Welcome to Math 170

Welcome to Math 170 at upenn! First let's start with some questions, or perhaps meta-questions, about the class. Why take it? What should I (as a student) get out of it? What does Professor Weber want; what are his aims? What does the University want?

The first question has a pretty obvious answer for a lot of people: because I have to! It's a graduation requirement; I need to fill in a circle in my quantitative reasoning section. Others are interested for reasons more closely aligned to the aims of the class. Some want to go further in math, but haven't taken any college mathematics before, and feel they require an introduction before getting to more serious subjects. Others found themselves interested in some of our subject material (and a lot of it I think will be very interesting!).

These are all perfectly valid reasons, but I'd like us to look deeper into the rationale behind the class. In fact, as some students have pointed out in the past, the rationale and aims for Math 170 can seem a little unclear. For example, in a calculus course, the aim is to become proficient in calculus; in an algebra course, the aim is to become proficient in algebra; is an east Asian history course, the aim is to become knowledgeable about east Asian history. In various English courses, one learns grammar, paragraphing, story-telling, critical reading, and effective written communication. What is the aim of Math 170?

Our aim is, in a way, broader than in many other classes you'll take here. This class' students are frequently interested in realms of human knowledge and practice that are less mathematical: the departments I see on my class list circle around Psyc, Biol, Hist, Engl, and so forth, with a decent smattering of UNDC. The purpose of this class is to help develop proficiency in another form of human activity: formal reasoning (which includes, but is far from limited to, reasoning with numbers), and to help develop knowledge in an immensely rich and layered world that is rarely glimpsed: the world of mathematical form and structure.

So that's it: from the point of view of your teacher, me, the class' purpose is for everyone to become more proficient in formal reasoning skills (precision formulation of problems, pattern recognition, shape, formal structures, and, yes, numerical facility), and to gain some knowledge of what mathematics is today and what is being studied and developed in that world. If by semester's end everyone has a greater ability to approach both abstract and real-world problems in a precise, formal way, and everyone has a bit of appreciation for the amazing mathematics that exists in our society today, then I will consider the course a success.

And the University's aims? Of course I can't speak for the university, but I can give my view on the matter. The University wants to graduate students who are knowledgeable and capable, not just in their fields, but in a wide array of human realms---it wants its graduates to possess not just a skill, but what it considers to be an educated mind. That is why engineers take English and history, and why pre-meds and comm. majors take some kind of math. In an even broader sense, the purpose is two-fold: first, it gives you, the student (fundamentally you are the client), value for your money and your trust. The second purpose is that it is a form of advertising for Penn: if it graduates impressive and successful human beings, then Penn's status rises, and the demand for its services rises.

Anyway, I hope this overview of our course goals is valuable to you. As always, your comments and feedback are appreciated!