Index Announcement Syllabus & Homework |
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We will cover material in

Week 1 (Aug 27) Chapter 1. What Is Meant by `An Advanced Perspective'?

Students will take part of the NYS Math III Regents Exam in class on Wednesday 8/29.

Homework 1 (due Sept 5) p 1-15 nos 1, 7, 8Week 2 (Sept 3; Weds only) Chapter 2. Real Numbers

omit sections 2.1.3 and 2.1.4 (except for proof of irrationality of

Homework 2 (due Sept 10) p 2-9 nos 5, 6, 12 p 2-19 nos 1, 4, 7

Week 3 (Sept 10) Chapter 2 (end) Complex Numbers. Chapter 3 Functions

- Team activity 1. How would you explain complex numbers to an 11th grader who had never heard of them. Think: what? why? where? how?
- Team activity 2. Data: the US Tax Schedule for 2000. Graph, as a function of x your adjusted income, f(x) your marginal tax rate and g(x) the total tax you owe. How are these two functions related? (Marginal tax rate is the percent you pay on the last dollar you earn).

Homework 3 (due Sept 24) p 2-58 nos 1bd, 4, 11 p 3-8 nos 3, 5 p 3-13 nos 4, 6ab p 3-21 nos 1, 2, 7, 8Week of September 17: No meetings

Week 4 (Sept 24; Mon only) Chapter 3 Functions (cont.)

- Handout: Chapter 5 (Recommendations for High School
Teacher Preparation) from
*The Mathematical Education of Teachers,*AMS & MAA, 2001 - Team activity: An unknown function
`f(x)`is in a box. It is either an exponential`A a`, a logarithm^{cx}`A log`, a polynomial_{a}cx`A`, a non-polynomial rational function_{0}+ A_{1}x + ... + A_{n}x^{n}`p(x)/q(x)`where`p(x)`and`q(x)`are polynomials with no common factors, with`q(x)`of degree at least 1, or a trigonometric function, say`sin x`or`cos x`. Find a scheme to determine what kind of function it is by asking three yes-or-no questions about its behavior.

Homework 4 (due Oct 3) p 3-32 nos 3, 6, 9, 10, 13 p 3-40 nos 1, 3, 7, 8 Understand Langrange Interpolation (p 3-84)

Week 5 (Oct 1) Chapter 4. Equations

- Team activity: team A makes up an interval
`[a,b]`and a function`f`invertible on this interval. They choose 4 points`x,y,z,w`from the image`f([a,b])`. On a separate sheet they record their proof of invertibility, and the inverse images`f`etc. They pass the first sheet to team B who calculate^{-1}(x),`f`etc. on their own. Teams compare answers.^{-1}(x),

Homework 5 (due Oct 10) p 4-6 nos 1, 2, 3, 7, 9 p 4-13 nos 1, 2, 3, 9, 16

Week 6 (Oct 8) Chapter 4. Equations

- Team activity: Use calculators to solve
x

^{5}+ x + 1 = 0 sin x = .6 x + sin x + 1 = 0. - Team activity: Write four or five constructive criticisms of the text.
- Team activity: use Newton's method with
`x`to solve_{0}= 1`x`. Do two steps.^{5}+ x - 1 = 0

Homework 6 (due Oct 17) p 4-21 nos 3, 5, 6 p 4-23 nos 2, 5 p 4-32 nos 1, 7 p 4-37 nos 3, 4, 10, 12

Week 7 (Oct 15) Chapter 5. Integers and polynomials (through 5.2.2)

- Team activity: give the proof by induction that the sum
of the integers from 1 to
`n`is`n(n+1)/2`. - Team activity: apply the Euclidean Algorithm to find the greatest common denominator of 3731 and 1517.

Homework 7 (due Nov 5) p 5-8 nos 1, 4, 5 p 5-16 nos 10, 12 p 5-21 nos 2, 8, 12 p 5-37 nos 2, 6 p 5-41 nos 6, 8, 9

Week 8 (Oct 22) Monday: Review for Midterm

Wednesday: Midterm Examination through Chapter 4. See Review for Midterm 1

Week 9 (Oct 29) Base representations (5.2.5), Division of polynomials (5.3.1), Equivalence relations, modular arithmetic (6.1.1)

- Team activity: divide
`3x`by^{4}-2x^{3}+6x^{2}-x+1`x`^{2}-2x+2 - Team activity: A relation on a set
`S`is a subset`R`of the Cartesian product`S x S`. What does the condition ``reflexive'' say about the subset`R`? .

Homework 8 (due Nov 7) p 5-64 nos 1, 3, 4, 5 p 5-73 nos 1, 3, 4, 5, 6 p 6-8 nos 1, 2, 5, 6, 14

Week 10 (Nov 5) Chapter 7: Isometries

- Team activity: prove ``Jason's Formula"
`T`._{-P}R_{P,theta}= R_{0,theta}T_{-P} - Calculate the coordinates of the image of
`(x,y)`after rotation by 60^{o}about the point`(2,1)`.

Homework 9 (due Nov 14) p 7-40 nos 1, 3, 5 p 7-48 nos 1, 4, 9, 10, 12a

Week 11 (Nov 12) Chapter 7: Isometries (cont.)

- Team activity: Let
`X, Y and Z`represent the`x`-axis, the`y`-axis and the line`x = y`, respectively. Calculate`r`o_{Z}`r`and_{X}`r`o_{Y}`r`and explain your results in terms of the 2-reflection theorem._{Z} - What happens (to the 2-reflection theorem) when the two lines of reflection do not intersect?

Homework 10 (due Nov 28) p 7-68 nos 1, 2, 3 p 7-98 nos 1, 2, 3, 4, 8 Know Theorems 7-17 and 7-18 and their proofs

Week of November 19: No meetings

Week 12 (Nov 26) Chapter 9: Trigonometry

- Team activity: A triangle has sides of length 10, 11, 19. Solve for the three angles.
- Team activity: The flagpole across the brook. Angles subtended
43
^{o}and 32^{o}from a point 100 feet further away from the flagpole. Calculate height. - Team activity: Calculate the addition formulas for sine
and cosine from
`e`and the law of exponents.^{ix}= cos x + i sin x - Team activity: Assume the moon is in circular orbit around the
earth at radius
`R`= 384,000 km, so its position is`(Rcos(ct), Rsin(ct))`for some angular speed`c`radians/unit time. Given that the moon makes one complete revolution about the earth in approximately 28 days (actually closer to 27.3) what is`c`? What is the velocity of the moon along its orbit?

Homework 11 (due Dec 10) p 9-7 nos 1, 2, 3, 8a p 9-13 nos 1, 2, 3, 6, 7 p 9-25 no 5 p 9-35 no 4 p 9-42 nos 1, 4

Week 13 (Dec 3)

See Review for Midterm 2.

Week 14 (Dec 10) Review.

Last day of classes: December 13

Final Examination: Monday December 17, 5-7:30 PM

Math Dept SUNY Stony Brook

tony@math.sunysb.edu

November 2001