas that changed the world August Caesar's world Archimedes and the Door of Science
  22. In 5th grade my ds studied Biology. For his assigned reading, he read 20 minutes every morning before breakfast (6 days per week which is 2 hours per week for 40 weeks). He read these 4 books for the year: The way life works (DNA, protein synthesis etc), The cartoon guide to genetics, The stuff of life, and Biozone's Evolution. This totals about 600 pages. This is absolutely NOT all he read about biology, just his assigned textbooks. He also read a lot of books from the library. For history, his literature overlapped with history (we studied ancient history). So he read things like Rosmary Sutcliff's Eagle of the Ninth about Rome. He reads assigned lit for between 1 and 1.5 hours per day, and I require 16 classics per year (4 per 10-week term). He does not read a history textbook independently, although he does read books from the library for fun which are about the topic we are studying. My husband reads aloud both historical fiction and history textbooks. For 6th grade, he spends 1 hour 3 times a week reading Tarbuck's Earth Science. Next year for 7th grade, he will need to spend 4 hours per week for Chemistry (this excludes lab time) because he will be studying for the Cambridge International exam. Plus, I will start adding in non-fiction books about science and history, like Guns, Germs, and Steel. History will continue to take a back seat. Ruth in NZ
  23. He needs physics in High School. You really do not want his first exposure to physics to be in university. If he gets a biology degree he will be required to take 1 year of physics, and this will not be "physics for poets" but real calculus-based physics. Also, remind him that there is quite a bit of physics in biology, especially anatomy: how the wing allows for flight, how the knee of a horse enables the faster mobility, how the movements of waves affect seashore ecology, how bats detect sound, how the eyes of bees vs mammals use optics to see etc. Don't skip physics! Ruth in NZ
  24. No, it depends on the visa. There are homeschooling children here who are on a student visa and must follow the laws of the state in the USA they are from. If your child is on a "permanent resident" visa or is a dual citizen you must apply to the New Zealand government for permission to homeschool, and then you get the homeschooling allowance which is between $700 and $2500 per year depending on the number of children you will be homeschooling. Ruth in NZ
  25. Probability leads directly to statistics: Biology (ecology, population dynamics) Earth Science (seismologist, geologist in mining) Business (marketing, surveys/polls, economics) Social Sciences (psychology, sociology) Mathematics (probabilistic nonlinear dynamics) Statistics applies to most things today. Ruth in NZ (who did 6 years of statistical modelling of nonlinear dynamics in population dynamics!)
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