### Math 424 -- Honors Real Analysis -- Fall, 2009 Prof. C. Ward Henson

This is a listing of all assigned homework; unless stated otherwise, all references are to the textbook, Introduction to Analysis by M. Rosenlicht.  There is a separate listing of what was done in each class.

All reading assignments should be completed before the next class.

Come to class ready to discuss any examples or problems that you were not sure of.

Classes are described in reverse time order.

Class 43 (W 12/09): no new homework.

Class 42 (M 12/07): do chap. 7 # 22, 24 and problems on 12/07 handout.

Class 41 (F 12/4): read the rest of 7.3 for M 12/7.

Class 40 (W 12/2): no new homework.

Class 39 (M 11/30): do chap. 7 # 18, 21.

Class 38 (F 11/20): read 7.3 for M 11/30; do problems on 11/20 handout, which gives another method for introducing the exponential function.  (Problem [1] makes use of the ratio test for absolute convergence of series.)

Class 37 (W 11/18): do chap. 7 # 6, 8, 9, 12, 13.

Class 36 (M 11/16): read 7.2 for W 11/18; do chap. 7 # 1, 4, 5.

Class 35 (F 11/13): read R, 7.1 for M 11/16.

Class 34 (W 11/11): no new homework.

Class 33 (M 11/9): R, chap. 6 # 23, 24, 25, and DW, chap. 17 # 22, 23, 28.

Hand in M 11/9: problems A on 11/2 handout, E on 11/4 handout, and H on 11/6 handout.  (Solutions sketches here.)

Class 32 (F 11/6): read R, chap. 6, section 5 for M 11/9; do problems G-J on 11/6 handout and R, chap. 6 # 12, 15, 16.

Class 31 (W 11/4): read DW pages 345-346; do problems E-F on 11/4 handout.

Class 30 (M 11/2): do problems A-D on 11/2 handout; use today's handout on properties of the integral to review what is done on DW, pages 341-344.

Hand in M 11/2: DW, chap. 17 # 15a and R, chap. 6 # 2, 7.  (Solutions sketches here.)

Class 29 (F 10/30): no new homework.

Class 28 (W 10/28): read DW pages 342-344; do DW, chap. 17 # 15 and R, chap. 6 # 4, 7.

Class 27 (M 10/26): read DW pages 341 and 345 for W 10/28; do DW, chap. 17 # 4, 5, 6, 11, 12; and R chap. 6, # 1, 2.

Class 26 (F 10/23): read DW pages 339-340 for M 10/26.

Reference for the next 6 classes is chapter 17 of Fundamental Mathematics by D'Angelo and West; this covers the Riemann-Darboux approach to defining an integral for bounded real-valued functions on a closed bounded interval.  Material from this chapter will be referred to as "DW" and the Rosenlicht text will be referred to as "R".

Classes 24 and 25 (M 10/19 and W 10/21): no new homework.

Hand in M 10/19: chap. 4 # 33a, 36, and chap. 5 # 2a.  (Solutions sketches here.)

Class 23 (F 10/16): do chap. 5 # 11, 14.

Class 22 (W 10/14): read 5.4 for F 10/16; do chap. 5 # 6, 8, 9a.

Class 21 (M 10/12): read 5.3 for W 10/14; do chap. 5 # 2, 4.

Hand in M 10/12: chap 4 # 14a, 27, 29a. (Solution sketches here.)

Class 20 (F 10/9): read 5.1 and 5.2 for M 10/12; do chap. 4 # 39, 41 (harder), 42, 43.

Class 19 (W 10/7): do chap. 4 # 33, 35, 36, 37.

Class 18 (M 10/5): read 4.6 for W 10/7; do chap. 4 # 24, 25, 27, 29.

Hand in M 10/5: chap. 4 # 3, 4, 9a.  (Solution sketches here.)

Class 17 (F 10/2): read 4.5 for M 10/5; do chap. 4 # 13, 14, 16, 17, 19, 20, 21.

Class 16 (W 9/30): read 4.4 for F 10/2.

Class 15 (M 9/28): read 4.2 and 4.3; do chap. 4 # 2, 3, 4, 6, 9a, 10b, 11.

Class 14 (F 9/25): read 4.1 for M 9/28.

Class 13 (W 9/23): no new homework.

Class 12 (M 9/21): look at chap. 3 # 38; check some details of our proofs that R and R^2 are connected.

Hand in M 9/21: problem A on 9/11 handout and chap. 3 # 28, 33.  (Solution sketches here.)

Class 11 (F 9/18): read 3.6.

Classes 9 and 10 (M 9/14 and W 9/16): read chap. 3 problems # 35-37, which we will cover in detail in class; do chap. 3 # 26, 27, 28, 29, 30, 32, and (harder) 33.

Hand in M 9/14: "(3) implies (1)" in problem B and problem D, on the 9/4 handout. (Solution sketches here.)

Class 8 (F 9/11): continue reading 3.5; do problems on 9/11 handout.

Class 7 (W 9/9): begin reading 3.5 for F 9/11; no new exercises (exam #1 today).

Class 6 (F 9/4): do chap. 3 # 24 and problems on 9/4 handout

Hand in F 9/4: problems A,B on 8/31 handout.  (These are due Friday because Monday 9/7 is a holiday; graded solutions will be handed back Tuesday 9/8 at the problem session and will also be available in the folder on Prof. Henson's office door, 310 Altgeld.)  (Solution sketches here.)

Class 5 (W 9/2): read 3.4; do chap. 3 # 10, 15, 16.

Class 4 (M 8/31): read 3.3; do problems A-D on 8/31 handout.

Hand in M 8/31: chap. 2 # 7, 12 and chap. 3 # 4. (Solution sketches here.)

Class 3 (F 8/28):  read 3.1 and 3.2; do chap. 3 # 1abc, 4, 5.

Classes 1 and 2 (M 8/24 and W 8/26): read chap. 1 and 2; do chap. 2 # 7, 12, 13.  (Also review pp. 16-17 and chap. 13 in Mathematical Thinking by D'Angelo and West, which is the textbook for honors sections of Math 347).  Begin reading chap. 3 for F 8/28.