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Mathematics

 

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Science Literacy Resources

This is the index page for a diverse range of WeirdWildWeb resources for students seeking basic literacy in the sciences and mathematics. This is not popular science, which skips the mathematics. Rather, it is pitched at the level necessary to gain access to a variety of literatures, including the philosophy of science, science and religion, and basic science journals. It is, if you like, the science and mathematics you need to begin to understand what scientists really do.

In addition to these resources local to the WeirdWildWeb, there are many World Wide Web resources useful for those seeking science literacy. A sampling of relevant links can be found here.

Pedagogical Remarks

We make use of several novel techniques to help learners grasp the material needed for science literacy. Here is a brief introduction to three of them.

  • Narrative methods for building familiarity with complex ideas. In the present context, there is no time to build familiarity with mathematical and physical concepts in the usual way--by repetition of calculation in problem set after problem set. There is also no need in most cases for sophisticated calculation abilities. When science literacy is the goal, understanding the equations is more important that being able to derive them and grasping theorems is more important that being able to prove them. Narratives can be extraordinarily effective as a substitute for the tried-and-tested (and actually grossly overrated) familiarity-through-calculation approach of traditional mathematics and physics teaching.
  • Deliberately confronting the problem of varying disciplinary perspectives. Biochemistry and quantum chemistry conceive of energy in molecular interactions in related but rather different ways. Physicists and organic chemists don't think about van der Waal's forces the same way. These kinds of conflicts are due to a combination of traditions of thinking that suit individual disciplinary needs and lack of communication across disciplinary boundaries. The goal of science literacy requires coming to terms with these differences in disciplinary perspectives because they are immediately obvious and quite confusing to the alert student whose scientific knowledge spans disciplines. We try to confront these differences of perspectives head on, which leads to some deep discussions even when the other science being covered is not advanced. While this may seem incongruous, the overall effect of this approach is greater learner satisfaction and a deeper appreciation for the social character of scientific activity.
  • Noticing and discussing boundary questions when they arise. This doesn't happen in most science and mathematics classes, but it should. Boundary questions are questions that emerge from within a discipline but that cannot be answered within that discipline. Sometimes another science is capable of answering such boundary questions, in which case the contrast of disciplinary capacities is fascinating to study. Most often, however, boundary questions have metaphysical, theological, or existential dimensions. Students find such questions engaging so the failure of teachers to address them is arguably evidence of a kind of ideological insistence on maintaining either somewhat artificial disciplinary boundaries or else proscriptions against certain kinds of non-scientific inquiries. The result is confusing and frustrating for students, particularly those who strive for an overarching understanding of science and mathematics rather than technical proficiency in a single area of scientific research. But there is no harm in pointing out such boundary questions, in linking them with classical philosophical debates, and in inviting students to regard the presence of boundary questions in the sciences and mathematics as one of the very important reasons why these enterprises are so exciting and important. 

Contents

Contents: Biological Sciences

Analytical Chemistry

Biochemistry

Cell Biology

Neurophysiology

Evolutionary Biology

Immunology

Contents: Physics

Electromagnetism [There is something under this heading!]

Special Theory of Relativity

General Theory of Relativity

Cosmology

Quantum Mechanics

Contents: Mathematics

Mathematics: One-Dimensional Calculus

Mathematics: Multi-Dimensional Calculus

Mathematics: Linear Algebra

Mathematics: Complex Analysis

Analytical Chemistry

[On the way...]

Biochemistry

[On the way...]

Cell Biology

[On the way...]

Neurophysiology

[On the way...]

Evolutionary Biology

[On the way...]

Immunology

[On the way...]

Electromagnetism

Maxwell's Equations of Electromagnetism (HTML format; imperfect)

Maxwell's Equations of Electromagnetism (MSWord 2000 format; better)

Special Theory of Relativity

[On the way...]

General Theory of Relativity

[On the way...]

Cosmology

[On the way...]

Quantum Mechanics

[On the way...]

Mathematics: One-Dimensional Calculus

[On the way...]

Mathematics: Multi-Dimensional Calculus

[On the way...]

Mathematics: Linear Algebra

[On the way...]

Mathematics: Complex Analysis

[On the way...]

The information on this page is copyright 1994-2010, Wesley Wildman (basic information here), unless otherwise noted. If you want to use ideas that you find here, please be careful to acknowledge this site as your source, and remember also to credit the original author of what you use, where that is applicable. If you want to use text or stories from these pages, please contact me at the feedback address for permission.