What is a mathematical condition? When do they arise?

Activities: The Rational Radical.

What are the features of a good explanation? What is entailed in using mathematical language carefully?

Activities: Discussion of alternative solutions from reading. This will include a treatment of Euclid's Lemma and Unique Prime Factorization.

Reading: What are the Features of a Good Explanation?

Due: Analysis of reading, submitted at online form by 4pm

Bring a copy of your analysis to class.

How do conditions affect solutions and explanations of solutions?

Activities: Discussion of the Prime Time System.

Mathematical considerations in selecting problems with radicals.
How division interpretations arise in word problems
Introduction to Leftover Sequences.

Due: A summary of your solution to the Prime Time System, submitted at online form by 4pm.

Bring a copy of your solution to class.

Look up before class: how to do long division on integers (for example, how to divide 10 by 3 to obtain 3.333... using long division)

Due: Problem Set 1, in envelope at East Hall 1856.

(no class: MLK)

What are ways of representing rational numbers? How does the division algorithm relate to termination/repetition in the decimal? Are there decimal expansions for rational numbers that cannot be retrieved from long-division?

Bonus warm-up activity: A Cute Radical Problem

Activities: Feasting on Leftovers -- leftover sequences and the rational expansion theorem.

What goes into a creating a mathematical definition? What are language issues that arise when discussing "roots", "factors", and "solutions"?

Activities: Working with Polynomials.
The Relationship between Factors and Roots of Polynomials.

How are roots of polynomials represented? What can it mean to be a solution to a polynomial equation (or for no solutions to exist)?

Activities: Methods for finding roots of polynomials.
Introduction to complex numbers.

Due: an email to Dr. Lai and Ms. Mende with your final presentation group members. This email should cc all group members.

How are roots of polynomials represented? What can it mean to be a solution to a polynomial equation (or for no solutions to exist)?

Activities: Methods for finding roots of polynomials.

Due: an email to Dr. Lai and Ms. Mende with your group project and presentation date preferences. You should rank all projects, and you are welcome to flag a few as particularly favored by your group. This email should cc all group members.

Understanding and using statements of mathematics.

Activities: The Rational Root Theorem

Why do complex roots of real polynomials come in pairs? What are other kinds of roots that always come in pairs? What are representations of these pairs? How might mathematical results influence the notation used to state them?

Activities: Introduction to complex numbers.
Algebra and Geometry of Complex Numbers.
Two for the Price of One: The Conjugate Pair Theorem.
Algebra and Geometry of other types of conjugates.

What are common ways to define and represent complex numbers? What is the geometry of n-th roots of a number?

Activities: Flexible Identities: Angles, Polar Form, and Notation for Complex Numbers.

Look up before class: special angles and their sine and cosine values.

DeMoivre's Theorem

By this date, you should have met with either Dr. Lai or Ms. Mende for a 1/2 hour appointment regarding your team project.

What does it mean to say something is mathematically "undefined"? What does it mean for a sequence of numbers to converge or diverge? What does it mean to have a convergent or divergent sequence of functions?

Activities: Arithmetic of Very Small Numbers.
Growing Weird Functions from the Familiar.

In what sense do Taylor Series and MacLaurin Series "work"? What is the geometric interpretation for algebraic substitution and variable changing?

Activities: Defining Limits.
Transformations: Using DeMoivre's Theorem with Variable Changes.
Function Transformations.