Date  Module  Theme  Assignments 
15 Wed 
I. Conditions and Conclusions: Primes, Rationals, Irrationals, and Radicals  What is a mathematical condition? When do they arise? Activities: The Rational Radical. 

110 Mon 
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. 

112 Wed 
How do conditions affect solutions and explanations of solutions? Activities: Discussion of the Prime Time System.
Mathematical considerations in selecting problems with
radicals. 
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) 

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

117 Mon 
(no class: MLK) 

119 Wed 
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 longdivision? Bonus warmup activity: A Cute Radical Problem Activities: Feasting on Leftovers  leftover sequences and the rational expansion theorem. 

121 Fri 
Due: Problem Set 2, in envelope at East Hall 1856.  
124 Mon 
II. Solutions and Representations: Polynomials and their Roots, Complex and Real Roots, Decimals  What goes into a creating a mathematical definition? What are language issues that arise when discussing "roots", "factors", and "solutions"? Activities: Working with Polynomials. 

126 Wed 
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 final presentation group members. This email should cc all group members. 

128 Fri 
Due: Problem Set 3, in envelope at East Hall 1856.  
131 Mon 
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. 

22 Wed 
Understanding and using statements of mathematics. Activities: The Rational Root Theorem 

24 Fri 

27 Mon 
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.


29 Wed 
III. Representations, Families, and Definitions: Sequences of Decimals, Complex Numbers, and Polynomials 
What are common ways to define and represent complex numbers? What is the geometry of nth 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. 
211 Fri 
Due: Problem Set 4, in envelope at East Hall 1856.  
214 Mon 
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. 

216 Wed 
Midterm Review  
221 Mon 
Performance Exam I  
223 
Midterm Exam (Written)  
228 Mon 
(no class: spring break)  
32 Wed 
(no class: spring break)  
37 Mon 
III., continued. 
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. 
Bring to class: a graphing calculator. 
39 Wed 
In what sense do Taylor Series and MacLaurin Series "work"? What is the geometric interpretation for algebraic substitution and variable changing? Activities: Defining Limits. 

311 Fri 

314 Mon 
V. Representations, Definitions, and Using Mathematical Parallels: Exponential, Logarithmic, and Linear Functions.  TBA  
316 Wed 
TBA  Due: First draft of the written component of your Final Project. This draft should contain at least an outline of all planned content.  
318 Fri 
Due: Problem Set 5, in envelope at East Hall 1856.  
321 Mon 
TBA  
323 Wed 
TBA  
325 Fri 
Due: Problem Set 6, in envelope at East Hall 1856. 

328 Mon 
TBA  
330 Wed 
TBA  
41 Fri 
Due: Problem Set 7, in envelope at East Hall 1856.  
44 Mon 
TBA  By this date, you should have met with either Dr. Lai or Ms. Mende regarding feedback on your draft.  
46 Wed 
Final Presentations  We will be inviting faculty from the School of Education and the Department of Mathematics to join us, as well as alumni of previous Math486 classes. Feel free to invite your friends to join us as well!  
411 Mon 
Performance Exam II  
413 Wed 
Final Presentations  We will be inviting faculty from the School of Education and the Department of Mathematics to join us, as well as alumni of previous Math486 classes. Feel free to invite your friends to join us as well!  
418 Mon 
Final Exam Review  
421 Thu 
Final Exam (Written)  Due: Written component of your Final Project, in envelope at East Hall 1856, in addition to as a PDF document emailed to Dr. Lai and Ms. Mende. All members of your team should be cc'd in this email. 