Finally...

[allegansveritatem]

II started going through a textbook written by Dr Earl Swokowski titled "Precalculus" in March of 2019.. It is a book written or at at least revised and published (for the ninth time) in the early years of the present millennium. A dry book. Anyway, I have just finished the last exercise of the last set of exercises of the last chapter and so, done at last! I started this math stuff 4 or 5 years ago with algebra. Two hours a day for 7/24/365, Not bad for an old man (70's) I guess. I have been thinking of going on and trying calculus (101). Am I too old a dog? Don't know. I suppose I will try after all and if interest falls down and can't get back up I will look for something else to play with...maybe I will take up electric motorcycling! I want to thank all the people here who have helped me with various problems along the way. I have learned from them, among many other things, that there are apter (?) minds by far than mine for this subject (or vast set of subjects) out there and thank God for that!

 

[JeffM]

Congratulations and well done.

I would not dare give you advice on what path to take for further intellectual adventures because that is so much a matter of personal taste. I find history far less dry than calculus.

I’ll make three more purely personal observations about calculus.

The way it is currently taught goes in a logical order, but it was developed and used for almost two hundred years before it was logically justified. If Newton and Leibniz could not provide a logically sound basis for calculus, that means the logical underpinnings are hard to grasp. Virtually all the hard work in calculus is crammed into one or two chapters, one of which is the very first. I am convinced that someday an intuitive but logically rigorous approach to calculus will be developed. Some people find non-standard analysis more intuitive than the way I learned it. (I learned standard analysis, which I think is unbelievably ugly).

As a practical tool, calculus is far less applicable to day-to-day life than algebra, geometry, and trigonometry unless you are an engineer, physical scientist, or theoretical economist. In a long career in banking, I never needed to apply calculus to any business problem.

From a purely intuitive basis, what calculus is about are two questions. When does what seems to be zero divided by zero have a determinate answer, and when does what seems to be a sum with an infinite number of terms have a finite answer. (The last question goes all the way back to Zeno).

 

[Cubist]

I agree with with JeffM, congratulations and well done!

I hope you find your next challenge(s) enjoyable. Note that maths isn't mutually exclusive with electric motorcycling ?️ I just typed bike into the emoji search and was presented with pictures of bikes AND a bikini. For a moment I thought I was on the wrong website ?

There will always be people who are more clever/ talented/ faster etc, but don't let that stop you from doing something that you enjoy or would like to reach a certain level at. There aren't many people who reach the levels of Einstein, Stephen Hawking, Usain Bolt, Jomo, Subhotosh Khan, etc ?

 

[jonah2.0]

Beer induced ramblings follow.

II started going through a textbook written by Dr Earl Swokowski titled "Precalculus" in March of 2019.. It is a book written or at at least revised and published (for the ninth time) in the early years of the present millennium. A dry book. Anyway, I have just finished the last exercise of the last set of exercises of the last chapter and so, done at last! I started this math stuff 4 or 5 years ago with algebra. Two hours a day for 7/24/365, Not bad for an old man (70's) I guess. I have been thinking of going on and trying calculus (101). Am I too old a dog? Don't know. I suppose I will try after all and if interest falls down and can't get back up I will look for something else to play with...maybe I will take up electric motorcycling! I want to thank all the people here who have helped me with various problems along the way. I have learned from them, among many other things, that there are apter (?) minds by far than mine for this subject (or vast set of subjects) out there and thank God for that!

I say stick to math as a hobby and keep away from such dangerous activities like electric motorcycling especially when you're already in your 70's. Avoiding chronic pain from injuries in your 70's is something that should be prioritized. Hiking and light weightlifting or calisthenic exercises are preferable to playing with potential disasters.

Take a page from a member here who's now in his 80's. A former teacher, he started his hobby sometime back in 2011.

rayroshi said:
... Any help would be much appreciated, as I'm eighty-years-old and am trying to learn calculus by myself, a task that would be nearly impossible, if it weren't for the internet and lots of good books...which isn't really 'by myself,' I guess.

 

[Deleted member 4993]

dangerous activities like electric motorcycling especially when you're already in your 70's

I was just planning to do that. Riding pedal-bi-cycle has become a torture for my knees.

Would you think riding around in the neighborhood park would be dangerous? I am 72.

 

[JeffM]

I was just planning to do that. Riding pedal-bi-cycle is become a torture for my knees.

Would you think riding around in the neighborhood park would be dangerous? I am 72.

I am 76. My wife says even looking at young women is quite hazardous to my health. Who knows what she might say if I started looking a motorcycles dressed (semi-dressed?) in bikinis?

 

[LCKurtz]

Start up a relationship with an airplane. It's exciting. And airplanes don't care if you look at other airplanes or read airplane magazines.

 

[jonah2.0]

Beer induced ramblings and filibuster follows.

I was just planning to do that. Riding pedal-bi-cycle has become a torture for my knees.

Would you think riding around in the neighborhood park would be dangerous? I am 72.

I gave up riding pedal-bi-cycle for the same reason.
I just do knee bends and the leg extension machine for my knees.
Maybe we should be asking for Mark's (mmm4444bot) views as he's more or less involved in the medical profession.

Thinking a little more about it, I realized that maybe allegansveritatem was referring more to electric bicycling. The kind where one doesn't have to pedal at all or the other hybrid kind where one's pedalling is assisted by an electric motor once a sensor detects the pedalling effort of a cyclist like the one described in the following link.
www.youtube.com/watch?v=AtxZcNYo3wk
Electric pedal assisted or not, senior citizens are always at risk from an accidental fall. A senior falling from a standing position either while walking or from an accidental slip or imbalance could lead to some serious pain. An accidental fall while riding a bicycle (pedal powered or electric pedal assisted) will definitely result to painful and debilitating fractures (if you're really unlucky, translation: chronic pain) or instant death (if you're lucky, i.e., a painless exit - I speak from experience as I experienced total blackout when I was just a boy and had a concussion when I got reckless while riding my bicycle . I didn't remember any kind of pain whatsoever when I regained consciousness. Death or blackout - the brain's way of protection from overwhelming pain. I experienced the same phenomenon again when I was in my mid 20s and was suffering from asthma while going through a fever. I must have had some kind of a temporary severe oxygen deprivation and blacked out while having the worst asthma attack ever while I was in the bathroom all alone. "Woke" up lying on the cold floor several hours later marveling why I'm on the floor and wondering if it might have been better I didn't regain consciousness at all. So yes, lucky is a term I'd use for instant death.) To minimize any major injuries, perhaps an electric pedal assisted quadricycle might be a good alternative like in the following links.
www.youtube.com/watch?v=037CAW4Yeug
www.youtube.com/watch?v=YLMo0ouNTtU
www.youtube.com/watch?v=QH_Cb8YfTYA
This is of course for just riding around in the neighborhood park purposes.
Riding these things to buy one's groceries might be dangerous as it will involve sharing the road with cars, unless of course you're living in the bicycle friendly city of Amsterdam.

 

[Steven G]

I agree with with JeffM, congratulations and well done!

I hope you find your next challenge(s) enjoyable. Note that maths isn't mutually exclusive with electric motorcycling ?️ I just typed bike into the emoji search and was presented with pictures of bikes AND a bikini. For a moment I thought I was on the wrong website ?

There will always be people who are more clever/ talented/ faster etc, but don't let that stop you from doing something that you enjoy or would like to reach a certain level at. There aren't many people who reach the levels of Einstein, Stephen Hawking, Usain Bolt, Jomo, Subhotosh Khan, etc ?

Wow!

 

[Cubist]

Wow!

Of course everyone who helps out here is great! However, I think that yourself and Subhotosh are particularly good at including some banter!

Beer induced ramblings and filibuster follows.

...

Terrible experiences. I'm very glad that you're still with us! (And I bet the breweries are too ). I guess that everyone has their own acceptable risk levels, based on their personality and life experiences. It's certainly wise to be cautious if you're on the roads given that some car and van drivers don't seem very aware of their surroundings!

 

[allegansveritatem]

Congratulations and well done.

I would not dare give you advice on what path to take for further intellectual adventures because that is so much a matter of personal taste. I find history far less dry than calculus.

I’ll make three more purely personal observations about calculus.

The way it is currently taught goes in a logical order, but it was developed and used for almost two hundred years before it was logically justified. If Newton and Leibniz could not provide a logically sound basis for calculus, that means the logical underpinnings are hard to grasp. Virtually all the hard work in calculus is crammed into one or two chapters, one of which is the very first. I am convinced that someday an intuitive but logically rigorous approach to calculus will be developed. Some people find non-standard analysis more intuitive than the way I learned it. (I learned standard analysis, which I think is unbelievably ugly).

As a practical tool, calculus is far less applicable to day-to-day life than algebra, geometry, and trigonometry unless you are an engineer, physical scientist, or theoretical economist. In a long career in banking, I never needed to apply calculus to any business problem.

From a purely intuitive basis, what calculus is about are two questions. When does what seems to be zero divided by zero have a determinate answer, and when does what seems to be a sum with an infinite number of terms have a finite answer. (The last question goes all the way back to Zeno).

I have watched a number of YT videos whose titles profess that they teach calculus in 10 minutes! I'm not quite sure they fulfilled the promise but I got some ideas from them. I don't expect ever to use any of the math I have learned these last 5 years for anything, at least not for anything except solving the exercises at the back of each section. Maybe that is enough. At any rate, I don't intend to make a do or die commitment with this subject. I will do as long as I DON'T die--from boredom or some other similar psychomalady with no name. Who knows...I may even like the stuff! Thank you so much for your analysis of the development of the subject. When I was in school many decades ago I had an intuitive grasp of one fact: the "unbelievably ugly" prospect of spending another semester or two chewing on the huge calculus text I flipped through one day and refused to take the course. I took typing instead--and of course I have gotten 100 times the use out of it I would have gotten from the calculus...or did I? Oh why oh why can't anything be cut and dry?

 

[allegansveritatem]

I agree with with JeffM, congratulations and well done!

I hope you find your next challenge(s) enjoyable. Note that maths isn't mutually exclusive with electric motorcycling ?️ I just typed bike into the emoji search and was presented with pictures of bikes AND a bikini. For a moment I thought I was on the wrong website ?

There will always be people who are more clever/ talented/ faster etc, but don't let that stop you from doing something that you enjoy or would like to reach a certain level at. There aren't many people who reach the levels of Einstein, Stephen Hawking, Usain Bolt, Jomo, Subhotosh Khan, etc ?

I have noticed that a lot of older males buy motorcycles and then swoop around on them with their grey locks flying who seem to have in mind making a dashing impression on the "bikini" crowd. Carrying fatuity to that level is beyond me at this point...

 

[allegansveritatem]

Beer induced ramblings follow.

I say stick to math as a hobby and keep away from such dangerous activities like electric motorcycling especially when you're already in your 70's. Avoiding chronic pain from injuries in your 70's is something that should be prioritized. Hiking and light weightlifting or calisthenic exercises are preferable to playing with potential disasters.

Take a page from a member here who's now in his 80's. A former teacher, he started his hobby sometime back in 2011.

rayroshi said:
... Any help would be much appreciated, as I'm eighty-years-old and am trying to learn calculus by myself, a task that would be nearly impossible, if it weren't for the internet and lots of good books...which isn't really 'by myself,' I guess.

I hear you. I have been riding light motorcycles for the last 5 or six years and have fallen off--at low speeds--a number of times. I wear gear so only once was I injured to the point that laid me up. Twisted ankle. Took a month to heal. Yes. That is why I was thinking electric. I have an electric car and have become seriously aware of how much more it costs me to drive fast than to drive slow and how much less range I get the faster I go...so I would be counting on this knowledge to hold me down to a sane rate of speed on my electric cycle.
Thanks for the quote from rayroshi--I can relate.

 

[allegansveritatem]

I was just planning to do that. Riding pedal-bi-cycle has become a torture for my knees.

Would you think riding around in the neighborhood park would be dangerous? I am 72.

I think you would be very happy with an ebike. I have ridden them. They absolutely take all the pain out of the experience of bicycle travel.

 

[allegansveritatem]

Beer induced ramblings and filibuster follows.

I gave up riding pedal-bi-cycle for the same reason.
I just do knee bends and the leg extension machine for my knees.
Maybe we should be asking for Mark's (mmm4444bot) views as he's more or less involved in the medical profession.

Thinking a little more about it, I realized that maybe allegansveritatem was referring more to electric bicycling. The kind where one doesn't have to pedal at all or the other hybrid kind where one's pedalling is assisted by an electric motor once a sensor detects the pedalling effort of a cyclist like the one described in the following link.
www.youtube.com/watch?v=AtxZcNYo3wk
Electric pedal assisted or not, senior citizens are always at risk from an accidental fall. A senior falling from a standing position either while walking or from an accidental slip or imbalance could lead to some serious pain. An accidental fall while riding a bicycle (pedal powered or electric pedal assisted) will definitely result to painful and debilitating fractures (if you're really unlucky, translation: chronic pain) or instant death (if you're lucky, i.e., a painless exit - I speak from experience as I experienced total blackout when I was just a boy and had a concussion when I got reckless while riding my bicycle . I didn't remember any kind of pain whatsoever when I regained consciousness. Death or blackout - the brain's way of protection from overwhelming pain. I experienced the same phenomenon again when I was in my mid 20s and was suffering from asthma while going through a fever. I must have had some kind of a temporary severe oxygen deprivation and blacked out while having the worst asthma attack ever while I was in the bathroom all alone. "Woke" up lying on the cold floor several hours later marveling why I'm on the floor and wondering if it might have been better I didn't regain consciousness at all. So yes, lucky is a term I'd use for instant death.) To minimize any major injuries, perhaps an electric pedal assisted quadricycle might be a good alternative like in the following links.
www.youtube.com/watch?v=037CAW4Yeug
www.youtube.com/watch?v=YLMo0ouNTtU
www.youtube.com/watch?v=QH_Cb8YfTYA
This is of course for just riding around in the neighborhood park purposes.
Riding these things to buy one's groceries might be dangerous as it will involve sharing the road with cars, unless of course you're living in the bicycle friendly city of Amsterdam.

" "Woke" up lying on the cold floor several hours later marveling why I'm on the floor and wondering if it might have been better I didn't regain consciousness at all." The older I get the more devoutly I wish for such an end.

 

[LCKurtz]

I rode a motorcycle to work at the university for years. Towards retirement I decided to quit while I'm ahead. So I put a bike rack on my car and drove into a university parking lot to ride a bike in from there. Best of both worlds. Easy and safe transportation to the university followed by a quick bike ride instead of a long walk to my office from the parking lot. However I found that riding my bike through the parking lot was very hazardous because of all the students zipping in and out of the rows of cars looking for parking spots and not for some old guy trying to survive on a bike. Made it though, and now I ride neither a bike nor a motorcycle. Did have a chance to drive a jet-ski for the first time this summer though.

 

[allegansveritatem]

I rode a motorcycle to work at the university for years. Towards retirement I decided to quit while I'm ahead. So I put a bike rack on my car and drove into a university parking lot to ride a bike in from there. Best of both worlds. Easy and safe transportation to the university followed by a quick bike ride instead of a long walk to my office from the parking lot. However I found that riding my bike through the parking lot was very hazardous because of all the students zipping in and out of the rows of cars looking for parking spots and not for some old guy trying to survive on a bike. Made it though, and now I ride neither a bike nor a motorcycle. Did have a chance to drive a jet-ski for the first time this summer though.

It would probably be wise to avoid bikes....but I seem to be addicted to these things.