I’m taking my Pre-Cal final tomorrow, it’s the last day of my junior year.
I already had all my other finals. I aced all of them with lil to no effort…for the record my other classes were Honors History and English, 2 different Speech classes, Spanish, and Poetry. It wasn’t even a problem to score A’s in those classes.
But I’m dreading math, and I should be studying for it right now. Why? Because every year of my life, I barely scrape by with a B. My problem is, I learn a concept, I even understand a concept, but I can’t REMEMBER that particular concept for more then a few minutes. The easiest type of math for me is equations. I love equations. Just plug numbers in and get the answer. But anything that recquires more of a memory than that is just difficult for me. And forget about geometry. That was the worse year of my life.
I also remember learning the theory of right/left brain people. I’m primarely right brained, so I work easiest with language, reading, etc etc. People who are primarily left brained oriented are more adept to math skills and analysis, and also more musically inclined. Most people are at a happy medium, and can easily function either way.
I don’t have anything for a cite, but I learned this last year in Academic Decathalon, and the main area of study was The Human Brain.
See what happens when we let mortals generalize about abstract things like mathematics?
Actually, it’s been my experience that the better mathematicians are quite musically inclined and vice versa. Probably because music, its scales, and its progressions can all be broken down mathematically.
Of course, not every mathematician can sing or play the piano, but they do have a thought process that makes them likely to understand music.
Where I get scared is the number of people in this world that should be able to use some mathematics but don’t have a clue.
About a year back one of the guys in the office was doing some landscaping around his house and asked anyone in the office if they could solve a problem for him. He wanted to place a regular octagonal border made of 4x4 lumber around some trees and needed to know how long to make each side. In an office full of DP professionals, I was the only one to solve his problem.
The most frightening incident was about 3 years ago when it was discovered that a checksum algorithm was breaking down on what should have been detected errors. The vendor that created the checksum spent 3 months trying to improve the algorithm, with little success. In an afternoon, I created one that solved the problem. (100% catch of the single digit errors and 99% or 100% catch of specific two digit errors.) The vendor spent 3 more months TESTING my work and when pressed, finally said that they weren’t able to reproduce the catch rate I’d stated, made some minor changes and had partially tested the new code. They claimed that their PC had been running the test for about 3 days, had tested about 30% of the permutations, and it appeared that their “improvements” would result in a slightly greater catch rate than my proposed algorithm. I plugged their changes into my code, ran the tests, and within an hour let them know the results. They wanted to know how I could have tested 1.0E+16 samples in such a short period of time, to which I replied, “I didn’t – I only need to test several thousand to test every case.” A huge argument ensued about the mathematics and finally the people that were in the business of mathematics threw up their hands and said that they didn’t understand it anyway.
I can forive my wife for not understanding the math. (But it would sure be neat if she did!)
SouthernStyle
Just because the Calculus was invented in 1687 doesn’t mean it was common knowledge in 1700. I doubt that more than 10-15% of the adult population of any country has passed a calculus course, now or at any time in the past.
I think math has an inaccessibility problem unique to the discipline, and that’s part of the reason why we have reduced expectations for people’s knowledge of math compared with other fields.
I’ve never taken a physics course, for instance, but have a half-decent picture of the basics of relativity and quantum physics. I admittedly had the help of a little math, but this was mostly due to some good books and articles written for the educated layman. Thanks to Quammen (who shoulda included more of the math), I’ve got a fairly good picture of the development of island biogeography. And while I’ve never taken a course in Shakespeare, I’ve seen his plays on stage and film.
This is much less possible with math; with a few exceptions, to understand it, you’ve got to learn it. Try explaining simple groups, or the Cauchy-Riemann equations, to someone who’s never taken calculus, for instance.
A question that I’ve asked myself and others, as a mathematically literate person, is what math we should expect most people to know. The only college-level course (which really could be a high school course, IMO) on my list is freshman statistics, including a bit of probability. Any thoughts from the gallery?
Kimstu - I see Brown has a department of History of Mathematics. Cool! (I know, its size is appropriately measured in epsilons, but still…)
I would consider myself to be well versed in math. I got up to a junior-level analytic geometry class in college before I decided that I wouldn’t need any more. Most of the people in that class were math majors, anyway.
On the other hand, I will freely admit that I haven’t read any Shakespeare since high school, and that only under duress. I love reading, but I find his stuff just puts me to sleep. On the other hand, I do enjoy watching his plays. I find them intellectually stimulating, unlike any of today’s entertainment. I loved Kenneth Branaugh’s Henry V and Much Ado About Nothing. Loved them.
So what does all that mean? I dunno. Maybe just that we all have different interests and aptitudes. Or not.
Actually, I think people are better in “math” than you give them credit for. When described and introduced properly, I find that most everyone grasps the relevant concepts. Problems seem to arise when rigor and precision are demanded (as they must be, of course). Unlike most everything else in school, or in ‘Human Discourse’, there’s no fudging math. No equivocation, no opinion, no arbitrariness, nor BSing is allowed. Unlike so many other subjects, in math the trees are as important as the forest (or at least that’s the way it’s evaluated on exams and such). So, people have no skills in dealing with this type of subject. Hey, how could they? Soft and imprecise topics predominate. Our schools “validate” everyone’s opinions, no matter how arbitrary. There are no rights or wrongs. Relative values are the absolute rule.
I took mostly math in pre-med in order to bolster my GPA and increase my chance of Med school acceptance - in math you can honestly get 90 or 95 percent, maybe even 100%. In artsy courses, there was a tacit ceiling in the low 80’s. More importantly, I loved math. If I had half as much ability in math as I do interest in it, I’d be a topologist, not an endocrinologist.
Also, there are too many links in the chain of mathematical education to be broken. Math is one of those subjects which is highly dependent on a strong foundation — if you didn’t pay attention during basic math or algebra, you’re going to have a lot of trouble grasping the concepts in calculus or other higher math courses. I speak from experience, since in order to do well in my calculus course, I needed to dig out my old algebra text more than once to brush up on the basic skills I should have learned in high school. On the other hand, I’ve taken 300 and 400 level liberal arts courses that anybody could jump into without taking the prerequisites. Try that with any math course!
I am a fairly educated and intelligent person. In my continuing education, I have breezed through psychology, sociology, and several law classes. But math…
I have found the remedial math class at my school to be a bit beyond my present capabilities, to put it mildly. Which may well illusrate junebeetle’s point. I have no foundation in mathmatics. Probably due to a very liberal attitude toward intoxicants in my formative years. Or maybe I’m just innumeraticlly challenged?
I am not advocating making English majors take Calculus. Certainly mathematics is a tool, but it is also a very elegant construct. Literature may have universal value to all but in whose opinion? The English professors. The artsy crowd.
My point is this. Can I be a good math professor without reading Shakespeare? Yes. Can reading Shakespeare make me a better math professor? No. I enjoy Shakespeare, and Milton, and Dante, and Faulkner, and Frost, but I also enjoy Niven, and Heinlein, whose works most English profs would not consider literature. On the other hand I couldn’t stand Hemingway, I think he was a terrible writer, or Burke.
The artsy crowd complains when they have to take a math class or two to get their degree, but they think we are barbarians when we complain about taking lit or theater courses.
I don’t disagree that reading literature is a good things, but I don’t think it hurts a person to take a math class or two.
Hey, I agree with you right down the line there, except for Burke, whose works I never read.
Well, that’s because to many artsy folks, math classes are hard, whereas Art Appreciation 101 is in most places pretty undemanding. Personally I always loved Lit courses (or dropped right away if I had a bad teacher) and usually liked math courses too. I’m firmly in the middle ground here between the technical and the artsy folks.
There is a corollary to the ‘barbarian’ jibe. That’s the one where scientists and mathematicians look down their noses at the folks who deal in the arts as being less intelligent or capable. So, it does kind of go both ways I think.
Actually, I think people are better in “math” than you give them credit for. When described and introduced properly, I find that most everyone grasps the relevant concepts. Problems seem to arise when rigor and precision are demanded (as they must be, of course). Unlike most everything else in school, or in ‘Human Discourse’, there’s no fudging math. No equivocation, no opinion, no arbitrariness, nor BSing is allowed.
That is an important consideration. Witness the furore a few years ago when the physicist, Alan Sokol, submitted an article to the postmodern journal, “Social Text.” The article, entitled,“Transgressing the Boundaries: Toward a Transformative Hermeneutics of Quantum Gravity,” was a farrrago of nonsense that the editors of Social Text were too dim to figure out. Pointy-headed lefty academics use buzzwords and jargon to hide lack of intellectual substance.
In science and math, either your results are reproducible, or they aren’t; no BS’ing allowed.
There are two important aspects of math: one, math is an indispenble tool for solving problems, making wise decisions, and saving money. Two, math has a beuty and elegance that more people should appreciate. I would recommend y’all read, “Journey Through Genius”, by William Dunham. It’s an account of great mathematical discoveries that will make even the most mathphobic person eager to learn more. I would also suggest “Mathematics:From the Birth of Numbers.” It’s an exhaustive collection of every aspect of modern mathematics organized in a user-friendly style, allowing the reader to plunge in anywhere in the book and learn something new. A good math book can be as intellectually rewarding as Shakespeare or Milton.
Another obligatory historian-of-science caveat required here: though I too can’t stand most postmodernist work on “science studies”, it should be noted that the Social Text editors weren’t “dim,” just ignorant of the math and science involved. As you can see from a number of sources at this very exhaustive site, the editors actually did not think much of the parts of the article they could understand, but decided to include it because they figured the scientific aspect might be of interest and they trusted the author to know what he was talking about. Bad call.
To my mind, the implication of this is not so much that the humanities—even modern cultural studies—are intrinsically totally BS’able (after all, no postmodernist editor would accept an article calling Shakespeare a nineteenth-century novelist or Michel Foucault a Hegelian fascist), but that most people in general are extremely BS’able about science. Yes, it’s a shame that a humanities scholar doesn’t know enough basic physics to spot a hoax about gravity, and it’s deplorable that an editor doesn’t get an opinion from a qualified referee before printing an article, but in what way does either of those lapses specifically discredit postmodernist scholarship per se? (I may wish they did—as I say, I don’t care for the stuff myself—but I don’t think they do.)
Oh, please! Are you trying to say there aren’t hoaxes, frauds, misunderstandings, controversies, and all-out wars in science and even math? How do you account for the fact that many reputable mathematicians and editors dispute whether Hsiang and/or Hales should get credit for proving the Kepler conjecture? And the fights in physics, astronomy, etc., about results and their interpretations are too numerous to count, and I’ve seen little hesitation in hurling around accusations of BS in those circles.
I understand what you seem to be thinking (and what KarlGauss expressed) about math and science at the elementary level being more rigorous than non-science subjects, and I agree. You both seem to be drawing the cynical conclusion that students therefore dislike the hard subjects because they prefer to be able to BS instead of reasoning carefully. If you want to look at it that way, fine (although I would prefer the somewhat more nuanced and generous view that people generally feel more comfortable with subjects that they can approach from lots of different perspectives, as opposed to the my-way-or-the-highway rationales of most math instruction). I just don’t think you can support that claim with anecdotes drawn from the professional scholarship level; there’s plenty of room for BS and “buzzwords and jargon hiding lack of intellectual substance” in the research echelons of any discipline, science and math not excepted.
Now, if you want to argue that pomo or cultural studies just happen to be more BS’y than most fields, I won’t argue. But that says nothing about the comparative BS’iness of the sciences versus the humanities in general.
(Oh, and just in case you felt like writing me off as another math-illiterate mushhead, let me note that my current paper is called “Fixed-point iterations and their convergence in medieval Indian astronomy”, so there. Guess I better get back to writing it…)
I haven’t looked at that particular site, but I’ve looked at a lot of the controversy and writings about the incident. To be a little more accurate, the editors claimed that they “did not think much …” after the hoax was revealed. We do not have records of what they thought before the hoax was revealed. There are several possible attitudes they could have had before the hoax was revealed; perhaps they did indeed feel as they claimed, perhaps they thought the article was the greatest thing since sliced bread and planned an entire issue around it, perhaps all sorts of things. The statement they issued after the fact is probably the only thing they could say, whatever the truth may be. If they were indeed taken in big-time, would you expect them to issue a statement to that effect?. Their statements are not proof. I’m not aware of any proof about their attitudes.
Omg! Math! The very word brings fear to my heart. I tried and tried but no matter how hard I studied or got extra tutoring I just couldn’t grasp it. I cried a lot trying to do basic story problems. Luckily my teachers understood how hard it was for me and that I was really, truly making a big effort and I graduated without taking algebra and the like. And I am doing fine in life.
I’m not saying that I can’t do the basics. I can do percentages, fractions and stuff like that. It was the higher learning stuff that got me. Some people just can’t do it.
I’m not sure why you’d really need calculus to understand simple groups, they’re so simple…oh, nevermind…
I’d still like to take a shot. The history of group theory shows that groups have been a central concept of mathematics. Simple groups are associated with the mathematician Galois, who died in a duel at age 20, and the romance of a brilliant but surly revolutionary dying young sometimes appeals to the not-necessarily-mathematical mind.
A group is any set of objects with an operation on those objects such that the operations always result in another of the set of objects. Also, (AB)C must be the same thing as A(BC), and one object in the group must be the identity, such that multiplication by it leaves any member of the group unchanged, and every member must have an inverse, so that any object times its inverse is the identity. That’s it. These requirements are vaguely familiar, right? From ordinary arithmetic?
These don’t look like imposing requirements, but groups are still a very powerful concept. I’ll barely begin to try to show how powerful. An elementary group is this one associated with flipping a coin: it has two objects: A, leave the coin alone; and B, flip it over. In this case, our “multiplication” just means “followed by”. A is our identity in this group, and B is its own inverse: BB = A. Whether we start with a heads or a tails on the coin, AA = AAA but BB does not equal BBB. This is one of the least complex groups–but it is not what we mean by “simple.” There is one group that is even less complex–and that would be the element A by itself. Every multiplication (AAAA*A…) equals A, A is the identity, A is its own inverse…not very interesting.
A simple group is a group which has noproper normal subgroups. A subgroup is just a subset of the group that is a group in its own right–like the element A above, except that it is not a proper subgroup. A proper subgroup must have more than one element, but it can’t have as many elements as the group of which it is a subgroup. Obviously, that two-element group that I described above has no proper subgroups, so it cannot possibly be a simple group.
What does normal subgroup mean? Normal subgroups are sometimes called invariant subgroups. If you take any element of the subgroup and multiply on the left by any element of the big group and by that element’s inverse on the right, and you still get an element of the subgroup–then the subgroup is invariant, or normal. If a group has no invariant subgroups, then it is a simple group. Galois showed that the smallest simple group has 60 elements–and certain types of groups are always simple. He used this fact to show that no equation of order five or higher could be solved by radicals–which had been a very famous problem in those pre-computer days. He died kinda young, before most of us learn calculus.
Took my Math final today. I’m in Pre-Cal…wait, WAS in Pre-Cal. Anyway, I bombed it. Badly. I’ll be lucky to get better then a C in that class. Why? Because I simple couldn’t remember what to do. I studied, we were even allowed a small cheat sheet. And I just couldn’t remember the process. It’s like when a word or name is on the tip of your tounge, but it just won’t come out! No matter how hard you think!
Despite of all of this, I am moving on to Calculas next year. I think I’m gonna start praying for some kind of Divine Intervention so I might pass that class.I’m sure God has better things to do, but one never knows until ones tries, right?
I was another student who excelled in the humanities instead of the mathematics. I can balance a check book, figure out percents pretty easily, and I can even subtract well enough to figure out who’s going to end up without a cookie after lunch (usually me, with 3 kids in the house).
I love to read everything I can get my hands on, Heinlein, Shakespeare, Rice, King, Steele… I was also good in the different sciences in high school, although don’t ask how I managed that with how bad I am at math, I haven’t got a clue! English lit. was my absolute favorite class in high school, and I was even the county spelling champ my 8th grade year.
I don’t say that I’m proud of being mathless, but I don’t look down on people who don’t spell as well as I do or understand Shakespeare in the original text. There are a lot of tough subjects in this world. Some I have down pretty well. On the others, I punt.
Certainly some people find some classes tougher than others. But math really is no tougher than English or History.
The problem with math, as was pointed out earlier in the thread, is that it is the one subject that has as a foundation, every math class you’ve ever taken. You break the chain anywhere in the process and you no longer have the basics needed for other classes.
And no other class has this level of dependency. American History requires no knowledge of the French Revolution. I can read Heinlein without first having to understand Chaucer. A geography class requires that you can identify the Rocky mountains, not the science to understand how the mountains were made.
I don’t blame those that claim to be “mathematically challenged”. In truth, they missed a building block somewhere along the way or failed to use the math that they learned enough to retain it into future classes.
Another misconception is the link between mathematics and science – particularly physics. Math is but a tool of the sciences. It’s entirely possible to have a reasonable understanding of the science without understanding its tools.
To Pepperlandgirl, I would suggest that you not delve into calculus until you have a good grasp on pre-calc. Trust me on this one.
SouthernStyle
: I know a Lincoln scholar who is amazingly erudite
: in history and the liberal arts, yet he had never
: heard of the concept of limits(this came up when I
: mentioned Zeno’s paradox in a philosophy discussion.)
It does not really surprise me to find people with liberal arts educations who don’t understand much math, having met many myself. My direct experience is now somewhat dated, but having taken both liberal arts classes and a boatload of mathematics at university, there is little comparison, IMHO. I found that there were single pages of math texts in some of the more esoteric classes which required more thought to understand than entire books in the liberal arts classes. In most math classes it is also difficult to cover up a lack of understanding.
: How is it possible for someone to graduate from
: university in the US without at least a basic grounding
: in elementary mathematics?
I wonder about this as well. I am of mixed opinion on the subject. Often, I cannot imagine going through life without at least a basic grasp of algebra, calculus, trig, and other similarly useful mathematical tools. In those moments I tend to hold the opinion that there is precious little one can really understand about the world without some grasp of math. The basics of a really large number of disciplines, from medicine to economics to materials engineering to circuit design depend on math. Not only that, but much of the day to day things my liberal arts friends are curious about, they could understand much better with just a little elementary math or physics.
But in other moments, I think perhaps it isn’t so important after all. I’m looking at it through the eyes of an engineer; we naturally want to understand how and why things work, which requires math. Most people don’t care or even need to know. If you goal is to get in your car and drive to work, knowing enough calculus to understand the various physics involved is not required. If you are not designing bridges or electronic circuits, then simple arithmetic serves quite adequately for virtually every task that life requires.
At yet other moments, I think that our culture is perhaps a bit too tolerant of underachieving, and that if people had at least a basic knowledge of math, physics, just how the world is “hooked up”, then many fewer people would fall prey to various scams, pseudoscientific fads, and so on.
I probably won’t be able to check in often enough to participate in this discussion, but there are a few other related thoughts I’ll put in a subsequent post.
Guess I better get back to writing it…)