Saturday, April 13, 2019

Onward to Leithold: Trying to learn Calculus

Since I focused my studies on finance, I never really was taught calculus. During high school I, with a friend, used to marvel at the enormous brick of a book that was kept in the school library The Calculus with Analytic Geometry by Louis Leithold. We were already having a hard time with algebra and imagined how much more difficult would it be to tackle that landmark book.  Picture it: between its covers one was not only getting the spooky, esoteric subject from hushed legend, but also receiving it awash with heaping doses of alchemical geometry. 

Eventually, my friend went on to study mechanical engineering and he did get to read at least some parts of the book. I, however, have remained mostly ignorant of the subject and a bit piqued by the fact that others successfully get hold of the subject all the time while I still lived in the dark ages.

A couple of years back I decided that I too would learn calculus for my own enjoyment and to read the book that has been beckoning to me all this time. For that, I refreshed my knowledge of algebra and took on plane geometry, which was another gap in my mathematical knowledge. I am now at the threshold of precalculus and I thought it would be a good time to start informally chronicling my journey. I am in no rush and this will take a while, but I'm really enjoying the slow pace without any external pressure.

In this post I describe my project in general and give the resources I'll be relying on.


I'll start with plane geometry which I'm about to finish. I have been almost exclusively reading on it from Rich's Geometry from Schaum's outlines series. This one is the best I found in my local library and I was fortunate to find it because it clearly states the principles on which each part of the geometry system is built upon; it is very condensed, meaning it has no fluff, and, as with the rest of the series, has loads of exercises. I have worked my way up to loci trying to solve every proposed exercise with pencil and paper and have been generally successful with it: only a few have left me stumped and I feel confident in my acquired knowledge.

As with logic, there's something very soothing in geometry that it's better than chess exercises. While in all three there is mental stimulation, one is left with nothing to show after doing chess problems (other than presumably getting better at it). The other two not only enhance one's skills, but say something about the world and with no competitive pressure.


For precalculus I chose Barnett's because my local library had many copies of it and found the more extended treatment of the subject better than Larson's Precalculus: A Graphical Approach which was my second best find. To be frank, this will be my second attempt with it. The previous one I had to cut it short someplace after function transformations because I had a bout of TMS at that time. Now, I'm all fired up back again and bought my own used copy online. Since this is going to be a leisurely stroll, I felt bad about borrowing one copy from the library for such an extended period, months at a time, even if no one else was requesting it; and also because I wanted to have a good reference book on the topics covered when I finally moved on to calculus proper.

Graphing calculator

I soon saw the need for a graphing calculator. My first shot was my brother's old HP 48 SX which he left in his drawer after he moved out. Overall I found it too complicated, glacially slow when working with graphs, but fell in love with RPN (reverse polish notation) on which it is based. In my first precalculus attempt, I decided instead to settle on the Educalc app for iOS for my graphing needs and use the 48 for quick calculations.

For this time around I researched for a perfect solution, meaning one that relied on just one piece of hardware. After going back and forth I realized that there was no physical calculator that met all my needs in one package: RPN, CAS, college oriented, fast, no rechargeable battery (I don't want my fancy calculator bricked when the battery finally gives up its ghost) and if possible, cheap. Why not go for multiple solutions? In the end, I decided to stick with the 48 for the straightforward operations, get a TI-89 titanium for the rest of the stuff except actually graphing, and the Educalc or Desmos apps for graph viewing.

One of the alternatives that I brushed off out of hand was the Voyage 200 because I thought that a standard-sized calculator was the obvious route.  A few days ago I got my titanium from eBay and dove in to learn how to use it. When I got to the split-screen feature it brought, front and center, the obvious smallness of the screen. I can manage it, but it is still uncomfortable. Then, there's the patent contriveness to getting many of the titanium's functions. This made me look back to the Voyage and while it seemed to alleviate these problems, it also had a big wart itself in that the ribbon that feeds the screen seems to lose contact in some cases after some years of use generating lines on the display. The similar shaped TI 92+, on the other hand is essentially the same as the 89 and Voyage and, judging by number of publications on eBay and mentions on Google, way less susceptible to pixel loss, even despite its age, than the latter. It is also cheaper. So I ordered the 92+ and plan to resell the titanium.

Dummies Books 

One of the incentives for getting a titanium, was that it had a Dummies book written for it. I read somewhere that this calculator had a learning curve, and since I like the approach of the Dummies series, I decided to get a copy. Now, that I have both in my hands I see that while it is true that that the titanium has a load of features buried in it, the manual from TI doesn't do a bad job explaining them, making the Dummies book a good head start, but not really necessary at all. It is also good for the TI 92+

Still, I'm not giving up on Dummies. I plan to acquire Calculus for Dummies. It has very good reviews and there's no harm in backup, since I don't have the benefit of a live instructor. If I want to compare something even further, I plan on borrowing Calculus by Stewart of which my local library has also many copies.

How I study

You won't get any insights from my study habits as they are quite ordinary and nothing special. I can allow myself to 60-90 min daily (including weekends). Most of my learning I get from solving exercises rather than through the dreary explanations, though I do both. In high school I discovered that music makes all the difference in the world and my best listening is during the studying periods. I allocate my favorite artists and vinyls for them which had so much to my overall enjoyment. I find math enjoyable, but this takes it to a different level and keeps me going. I am frequently looking forward to getting back to my exercises.

Now, I have noticed that many of the concepts while the look transparent and almost obvious in retrospect, are not immediately accessible to me. It takes a few tries for those aha! moments and for comprehension to settle in. It is in these instances that I can see what the difference is between highly intelligent people and regular ones is: they 'get' it right away. Once I get traction, I acquire the skill and even, at times, some speed.


Prof. Leithold appears to have passed on already. The latest edition of The Calculus is the seventh and I'm getting that.

The journey

I'll be tweeting my journey with the hash tag #onwardtoleithold , just don't expect any frequent posts