# Mathematics: Calculus, Statistics, and Logic Courses

Approved courses introduce students to or extend their knowledge of precalculus, calculus, discrete mathematics, probability, statistics and/or data analysis. Courses may be offered in the Department of Mathematics and Statistics and in other departments that have expertise in quantitative reasoning and data analysis and that offer appropriate courses, particularly in statistics or discrete structures.

A student who has achieved a score of 85 or above on the Regents “Math B” Exam (former “Mathematics Course III” Exam) or on a recognized standardized examination indicating readiness to enter precalculus will be considered to have fulfilled this requirement.

### Learning Objectives for Mathematics: Calculus, Statistics, and Logic

Courses in Calculus enable students to demonstrate:

- an understanding of basic mathematical functions and their graphical representations together with an ability to understand how many quantities of interest in mathematics, the sciences, and the social sciences can be modeled by functions and their properties understood graphically;
- an ability to calculate derivatives and use them to analyze graphs, solve problems (growth/decay, optimization, rates of change), and make approximations;
- an ability to use integrals to calculate quantities of interest (area, volume, work, moments, probabilities).

Courses in Statistics enable students to demonstrate:

- an ability to find the values of basic measures of center (mean, median), location (percentile), and spread (variance, standard deviation, interquartile range);
- an ability to extract information from graphs and other displays (such as scatter plots and histograms);
- an ability to choose and appropriate statistical procedure for evaluation of various types of data;
- an ability to calculate confidence intervals (mainly for means of one and two sample tests) and to set up and interpret the result of standard hypothesis tests, which require the use of tables (mainly of the normal and t distributions).

Courses in Logic enable students to demonstrate:

- an ability to translate sentences and arguments from English into the formal systems and to demonstrate or prove arguments within the formal systems;
- an ability to evaluate formal properties of sentences (and sets of sentences) using truth tables and to prove formalized arguments;
- an ability to examine, interpret, and represent the logical structure of the original English expressions and draw communicable conclusions (e.g. that an argument is invalid).