Science & Quantitative Reasoning

QR Courses without Prerequisite

Astronomy

ASTR 160 - Frontiers and Controversies in Astrophysics

DESCRIPTION:
This course addresses three topics in astrophysics that are currently subjects of intense research and debate: 1) planetary systems around stars other than the Sun; 2) pulsars, black holes and the relativistic effects associated with them; 3) the evidence for dark matter and dark energy, and their implications for the ultimate fate of the Universe.

PACE OF QUANTITATIVE TRAINING:
There will be some discussion in the lectures and in the discussion sections about approaches to the quantitative problems. These issues will be continually reinforced by the problem sets, which will be due approximately once per week. There will be ample opportunity to discuss the quantitative problems in the discussion sections, in the on-line forum, and in office hours.

EXPECTED QUANTITATIVE PREPARATION:

Astrophysics is an intrinsically mathematical subject, and this course makes use of algebra, geometry, and some trigonometry along the way. As we tend to deal with a very big (astronomical) numbers, experience with scientific notation would be useful. Neither calculus nor pre-calculus is used anywhere in the course. We will review all of the mathematical techniques as they arise, so it isn't a problem if your skills in algebra, geometry, and trigonometry are a little rusty. In other words, what's important for this course is that you COULD deal with problems in this area if you were given a brief reminder of how to do so. Some sample problems are included below to give you a feel for the kinds of questions that you'll need to be able to answer.

Doing word problems in astrophysics is seldom a simple matter, and many students find the problems that we will solve in this class to be *very* challenging! In this regard, some degree of comfort in applying algebra and geometry to real-life situations is much more important than knowledge of any particular mathematical technique.

Some previous experience with college-level science, either through high-school AP courses or prior course work at Yale, also is recommended (note, though, that AP math is not required for this purpose, as we don't use calculus in this course).

If you are uncertain about whether you are ready for this course, please talk with the instructor.

SAMPLE PROBLEMS:

What's more important than these technical manipulations is the use of math to address real world problems. Since you don't know the context, I can't give any specific examples from the course itself, but here are a couple of sample problem using the traditional formula V = D / T, where V is the velocity of an object (say a car going from city A to city B), D is the distance travelled, and T is the time it takes.

1. Easy problem: If Chicago is 1000 miles from New York, how long does it take to drive between the 2 cities at an average speed of 50 mph?

2. Hard problem: If your car gets 20 miles to the gallon, and you put 10$ of gas in your car, how many hours can you drive at 50 mph before you have to refill?

The reason the second problem is hard is that it doesn't use the formula in an obvious way, and the problem doesn't provide complete information within itself. Many of the problems in this course will have these features.

Answer key