JHR's MA306 page

MA306
Real Variables

Textbook: Understanding Analysis, by Stephen Abbott.
MTRF 2, G310
John Rickert, Associate Professor of Mathematics
Office: G-215A, Crapo Hall
Phone: (812) 877-8473
Campus mail: CM 141
e-mail: john.rickert@rose-hulman.edu
Office hours: MTRF 3,7, or stop by and see if I'm in. My schedule
policy       grade weights       Notes       Greek alphabet       Mathematical shorthand page      
Information about mathematical typesetting is available at http://www.rose-hulman.edu/class/ma/courses/software/tex/tex.html.

Homework

For Tuesday December 3: Read sections 1.1-1.3. We will have a short quiz covering material discussed in class Monday.
For Thursday, December 4: Read Sections 1.3-1.4. Review your notes on least upper bounds. We will have short quiz covering the material discussed in class Tuesday.
For Friday, December 5: Read Section 1.4. We will have a short quiz covering properties of rational/irrational numbers.
For Monday, December 9: Read Sections 1.5, 2.1. At the end of class, the question was raised: "Are the irrational numbers uncountable"? Are they? Think about it over the weekend.

Homework due Monday, December 9: 1.2.1, 1.2.3, 1.2.10, 1.2.12, 1.3.1, 1.3.4, 1.3.6, 1.4.2, 1.4.4, 1.4.7, 1.4.9, 1.4.12. Some solution sketches.
It's strongly recommended that you work on these exercises as we cover the sections, and ask questions during the week before they are due.
Extra Credit: Compute, with proof, the supremum and infemum of the set     { 1/n+ 1/m + 1/r   :   m,n,r are natural numbers, 1/n + 1/m + 1/r < 1 }.
Extra Credit: Explicity construct a map from the natural numbers to the rational numbers using the alternating diagonal function described in class.

For Tuesday, December 10: Read Sections 2.1-2.2. No quiz Tuesday(!).
Get ready to think about sequences and series.
For Thursday, December 12: Read section 2.2-2.3.
For Friday, December 13: Read sections 2-3.2.4.
Homework due Monday, December 16: 1.5.2, 1.5.4, 1.5.5, 1.5.9, 2.2.1, 2.2.4, 2.2.7, 2.2.8, 2.3.3 ,2.3.4. Some solution sketches.
For Tuesday, December 17: Read sections 2.4-2.5. There will be a quiz asking for some sort of epsilon-N proof.
For Thursday, December 19: Read sections 2.4-2.6. Pay special attention to the epsilon-N and epsilon/2 proofs. We will be spending some time reviewing how these proofs are constructed.
For Friday, December 20: Read sections 2.5-2.6. There will be a quiz asking for some sort of epsilon-N proof.
Homework due Monday, January 6: 1.4.9, 2.3.1, 2.3.7, 2.3.11, 2.4.2, 2.4.4, 2.4.5, 2.4.6. Some solution sketches.
Reread through Section 2.7. Read through the end of Chapter 2.
Homework due Monday, January 13: 2.5.3, 2.5.4, 2.6.1, 2.6.4, 2.7.4, 2.7.9, 2.7.12, 2.7.13.
Homework due Monday, January 20: The three supplemental exercises, and 2.7.13, 3.2.1,3.2.2,3.2.3,3.2.5,3.2.13,3.3.1.
For Thursday, January 23: Let Ox = (x/x, 3x/2) for all x in (0,1), and let O0=(-epsilon,epsilon) for some epsilon>0. Then this collection is an open cover of [0,1]. Find a finite subcover. Homework due Monday, January 27: 3.3.1, 3.3.3, 3.3.5, 3.3.8, 3.3.9, 3.4.1, 3.4.2, 3.4.4, 3.4.8.
Homework due Monday, February 3: 4.2.1, 4.2.3, 4.2.6, 4.2.7, 4.2.9, 4.3.1, 4.3.3, 4.3.6, 4.3.9, 4.3.11.
Homework due Monday, February 10: The supplemental exercises and Section 4.4 #2,4,6,9; Section 4.5 #2,.7; Section 5.2 #5; Section 5.3 #5,10. Some solution sketches.
Homework due Monday, Februrary 17: Section 6.2 #1,3,7,16; Section 6.3 #1; Section 6.4 #1,2,6; Section 6.5 #1,5; Section 6.6 #1,2.

Notes

Monday, December 2: We discussed Proof by Contradiction and Proof by Induction, and went through some elementary set theory and mathematical shorthand.
Thursday, December 5: At the end of class, the question was raised: "Are the irrational numbers uncountable"? Are they? Think about it over the weekend.
Regarding the trivia quesiton on the quiz
Thursday, December 12: We saw our first epsilon/2 proof today.
Tuesday, Febrauary 18: For a Maple look at the function g(x) defined today in class, you may try the following code;
f1:= x->piecewise( -1 < x and x <= 1,abs(x));
h := x->add( f1(x-2*k),k=0..32);
plot( h(x)+h(2*x)/2+h(4*x)/4+h(8*x)/8+h(16*x)/16+h(32*x)/32,x=0..2);
or
f1:= x->piecewise( -1 < x and x <= 1,abs(x));
h := x->add( f1(x-2*k),k=0..128);
g7:= add(h(2^k*x)/2^k, k=0..7);
plot( g7,x=0..2);
What seems to be the maximum value of g(x)?

Course Policy

Multi-page homeworks should be stapled together, not mutilated.
Place your name and Campus Mailbox number in the upper right-hand corner of your homework. Homework is due when I collect it, typically at the beginning of class on the due date. Homework may be turned in later but will be penalized based on just how late it is - typically
    1 point off for turned in late during the class,
    10% off for being turned in late the same day,
    20% off per day. (weekends count for two days) i.e. 5 days later, it's too late to get a makeup homework turned in.
When writing up homework, you should circle (or otherwise clearly indicate) your answers.
It's good to work together, but you should write/type your own homework. Simply copying another person's work is not acceptable. Homeworks that are too similar to each other will be worth no credit.
I reserve the right to return as unacceptable any homework that is inadequately prepared. (full of scratch work, problems out of order, submitted on crumpled or fringed paper)
If you have any questions while I'm not around, you may e-mail me at john.rickert@rose-hulman.edu and I will reply as soon as I can.

You should come to class prepared. This means that I expect you to have done the homework, read the material, and brought your book to class.

A summary of the grade weights

Quizzes will be worth 10%
Pre-final exams will be worth 30%
The final exam will be worth 20%
and homework will be worth 40%
Go to