# Overview of Lower Division Courses

#### General Information for Freshmen and Sophomores:

Most freshmen 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 and 202 can be taken in either order.

More mathematically inclined students, especially prospective physics majors, may opt to replace 201-202 with 203-204 for greater emphasis on theory and more challenging computational problems.

Students who are not prepared to begin with 103 may take 100, a rigorous precalculus/prestatistics refresher. 100 may be followed by 102 or 103; 102 is a one-semester survey of selected topics from 103 and 104, for students who do not intend to take further calculus courses. Students who will later need 104 should not take 102.

Prospective economics majors can minimally fulfill their mathematical prerequisites with (100)-102-175, but 103-175 is strongly preferred. 175 covers selected topics from 201, with biology and economics applications in mind. Some future economics majors will need the standard sequence 103-104-201-202 instead, especially recommended for those who plan to take math-track econometrics and finance courses. Economics majors who plan to continue with 300-level mathematics courses and/or go on to graduate school in economics or finance should take 201-202 instead of 175.

Prospective mathematics majors must take at least one course introducing formal mathematical argument and rigorous proofs. For many this will be 215, but 214 or 217 are more algebraic alternatives. One recommended sequence for prospective majors is 215-217-218, especially suitable for those who already have some experience with constructing proofs. Other possible sequences for prospective majors include 214-217-203 and 203-204-215, although the latter is relatively rare. Note that 215 and 217 may be taken in either order, as can 203 and 204.

#### Placement Overview:

Students with little or no background in calculus are placed in 103, or in 100 if their SAT mathematics scores indicate insufficient background in precalculus topics. To qualify for placement in 104 or 175, a student should score 5 on the AB Advanced Placement Examination or a 4 on the BC Advanced Placement Examination. To qualify for placement into 201 or 202, a student should have a score of 5 on the BC Examination. Students who possess in addition a particularly strong interest in mathematics as well as a SAT mathematics score of at least 750 may opt for 203 or 214 or 215 instead. Initial placement into 217 or higher for incoming freshmen requires consultation with the placement officer.