### Extra Office Hours

I will be holding extra office hours in the run-up to the final exam. These will be

- Tuesday 11am-1pm
- Wednesday 2pm-3pm.

June 4, 2011

I will be holding extra office hours in the run-up to the final exam. These will be

- Tuesday 11am-1pm
- Wednesday 2pm-3pm.

May 30, 2011

The final exam is scheduled for Thursday, June 9, 11:30am-2:30pm, in the usual lecture room. No books, notes, cheat sheets, calculators, cell phones or other aids are allowed. The exam will cover all the lecture topics, along with the relevant reading material in Eccles, and the unit on limits and continuity from lecture (notes are available on this material below. You may want to use the following to help while studying:

- Practice problems. Some of the problems on the test may be very similar to these. On the other hand, some of these problems are harder than what will appear on the test.

May 9, 2011

The class calendar and homework assignments have been updated. Please make sure you have the most current versions.

May 9, 2011

The midterms have been graded and are being returned in lecture. Sample solutions are available here.

April 30, 2011

Ameera has rescheduled her office hours from now on to be Thursdays 8am-12pm.

April 27, 2011

The midterm exam is scheduled for Friday, May 6, during the usual lecture time. No books, notes, cheat sheets, calculators, cell phones or other aids are allowed. The exam will cover Chapters 1-11 (inclusive) in Eccles, and the unit on limits and continuity from lecture (notes are available on this material below. You may want to use the following to help while studying:

- Previous exams: 2007, 2009.

Caution: The above exams are provided "as is", exactly as they appeared when administered and without answers; in addition, they may differ in form and content from the exams given this term. - Practice problems. Some of the problems on the test may be very similar to these. On the other hand, some of these problems are harder than what will appear on the test.

April 23, 2011

Since the schedule has been shifted a bit, I've modified the questions on Homework Exercises 5 and 6.

April 21, 2011

Ameera is away at a conference this coming week (Apr 25-29). Patrick Driscoll will be covering her sections and office hours. His office hours are Wednesdays 1-2 in Calc Lab and Thursdays 10-11 in APM 6351.

April 15, 2011

To give you some more time to digest the definitions of limits and continuity, the addendum question on continuity that is part of Homework Exercise 3 will not be graded. I still recommend you look at it and try to do it (and solutions will be posted) since the second Longform Homework deals with these concepts. As promised, I've uploaded a short writeup with the definitions and some examples below.

April 14, 2011

Ameera has rescheduled her office hours this week to be Friday, April 15, 11am-1pm.

April 11, 2011

Homework 3 has been updated to include a question on continuity (to be discussed on Friday, April 15).

April 11, 2011

Cody Heiner came up with this ingenious proof of the statement we were discussing at the beginning of today's class. We want to prove that for all positive real numbers, x, x + (1/x) >= 2. Notice that (for positive x), this inequality is equivalent to x^2 + 1 >= 2x, which in turn is equivalent to x^2 - 2x + 1>=0. But, we can rewrite the left hand side as (x-1)^2, which is always non-negative. Therefore, the inequality is true, as required.

April 4, 2011

After homework is due, you can find solutions to it posted on this website.

Also, after each section, the worksheet discussed during the section is available below, along with solutions.

March 16, 2011

Welcome to MATH 109. This webpage will be your main source of information for this course. It will be updated frequently with announcements and assignments, so check back often.

Important information about the textbook, homework, and exams is on the Schedule and Syllabus page. Also there, you can find a calendar with the current information on important dates for this course.

Below you can find all homework assignments and any additional handouts.

Exercises listed in parentheses ( ) are recommended but

- Homework Exercises 1
(Due 4/4) Solutions*Chapter 1*: 2;*Chapter 2*: (1), 5;

*Chapter 3*: (1), 2, 6;*Part I Problems*: 1.

- Homework Exercises 2
(Due 4/11) Solutions*Chapter 4*: 2, (3), 7;*Part I Problems*: 7;

*Chapter 6*: (1), 2, 6;*Part II Problems*: (4).

- Homework Exercises 3
(Due 4/18) Solutions*Chapter 7*: (1), 2[i,iii,v], 4[iii,iv], (7);*Part II Problems*: (11);

*Chapter 8*: 1, (3), 4;*Continuity*: attached.

- Homework Exercises 4
(Due 4/25) Solutions*Chapter 9*: 1[i, ii], 4, (5);*Chapter 10*: 3;

*Chapter 11*: 2;*Part III Problems*: 2.

- Homework Exercises 5
(Due 5/2) Solutions*Chapter 10*: 1;*Chapter 11*: (1), (5i), 5ii;

*Chapter 5*: (1), 2, 4;*Part I Problems*: 13.

- Homework Exercises 6
(Due 5/16) Solutions*Chapter 12*: 4, (6);*Chapter 14*: 1, (2), 4;

*Part III Problems*: (11), (28);*Chapter 15*: 1[i,ii], 2, (3).

- Homework Exercises 7
(Due 5/23) Solutions*Chapter 16*: (1);*Chapter 17*: 1, 2

*Chapter 18*: 1*Part IV Problems*: 14, 15i;

- Homework Exercises 8
(Due 6/1) Solutions*Chapter 22*: (1), 3;*Chapter 19*: 2, (4ii)

*Chapter 20*: 1i, (1[ii-iv]), (2i);*Chapter 21*: 3, (5i);

*Chapter 23*: (1), 2.

The long-form homework will be graded according to the following rubric.

The discussion on pages 21-22 of Eccles' book is useful in thinking about writing up proofs.

- Sample long-form homework Sample solution
Annotated sample solution
Do there exist propositions p and q such that both "p implies q" and its converse are true? Do there exists propositions p and q such that both "p implies q" and its converse are false? Justify your answers.

- Long-form homework 1
(Due 4/8) Discuss the existence and non-existence of least and greatest numbers by answering all the components of Problems 9, 10, and 11 in Eccles, page 54. Remember that you must use full and grammatical sentences in your write-up.

- Long-form homework 2
(Due 4/22) There are two common intuitive explanations of what it means to say that a function f is continuous.

1. You can draw the graph of f without lifting your pencil.

2. For any point a, f(x) is near f(a) whenever x is near a.

Discuss how these explanations are connected to the definition of continuity we discussed in class. You may want to use formalizations of these statements with quantifiers (if possible) and examples of functions. - Long-form homework 3
(Due 5/4) Discuss the existence and non-existence of minima and maxima of finite sets of numbers by answering all the components of Problems 5, 6, and 7 in Eccles, page 183.

- Long-form homework 4
(Due 5/20) Investigate the properties of the least common multiple of two non-zero integers by answering all the components of Problem 13 in Eccles, page 226.

- Long-form homework 5
(Due 6/3) Investigate the properties of rational solutions of polynomials with integer coefficients by answering all the components of Problem 12 in Eccles, page 296.

- Course syllabus in pdf
(Uploaded 3/23) - Definitions and examples of limits and continuity
(Uploaded 4/15) - Worksheet from section on 3/31, and its solutions
(Uploaded 4/4) - Worksheet from section on 4/7, and its solutions
(Uploaded 4/11) - Worksheet from section on 4/14, and its solutions
(Uploaded 4/15) - Worksheet from section on 4/21, and its solutions
(Uploaded 4/24) - Worksheet from section on 4/28, and its solutions
(Uploaded 4/29) - Worksheet from section on 5/12, and its solutions
(Uploaded 5/16) - Worksheet from section on 5/19, and its solutions
(Uploaded 5/24)

Tue 2:00PM-3:00PM

and Thur 1:00PM-3:00PM

MWF 1PM-1:50PM PETER 104