The Calculus in Perspective

(This site is under construction)

A warning to all Art Students:
This is a book about mathematics.

A warning to all Math Students:
This is a book about art.

Now that I have chased away the majority of my audience, I should explain. The Calculus in Perspective is an unique approach for introducing students to the rich language of the calculus. In this work, I present the student with model of visual perspective, then extend visual perspective into an overall model of the calculus.

I believe that this approach will be an enjoyable introduction into the fascinating field of Calculus and higher mathematics. I do not intend the work to be a replacement to a rigorous college course on the subject. Rather I hope to create an enlightening series of essays that will help encourage you to learn more about mathematics.

By The Way, this site is underconstruction. So don't expect much yet.

Visual Perspective

The Calculus

Anyone who adds to the plethora of introductory calculus texts owes an explanation.

Calculus: An Intuitive and Physical Approach; Morris Kline

Morris Kline provided the world with one of the most accessible introductory texts for the calculus. The work is currently part of the wonderful collection of paperback math books provided by Dover Publishing group...which means that it is available at only a fraction of the cost of the calculus texts used in many major universities. I envy those students fortunate to take classes using Kline's text. Not only do they save a ton of cash, Mr. Kline's physical approach does a superior job in conveying an intuitive understanding of calculus, mathematics and Newtonian physics.

Kline's work begins with an interesting note that authors wishing to contribute to the crowded field of introductory texts owe an explanation for their efforts. Quite frankly, I have the exact opposite feeling. I believe that one of the greatest challenges of a culture is to preserve the gems of the past. While it is exciting to be on the cutting edge of a new science or technology, the role of the untold masses that work on the maintenance of the foundations of a subject play as important a role as the adventurers who get to explore new territories.

For that matter, I see problems with our current notion that all worthy books must be original from start to finish. Science generally works by extending, refining or correcting existing ideas. We might get a good paradigm shift once every other generation. Our preference for new ideas over refined ideas has created an absurd comedy where every other month a wannabe guru claims the existence of a new fundamental dichotomy.

Astute readers will notice that this work is completely lacking in new ideas. It is merely a reworking of the presentation of ideas. It is my contention that liberal art students would find calculus more intriguing if the class began with a presentation of visual perspective.

I steal from Morris Kline the idea that the primary goal of an introductory calculus course is to convey an intuitive understanding of the subject. Wishing to avoid the metaphysical difficulties of infinitesimals and limits, I take the questionable shortcut of finding the equation for the y-intercept before finding the slope of a tangent.

Generally, visual perspective is treated as an insignificant subcategory of optics. Using perspective as an intro to calculus gives the subject flair. Preceding calculus with a discussion of visual perspective also fits well with the historical order of scientific discoveries. In my opinion, this minor reworking of the syllabus would make the subject more compelling and interesting. When I first came up with the outline for "The Calculus in Perspective" I had grandiose visions that the simple change in order would be so compelling that it might even be possible to using the outline for a junior high or high school class.

It is my hope that the future sees a large number of authors of the caliber of Morris Kline working on the foundations of Calculus and that each generation produce celebrated figures who work honing the methods used to teach introductory mathematics and science.

Mathematics is never finished. There will always be a need for writers of strong minds and character to rework foundations, and that such writers need no explanation for their work. Perhaps a true mathematicians might seize on the idea of a real textbook that follows the outline of this presentation.

Open Source Textbooks

The pedagogy of mathematics is as important as the cutting edge. In this regards, I think one of the most exciting developments in the current intellectual landscape is the open source movement. Open Source Software openly invites developers to work on and extend a common framework.

It is my hope that the same spirit leading to the open source development of software leads to open source textbooks. It is my hope that open source textbooks could lead to a new age of intellectual inquiry where mathematics teachers actively participate in the creation of both the text and curriculum of their class. Open source textbooks wouldn't lead to simply one or two new calculus texts, but would lead to literally thousands of new introductory calculus texts and different schools and professors try to hone in on the methodology that they find most conducive to the needs of the student.

Open source textbooks would allow the community of teachers to hone and perfect the introduction of a subject.

There is no need for an explanation for teachers to actively engage the subject that they love. In my opinion, what the next generation of calculus instructors needs is a large base of source materials from which they can generate their ideal textbook. In my ideal world, every teacher would be actively engaged in the creation of their curriculum.

In writing this work, I have given a great deal of consideration to contributing it as the foundations of an open source effort. For that matter, if there ever is any legitimate interest in using basis of an open source math class, I would be eager to pursue the idea. At the moment, I am developing the class as a proprietary ultra copyrighted, capitalistic effort.

Unfortunately, there seems to be one minor block to the success of this outline as an open source project. It just so happens that the overriding number of math professors that I have approached with my version of the calculus seem to think that my vision of the calculus is flawed from the ground up.

The rejection of this work has been so outright and complete that I worry anyone foolish enough to partake in an open source effort would have their academic career ruined.

Of course, I have about as much respect for the dialecticians that haunt ivory towers as they have for amateurish clowns like me. I hold with Poincare in the assessment that the approach to calculus based on transfinite theory is a disease. I would have loved to be a teacher, but when given the choice of the street or transfinite theory, I take the street.

Oh, if you happen to be a student hoping to glean an understanding of calculus from this web. Well, uh, I guess I should mention that I flunked math.

Descriptive, Diagonal
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