I was able to hunt down an old Calculus text by Douglas F. Riddle (c.1984) - Calculus and Analytic Geometry. I also hunted down
the solution manual for $1.24. It is listed wrong on Amazon (as A. Riddle with wrong title), but using ISBN, 978-0534045845, I verified it was
the correct solution manual for
the textbook, ISBN13: 978-0534014681.
I received it. Even though it is nearly 30 years old it looks as though it has never been used. It is listed wrong all over the world (
internet), but I can verify this is the correct solution manual to DF Riddle's Calculus AND Analytic Geometry, 4th edition, circa 1984!
The text, on the other hand, is worn in ... discolored pages ... yellowish tint ... in a way, very beautiful to me. It contains everything from analytic geometry through differential calculus, integral calculus, conic sections, parametric equations, polar coordinates, as well as infinite series, solid analytic geometry, multiple integrals, line and surface integrals ...
I have decided to go through these along with other texts in my own slow manner. I've been going through
the Hoffman text, and I stopped at Conic Sections to take a detour into analytical geometry and polar coordinates ... I had hesitated in investing in a big fat calculus book, but I did some research and have a good feeling about Riddle's pre-graphing calculator, pre-CAS text. In the solution manual, the sketches are by hand, which is very encouraging.
I have found that what might be most frustrating to the youth is when, in examples in texts, the author says, "and solving these equations, we get" --- but he does not show the details of the work involved! I'm afraid Riddle is no exception, but I am filling in the gaps to my heart's content.
This is what I am using my notebooks for now.
I also realized that, while it is a noble idea to wish to discover some ways to make this more accessible to the youth, the bottom line is that it is we who have been compelled to re-educate ourselves in a slow manner. If anyone stumbles upon our attempts and becomes inspired to reject the fast pace of systematic schooling, then this is up to Fate, and really not in our control.
All we can do is stubbornly insist that what we are up to, even though it has nothing to do with careers or productivity, is essentially very important to us.
I very well could have been one of these suicides at age 19, and again at age 33 ...
For whatever reason, my mental stability seems to be hinged on grabbing this bull by the horns.
While some may brag about not having to write things down, I intend to show all the work!
I am doing this primarily for myself. It is an added blessing to involve you in this process.
Our lives would make for a boring novel and an even more boring film, but, as Schopenhauer said in the beginning of the World as Will and Representation, Volume Two:
"Why wilt thou withdraw from us all
And from our way of thinking?" ----
I do not write for your pleasure,
You shall learn something.
an aside:
Do you remember when you were asking me what I thought about the long section in On the Will in Nature about magic and animal magnetism? We wonder what Schopenhauer thought of ghosts ...
Well, a childish part of my psyche wants to believe that I have made some kind of contact with this "Douglas F. Riddle", author of "Analytic Geometry" (c.1996) and "Calculus and Analytic Geometry" (c.1984).
* Douglas F. Riddle died in 2010 at age 81. This means he published the 1996 book when he was (81 - (2010 - 1996)) = 67, and the 1984 book when he was (81 - (2010 - 1984)) = 55. They are the most recent editions.
While going through one of the examples having to do with application of vectors in calculating forces, I found an error. Not only does he not show the work in solving a system of equations, but his results are incorrect. They do not satisfy the second equation. I found the correct solutions and scribbled it into the margins of the textbook. Of course, in my own notebook, I show the work to prove it to myself. The thing is, most kids are just going to become confused and filled with doubt when something like this occurs.
I told the ghost of DFR, "Shame on you Mr. Riddle!"
"Here I am putting my faith in you, sir, and now my faith is in jeopardy. I will have to proceed with caution."
The ghost wasn't troubled too much by my discovery of the error ... but he should have been. Such errors could be all that is necessary for a less determined student to call it quits. So, please, Holden, do not put too much faith in anyone's calculations and computations, not even your own, especially not your own. We have to check our work ... Whoever said that to err is human must have tinkered with mathematics (specifically arithmetic).
Sometimes when our error is from merely adding when we should have subtracted (for example, when the sine of an angle is negative but of we write the positive), we may be able to spot our error by considering a geometric representation. The thing is, how much time and mental energy does anyone really want to spend checking their results? I tend to gravitate towards working on exercises that I have solution manual for ... often I will only work on problems that have solutions available. This probably has to do with the way I study - alone. Still, if there is a conflict between my solution and the textbook's, I have the support of computer algebra systems like Sage and the TI-Nspire to check the results.
There is no way to race through any of this. That may be one of the main causes of these suicides. I really would prefer to jump into multivariable calculus (since I supposedly got an A in that class in the year 2000). I want to dive into Physics and Computational Physics ... but this ghost (DFR) seems to be guiding me back to fundamentals to show me where the gaps are, what void needs my attention!
As long as there is a sense of rank and social hierarchy involved in various areas of mathematics, students will dread having to return to the fundamentals as they will interpret this as some kind of failure.
And yet wasn't Husserl interested in the Foundations of Arithmetic?
What I suggest is that you join me in this return to the fundamentals: algebra, geometry, trigonometry, calculus ... along with all the arithmetic involved ... and we do this in the spirit of re-education, showing as much of our work (to ourselves) as time will permit.
What will be different this time as opposed to when cramming for exams and anxious to land a job so as to purchase a used Volkswagen Jetta, is that we will have removed careers and usefulness from the equation. We can keep track of just where we ourselves experience frustration, despair, and deep depression. Do these moods strike us when we consider the enormity of the subject matter, and how long it takes to just peck away at one little problem in a big fat book?
We may not get to the bottom of this, but, in the process, we are allowing ourselves to return to the study of mathematics proving to ourselves, at least, that this "failure" that is causing the epidemic of suicides among students is purely imaginary, albeit reinforced by the authoritarian gorts in charge.
My message will be simple: Take your time. There is no such thing as failure when it comes to mathematics. The math is not going anywhere. Our societies impose these grids and time constraints. They make fools of us all. They want well-trained super-chimpanzees who can calculate rapidly. God forbid we should take years or decades to compute ...
We can forget all that nonsense and approach mathematics education, primarily our own education, keeping Schopenhauer's few comments on the subject in mind, especially as far as the disagreeable process of describing geometric problems algebraically and algebraic problems geometrically.
Feel free to go in any direction you wish, and when you find yourself stupefied by a textbook, allow yourself to discover why you are stupefied. It most likely is because the author of the text has skipped some steps, as in "solving these equations, we get" without taking you through the thought processes involved. Take as long as you need to to eliminate the stupefication.
The time constraints and the big rush to get nowhere fast is the root of the stupefication, not in your brain. So we can take it slow ... and not allow ourselves to be overwhelmed with psychological despair ...
Maybe the most intelligent thing to do is to drop out of school and study at your own pace.
In the meantime, I don't think anyone can judge any of these kids who are ending their lives over this unless they are willing to go on this little intellectual adventure themselves ... We might even want to imagine Schopenhauer himself going through such textbooks. Now, no one doubts that Schopenhauer had an exceptional intellectual capacity, but he was also extraordinarily honest. It would be very interesting to know how he would go about solving the problems. Surely, he would not be racing through them.
Maybe nobody really knows how to teach ... Didn't the Buddha say that "this can not be taught" ?
The best approach you can take might be to imagine how Schopenhauer would approach these mathematics problems. Again, I hate to be so repetitive, but I can't see him try to calculate rapidly. I imagine him observing his own thought processes in slow motion to make observations on how dreadfully torturous the process is!
Maybe we can only approach mathematics as individuals at our own pace, and that systematic mass-hypnosis is not the best way to go about educating ourselves. So much has to do with moods and temperaments. It can be delightful as long as nobody is standing over you filling you with dread.
to them this board shall remain unknown, and few of them would know when it would ceased to be
I have been experiencing some difficulties accessing our board recently, so I used
HTTrack Website Copier to copying the entire site (as of 2016 Aug 9) ... it's about 1.2 GB on my home directory.
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