mae301 - syllbus F01

## MAE 301 Syllabus & Homework    Fall 2001

We will cover material in High School Mathematics: An Advanced Perspective. by Usiskin, Peressini, Marchisotto and Stanley.

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, 8
```
Week 2 (Sept 3; Weds only) Chapter 2. Real Numbers
omit sections 2.1.3 and 2.1.4 (except for proof of irrationality of e)
```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, 8```
Week 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 acx, a logarithm A logacx, a polynomial A0 + A1x + ... + Anxn, a non-polynomial rational function 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-1(x), etc. They pass the first sheet to team B who calculate f-1(x), etc. on their own. Teams compare answers.
```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
```x5 + 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 x0 = 1 to solve x5 + x - 1 = 0.   Do two steps.
```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 3x4-2x3+6x2-x+1 by x2-2x+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 RP,theta = R0,thetaT-P.
• Calculate the coordinates of the image of (x,y) after rotation by 60o 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 rZ o rX and rY o rZ and explain your results in terms of the 2-reflection theorem.
• 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 43o and 32o from a point 100 feet further away from the flagpole. Calculate height.
• Team activity: Calculate the addition formulas for sine and cosine from eix = cos x + i sin x and the law of exponents.
• 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) Wednesday Dec 5 Midterm 2 on material in chapters 5, 6, 7
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
Anthony Phillips
Math Dept SUNY Stony Brook
tony@math.sunysb.edu
November 2001