# Overview of Lower Division Courses

*We offer two main types of courses at the 100 and 200 level.*

**Example-Based (100, 103, 104, 175, 201-202, 203-204)**

**Who takes these courses? **These calculus and linear algebra courses are organized around concrete examples and applications with a minimum of abstract theory and are intended for a general audience of students interested in the natural sciences, engineering, finance, economics and social sciences.

Most first-year students and sophomores interested in science, engineering, or finance take courses from the standard calculus and linear algebra sequence 103-104-201-202, which emphasizes concrete computations over more theoretical considerations. Note that 201-202 can be taken in either order. More mathematically inclined students, especially prospective physics majors or students generally interested in applied mathematics, may opt to replace 201-202 with 203-204 for greater emphasis on theory and more challenging computational problems. Note that 203-204 can be taken in either order, but 203 is offered only in Fall and 204 only in Spring.

MAT100 is typically offered only in the fall semester and intended for students who need to review precalculus before starting 103.

Prospective economics majors can (minimally) fulfill their mathematical prerequisites with (100)-103-175. MAT175 covers topics selected mostly from 201, with biology and economics applications in mind. Students who wish to take ECO312, pursue graduate studies in economics or finance, or pursue a finance certificate are strongly advised to take 201-202 instead of 175.

Some of our successful majors became interested in mathematics as a major after taking courses at the 100-level. As an alternative to MAT104, and as a lead-in to MAT215, students may opt to take MAT210 in the fall, followed by MAT215 in the spring. Such students should consult with the Junior Advisor or the Associate Director of Undergraduate Studies as soon as possible to plan a course of study.

**Proof-Based (210, 214, 215-217, 216-218)**

**Who takes these courses? **These courses are intended to prepare prospective majors for upper division course work in the department. They are also useful for theoretical analyses in physics, applied mathematics, computer science, engineering or economics.

MAT215-217 and MAT216-218 are designed to give students an authentic experience of how mathematicians think about problems and introduce the basic tools of logical argument and abstraction that are needed in upper division mathematics courses. They introduce students to rigorous mathematical argument and formal proofs while at the same time they provide a robust theory-based introduction to the main ideas and techniques of linear algebra and analysis (calculus) in one and in several variables.

Students in MAT216-218 are expected to start this sequence of courses with substantial experience with proof-based mathematics (for example, some students have already taken an introductory analysis course at a nearby university while still in high school). The placement officer or other representatives of the math department can advise students unsure about where to start in the first semester at Princeton. (Advice from other math majors is very helpful but it sometimes does not take into account that different students learn these topics with a very different pace and style.)

MAT210 is a new course, offered for the first time in Fall 2023. It is equivalent to MAT104 and its prerequisite is MAT103 (or equivalent). It is primarily aimed at prospective math majors who want to consolidate their single variable calculus knowledge and simultaneously get a jump start on the rigorous proof techniques that are further developed in MAT215. (It is offered at the same time as one section of MAT215 to facilitate any needed placement adjustments.) This course is also suitable for for anyone who wants to get an introduction to rigorous mathematical thinking, so may be of interest to prospective majors in philosophy, physics or math track economics who plan to take MAT104 in the Fall semester.

Prospective math majors with a very strong calculus background can choose to start in MAT215 or they may opt to start in MAT**210 **and continue with MAT215 in the spring. More information can be found on the math department website or at the placement workshops during orientation in August.

MAT214 is an introduction to formal mathematical argument in the context of an introduction to number theory, and may be particularly appealing to prospective philosophy or computer science majors. (Most mathematics majors learn about these topics in the 300-level algebra courses.)

**General Surveys:** In addition to our example-based and proof-based courses we usually offer at least one course every year aimed at a general audience with relatively little in the way of mathematical prerequisites, for students who want to satisfy the Quantitative and Computational Reasoning (QCR) requirement while pursuing their primary interest in other non-quantitative disciplines. In recent years we have offered **MathAlive (APC/MAT199)** in the spring semester. This course is a survey of modern applications of mathematics (e.g. digital music, sending secure emails, using statistics to explain, or hide, facts) with an emphasis on ideas rather than sophisticated mathematical techniques. Other courses of this type may be offered occasionally, on a one-time-only basis, usually in the spring semester. Check the registrar's course offerings for a current listing of QCR courses offered.