# Homework Assignments

Unless otherwise stated, all problems are taken from Lay's Analysis (5th edition). Problem sets should be stapled together, with your name and collaborators clearly identified, and turned in to your instructor at your Thursday recitation section. Because we will post selected solutions on this page soon after the due date, no late homework will be accepted. See the course information sheet for information on how homework is graded.**Assignment 1, due Thursday, January 25th**

**1.1:**4, 7ab (meaning, here and elsewhere, parts a and b only), 8a, 9ace, 12.

**1.2:**4, 5, 7, 8, 10ab, 12abcf, 14.

**1.3:**3, 4.

- Note: The problems from Section 1.3 above are officially moved to be part of homework 2, but
we give the solutions in the solutions set for Homework 1 since some students might be working ahead and want to see the answers now.
**Assignment 2, due Thursday, February 1****Assignment 3, due Thursday, February 5****Assignment 4, due Thursday, February 15th****Assignment 5, due Thursday, February 23rd****Assignment 5, due Thursday, March 1rst****Assignment 6, due Thursday, March 8th****Assignment 7, due Thursday, March 22th****Assignment 8, due Thursday, March 29th**

**1.4:**3, 7, 8, 15, 18, 21, 28

**2.1:**4(acfg), 7, 10, 15, 16, 20, 22

**2.2:**11(a-f), 12(a-d), 14, 17, 30, 31(abde) .

**2.2**13,21,25,26,28

**2.3:**3 a,b,d; 5b;6c;9;10;19

**2.2**13,21,25,26,28

**2.3:**3 a,b,d; 5b;6c;9;10;19

**2.4:**1;3a,c,d,e; 4;5;9a,b (note: you can use here, without proving it, the fact that any polynomial with real coefficients has a finite number of roots.);11;15;17;21

**3.1:**3;6;9;14;17;20

Note also: be careful when using ordinal numbers that you are comfortable with exactly what they represent. For example - problem 15 on the above homework is not straightforward at all to do - in fact as far as I know, you have to use the Theorem mentioned in Problem 13 in the text (the Schroeder-Bernstein theorem.)

**3.2:**2;3a,b,e,i;4;6;7;10;12

**3.3:**2;3a,c,e,i;4a,c,e,i;6;10;11;14.

**3.2:**2;3a,b,e,i;4;6;7;10;12

**3.3:**2;3a,c,e,i;4a,c,e,i;6;10;11;14.

**3.4**1a,b,c,d,h,i;3a,b,c,e;4a,b,c,e;5a,b,c;6a,b,c;7a,c,d;10;15

**3.5:**2a,b,c,d,e;3a,d,e;4;5;6,7,8,9,12

**4.1:**2 a,b,d; 4;6a;7b,c;8b,d;12.

**4.2:**3a;5a (More will be assigned from this section on next homework.)

**4.1:**2 a,b,d; 4;6a;7b,c;8b,d;12.

**4.2:**3a;5a,c,i,j; 6;9; 14;15;16;17.

**4.3:**3a,d;4;8;9.

**Assignment 9, due Thursday, April 5th**

**4.3:**3a,d;4;8;9.

**4.4:**3a,b,d;7;13;16;17, 18

**(there will be no additional sections coverd on this homework!)**

**Assignment 10, due Thursday, April 12th**

**8.1:**3;4c,d;5b,d,f;7;11

**8.2:**1a,b;2a,b,c;3b,d,f;5b,d,f

**8.3:**3a,c,e,g,i;5a;7

**Assignment 11, due Thursday, April 19th**

**8.3:**3a,c,e,g,i;5a;7

**Assignment 12, due Thursday, April 26th**

**5.1:**3a,b,c,d;4;6b;7b,c;13;18

**5.2:**3;5;10;14;16;17

**5.3:**3a,b;4;7;8;16.

**Assignment 13, Due Thursday, May 3.**

**6.1:**4a,e;6

**6.2:**5b,c,h;8b;12

**6.3:**3a,b,f;4e

**6.4:**3, 4, 5