Can you prove p → q |- ¬p ∨ q without using the law of the excluded middle or its equivalent? I'm going through a logic book (introductory) and I have an intuition that proving this isn't possible constructively, but I'd like a confirmation.
My department is interested in transitioning to a "mastery-based" precalculus class at the college level. The basic idea is that students would be allowed (somehow) to work at their own pace, and success in the class would be by demonstrating mastery of most of the material (80%?). Somehow. Does anyone have any experience with this sort of teaching, in any discipline? [more inside]
How do I write an Excel formula to weight a rating by the number of ratings, so that a 4 with tens of thousands of ratings weighs more than a 5 with three ratings? [more inside]
Sometime within the last two years, I read a positive review of a mathematics book for children of at least kindergarten age that introduced math concepts using the number line as a conceptual focus. I'd appreciate any help in trying to identify this book. [more inside]
I am aiming to create extracurricular programming for people of all ages (but I'm particularly focused on teens and adults) to illuminate the neat areas of math that aren't covered in school. (Graph theory, mobius strips, pascal's triangle, things like that.) However, I don't have a very official background in mathematics myself. 1) What resources can I use to teach myself about math in those areas, or math leading up to those areas? 2) What resources are out there for kids/teens/adults to increase their math awareness? [more inside]
Our three year old LOVES to say his letters and numbers. When he gets to Z, he triumphantly (and accurately) announces "and that's all the letters!" When he gets to 100 he proudly informs us, "that's all the numbers!" I've tried to tell him about 101, 102, etc., but he does not believe me. He would believe it if a YouTube video or app told him so. Any suggestions? (Yep, I know this is not a big deal. I just like watching the light bulb go on when he realizes just how big the world is.)
I am in the process of trying to create a complex pricing calculator for internal use in our business. I have most of the data, however I am hoping to engage someone on a freelance basis to help me complete the data set, as well as give some expanded detail on how this data (pricing) can change geographically. What specific professions should I be engaging, and where can I find them? More information below the fold. [more inside]
I'm looking for challenges, puzzles and "teach yourself" courses that involve maths and logic, probably related to computing. Ideally I'd like a curated source (mailing list or regularly updated website), but perhaps the best we can do is collect them here. Inside I will give examples of what I mean by "challenges, puzzles and courses". [more inside]
Hi, parents of young children. I've been commissioned to design and format a series of small books aimed at you and your kind. How do you want it to look? [more inside]
So the school year is close to starting here and I was recently told I need to teach a STEM elective course. This is a brand new course and there are no real guidelines so I need to build it from the ground up. I have some ideas but I need to quickly find ways to get material resources most of all, but also a strategy to plan a cohesive year-long course. [more inside]
My math is a bit rusty, I would like to calculate the surface of a helix [more inside]
I want to learn math. I signed up for Khan Academy and I like the format a lot. I really like that there are short lessons that I can complete, and that the software automatically checks the answers and lets me continue when I completed a string of 5 good answers in a row (or something similar). I don't like the video explanations though. I'm just not a video person, I learn much better from text. Is there something like Khan Academy where you can do math exercises online but where the explanation is in text?
How much and what type of math is beneficial to programming? What are the prerequisites / pathways to grokking this kind of math? [more inside]
I need to use math to figure out how to fill my pill organizer correctly. [more inside]
What are some good, free online resources for an adult who needs to brush up on basic math operations such as working with fractions, percentages and ratios? Other than Khan Academy. The more interactive the better.
I'm interested in teaching high school students mathematics through a tutoring agency. I have the required experience in mathematics, but very little in teaching. This doesn't seem to be a massive problem for many tutoring agencies, but I want to know: do you have any specific tips/advice about teaching mathematics? And more broadly, any advice about applying for and going to work for a tutoring agency? [more inside]
Mathematically, in a 6-way race with 5 winners, should I vote for the 2 candidates I like, or all 5 who I don't hate? Details inside. [more inside]
I teach math to high schoolers in the San Francisco Bay Area. I'd like to get them out of the classroom on a field trip to a local math-themed destination. Any suggestions? [more inside]
I have just completed my MSc in mathematics in Europe. I do enjoy math, but I spent my uni years feeling like a autodidact hippie marooned on an island full of Mr and Mrs I-Want-A-Good-Job. My main interests revolve around humanities (literature/history/anthropology) and economics (but not finance), and instead of starting a "stable" well-paying career I dream about something inter-disciplinary. I am very open to earning little money and relocating just to do kind of work that engages those skills. What are some random uses of my degree? [more inside]
Non-obvious careers for someone with a B.S. in Applied Mathematics? [more inside]
At the age of 24, I just completed my first year of undergraduate studies at a good public university. I am a strong student with a 4.0 GPA, but I feel that my interests are so broad and varied that I don't know how to narrow down on a specific path of study. Compound these problems with the ubiquitous financial and career concerns of the modern college student, and you have one confused student. How can I resolve this inner turmoil and structure a long-term plan that will bring me (at least some) peace of mind? [more inside]
I've been reading Godel, Escher, Bach and I want to find more mind-expanding concepts that give the sense of understanding some fundamental truth. [more inside]
For the grad-level education I want, I need an understanding of chemistry, physics, and calculus at a minimum. I have a BA in a tangentially related field (or will in a couple months). What are the best resources for learning these subjects without spending even more time/money on tuition? [more inside]
Can/how can one improve the estimate for a chance of an event with a small historical sample size by utilizing the chance of a related event with a large historical sample size? Example and half-assed guess inside. [more inside]
Why do we have order of operations rules in arithmetic instead of just strictly evaluating expressions from left to right (possibly with parenthesis for grouping if we really wanted to change the order)?
What do you do to teach your children math (or maths)? [more inside]
I'd like book/course suggestions to do a slow gentle study of higher Math by myself. I did a bachelor's degree in Math (and Economics) several years ago by myself as an external course (from the Univ of London and LSE), on the side of a whole lot of other things. I did reasonably well, enjoyed parts of it very much, but I've forgotten most of it now. I taught high school Math for a couple of years after that but now work in a totally different field (communication design). I love my work, but miss the brainwork Math required. I'd also like to slowly internalise more Math vocabulary and the structure of the subject, which didn't happen during my Bachelors. [more inside]
Dropped out of school several years ago, drifted for a bit, but now I want to return and get AT LEAST a BS in mathematics. What sources are there for someone returning to school? Should I bite the bullet and pay for college counseling, or are there good free resources I'm missing? [more inside]
I have a series of physical data with a fairly straightforward property: it follows a path in space. If I plot a bunch of successive (x, y) values from the data, they follow a curving, looping line rather than randomly jumping all over the plot. More formally, if I have a point (x[t], y[t]) at time t and (x[t+1], y[t+1]) at time t+1, there is an upper limit on the distance between these two points (and this limit is small relative to the overall variation in the data). Is there a well-defined technical term for this property? [more inside]
I am looking for adult-oriented iOS apps that will help improve my math skills. [more inside]
I'm developing a Data Design curriculum for Art college students, and I'd like to teach some basics of maths and statistics in ways that the non-numerically inclined will understand. For this, I need some simple explanations for complicated ideas. [more inside]
I plan on applying to graduate mathematics programs for the 2014-2015 school year and I'm starting to get a little nervous about my chances at landing a spot in a funded program. My major concern is that I have absolutely zero research experience from my undergrad years, and am having trouble focusing in on what kind of work I would be interested in anyways, and I don't know where to start! And the research papers that do seem interesting to me are so specialized, I have trouble understanding them! [more inside]
I'm struggling to understand likelihood ratios (LR) in the context of diagnostic tests, and why a positive LR is influenced by the sensitivity of the test. [more inside]
I'm learning to accessorize! I'd like to find some little mathematics-related accessories, kind of like the women's equivalent to a (relatively subtle) mathematics tie or cufflinks, that are work (think secondary school educator) appropriate. Simple and relatively understated is preferred. I'm also interested in clothing that would be work-place appropriate (not t-shirts!). I had a lot of fun with my regex skirt from XKCD a few years ago. [more inside]
My son is 10 years old and going into 5th grade in the fall (but he usually does 6th grade math). He likes Stack the States, and we're looking for a math app with similar appeal. We already have Sushi Monster and his younger sister loves it, but I'd like something more challenging for him.
Help me with statistics and Excel. Especially help me if you know any labor saving methods. I want the median, mean and standard deviation for the average price of all items sold, but my spreadsheet-full-of-data doesn't tell me the price of each sale -- just the average price per store, and the number sold at that store. Something like this: [more inside]
Dear math people: please help me understand fractions and ratios intuitively. [more inside]
My math knowledge ends just past Newton. What books provide a good, relatively general-audience introduction to the past 150-250 years of problems and developments in mathematics? [more inside]
For all we know, some mathematical truths might be unknowable. E.g., for all we know Goldbach's conjecture (or its negation) is this way. Yet, if there are unknowable mathematical truths, why might this be? Here are some initial considerations/hacks in the dark: (a) Presumably any computing device would have a finite number of parts. Maybe this would limit its processing power in some relevant way; (b) maybe some of the proofs are too long.
I'm wondering, after breakfast, and a shower, and a commute, and coffee - what is next? [more inside]
For a work assignment, I need to come by a conceptual understanding of modular forms that's light on jargon and, ahem, actual math. If such a thing is possible.
My son is now 15 months old, and I would like for him to have the best possible mathematics education. What should I be doing now and what sort of long-term plan should I have in order to help him both to learn and to love mathematics? (He doesn't have to be a mathematician when he grows up, but really knowing mathematics is non-negotiable.) [more inside]
I'm a 21 year old college senior liberal arts major who has managed to slide by in school (and life) without ever really learning math beyond a middle school/very early high school level. For no reason in particular, I've decided that I want to get serious about bettering myself in the math department. How can I teach myself the academic math skills I missed out on? [more inside]
Mathematics-filter: If there are seven funds with various charges, how can I work out the allocation to these funds of a fixed amount so that the weighted mean charge is below a certain level and the allocations are of similar sizes? [more inside]
Economics Mathematics: I have a Maths degree but lately I've become interested in Economics (Microeconomics and Macroeconomics) and have been reading some textbooks and classic texts and doing some online lecture courses on Economics. But find many of that the "handwaving" graphical "proofs" of economic theories lack a sense of mathematical robustness. Do more thorough mathematics for these ideas exist? Where can I find them? [more inside]
Can anyone point me towards a good resource for learning more about Poul la Cour's work on wind turbines? Or other historic wind turbine work? [more inside]
What is the cardinality of the set of all people who shall expel us from the paradise that Cantor has created?
Sweet descriptions of the empty set? [more inside]
I have a very strong background in humanities but I've completed three-year undergraduate course in math. Though I passed it without trouble, I feel like traditional textbooks didn't teach make me understand a lot. What are best math resources (books, but not necessarily) that instead of trying to look like PM read more like literature or work on your intuition and talk about big picture implications instead? Something like Godel, Escher, Bach for various areas of mathematics. [more inside]
My math skills are no where near where I'd like them to be. Can you recommend a self-paced math learning site? Pretty much any branch of math can apply. [more inside]
I was helping my 4th grade age sister-in-law with her math homework, and came across a question that I couldn't figure out. Can you do it? [more inside]