 # The University of Texas at Austin: Discovery Precalculus: A Creative and Connected Approach

Strengthen your critical thinking skills in this inquiry-based Pre-calculus course.
15 weeks
10 hours per week
Self-paced

In this interactive pre-Calculus course, you will deepen and extend your knowledge of functions, graphs, and equations from high school algebra and geometry courses so you can successfully work with the concepts in a rigorous university-level calculus course. This course is designed to engage learners in the “doing” of mathematics, emphasizing conceptual understanding of mathematical definitions and student development of logical arguments in support of solutions. The course places major emphasis on why the mathematics topics covered work within the discipline, as opposed to simply the mechanics of the mathematics.

### At a glance

• Institution:

UTAustinX

• Subject: Math
• Level: Introductory
• Prerequisites:

A mastery of mathematics up through the Algebra II or College Algebra level.

• Language: English
• Video Transcript: English
• Associated skills: Critical Thinking, Algebra, Student Development, Precalculus, Geometry, Calculus, Basic Math, Legal Discovery, Mechanics

# What you'll learn

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• How to make conjectures, construct logical arguments, and justify your reasoning
• The concept of function in mathematics, function characteristics and properties, and rate of change of functions
• Modeling of common relations and functions such as linear, power, exponential, and logarithmic functions using statistical regression and matrix methods
• An exploration of algebra and geometry, and the connections between the two in analytic geometry
• Properties and applications of exponential and logarithmic functions including exponential growth and decay and The Logistic Function
• The development of the trigonometric functions and identities along with applications of trigonometry
• Limits and rate of change of functions as a precursor to Calculus
• Other Coordinates Systems – an investigation of parametrization of the plane and the polar coordinate system along with exploration and use of vectors
• Sequences and Series including The Method of Induction
• Basic probability and combinatorics used in an investigation and development of the Binomial Theorem and its connections to Pascal’s Triangle

# Syllabus

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The course is organized around the following seven units:

1. Functions, Rates, and Patterns
2. Algebra and Geometry
3. Exponential and Logarithmic Functions
4. Trigonometry
5. Limits and Rate of Change of Functions
6. Exploring Other Coordinate Systems
7. Sequences and Series