# Math 314, Spring 2016 Class Announcements Page

Welcome to the class announcements page. This page will contain Useful Information for the class, including all posted homework assignments and their due dates and test scheduling. Get into the habit of looking at this page regularly.

New information will be added at the top.

## Test III and Course Grades

Find here the grades on Test III and a report of your final letter grade in the course.

## The Lecture Notes (and other things kept at the top)

Here are a set of class notes I developed in Fall 2011 and Fall 2014. I will be editing these into our own notes as we go along.

### Office Hours

I am teaching Math 314, Real Analysis, TTh 12--1:15 MB 124 and Math 406, Advanced Number Theory, WF 10:30--11:45 MB 139. I participate in the logic seminar, which meets 3-4 PM W in MB124. I am tentatively defining my office hours as 9:15 -- 11:45 am TTh, 9:15 -- 10:15 am WF, 3 -- 5 pm TF (not WTh). I expect not to be routinely on campus at all on Mondays, though you are welcome to request an appointment if you need to meet me on a Monday. I expect to be around most of the day TWThF.

## Sample Final from 2014

I give the final exam from 2014 which has similar coverage to the exam I will give you. I'll give it a better format, and I may have different ideas about what review questions will appear in it. Expect a better formatted practice test to appear soon (today or tomorrow).

Here is the 2014 test in better format. I think it is quite a good review test for you all.

## Assignment X

This is due on the last day of class.

chapter 8 in Spivak: problems 15 and 16. These are quite hard. I want you to think about them over the coming weekend -- I am likely to lecture on this approach to the big theorems of chapter 8 on Tuesday. problem 17: much easier. chapter 22: problem 1 parts i,ii,iv; problem 2 parts i, v, problem 3, problem 4, problem 7 parts a,b (look back at the problem in chapter 2 that is mentioned), problem 11, problem 20, problem 23. Chapter 22 material I will start lecturing today.

Here are some hints on this homework set which I may expand on during the weekend. I will post the practice test by the end of the day Sunday.

## Test II Results

Here are the Test II grades, posted by the ID number on your paper.

## Practice Test II

Here is the practice test. It is larger than the actual test will be, and it does not yet contain any theorems and definitions which I might supply.

## Assignment IX

This is due Thursday April 7th. Whatever appears on this assignment is fair game for the test on the 14th. Turning this assignment in the following Tuesday will not be disastrous for your homework grade, but I then do not guarantee getting it back to you graded before the exam.

Spivak problems 6.1, 6.3, 6.4, 6.7, 6.9, 6.15, 7.1, 7.2, 7.5, 7.10, 7.11, 7.21a[7.21a is extra credit, hard], 8.1, 8.2. I am taking the view that I do not require all of these problems to be completed for satisfactory performance: what is expected is 6.1, 7.1, 7.2, 8.1 (definitely do all of these) and six other problems. I am likely to give substantial hints on several of these all on my own, and you should feel free to ask me about any of these problems that are puzzling you. Start working on them promptly so that you know what you need hints on...

## Solutions to Test I

Here are solutions to Test I. These do not include complete solutions to the big formal arithmetic proofs, which I will never post, as these would destroy the usefulness of these exercises as homework in the future; I'll be happy to discuss these proofs individually. I did post outline solutions to these earlier, and you can look at the proofs of commutativity of addition and right distributivity in the notes.

## Test II announced (and remark about Test III)

I am intending to give Test II, covering roughly chapters 5,6,7 (including statements and applications of the Intermediate Value Theorem and Extreme Value Theorem but not the new axiom used to prove these theorems) on April 14th. Basic definitions from chapter 8 may also appear. A full practice exam will appear here.

Test III will be in the final exam period. It will include new material from chapters 8 and 22, and will include some cumulative material with opportunities to improve earlier grades.

## Assignment VIII

Extended to Tuesday the 29th: chapter 1 in Spivak, problems 20 and 21: these are lemmas needed to prove the addition and multiplication properties of limits; proving them gives practice in using properties of absolute values; chapter 5 in Spivak problem 3 parts ii-v, viii; problem 8, problem 9, problem 12. If you are mystified by some of these...I want to hear about it, in class or in my office. If you turn in a paper to me on the 17th or 18th, complete or partial, I will comment during the break by email (retain a copy and keep working on it!)

## Assignment VII

Do the three problems on p. 88 of the notes (section 6.4). Due Thursday March 10th (I'll be generous about accepting it late since I'm posting it rather late, but I am leaving the official due date on the 10th and I intend to grade it by the following Tuesday). Examples that I have already done and examples I plan to do on Tuesday should give substantial hints. Start on it now so that you know what to ask me about (or what to watch for) on Tuesday.

I extended this assignment to Tuesday after giving some hints in class.

## Assignment VI

Do chapter 1 problem 5, p. 14, as many parts as you can (a good score does not require anything like all of them, and I may give some of them away in class). and problem 8 on the next page (this is harder). These are due on March 8 (the Tuesday after the exam) but they are exam relevant. In these problems, you may do completely common sense algebra manipulations with addition, additive inverses, subtraction and multiplication: all your reasoning about order (or positive numbers) should be explicit. Your problem 5 arguments should use (P10), (P11), (P12), not the alternative versions in problem 8.

## Timetable to complete Assignment IV and Test I announcement

Final form of Assignment IV due in class on March 1 (Tues).

## Assignment V (assigned 2/18/16, due 2/25/16):

see p. 82 of the notes (and notice that for the moment I am just assigning the first three problems mentioned there). Due on the 25th. Of course we still have completion of Assignment IV hanging over our heads. I strongly encourage you to read the notes on Spivak chapter 1 and attempt the little proofs that I suggest. The final form of the optional Marcel lab is posted.

## Lab II (ready for prime time)

Here is the text needed for the optional Marcel quantifier lab. As promised, one of the exercises is precisely the proof I did as the class demo. The other two are simpler. Section 4.6 of the notes on p. 53 contains some comments on the additional features of Marcel needed for this lab. If you are working on it and visit me in the office, I will be happy to show you how to do bits of it; I may at some point do a little more in-class demo.

## Assignment IV, 2/11/2016, due 2/18/2016 in draft.

Section 5.8 in the notes starting on p. 65. This is a hard writing assignment. You will get rewriting instructions when you hand in your draft and a final due date for a finished product. You are welcome to turn in drafts early for review, and even more than once if the cycle permits.

## Assignment III, 2/4/2016, due 2/11/2016

Section 4.5 in the notes on p. 52. This is due on 2/11/2016.

## Computer Lab 1/28/2016

Please bring your laptop computer to class on Thursday the 28th! It would be a good thing if you had Python installed on it.

Here is the lab document. It is also in the notes (section 3.8, p. 45)

## Assignment II, due 1/28/2016

See p. 28 and 29 of the notes, section 3.6.5.

Notice that the example proof done in class is found on pp. 33 and 34 of the notes.

## Assignment I, due 1/19/2016

See the lecture notes, p. 9.

The Old Stuff below is from the last time I taught the course, and will be moved to the top when it is found to be useful.

# Old Stuff which might be Useful

## my handwritten solutions (not guaranteed in any way) to Tests I and II.

Here are my handwritten solutions to Tests I and II. They are not guaranteed in any way, and you should remember that some problems in Tests I and II are likely to be changed.

Happy studying!

## Practice Questions for Test II are Here

Here are the practice questions.

## Practice test questions for Test I

Find here the practice exam.

## Old Test I papers

Practice test from fall 2009 with some solutions

Part I; Part II: The test from Fall 2011, which was given in two sittings. I am not thinking of giving a test in two sittings.

## New assignment posted on Oct 12

Here is the assignment. The assignment is also found in the notes.

This is officially due on Oct 24, after the test on Oct 22, but if you turn it in by October 17th I will grade it before the test.

## Computer Lab I

Here is the first computer lab. The lab should be submitted officially by next Friday at midnight (though I am quite patient about late computer labs).

## Class notes from Fall 2011 and assignments due 9/10/2014 and 9/12/2014

Here are a set of class notes I developed in Fall 2011. I will be editing these into our own notes as we go along

## The book

The author is Michael Spivak, the title is Calculus (it pretends to be a Math 170/175 book, but isn't) You want the fourth edition (this matters).

ISBN 978-0-914098-91-1 (accept no substitutes!)