<p>Y'ever have a good <em>class</em> in high school, where the teacher really knew what they were doing, and you felt confident in the knowledge that you received from him or her, and really knew that you could knock people over with your knowledge of whatever subject they taught you?</p>
<p>What about a bad class, where you hope that nobody asks you about that subject ever again, because while you spent an entire year learning it from a particular teacher, you're not entirely certain that you learned anything of value?</p>
<p>If you had a good course in a particular subject, maybe it was followed up by another good course, with more complicated material, that built upon the first course. Sounds like you were particularly influenced by math in high school. Perhaps one of the things that influenced you was that you had good courses in that subject, that the teachers taught you a lot and made you feel confident in your knowledge of the subject. That'd be one indicator that your high school had a good math program. If instead your high school math program made you feel unconfident in your abilities and you hoped that nobody would ever ask you a math question ever again, that might be an indicator that your high school had a pretty lousy math program.</p>
<p>Same thing applies to college programs, as well. It's a particular strength in a particular department, which provides its students with the necessary tools (software, facilities, whatever) to learn that subject, and it has talented faculty who possess the necessary tools to teach the subject to the students... The students who graduate with a degree from that department have been imparted a certain confidence and talent and knowledge for that particular subject. In turn, that confidence and talent and knowledge is highly regarded by potential employers and other professors of that subject. That's kind of what it means to have a good program. You're right in that a good program may also have a more broad selection of courses within a particular field, but it's only one of many factors that make up a good program.</p>
<p>That's not to say that all "good programs" have their respective departments populated by amazing teachers. There are some bad teachers, because there's sometimes a discrepancy between people who are good teachers and people who are good researchers (research is where profs study a subject in great detail and convince people or companies or the government to give them money to do so... part of the money they get goes to the university, and universities like money... so sometimes a person who can convince a lot of people to give them money to study a particular subject aren't necessarily the best teachers... they're valued as faculty members for a different reason) so in addition to finding out whether or not a college or university has a good program in ______, it's also good to find out whether the teaching quality is as high as the overall program quality.</p>
<p>Rankings, like the ones you'll find in US News & World Reports, are a rough indicator of which places have better programs in what subjects. Don't take those rankings as fundamental truths, though... They use a very debateable algorithm to determine which places have better programs in which fields, and it's the subject of much argument within both the collegeconfidential community as well as within academia.</p>