# Mathematics

As students move through our mathematics courses, they’ll learn how to apply theorems; create and solve equations and inequalities involving linear, exponential and quadratic expressions; and apply methods from probability and statistics to draw inferences and conclusions from data. Our fourth-year Mathematical Reasoning with Connections course then reinforces and builds upon what students learned in the Integrated courses and prepares them for college-level mathematics.

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## Integrated Math I

For the Mathematics I course, students learn how to:

- Extend understanding of numerical manipulation to algebraic manipulation
- Synthesize understanding of function

Deepen and extend understanding of linear relationships - Apply linear models to data that exhibit a linear trend
- Establish criteria for congruence based on rigid motions
- Apply the Pythagorean Theorem to the coordinate plane

## Integrated Math II

For the Mathematics II course, students learn how to:

- Extend the laws of exponents to rational exponents
- Compare key characteristics of quadratic functions with those of linear and exponential functions
- Create and solve equations and inequalities involving linear, exponential and quadratic expressions
- Extend work with probability
- Establish criteria for similarity of triangles based on dilations and proportional reasoning

## Integrated Math III

For the Mathematics III course, students learn how to:

- Apply methods from probability and statistics to draw inferences and conclusions from data
- Expand understanding of functions to include polynomial, rational and radical functions
- Expand right triangle trigonometry to include general triangles
- Consolidate functions and geometry to create models and solve contextual problems

## Introduction to Data Science

Introduction to Data Science (IDS) was developed by UCLA to introduce students to the exciting opportunities available at the intersection of data analysis, computing and mathematics through hands-on activities. Data are everywhere and this curriculum will help prepare students to live in a world of data.

The curriculum focuses on practical applications of data analysis to give students concrete and applicable skills. Instead of using curated data sets as in a traditional statistics curriculum, this curriculum engages students with a wider world of data that fall into the “Big Data” paradigm and are relevant to students’ lives. In contrast to the traditional formula-based approach, in IDS, statistical inference is taught algorithmically, using modern randomization and simulation techniques. Students will learn to find and communicate meaning in data and to think critically about arguments based on data.

## Mathematical Reasoning with Connections

Mathematical Reasoning with Connections (MRWC) is a new fourth-year mathematics course designed to prepare students for the expectations and rigor of college mathematics courses. It reinforces and builds on mathematical topics and skills developed in Integrated 1-3. It is designed as a bridge to both STEM and non-STEM majors.