The midterm will cover material from the first half of the course (through exponents), with a focus on revisiting secondary school mathematics from new perspectives, especially as a coherent system … Read More
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The intuitive idea of an axiomatic system is very simple. Suppose we want to explain a given assertion A. In so doing, let us say we have to
Complex numbers are an area where algebraic and geometric perspectives provide very different strengths and intuitions. Having a firm grasp of both perspectives and being able to switch from one … Read More
What does it mean to raise a number to a power?
What if the power is whole number? An integer? A rational number? A real number?
For a specific example, … Read More
Polynomials and their roots
What are the polynomials? They are a particular collection of functions.… Read More
I wanted to pass along this resource (thanks to Rachel for sharing!). These guides have hundreds of questions (about six years worth of Regents exams) organized by topic, … Read More
Why do we spend so much time studying quadratic functions, but relatively little time on cubic functions, quartic functions, quintic functions, and so on?
Putting together our work from yesterday, can we answer the following?… Read More
Definition. A parabola is the set of points equidistant from a given point $P$ and a given line $L$ (not containing the given point).
Definition. A quadratic function
How do we define the slope of a line?
The coordinate plane
The coordinate plane, labelling each point in the plane with a pair of numbers (coordinates), allows us to … Read More