Any adult in today's world is at a serious disadvantage is they don't grasp basic prob/stat principles. Anyone that grew up a sports fan has to have developed an appreciation of statistics.
Should college students be forced to take calculus to graduate.
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I recall using the Pythagorean theorem twice in my life. Once when I was building a shed and wanted to make the walls square and also when I was laying out the island in the kitchen that had two sections at a right angle to each other with a stove in between them, and I wanted that square also. I do not believe I have calculated the square root of anything in my life. Parallel parking turned out to be pretty useful, but I have watched a whole lot of people who never mastered that. And if Saint Peter starts my entrance exam into heaven with 'if a train leaves New York at 55 mph and another leaves Chicago at 45 mph," I am just going to jump head first into the chute that goes straight to hell because I have not got that question right yet in my life.Euclidean geometry (the way they used to teach it when I took it in high school - with rigorous proofs starting from a few definitions and clearly stated axioms) was meant to teach students how to think. Most graduates rarely used the Pythagorean theorem, but they knew where it came from and, more importantly, how to use logical deduction. Learning to think logically is difficult, but well worth the effort. Legend has it that the following was inscribed above the entrance to Plato's Academy:
"Let no one ignorant of geometry enter"
You asked a general question but applied it to your son majoring in Marketing. Your son needs to study calculus. Lots of reasons above and I'll give a few more. Many things are based on the calculus and it's not possible to truly understand them without understanding the calculus. Statistics, economic models, forecasting, etc are all based on the calculus.
You may be able to use these "tools" without truly understanding but that would never be satisfactory.
BTW: Calculus for business students rarely involves trigonometry so it's not very difficult.
BTH: Big Time Hint: The derivative is the "instantaneous change" of something, something being what's changing. Think velocity changing while you're pushing on the accelerator (gas pedal) of your car. ...what happens is that the velocity changes and that's called acceleration. Understand this and you'll understand Calc I. Thank me later.
You may be able to use these "tools" without truly understanding but that would never be satisfactory.
BTW: Calculus for business students rarely involves trigonometry so it's not very difficult.
BTH: Big Time Hint: The derivative is the "instantaneous change" of something, something being what's changing. Think velocity changing while you're pushing on the accelerator (gas pedal) of your car. ...what happens is that the velocity changes and that's called acceleration. Understand this and you'll understand Calc I. Thank me later.
You're right most do------1 semester of Calculus and 1 semester of Statistics are mandatory for all incoming Freshman at ND.
Sweet Jeebus -35 years later those two words still give me the shakes. Along with Fourier Analysis.
I'm going through the same thing with my son. I am an engineer and loved math. I graduated from PSU in '86. Back then, the highest level required in the major was differential equations.
I have worked in several different industries and have never used any type of math above the algebra level. I have needed lots of statistics, but even then, very basic statistics.
I have also wondered about the value of taking all the higher level math classes. I'd think students would get more value of going more in depth in their major.
Take graduate level thermodynamics if you want torture. You have to be able to eat, sleep, and breath differential equations. But after that I never had any trouble explaining basic thermodynamics to first year chem students.
We did have one prof who expected all chem students (including freshmen) to be able to derive the Schrodinger equation.
I did see an article somewhere recently where there was a complaint that calculus and chemistry were "unfair" as they prevented people from getting high paying STEM jobs. I was flabbergasted. It's like saying I want a drivers license because I can operate a Big Wheel. You have to have this stuff to do the work.
You man never use the math in everyday life, but it gives you a much deeper understanding of the topics that use it. Like my thermodynamics example. I don't think I ever used that math again in my life. But I really understood thermodynamics after that at a much deeper level.
The class at PSU that really ticked me off (one of my few "C"s) was the combined matrix algebra/stats course. The prof got behind and only gave us a week of stats. The final had a lot of statistics question. This was in the day when the TI calculator that could do standard deviations had just come out. Those who had them passed the exam. Those who didn't, did not--and he did not grade on the curve. I finally learned how to do basic stats from a TI instruction book two years later.
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I think calculus helps you develop a logical thought process. It reinforces that process so you can get through other issues using a logical thought process rather than some emotional process. JMO!
As someone who started at PSU as a math major, I wouldn't consider Calculus higher level math. The Calculus class that I took my first semester was the same as what I took in high school. When I got to real higher level math classes, I realized that I had to change my major!
As far as the argument that students shouldn't have to take it because they won't use it in life, then I would ask what classes do they need to take? I didn't learn much in any classroom (undergrad or grad) that I use regularly.
As far as the argument that students shouldn't have to take it because they won't use it in life, then I would ask what classes do they need to take? I didn't learn much in any classroom (undergrad or grad) that I use regularly.
Because of his major? Or does the college require calculus for all students?
The biggest problem for students taking calculus is, in my opinion, that you have to study it in a different way than your other classes. Getting used to reading the textbook is a challenge, for one thing. Generally speaking, if you spend 90% of your time doing the problems, you’re golden.
I have used it in my work but not often. Algebra is something that is used the most. I have never used theater, creative writing or fly tying in my career. I have used them in my life in some way. If we just want what we need to do a job, college would take no more than two years. For some majors less. I am an engineer but really like art, cannot spell for shit and think most of may knowledge is what god gave me. I have the knack - I have never posted videos but there is a Dilbert clip on this.
I took Architectural Engineering (maybe 20 classes devoted to the field) and much of what I learned in them help me in my work. The rest was just fluff.
I took Architectural Engineering (maybe 20 classes devoted to the field) and much of what I learned in them help me in my work. The rest was just fluff.
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wow, Fourier Series, modeling everything as a sine or cosine function. I got A's in every math class i ever took. Just came natural to me. Math 140, Math 141, Math 220, breezed right through them. Math 251 was hard but still was getting an A until the last couple of weeks when Fourier Series was taught. First time in my entire life that I could not really understand the math. Teacher was really hard as i took it at Penn State York over the summer (all my friends took up at main campus next semester and I tutored them all and they got A's and it was not anywhere near as difficult as that PSU York professor). I remember it was only one test (the last test of the course as he didn't have a final) and I had a decision to make, either I had to study 4 hours per day every day for a week before the test to keep my A and really try to understand, or just study enough to pass the test and recognize my streak of A's in math was coming to a close. I got a B+ in the course.
So, this thread has devolved bit....so let me add to it..
1. Yes, take calculus. Because only taking classes. you need will not help you advance in your career or in life. Challenge yourself academically and you will find you can take on challenges professionally. By and large, the individuals with more professional success are those who are challenged academically as students. There are always exceptions, but they are just that - exceptions.
2. College is not a job placement program. You want a guarantee of a job doing what you want to do after you finish coursework?....then go to PennCoTech and become a welder. The world needs welders also.
3. Story time - I worked for a manager who took one of the "soft sciences". She started with the company when it was a start up (she was still in college) and grew with them - good for her. We butted heads a number of times because I am, based on my academic background (which included calculus), a trained problem solver. I look at constants and variables and I figure out a solution to achieve a final goal. Her academic background did not offer her that training. She had to take on managing another office, which left me without her oversight and limitations, and that was exactly what I needed - I was able to work through problems for the client and provide solutions which resulted in the successful solving of problems for the clients. So much so that they rewarded me with some awards (they did this as a matter of practice to their consultants on an annual basis). And this was after 1 1/2 years of dealing with my manager. During the awards ceremony, my manager sat silent and red faced - much to my enjoyment. Fast forward over 20 years and when I run into her at professional meetings, she is still red faced and irritated - again, to my enjoyment.
All of that because I took on academic challenges and then was able to take on professional challenges.
4. Regarding things you learn in college vs. out in the job. As someone told me when I was lamenting the same issue - "You are correct - your employer will teach you want they want and you may not use what you learned in college.. But, guess what - you are not working yet. You are in college, and your responsibility is to learn what is front of you. So do it". Looking at college as a ratio of what you learn to what you will use is a myopic way to look at things.
5. I attended Penn State in the mid 80s. I have forgotten more stuff than I remember - or so I thought. Recently, I was perusing some information for taking a private pilot's exam and in review of some documents, which discussed air pressure, some basic physics of flight, etc, a lot of stuff I learned in physics and math classes so many years ago came back to me. So, the stuff you learn is in there - it just needs to have a reason to come back out.
1. Yes, take calculus. Because only taking classes. you need will not help you advance in your career or in life. Challenge yourself academically and you will find you can take on challenges professionally. By and large, the individuals with more professional success are those who are challenged academically as students. There are always exceptions, but they are just that - exceptions.
2. College is not a job placement program. You want a guarantee of a job doing what you want to do after you finish coursework?....then go to PennCoTech and become a welder. The world needs welders also.
3. Story time - I worked for a manager who took one of the "soft sciences". She started with the company when it was a start up (she was still in college) and grew with them - good for her. We butted heads a number of times because I am, based on my academic background (which included calculus), a trained problem solver. I look at constants and variables and I figure out a solution to achieve a final goal. Her academic background did not offer her that training. She had to take on managing another office, which left me without her oversight and limitations, and that was exactly what I needed - I was able to work through problems for the client and provide solutions which resulted in the successful solving of problems for the clients. So much so that they rewarded me with some awards (they did this as a matter of practice to their consultants on an annual basis). And this was after 1 1/2 years of dealing with my manager. During the awards ceremony, my manager sat silent and red faced - much to my enjoyment. Fast forward over 20 years and when I run into her at professional meetings, she is still red faced and irritated - again, to my enjoyment.
All of that because I took on academic challenges and then was able to take on professional challenges.
4. Regarding things you learn in college vs. out in the job. As someone told me when I was lamenting the same issue - "You are correct - your employer will teach you want they want and you may not use what you learned in college.. But, guess what - you are not working yet. You are in college, and your responsibility is to learn what is front of you. So do it". Looking at college as a ratio of what you learn to what you will use is a myopic way to look at things.
5. I attended Penn State in the mid 80s. I have forgotten more stuff than I remember - or so I thought. Recently, I was perusing some information for taking a private pilot's exam and in review of some documents, which discussed air pressure, some basic physics of flight, etc, a lot of stuff I learned in physics and math classes so many years ago came back to me. So, the stuff you learn is in there - it just needs to have a reason to come back out.
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Board irony:
Board name - Cletus (immediately a toothless hill jack with overalls and an Ohio State baseball cap comes to mind)
Educational background - math wizard
Funny, I knew a cletus in law school who was brilliant as well and thought the same thing.Board irony:
Board name - Cletus (immediately a toothless hill jack with overalls and an Ohio State baseball cap comes to mind)
Educational background - math wizard
best was college roommate who had a friend in Hanover named buck, who was dubbed “buck the dumb ****”.
So out of the 40 or so classes you took in college, a history professor’s skepticism and one paper stick out? Given your posts over on the test board, many would argue that you don’t understand those issues today but that’s another topic.
Since you work in the field of your major, those classes are helpful, but the vast majority of graduates end up in a career unrelated to their major. So all of those classes essentially become electives as well.
Tell him to take the class, get a good grade, and move on. It’s the same process that everyone goes through
No.....but they should be forced to take it and get a B or higher before they can play football for Ohio State.
The person they paid to take the class for them should get a B or higher before they can play football for Ohio State.
Fixed it for you. You are welcome.
As far as Math goes today watch the kids at the register when they have to make change when the register doesn't tell them what they should give you back or you decide to give extra to avoid a pile of coins - it's painful.
My son went through ND a few years ago. I don't remember him taking any math while there as a Marketing major. Maybe a stats course, but that's it.
Yes if you are in a program that has a need for it like STEM, business, education and no for arts and the like.
I was a freshman at Mont Alto in 82 and took calculus. The professor was a devout Christian. His lectures would draw analogies between calculus and the Bible. For the final he told us that if you don't know the answer to not give up. Pray for help. Then he wrote Seek and ye shall find on the chalkboard. We later found out that he was at UP and no one would sign up for his class so they mover him to Mont Alto.
Obviously, I had to retake it. This time the professor was from India. Great guy. Mathematical genius. On the downside he didn't prepare for exams. On the final he winged a question about a plane flight. The answer ended up being a negative number so most changed their calculations and got it wrong.
I was a freshman at Mont Alto in 82 and took calculus. The professor was a devout Christian. His lectures would draw analogies between calculus and the Bible. For the final he told us that if you don't know the answer to not give up. Pray for help. Then he wrote Seek and ye shall find on the chalkboard. We later found out that he was at UP and no one would sign up for his class so they mover him to Mont Alto.
Obviously, I had to retake it. This time the professor was from India. Great guy. Mathematical genius. On the downside he didn't prepare for exams. On the final he winged a question about a plane flight. The answer ended up being a negative number so most changed their calculations and got it wrong.
Yeah, ND used to require calculus but that changed about a decade ago. I tried to figure out exactly what is now required but it seems that only a QR course is required. That’s fine.
I agree with a couple of the earlier post regarding proof based geometry. Students that I have worked with who come from systems still using it for extended periods of time in their geometry classes always tend to be better analytical thinkers and able to process better than those who studied a geometry that is more based on shapeshifting and volumes and such.
I'm also amazed at some people agreeing about the need for statistics for everyone. Especially since if my AP Statistics students reported their data the way that media reports it most of the time they would get ones on their exam but these poster swear the media doesn't lean one way
I'm also amazed at some people agreeing about the need for statistics for everyone. Especially since if my AP Statistics students reported their data the way that media reports it most of the time they would get ones on their exam but these poster swear the media doesn't lean one way
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I don’t care for it to be a requirement, but it certainly helps many challenge themselves. Like many college subjects there are two levels of attainment: knowing what it takes to pass it, and developing an understanding of it. For those that only strive for the first, it’s useless.
I would prefer that universities stress these things:
1. How to think critically. This would include both understanding logical constructs as well as knowing what actually answers a question.
2. How to optimize in general. Calculus at the understanding level of attainment helps facilitate this one. So much in life can be made better if people could free up their time, money, etc. I’m made fun of for doing this stuff in everyday life, but I wear that as a badge of honor.
Combined these should help with what I encounter way too much in the professional world: people lose sight of what they’re actually trying to solve and why. I work (figuratively in 2020) side by side with 50 PhD level Decision Scientists, with majors of engineering, comp sci, physics, math and econ. 80% of them have no idea how their work fits into the entire digital ad serving and performance measurement system we have built. Truth is, that’s a manager/exec’s fault, but there’s a lack of ownership at the scientist level as well. But the good news for them is they have tangible projects that they can write into their reviews and score well. Too bad they’re the pieces to somebody else’s puzzle.
For reference my degrees are BS Econ, MA Econ, and MS Stats. Never did get around to finish the MS Operations Research.
I would prefer that universities stress these things:
1. How to think critically. This would include both understanding logical constructs as well as knowing what actually answers a question.
2. How to optimize in general. Calculus at the understanding level of attainment helps facilitate this one. So much in life can be made better if people could free up their time, money, etc. I’m made fun of for doing this stuff in everyday life, but I wear that as a badge of honor.
Combined these should help with what I encounter way too much in the professional world: people lose sight of what they’re actually trying to solve and why. I work (figuratively in 2020) side by side with 50 PhD level Decision Scientists, with majors of engineering, comp sci, physics, math and econ. 80% of them have no idea how their work fits into the entire digital ad serving and performance measurement system we have built. Truth is, that’s a manager/exec’s fault, but there’s a lack of ownership at the scientist level as well. But the good news for them is they have tangible projects that they can write into their reviews and score well. Too bad they’re the pieces to somebody else’s puzzle.
For reference my degrees are BS Econ, MA Econ, and MS Stats. Never did get around to finish the MS Operations Research.
I struggled big time as a freshman with calculus. Never really had a clue what I was doing and, having spent a career in a non-technical field, I've had no use for calculus itself. However, i took Statistics as a grad student and considered it then very real-world and have applied Stat principles many times in everyday work since. Just understanding how to examine and question statistics is very useful in everyday life. If you're not an engineer or a scientist, I don't see why calculus should be a requirement. I do believe Statistics should be a high school or undergrad requirement.
Our current times have confirmed in my mind that Americans receive very poor education in civics and in scientific process. Much more important to the average citizen than calc.
Our current times have confirmed in my mind that Americans receive very poor education in civics and in scientific process. Much more important to the average citizen than calc.
Calculus is useful for understanding finances too, even if you are just investing on your own. It helps you optimize risk return portfolios and also fixed income and futures when looking at duration and convexity. MS in finance here and we touched on derivatives, but it was not stressed heavily. Stats and algebra ruled the day. The calculus is left for the PhD quants, who oftentimes have degrees in something like physics.
but really, all math is, is your ability to read and understand. if you can't do math you can't really read and comprehend.No, it should not be required. The emphasis on math as opposed to English and writing is ridiculous in my opinion....of course, I was not a big fan of math and was very strong in English and writing.
If it's relevant to their major and career track then yes. If not, then no. I'm opposed to forcing students to take courses that aren't directly part of their area of study. Eliminating this requirement is one way that students could shave a semester or 2 off of their time in college and help to reduce the amount of debt they carry when they graduate. I completely "mailed it in" in all of my general elective courses, I got almost nothing out of them. I still did enough to get decent grades but I had no interest in the subject matter whatsoever.
Both of you used the idea of optimizing or optimization. Related rates and optimization are my two favorite units to teach in calculus and yet every year AP makes those two units less and less of a priority on the exam. After the exam I always come back with the underclassmen and we do more examples for optimization since it definitely leads to engineering principles.
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If you are in a major that is science or math-focused, then yes. It's about problem-solving skill in general, not necessarily about specific problems to solve. If you are not in a math or science major, it's ridiculous to make people take calculus. I can see a watered-down calculus being required ("business" calculus, which always gives me a chuckle) if the jobs you are training for involve problem-solving. But even then it's a mild stretch I think.
OMG! Thank you. I finally understand calculus. But now I've got a question. Before I press the gas pedal in my car, my acceleration is zero. As I press the gas pedal I know my velocity increases, but it must also be true that my acceleration is changing, too. So, what is the one word that describes the instantaneous rate of change in acceleration?
