Math
147,
The Language of Mathematics,
Spring 2012

This site updated April 23, 2012

(Recent
updates
will usually be above the first horizontal line.

Looking for something? See the page index here.

Looking for something? See the page index here.

HW due Wednesday, April 25: None, but here is an old final exam and I will answers questions about it.

HW due Friday, April 27: None. I will review. Come with questions.

Our final exam is 8:00-9:50 am, Thursday, May 3, during exam week, in the usual room.

(You can find your other exam times here: http://www.montana.edu/registrar/exams/ )

April 16

Revised HW for Wednesday, April 18: Do the exam I handed out and come with questions about it.

The HW formerly due Wednesday on Chapter 5.0 and 5.1 will be due Monday after the exam Friday.

Friday, April 20: No HW due. Exam 4 (100 points) emphasizing Chapter 4 (and relying on all earlier material).

Here is a Harvard article on learning and how it relates to time and sleep.

April 9

The last day to drop without a letter grade is Friday, April 13. If you are not attending regularly, it is time for you to drop. It is very rare for non-attending students to do well enough on exams to avoid bad grades. Come to class Wednesday and I will sign a drop form for you (I will bring blank copies).

If you do not want a letter grade, fill out a "Drop form," get two signatures, and submit it to Montana Hall by the end of Friday, April 13, in which case you will get a "W" (withdrawn) which does not affect your GPA but gives you no credit for the course. The "instructor's signature" can be satisfied in two ways-- Dr. Esty can sign it or it may be signed by an administrative assistant in the main math office (Wilson Hall 2-214). However, you also need your adviser's signature, so allow some time to find that person. If you stay and get a low grade, it will count in your GPA, but it can be replaced if you take the course again and do better. Low grades are replaced and erased by taking the course again and doing better. This course won't be offered again until next Spring semester.

HW due Friday, April 13: Section 4.5: A20, 21, 22, 23, 24, B1, 7, 10, 14, 19, 30, 49, 50

HW due Monday, April 16: Section 4.5: B61, 64, 90. Read Section 4.6. Section 4.6: A1, 4, 8, 12, B1, 2, 5, 7, 8, 16

HW due Wednesday, April 18: Revised--this is now due Monday: Read Sections 5.0 and 5.1. Section 5.0: B1, 2, 3, Section 5.1: A1, 3

Friday, April 20: No HW due. Exam 4 (100 points) emphasizing Chapter 4 (and relying on all earlier material).

April 2

HW due Monday, April 2: Read Section 4.3. Section 4.3: A1, 2, 3, 5, 8, 13, 16, 21, 29, B1, 2, 3, 9, 10, 12, 29, 30

HW due Wednesday, April 4: Reread Section 4.3. Section 4.3: B8, 31, 32, 39, 40, 45-48

Friday, April 6 is University Day, with no classes.

HW due Monday, April 9: Read Section 4.4. Section 4.4: A1, 4, 5, B1, 2, 5, 9-12, 24, 25

HW due Wednesday, April 11: Section 4.5: Read Section 4.5. Section 4.5: A1, 2, 3, 5, 9, 14, 51, 54, 61

QUIZ Wednesday, April 11, on logic through Section 4.4. 25 points.

There will be an important unit exam on Chapter 4 at the end of Chapter 4.

There will be a comprehensive Final Exam at the scheduled hour of exam week, 8:00 - 9:50 am, Thursday, May 3.

These two exams will have a very large impact on your course letter grade. If you do well on them you will get a good grade, regardless of any weak performances from earlier in the semester.

March 26

I hoped you would notice and report to me examples of sentences in English that were open to two interpretations. I noticed one:

Interpret this: "[If you employ this strategy] your business will have more satisfied customers."

Does this mean more customers who are satisfied, or customers who are more satisfied? Does the "more" apply to the customers or to the satisfaction level? If you want "more" to apply to the satisfaction level, you could use a hyphen: more-satisfied customers. If you want it to apply to the number of customers, you could try to reorder it to put "more" next to "customers: "more customers".

March 22

Exam on Chapter 3, Monday March 26. No HW due. Look at an old exam (the same one mentioned below the homework for March 23.).

HW due Wednesday, March 28: Read Section 4.1. Learn the terms. If you didn't finish the Friday HW on 4.1, hand it in today, as well as Section 4.1, page 211: A4, 5, 6, 14, 17, B3, 4, 6

HW due Friday, March 30: Read Section 4.2 (as usual, read the section). Section 4.2: A1, 4, 5, 9, 14, 19, 20, B2, 38

March 20

In class Monday I gave examples of sentences in English that were open to two interpretations because of the connectives. I am offering four points extra credit to any student who notices and reports to me first another example actually used in print or on TV or on the web. Tell me the sentence, the citation, and how it could have two different meanings. We will discuss it in class.

There will be a short True/False quiz on connectives, much like some homework in 3.3 and 3.4, Wednesday in class.

Our final exam is 8:00-9:50 am, Thursday, May 3, during exam week, in the usual room.

(You can find your other exam times here: http://www.montana.edu/registrar/exams/ )

March 19

Every textbook section: This is a language course. Terms facilitate communication. If you were taking German, you would have to memorize what the words mean. Similarly, in this class you must memorize what the terms mean so we can communicate using those terms.

At the end of each section there is a "Conclusion," and at the end of the Conclusion there is a part labeled "Terms." Learn those terms, just like you would have to learn what "aufwiedersehen" means if you were studying German.

March 6

HW due Wednesday, March 21: revised 3/9 Section 3.4, page 194: B12, 14, 20, 22, 31, 35, 36, 45, 46, 47

HW due Friday, March 23: revised 3/9 Section 4.1, page 211: A1, 2, 3, 13, 16, B1, 7, 9

Here is a copy of a previous exam on Chapter 3. This semester's exam will also repeat types of questions from Exams 1 and 2 this semester. The material is cumulative (as is any language) and you are building on the material from Chapters 1 and 2.

Monday, March 26: EXAM emphasizing Chapter 3

The purpose of Chapter 3 is not to teach you how to do truth tables. The chapter is intended to help you acquire a genuine understanding of the five connectives and how they combine with one another, and what can be deduced from what. Make sure you recognize and can use the results that are given in the chapter. Truth tables will be a small part of the exam. Of course, the material from Chapter 1 and 2 is critical prerequisite material and will be part of the exam.

March 1

In Chapter 3 your job is to figure out what the five connectives mean and how they combine.

3.1: Distinguish "and" and "or". Understand "if..., then..." and why a conditional sentence is true if its hypothesis is false. Understand that "iff" does not assert that either component is true, just that they are true or false together.

3.2: Logical equivalences give you alternative ways to think about sentences with connectives. The contrapositive of a conditional is logically equivalent to the conditional, but the converse is not. Theorem 3.2.8, "A Hypothesis in the Conclusion," is very important because it is frequently used to reorganize proofs.

3.3: The negation of a conditional is not a conditional; it is a sentence with "and". We anticipate generalizations (next chapter) and note that a single counterexample proves a generalization is false.

3.4: How to make deductions from given assertions.

Results from Chapter 3 are summarized on pages 199-201.

After Chapter 3 there will be an exam on it.

HW due Friday, March 2: Section 3.1, page 156: A10, 12, 16, 34, 37, 47, 70, 76, B2, 3, 5, 6, 9 [some of these, such as B5 and B6, you have to figure out]

HW due Monday, March 5: Section 3.2, page 169: A1, 2, 8, 11, 15, 18, B1

HW due Wednesday, March 7: Section 3.2, page 170: B3, 4, 6, 10, 13, 16, 22, 24, 33

HW due Friday, March 9: Section 3.3, page 182: A2, 6, 15, 18, 21, 25, 33, 34, 61, 78, B3 [a famous problem]

March 10-18 is Spring Break. No classes.

HW due Monday, March 19: Section 3.3, page 183: A11, 20, 23, 79, B1 [Don't tell me that it is right; tell me why it is right. Do a good and convincing job], 2, 4, 6, 14, 21, 27

also, Section 3.4: page 193: revised 3/9 A1, 3, 5, 6,10, B1-6, 9, 10, 11, 13, 19, 21

Feb. 21

The exam emphasizing Chapter 2 will repeat some types of questions from Exam 1. Please be sure you know how to do the questions on this semester's Exam 1.

Feb. 15

Revised HW for Friday, Feb. 17: (2.3) A34, B15, 58, 65, 66 (2.4) A1, 2, 3, 4, 5

Monday, Feb. 20 is President's Day, a holiday. No classes.

HW due Wednesday, Feb. 22: (2.4) page 136. A9, 10, B3, 4, 5, 16

Here is an old exam on Chapters 1 and 2.

Bring questions about it on Friday because Friday we will do some review prior to Monday's exam.

HW due Friday, Feb. 24: (2.4) page 136. B7, 10, 20

Exam on Chapters 1 and 2, Monday, Feb. 27.

HW due Wednesday, Feb. 29 (Leap year!): Section 3.1, page 156: A1, 2, 4, 6, B1

HW due Friday, March 2: Section 3.1, page 156: A10, 12, 16, 34, 37, 47, 70, 76, B2, 3, 5, 6, 9 [some of these, such as B5 and B6, you have to figure out]

Feb. 10

When people think of math, many of them think of numbers. However, for algebra, you must also think about operations and order (and equations and inequalities, which are relations [between expressions]). In Section 2.2 on functions we are thinking about operations on numbers. In 2.3 we are thinking about even more abstract "things": operations on equations. Take a given equation and do something to it to change it into a new equation you like better.

HW due Monday, Feb. 13: Reread Section 2.3. Section 2.3, page 121: A2, 3, 20, 26, 30, 33, 37, B1, 2, 5, 10, 25

HW due Wednesday, Feb. 15: Section 2.3, page 123: B3, 6, 9, 10, 24, 28, 30, 38, 39, 47

[revised, see above] HW Due Friday, Feb. 17: Section 2.4, page 136: A1, 2, 3, 4, 5, 9

Monday, Feb. 20 is President's Day, a holiday. No classes.

Feb. 9

Comments on the purpose of homework.

Feb. 2

Exam 1 was administered Feb. 1. If your letter grade was good, congratulations! Your foundation is good.

However, if your letter grade was not good, you will still need to learn that material. It was mostly on basics of the language that mathematics uses a lot. If you stick with it, come to class, and read the material with the intention of learning it, you will do better in the future. (When people continue to study a language, they get better and better at it.) To encourage you to do better, I offer an incentive. If you do better on Exam 2, I will raise your lower score on Exam 1 to the better score you got on Exam 2.

Remember the philosophy: This is a language course. If you are competent or fluent at it at the end of the course, you will get a good grade. However, competency takes frequent involvement and substantial effort. Here is a tried and true method of learning.

Read the section each day. You are learning to read and grasp Mathematics. This requires practice. Read for comprehension every day.

If something is unclear, ask about it in class, or see me in my office. I love this stuff and am in my office a lot. I'd be happy to see you.

HW Due Monday, Feb. 6: Section 2.1, page 87: B8, 14, 15, 16, 20, 21, 22, 28, 29, 30, 31

Read Section 2.2. Section 2.2, page 99: A1, 4, 10

HW due Wednesday, Feb. 8: Reread Section 2.2, page 100: A28, 29, 30, 35, B1, 3, 4, 6, 7, 10, 13, 35

Friday, Feb. 10, Quiz on sets and functions. 20 points. Questions will resemble the homework questions.

HW due Friday, Feb. 10: Section 2.3, page 121: Read it! (as always. It's long.) A1, 4, 7, 9, 15, 21, 25, 29

HW due Monday, Feb. 13: Reread Section 2.3. Section 2.3, page 121: A2, 3, 20, 26, 30, 33, 37, B1, 2, 5, 10, 25

Jan. 25

HW for Monday, Jan 30: Review Sections 1.1-1.5. Read Section 2.1. (2.1) page 85: A1, 3, 5, 15, 17

If something is unclear, ask about it in class, or see me in my office. I love this stuff and am in my office a lot. I'd be happy to see you.

Here is an old exam on Chapter 1.

Wednesday, Feb 1: . Exam 1 on Chapter 1.

The exam will emphasize terminology. Learn our language terms!

The questions resemble the homework questions and reflect the required reading.

Remember the philosophy: This is a language course. If you are competent or fluent at it at the end of the course, you will get a good grade. However, competency takes regular involvement and substantial effort, including reading the sections with intent to make sense of them.

HW for Friday, Feb. 3: Reread Section 2.1. (2.1) page 85: A18, 19, 23, 27, 31, 32, 35-40, B1, 2, 5, 19

Jan. 19

HW due Wednesday, Jan. 25: Read Section 1.5. Hand in from pages 65ff: (1.5) A1-6, A13-20, A33-36, B1, 2, 3, 7, 9, 10, 17, 21, 25, 26

HW for Friday, Jan. 27: Reread Section 1.5. (1.5) B8, 11, 13, 15, 18, 19, 22, 27-32, 37, 39, 44

Did you visit

http://www.wolframalpha.com/

to see what it can do? Not only does it show the future of math, it shows the present!

Can you get it to do something? Say

solve x squared plus 3 x minus 8 equals 0

find the derivative of x cubed

find the integral of x cubed.

graph x squared plus y squared equals 1

If you are a future educator, it is important to know what is worth teaching and what is not--what needs emphasis and what doesn't. I hope that throughout the course, and especially near the end, you will be thoughtful about what math needs to be taught in various grades. What should be the balance between facts, skills, repetition, concepts, understanding, etc.?

Jan. 17

Bookmark this page and check it frequently for updates about exams, homework, etc.

The homework for Jan 18 and following dates has been changed. See below.

Index:

Assignments are on this page.

Exams and Grading

Times, room, and instructor (office hours, etc.)

The course policies are here

Advice about how to do well.

What is the prerequisite?

What is the workload?

Every homework: Put your name high in the upper right corner of your HW page. Put the section number of the homework below it. I do not need your student ID number or the date. If you have questions about any problems, write the problem number(s) (e.g. "B5") on the side board before class and we will go over it.

If you use spiral-bound paper, please trim the ragged edge before handing it in.

HW due Friday, Jan. 13: Read the course policies. This is a language course. Mathematics is primarily a written language, and you will get good at it by reading and writing it (and you won't get good at it if you don't read it). Reading comes first. Read each section (really!) to get better at reading.

Read "To the Student" (page v) and Section1.1 (It is rather long). Do and hand in: Section 1.1, page 14: A1, 2, 3, 4, 5-6, B1, 2, 3

Note: In a language course, you must memorize what the foreign words mean. The words you use most frequently are the most important words. This course also has words you must memorize. The ones we use most frequently are the most important words. In class you will hear some terms frequently and I will emphasize the most important words. Each section mentions its terms in a list just above the exercises.

HW due Wednesday, Jan. 18 (Monday is a holiday): Read Section 1.2: Do Section 1.2, page 21: A1-7, 17, 33, B1, 2, 3, 4, 5, 6, 11, 13, 15, 16, 21, 23, 27, 28

HW due Friday, Jan. 20: Read Sections 1.2 and 1.3: Do Section 1.2, page 23, B7, 11, 30, 31, 33

and Section 1.3, page 31ff: A1, 2, 3, 7, 10, 15, B1, 2

HW due Monday, Jan. 23: Read Section 1.4. Pay attention to what you are learning. It is not just arithmetic. It is how to write the methods of arithmetic, and how results are organized in order such that the current result may depend upon prior results.

HW to hand in: 1.3, page 32ff: A18, A25-30, B3-7, 11, 12, 18, 23-26

1.4, page 55ff: A1, 5, 11, 15, 21-28, B1, 2, 5

Section 1.5: There are things you might have to "unlearn" or at least revise (page 57) if you tend to think only of positive numbers. Algebra permits 0 and negative numbers, which can cause problems if you are not careful.

The exam questions will resemble the homework questions.

I will put old "The Language of Mathematics" exams (Adobe pdf files) on the site here shortly.

Advice

Every textbook section: This is a language course. Terms facilitate communication. If you were taking German, you would have to memorize what the words mean. Similarly, in this class you must memorize what the terms mean so we can communicate using those terms.

At the end of each section there is a "Conclusion," and at the end of the Conclusion there is a part labeled "Terms." Learn those terms, just like you would have to learn what "aufwiedersehen" means if you were studying German.

We will cover all sections from 1.1 through 5.2, with some homework from each section. Problems are grouped by difficulty. Each section has "A" problems and "B" problems. The "A" problems should be straightforward if you have read the section. The "B" problems reflect the level of understanding expected of you. (You are not responsible for the "C" problems.)

Assignments: Every day you must read the section. Mathematics is primarily a written language and you must learn to read it. One goal of this course is to improve your reading ability. The best way to learn to read well is to practice reading (even if it is hard for you). If you have any questions, ask me in class or in the office. I want to help. I do not expect you to be good at reading mathematics near the beginning of the course. "Practice makes perfect." If you are good by the end of the course -- many weeks away -- you will get a good grade, regardless of your skills near the beginning. This is a language course. If you were learning Japanese, no one would expect you to be good at it in only a few weeks! Similarly, I do not expect you to be good at reading and writing math in only a few weeks. This is important for the grading of this course.

Here is an important page on how to study and learn mathematics.

Class meets MWF at 2:10 pm. The class room is AJM Johnson 222 next to and southwest of the SUB (Not Leon Johnson).

Instructor: Prof. Warren Esty

Department of Mathematical Sciences

2-238 Wilson Hall

Montana State University

Bozeman, MT 59717

(406) 994-5354

westy at math.montana.edu

I will be in my office most of the time MWF 9-10:50, 1:30-1:55 (before class) and at 3 (after class). I will be in a lot of the time Tuesdays and Thursdays too. I love this material, so come visit and ask me questions anytime. I hope you will also make friends in the class and meet with them to talk about the math you are studying and your homework. Mathematics is a language and you should practice communicating in it.

Here are the course policies. Read them.

Wikipedia on math as a language: http://en.wikipedia.org/wiki/Mathematics_as_a_language

You can see old Math 147 exams (Adobe pdf files) here soon (when I get them posted).

This is the end of the Math 147 material.

Pages and links relevant to all learning:

"Is the internet making us stupid?" Read about it here:

http://www.npr.org/templates/text/s.php?sId=91543814&m=1

(Really, it is short, so read it!)

The original article, "Is Google making us stupid?" in The Atlantic magazine is not short (I don't expect you to read it):

http://www.theatlantic.com/magazine/archive/2008/07/is-google-making-us-stupid/6868/

It has provoked quite a buzz, so search on the title will get many hits.

Here is a summary of new research on multitaking. "Study: Multitasking hinders learning: Distraction-free studying is more efficient and effective, new brain research suggests."

How do you study? Here is research on multitasking.

"Eating fatty food appears to take an almost immediate toll on both short-term memory and exercise performance, according to new research on rats and people. 'We expected to see changes, but maybe not so dramatic and not in such a short space of time,' said Andrew Murray, the study’s lead author.’’ Continued here:

http://well.blogs.nytimes.com/2009/08/13/fatty-foods-affect-memory-and-exercise/?hp

"Amusing Ourselves to Death" is a prophetic book that was written in 1985. Here is a cartoon that illustrates its preface. http://www.recombinantrecords.net/docs/2009-05-Amusing-Ourselves-to-Death.html

The book itself is extremely interesting. It is amazing the something written then could still be so relevant (even more relevant) now.