## First-Year Students' Guide

Mathematics embodies the spirit of the liberal arts. Mathematics is an art, a pure science, a language and an analytical tool for the natural and social sciences. Statistics is becoming increasingly important in analyzing data in many fields, from biology to computer science to economics. The first-year mathematics curriculum is deliberately flexible. Our intent is to provide appropriate entry points whatever a student's level of preparation.

**Most first-year students who take a mathematics course will begin in the calculus sequence:**

Consult the Calculus Placement Decision Chart or visit the Calculus/Statistics Placement page to determine which calculus course.

Math 101: Calculus with Problem Solving. This course provides an introduction to the two fundamental notions of calculus: the derivative and the integral. The five days a week meeting format allows for review of pre-calculus topics as needed. Admission to Math 101 is by placement via Carleton Placement Exam #1 only. After completion of Math 101, students may take Math 121.

Math 111: Calculus 1. A first introduction to the calculus that develops the derivative and the integral. Designed for students with little or no previous exposure to calculus. Upon successful completion of Math 111, students may take Math 120.

Math 120: Calculus 2. Inverse functions, integration by parts, improper integrals, modeling with differential equations, vectors, calculus of functions of two independent variables including directional derivatives and double integrals, Lagrange multipliers. Upon successful completion of Math 120, students may take Math 210.

Math 210: Calculus 3. Vectors, curves, calculus of functions of three independent variables, including directional derivatives and triple integrals, cylindrical and spherical coordinates, line integrals, Green's theorem, sequences and series, power series, Taylor series. (Not open to students who have already received credit for Math 211.)

Math 211: Multivariable Calculus. This is the entry point for students who received an AP BC exam score of 4 or 5. It develops the calculus in two or more dimensions. Upon successful completion of Math 211, students may take Math 232.

**If you have completed the calculus sequence consider:**

Math 232: Linear Algebra. Topics include linear spaces and linear transformations, eigenvalues, eigenvectors and determinants.

Math 236: Mathematical Structures. An introduction to proof techniques (induction, proof by contradiction) as well as other foundational aspects of mathematics (equivalence relations, cardinality, etc.).

Math 265: Probability. An introduction to discrete and continuous probability culminating in the Central Limit Theorem and Law of Large Numbers.

Refer to the Course catalog for a complete description.

**Statistics:**

There are several options for statistics.

**Math 115:**Statistics: Concepts and Applications. This course emphasizes statistical literacy.

**Math 215**: Introduction to Statistics. This course includes more data analysis than**Math 115**. If you plan to major in the natural sciences, environmental studies, economics or sociology/anthropology, you should take**Math 215**. If you plan to major in Political Science, you have the option to take**Math 115**or**Math 215**, but we encourage you to consider**Math 215**.

**Math 265-276**: Probability and Introduction to Statistical Inference. If you have completed Calculus through Math 210 or 211 (Calculus 3), we encourage you to consider this sequence (instead of**Math 215**). These two courses are required if you plan to major in the Mathematics/Statistics track.

**Math 245**: Applied Regression Analysis. If you have received a 4 or 5 on the AP Statistics exam, consider Applied Regression Analysis (Math 245). Completing this course with a C- or better will earn you 6 credits for Math 215.

**Questions:**

If you have questions regarding placement, please contact the Math Placement advisor.