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Online Astronomy eText: Introduction to This eText
The Use of Mathematics in My Lecture Classes
 ; Astronomy is a science, and the universal language of science is mathematics. As stated by Galileo (taking the liberty to leave out parts of his statement, for emphasis), "This universe... is written in the language of mathematics... without which it is impossible to understand a single word of it..."
 ; This does not mean that one cannot learn astronomy without learning mathematics. Although it is difficult or impossible to do advanced astronomy without a thorough knowledge of mathematics, one can obtain a basic understanding of things with little use or knowledge of mathematics, and I use mathematics as little as possible in my lectures, and never require any use of mathematics in the examinations for my lecture course.
 ; Despite this, there are times when I feel that it is either necessary or desirable to use mathematical equations to show how various quantities are related to one another, especially in the online text. I do this for two reasons. First, for those students who understand the mathematics involved, using mathematical equations provides a much clearer and more precise understanding of the relationships. Second, even for those students who do not understand the equations, the various parts of the equations can at least show how things are related. Thus, in the equation

P2 = a3,

which is the mathematical formulation of Kepler's Third Law, even if you have very little idea how equations work you can see that if a, the semi-major axis of an orbit, is big, then P, the orbital period, must also be big, so that bigger orbits have longer orbital periods. Understanding how the exponents (the small numbers above and to the right of each letter) work would give you a clearer idea of things, but even if you don't understand the exponents, you can get the basic idea.
 ; In most of the topics covered in my class and on this web site, the mathematical equations are as simple as Kepler's Third Law, or even simpler, and even those students who are mathematically illiterate should be able to follow what is going on, particularly after being reassured that they will not actually have to use the equations, so that they have no reason to panic. However, there are a number of places where a thorough discussion requires a considerable use of mathematics, and rather than ignore the mathematics and penalize those students who can follow the equations, I include the appropriate equations and derivations, but refer everyone to this page.

Summary of Important Points
 ; If you are mathematically literate, and can follow equations and mathematical derivations, please do so, so that you gain the most accurate understanding of the material involved. If you are mathematically illiterate, and cannot understand the equations, then just follow the discussion as well as you can, concentrating on the words which describe what is going on, and the basic ideas which underlie the equations. You may not get as clear and precise an idea of what is going on as mathematically literate students, but you should be able to understand the results.
 ;In either case, keep in mind that none of the examinations for my lecture classes require any mathematics. If, in answering an essay question, you can use mathematics to explain something more clearly and quickly than with words alone, please do so. If you can illustrate a particular answer with numbers calculated with some simple equation, please feel free to do so. But do not feel that you have to use mathematics, and do not use mathematics unless you know how to do so in a correct manner.