Fall 2013

Email Address: blair ["at"] math.unm.edu

Course Web Page: http://www.math.unm.edu/~blair/math401_f13.html

Office: SMLC 330

Office Hours: 2-3pm on Tuesdays and 11am-Noon on Thursdays. Also by appointment.

**Text:** *Foundations of Analysis* by Joseph L. Taylor.

**Meeting times/location**: Tuesdays and Thursdays at 12:30-1:45pm in DSH 334.

**Recitation**: Wednesdays at 12-12:50pm in DSH 334.

**Recitation leader**: David Weirich (dweirich ["at"] unm.edu)

**Course Description** From the catalog: *Rigorous treatment of calculus in one variable. Definition and topology of real numbers, sequences, limits, functions, continuity, differentiation and integration. Students will learn how to read, understand and construct mathematical proofs*.

**Prerequisites** (from the catalog): 264 and two courses at the 300+ level.

Check back for any announcements. Homework

Assignment #1--Due Thursday, August 29

Problems from Chapter 1, Lay: 2.4, 2.6(c,d), 2.10(a,b,c,d), 3.3(a,c), 3.4(a,c), 3.6(a,f,i), 3.7(a,b,c,g), 3.8, 4.3, 4.4, 4.10, 4.11, 4.13, 4.16

Assignment #2--Due Thursday, September 5

See handout

Assignment #3--Due Thursday, September 12

Problems from Taylor's text:

1.2: 9, 13, 15, 16, 17

1.4: 1, 2, 3, 9

1.5: 2(a,c)

Reading: Taylor, Ch. 1 and start 2.1.

Notes: For #9 in 1.4, you may take the full result in #8 for granted (you proved something similar in the first homework set). For 2c in 1.5, you may want to use Theorem 1.3.9.

Assignment #4--Due Thursday, September 19

Problems from Taylor's text:

1.5: 3, 7, 9, 10

2.1: 2, 5, 6, 7, 10

Reading: Taylor, 2.1, 2.2.

Not collected: 1.5: 4,5, 2.1: 3

Notes: For 9c in 1.5, don't forget that you can complete the square.

Assignment #5--Due Thursday, September 26

Problems from Taylor's text:

2.2: 1, 3, 12, 15

2.3: 2, 6, 7, 8, 10

Reading: Taylor, 2.3, 2.4.

Not collected: 2.2: 6, 2.3: 1,3,4

Assignment #6--Not collected

Problems from Taylor's text:

2.4: 1, 2, 3, 4, 8, 9

Reading: Taylor, 2.4.

Assignment #7--Due Thursday, October 17

Problems from Taylor's text:

2.5: 2, 7(b,c), 8, 9

2.6: 1, 3

Reading: Taylor, 2.5, 2,6, 3.1.

Not collected: 2.5: 1, 4, 5 and 2.6: 4

Assignment #8--Due Thursday, October 24

See handout

Assignment #9--Due Thursday, October 31

Problems from Taylor's text:

3.2: 7, 8, 12

3.3: 4, 8, 9, 10

Reading: Taylor: 3.3, 4.1.

Not collected: 3.3: 1, 2, 3

Notes: For 3.2 #12, consider a proof by contradiction. For 3.3 #9, 10, consider applying Theorem 3.3.5 or Theorem 3.3.6.

Assignment #10--Due Thursday, November 14

Problems from Taylor's text:

4.1: 6, 8, 11

4.2: 3, 8, 11, 12

Reading: Taylor: 4.1, 4.2, 4.3.

Not collected: 4.1: 1, 2, 3, 4, 5, 9 and 4.2: 1, 2, 4, 7

Assignment #11--Due Thursday, November 21

See handout

Assignment #12--Due Thursday, December 5

See handout