Your final exam has been graded and I encourage you to pick it up in the Main Math Office. Your letter grade in the course in on its back page and will be on your "myinfo" site Wednesday, May 13.

Have a great summer!

April 21

Here is a copy of last semester's final exam. We can talk about it on Wednesday and Friday.

Final exam times for other classes

 

HW due Monday, April 27: 

Hand in (5.1) B2, 3, 5, 8, 22. 

 

HW due Wednesday, April 29:

Learn 5.2. Hand in (5.2) A1, 7, B1, 3, 4, 5, 11, 14

Webwork problems that might help with 5.2

 

No HW to be handed in Friday, May 1:

Nevertheless, learn the concept definitions in 5.2. Read the conjectures and think about how you would address them. We will go over problems like these because this context yields good examples of proofs and disproofs.

Final Exam: Thursday May 7th 6-8pm in the usual classroom

April 6

Exam: Wednesday April 8th on Chapter 3

HW due Friday, April 10: 

(4.1)  A12, 14, B14, 27, 34


Due Monday, April 13: 

(4.1) B35, 36, 37, 54 
The will be 10-point quiz based only on attendance. I really want you to come, because I will be lecturing on the math behind RSA cryptography which is critical to using the internet, credit cards, and banking. You can understand something super-important in the modern world in one 50-minute lecture. Come! If you don't come, I will notice! (Also, a small amount of it, just enough to show you were paying attention, will be on the next exam.)

Due Wednesday, April 15: 

Read all of Section 4.2. Hand in  (4.2) A18, 25, 28, 29, 32, 37, 38, 45 (prove it), B1, 3, 14, 16, 17, 30, 32

HW due Friday, April 17: 

(4.2)  B1, 3, 14, 16, 17, 30, 32, 33

Last semester's exam on Chapter 4. If you look at it before Monday's class, we can talk about it in class.

HW due Monday, April 20: 

Read 5.1 at least through the definitions of "one-to-one" and "onto". (4.2) B35, 36, 41 (5.1)  A2, 8, 11, 14, 17, 19

Wednesday, April 22:

Exam on Chapter 4 and all earlier material. It has definitions, counterexamples, and proofs. It does not ask for creative proofs--rather proofs that are very similar to those you have seen. Study the forms of the proofs we have done and notice what they have in common. Mastery of the definitions is critical. So is mastery of alternative logical forms. In addtion to Chapter 4 material, it will have some problems resembling those on the Chapter 3 exam. It has a small amount on RSA cyrptography from my talk.

HW due Friday, April 24: 

Read 5.1 closely, including the proof of Conjecture 7 and the bad proof of Conjecture 9. [Learn to recognize characteristics of bad proofs.] Make sure you follow the given examples closely. Hand in (5.1) A15, 18, 21, B7.

March 23

HW will be put on the front, side, or back whiteboard by (self-selected volunteer) students before class each day. Put something up once in a while. [It does not have to be right. It is a conversation-starter.]

HW due Monday, March 23:  

(3.3) B65.  Read Section 3.4.  Be sure you understand Example 1. Then also hand in (3.4)  A1, 4, B2, 3, 4, 5

HW due Wednesday, March 25: 

Read Section 3.5 and do (3.3) B77, (3.4) B8, 11 (two proofs, not three), 23

HW due Friday, March 27: 

(3.5) A2, 4, B2, 8, 13


HW due Monday, March 30: 

(3.5) B10, 12, 18

 

HW due Wednesday, April 1: 

(3.6)  A1, 2, 7, 8, 9, 10, 11, 12, 15, 19, B26, 33

Friday, April 3: University Day - no classes

HW due Monday, April 6: 

Read 4.1. (4.1) Memorize the sentence-form definitions of the set-theory terms. A2, B7 (Be specific--find it in the text), B11

Wednesday, April 8: Exam on Chapter 3

HW due Friday, April 10: 

(4.1)  A12, 14, B14, 27, 34

March 6

About homework.
Read if your exam did not go well.


HW due Monday, March 16:

(3.1) B21, 24, 42, 47  (3.2) B7 [again], 8, 11, 12, 13, 14, 37

  • One goal of Chapter 3 is to instill an attitude change. You should become skeptical. 

 

Upcoming homework: 

Please do your exploration on scratch paper and select the good parts to recopy and hand in. We do not want to see the things you wrote down that did not work. Just show us the good parts! Use scratch paper to begin proofs.

HW due Wednesday, March 18:  

(3.2) 39, 40. Quiz on material up through 3.2 

Friday, March 20: 

Read Section 3.3 (of course). Also hand in: (3.3) A1, 2, 7, B1, 2, 3, 5, 11, 12, 57, 61

March 5

Things not to do in proofs.

On prior results and citations. In this course, you are expected to cite prior results from the current and immediately previous sections, but not from sections on lower-level material studied long ago. At some point you get to stop citing old and well-known results. For example, when doing a calculus proof you do not need to cite results on inequalities from 3.1. By then, you are supposed to know what is true and what is not, and inequalities are supposed to be so much lower level and so far prior to calculus that we can assume you use them correctly, even without citation. (I know, from experience, that this is an incorrect assumption because some students manipulate inequalities and absolute values incorrectly in the context of calculus. Nevertheless, I will not expect citations of prior results that are much lower level than the current work.)

Handout on writing proofs. 

March 3

Comments for "Distraction" assignment submited by students

Exam 2 page notes.

The lowest A- was 80, the lowest B-, 70, the lowest C-, 55, and the lowest D-, 50. The median was 74. 

Comments:

Every question on the exam is important. It is all relevant to the rest of this course and all future math courses, either indicating your reading skills or your logical skills. It is possible to improve both with practice, and that is what we will be doing for the rest of the semester.

  •   If you did well, congratulations. I expect you will only get better because you are working correctly.
  •   If you did poorly, I suspect it is because you have not yet learned how to remember and grasp what you read and are told in class. I suspect your concentration and study habits are at fault. Reflect on these for the assigned homework for Wednesday (below).

 


Solutions to many exercises in Chapter 3.

HW due Monday, March 2:

Read some of 3.1 and do (3.1) A2, 4, B1, B3

In Section 3.1, study the given proofs line-by-line. Make sure you know the reason for each assertion. Every "=" requires a reason. Every ">" requires a reason. Every sentence requires a reason. For this section, the work you need to do is to read carefully. You need to seek justifications for every step and realize how details are important. The homework to be handed in is only a small part of what you are to do. Read (slowly and thoroughly) first. Then apply the lessons to the homework. (You may use lower-numbered results to prove higher-numbered results.)  If you find anything hard to read, I hope that you will ask questions about it in class.

HW due Wednesday, March 4:

(3.1, part 2) B10, 12, 18, 19.  Here is the bulk of your work for Wednesday and the most important for you. Read two internet articles (links below) and write and hand in electronically, in an e-mail to me at estymsu at gmail dot com (as an e-mail, or as an attached doc file or text file), this:

  • Send me your reaction to these two articles. Does media distract you? Include a description of how you study, what you think works and what doesn't, and what you intend to do differently in the future. Please be specific. I would be interested to hear how you have successfully learned things in the past, or any analysis of your learning that you want to do.
  • Here is one thought you may or may not choose to address.Most people are really good at something (and I don't mean just academic things). How did you get good?
  • I think such an analysis of your own learning might be beneficial to you--that's why I'm asking. But, before you do this, I want you to read the articles.
  • I care and am taking this seriously. I hope you will too.


The first article: "Is the internet making us stupid?"  (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, but I did): 

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

The second article

Additional comments: Here is a summary of some surprising research on multitasking. 

New policy: 

HW will be put on the front, side, or back whiteboard by (self-selected volunteer) students before class each day. Put something up once in a while. [It does not have to be right. It is a conversation-starter.]

HW due Friday, March 6: 

(3.1)  20, 23  (3.2) A2, 5, 8, 10, 14, 19, 25, B 6, 7.

  • Begin to read 3.2. In Section 3.2, pay attention to the order in which the results are listed. Each one joins the list of prior results for purposes of proving the next. The inequality facts from Section 3.1 are also prior.

 

March 9-13: Spring break no classes

We will continue straight through the text. You may read ahead and be sure it is important material we will cover.

HW due Monday, March 16:

(3.1) B21, 24, 42, 47  (3.2) B7 [again], 8, 11, 12, 13, 14, 37

  • One goal of Chapter 3 is to instill an attitude change. You should become skeptical. 

Upcoming homework:  Please do your exporation on scratch paper and select the good parts to recopy and hand in. We do not want to see the things you wrote down that did not work. Just show us the good parts! Use scratch paper to begin proofs. 

Feb. 19

Exam: Friday February 27th on Chapter 1 and Chapter 2

February 23rd quiz with solutions

Negations of generalizations are existence statements. Never omit "there exists" when it is intended.
The negation of "ab = ac => b = c" is NOT "ab = ac and b ≠ c."  It is "There exist a, b and c such that ab = ac and b ≠ c."  I am seeing this error far too often and I intend to score it as a major error on the upcoming exam.

For Exam:

Memorize the Quadratic Theorem and the definitions related to bounded, increasing, even, and rational. Be sure you know the logic of quantifiers and negations, and the technical terms we have discussed (e.g. placeholder).

Feb. 12

Exam 1:  Letter grades and the lowest number score that earns that letter: A 90, A- 85, B+ 80, B 75, B- 70, C+ 67, C 62, C- 60, D+ 57, D52, D 50. Below 50, F.

If you did well, congratulations. If you did not do as well as you would like, you will certainly have more time to learn this same material. We never drop a subject. This is a language course and if you participate (read the text, do the work, and come to class) you will get better and better.

If you demonstate on the exams on Chapters 3 and 4 and the final exam that you have learned the material, you will get a good grade. If you learn it, you will not be penalized for not knowing it now.

MSNBC views are why math and stats are good jobs

HW due Wednesday, Feb. 11 

(2.2, part 2) B1, 2, 3, 11, 18, 19, 25, 30,  81, 84, 87, 88

If you mean "there exists" do not omit saying it. For example, the negation of  "If |x| > 5, then x > 5"  is not "|x| > 5 and x ≤ 5."  It is "There exists x such that "|x| > 5 and x ≤ 5."   It is common to suppress "for all" when it is intended, but it is not okay to omit "there exists" when it is intended.

Suppose you are to give the negation of  "If ab = ac, then b = c."  It is not "ab = ac and b ≠ c."  The negation is "There exists a, b, and c such that ab = ac and b ≠ c."   Never omit "there exists" if you mean it!

HW due Friday, Feb. 13:

Read Section 2.3.  (2.2, part 3) B32, 33, 40, 46   (2.3) A1, 2, 3, 6, 13, 15, 59, B1, 3, 11, 15, 25, 40

Monday, Feb. 16: President's Day no classes

HW due Wednesday, Feb. 18: 

[I hope you realize your job is to read and learn. The purpose of the homework is to help you see what you were supposed to get out of the reading. Too many students think the goal is to get the homework done.  No. The goal is to learn to read mathematics and to learn how to do all similar problems. The homework is evidence of how your learning is progressing.] (2.3, part 2)  B2 [changed away from B3], 7, 21 (2.4)  A1, 7, 12, 16, 18, 19, B1, 2, 10, 16

HW due Friday, Feb. 20

(2.3 part 3) B89, 105 (2.5)  A1, 3, B1, 2, 14, 17, 18

HW due Monday, Feb. 23: 

(2.2 [sic])  B59-62, B74, 78, 84, 85  (2.5, part 2) B20, 37

HW due Wednesday, Feb. 25: 

Review for the exam by doing and handing in a previous version of Exam 2 and coming to class with questions.

Friday, Feb. 27: Exam 2 on Chapters 1 and 2.

Memorize the Quadratic Theorem and the definitions related to bounded, increasing, even, and rational. Be sure you know the logic of quantifiers and negations, and the technical terms we have discussed (e.g. placeholder).

HW due Monday, March 2:

Read some of 3.1 and do (3.1) A2, 4, B1, B3

HW due Wednesday, March 4:

(3.1, part 2) B10, 12, 18, 19, 20, 21, 24

New policy:

HW will be put on a side or back board by (self-selected volunteer) students before class each day. Put something up once in a while. [It does not have to be right. It is a conversation-starter.]

March 9-13: Spring break no classes

We will continue straight through the text. You may read ahead and be sure it is important material we will cover. 

Feb. 3

Here is a link to solutions to many exercises in Chapter 2. 

About homework.

Most homework gets a check. You did it and it displays effort, even if some is wrong. Some really good homewriok gets a check plus which says that type of work will result in a high grade. However, some homework earns (at the end) a check minus. That is my way of warning that the work is poor (and displays little effort at reading the material) and a very poor letter grade will result if things don't get better. 

Jan. 24

Exam: Friday February 6th on Chapter 1

 

HW due Wednesday, Feb. 4: 

(2.1) A10-11, 17, B1, 2, 3, 4, 5, 7, 17, C2

Exam 1 from last fall.

Friday, Feb. 6: Exam in class, no homework due

HW due Monday, Feb. 9:

(2.2, part 1) Read 2.2 yourself. Then do A1, 2, 3, 9, 17, 24

Solutions to many exercises in Chapter 1.

 

HW due Monday, Jan. 26:  

(1.3, part 2) B1 [Do it all in one wide table] (1.4) A1-4, 6, B15.

 

HW due Wednesday, Jan. 28:  

(1.3, part 3) B2  (1.4, part 2) A12, 18, B1 (do a good job), 2, 10  (1.5) A2, A10, 25  [One more problem] You have heard the phrase "cruel and unusual punishment." Where does it come from? (Do a web search.) If it had been written by mathematicians, would they have used "and" or "or"? Restate the entire sentence to state clearly what you think it says using the mathematical connective correctly.

HW on the web at our WeBWork site

Each day read the entire section. One goal of the course is to have you learn to read mathematics well enough to lean math by reading it. Watching me and listening in class will help, but you learn to read by reading. If something is not clear after you read it, slowly and with intent, several times, ask!

HW due Friday, Jan. 30:

(1.5)  A6, 11, 15, 21, 27, 31,  B1, 2, 3, 8, 17 

HW due Monday, Feb. 2: 

(1.5) B4 (1.6) A1-7, B1, 10, 15, 27, 29, 52   (2.1) A1, 3, 6, 9

  • Learn the names of the results from logic (pages 86-88). These address forms that will reappear frequently, so they are worth knowing,

 

HW due Wednesday, Feb. 4: 

(2.1) A10-11, 17, B1, 2, 3, 4, 5, 7, 17, C2

Exam 1 from last fall.

Friday, Feb. 6: Exam in class, no homework due

HW due Monday, Feb. 9:

(2.2, part 1) Read 2.2 yourself. Then do A1, 2, 3, 9, 17, 24

Jan. 20

I mark your homework. I mark it to help you, not to grade you. If you don't pay attention to my marks my time is wasted. 

If possible, you should come to class early, pick up your homework, and check everything you did wrong (with an X) against the question in the text. Bring your text and open it up in the minutes before class and if it is not clear why your answer was wrong, put the problem number on the side board, e.g. "1.1, A11" . I will remember the errors made on that problem and will address them (rather than just your particular error).


Please have your cellphone off in the classroom. Put problems numbers on the board if you have questions and get your text out and check any errors on the homework that was just returned. If you have extra minutes, begin to read the next section or talk to your neighbors. We will usually begin with smiley-face problems from the current section. Make sure you understand them. If you don't, ask. 

Jan. 16

Some of the most straightforward problems can be marked by a machine. They are distinguished with a superscript W in the text. You can get immediate feedback on similar problems here.


Login with the "Guest Login" button. No password is required. Problems are labeled by section, e.g. "Sec1.1". If the machine marks something wrong, be sure you understand why. Try again and ask me if you don't figure it out. Be aware that these problems are not at the level of the course, rather they are lower-level and prerequisite material for the level of material we are actually studying.

Our first quiz will be Monday, Jan. 26, on 1.1-1.3, as noted below. See the old sample quiz there to see what it will be like. This is not a computation course. Learn our terms and use the homework as a guide to what you are supposed to learn. 

Jan. 12

This web site will be updated frequently. Upcoming HW will be listed, quiz and exam dates will be posted, and mathematical advice will be posted. Basic course information and some relevant web links.

First day of class: Wednesday, Jan. 14, 2015  

We will discuss the course and cover Section 1.1.

 

For Friday, Jan. 16: 

Read all of Section 1.1. Mathematics is a written language (much more than it is a spoken language). Therefore, this is a reading and writing course. You learn to read and write by reading and writing. Read the text thoroughly. Every section, learn the meaning of the terms listed at the end of the section's conclusion (just above the "Exercises." If you don't recall where a term was introduced in the text, use the index at the back to look it up). For this section, hand in written homework at the beginning of class Friday:

  • Bring your text to class every day. We will use it in class every day.

 

HW Due Friday, Jan. 16:

(1.1) A2, 3, 4, 7, 9, 11, B1, 2, 5, 7, 8, 12, 14, 23, 26, 29.

Label your homework with your name at the very top right of the page and the section number (this time, "1.1") of the homework just below it.
Also for Wednesday, read:  "Is the internet making us stupid?" (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, but I did): It provoked quite a buzz, so search on the title will get many hits.

Additional comments:

Do you multitask well?  Here is a summary of some surprising research on multitasking.

 

Monday, Jan. 19: Martin Luther King Day - no classes

HW Due Wednesday, Jan. 21: 

Section 1.2:  A1, 6 (both parts!), 11, 25, 29, B1, 5.

Some of the most straightforward problems can be marked by a machine. They are distinguished with a superscript W in the text. You can get immediate feedback on similar problems here

Login with the "Guest Login" button. No password is required. I do not keep track of how you do or even if you visit the site. But, you might find it helpful. If the machine marks something wrong, be sure you understand why. Try again and ask me if you don't figure it out. Be aware that these problems are not at the level of the course, rather they are lower-level and prerequisite material for the proofs we are actually studying.

In this course you will learn how to learn math by reading it. One way we teach you to read is to require you to do it. You learn to read by reading. Therefore, many days there will be homework due on material we have not yet covered in class. You will read the section and learn how to answer the questions. Then the following lecture will clarify any remaining issues.

If you have tried, but are still uncertain about a problem, on your HW put a big question mark, ?, in the margin. Also, put the problem number on the side board before class and I will try to make sure it is covered in class. If it is not covered in class, when I mark papers I will note those problems and possibly devote time during the next class to them.

 

HW due Friday, Jan. 23: 

(1.2, part 2): B3, 4, 18, 21, 22, 26, 42, (1.3) A1, 6, 9, 14, 18. Be sure you can pronounce all the mathematical expressions and grasp all the "grammar" exercises. Little typographical differences can make a big difference in the referent (the thing being named or referred to). For example, there is a major difference between a and A and a major difference between (, [, and {.

Mathematics is a written language. To get good at math, you must read it. Read!
If you are coming to class and feel yourself slipping even the slightest bit behind, please come see me in the office. I want to help!
Fortunately, we will use the language of mathematics every day and we never drop any topic, so you will see every usage and hear every pronunciation again and again. Pay attention and notice what is giving you trouble. Let me know and I will help.

HW due Monday, Jan. 26:  (1.3, part 2) B1 [Do it all in one wide table] (1.4) A1-4, 6, B15.

[To be continued at the top of this page.]

 


Pearls

Pearls before Swine comic strip


Can Smart Machines do Your Job?
January 25, 2013, this article came out. It begins by discussing a man who makes $67,000 a year whose job is being replaced by machines. It continues with a broader discussion of the economy and how many good jobs are disappearing.

A very similar article,  "New technology is erasing many middle class jobs,"  was printed in the Bozeman Daily Chronicle Sunday, Jan. 27, 2013: The full URL is here:

 


Course policies for Methods of Proof, M-242, at Montana State University, Spring 2015.

Time and Room:

10:00-10:50 am, MWF, in Wilson 1-142.

Goals:

You will learn to read, write, and think like an advanced mathematician. You will learn to read symbolic mathematics with comprehension, express mathematical thoughts clearly, reason logically, recognize and employ common patterns of mathematical thought, and read and write proofs.

Instructor:

Dr. Warren Esty, 994-5354, Wilson 2-238 (East wing, South wall, near the catwalk).  estymsu at gmail dot com
Phone calls and e-mails are both fine. Appointments are easier to arrange on the phone. 

Office hours:

I love this material and am happy to help.
Mondays, Wednesdays, and Fridays:  8:30-9:40. Also, Mondays 1:30 - 2:00 and Wednesdays 1:30-3:00.  Many other hours, including Tuesdays and Thursdays (usually 9-11:30, but other hours are fine too). You are more than welcome whenever I am in the office. If you want to arrange to meet some other hour, just ask in class, call (994-5354), or drop in. 

Required text: 

Proof: Introduction to Higher Mathematics, seventh edition, available at the bookstore, by Warren W. Esty and Norah C. Esty.

  • This course has almost nothing to do with calculation, so no calculator is required. 
  • Bring your text to class every day. We will use it in class.

Course Content:

We will proceed straight through the text, covering every section through Chapter 5.

  • Chapter 1:  Preview of proof, sets, logic for mathematics (including truth tables and important logical equivalences that provide alternative forms). 
  • Chapter 2: generalizations, existence statements, negations, reading symbolic mathematics with full comprehension, logical form and deduction, and practice with alternative forms in the context of rational and irrational numbers. 
  • Chapter 3:  Proof of theorems about inequalities and absolute values, theory of proofs, proofs by contradiction or contrapositive, proofs by mathematical induction, and common types of mistakes in proofs. 
  • Chapters 1 through 3 complete the theory. The rest of the course provides practice in several content areas of mathematics.
  • Chapter 4 is Set Theory including bounds and suprema.
  • Chapter 5 is about the concepts of one-to-one and onto, functions applied to sets, and cardinality.
    • We will cover through Chapter 5.

Prerequisite:

Math 172 (two semesters of calculus). The mathematical sophistication provided by additional mathematics such as Math 221 (Matrix Theory) and Math 224 (Calculus of Functions of Several Variables) would be very welcome, but the material covered in those courses is not a prerequisite. In fact, the material in Calculus is not a prerequisite either--we just want you to have read a lot of mathematics.

This course is primarily for students who wish to be math teachers or math majors, and others, such as computer science students, who need to grasp proof. It is a through discussion of the most important types of thought processes in mathematics.

I will:

  • Have passion for the material
  • Enjoy the class
  • Give you your work back promptly
  • Give you lots of helpful criticism and feedback on your work
  • Listen and respond to your concerns
  • Realize that students have a life outside of class and not make unreasonable demands on you
  • Take questions seriously 
  • Help outside class if you are trying hard and want help

You will:

  • Attend (almost) every class, be on time, and be prepared
  • Enjoy the class 
  • Appreciate learning during class time
  • Read all the material in the text outside class
  • Do and hand in the homework--almost always on time  
  • Try hard to get good at math 
  • Ask for help when trying isn't working
  • Observe proper etiquette

Attendance:

Attendance every day is expected. More than a couple unexcused absences is unacceptable. Of course, excuses for academic reasons, illness, participation in university sporting events, and significant life events will be accepted. Every day in class you will learn about common mistakes and how to avoid them. It is not possible to recognize your own errors in logic, so you must take every opportunity to see deceptive errors in reasoning explained and to get feedback about your own and your classmates errors in reasoning. Students who miss a day are missing a significant lesson that cannot easily be recovered from the text alone.
   If you miss a day, I will not be able to recreate the class experience for you. Find a friend who can help you catch up, read the text thoroughly, and then I will be glad to help you with specific questions

Homework:

There will be homework due almost every day. If something on your homework is wrong, I will mark it wrong with a big X at the place where it goes wrong. Please make sure you understand why. Do not treat your homework as just part of your grade. Treat it as an occasion to learn. Anything you got wrong must be looked at again and studied much harder than anything you easily got right. Some things are easy. It is not much of an accomplishment if you can learn the easy stuff. Some things are harder. Put substantial effort into making sure you understand the harder stuff too. 
    It is important that it be attempted on time. The work you hand in need not be all correct, but it must display serious effort. More than a few late homeworks is not acceptable and will result in your course letter grade being lowered a notch. I will give you important and useful feedback on all the HW you do on time.

  • You may work on homework with other current students. You are even encouraged to work with others. You may ask previous students about individual problems. But obtaining work from others and presenting it as your own is unethical and forbidden.
  • You are expected to work, on average, about two hours outside class for each class hour.
  • You must read the assigned sections. Learning to read math with full comprehension is one of your goals, and you learn to read by reading. Reading is part of those two hours.
  • Bring your text to class every day. We will use it in class regularly.

Exams and Grading.  There will be unit exams at the end of each chapter, frequent quizzes, regular homework, class participation, and a comprehensive final.  

Exam dates will be announced on this site.

Homework and its due dates will be announced on this site.

Your course letter grade will be based almost entirely on exams and quizzes. Nevertheless, homework is mandatory. More than a few late homeworks is not acceptable and will result in your course letter grade being lowered a notch from the grades your exms would suggest. Homework is intended to help you learn and its impact on your grade is primarily that it serves as evidence of your attempt to learn, and, of course, it is necessary practice so you can do well on the exams. Getting a few problems wrong or incomplete will be noted, but it will not lower your grade if you display appropriate effort. I want to help. If you have difficulties come see me.

The final exam is 6:00-7:50 pm, May 7, Thursday of Exam Week. Arrange your summer break schedule so you can take the final at the scheduled time.

Final exam times for other classes

Conflicts:

You are required to take all exams and the final exam at the scheduled hours (unless you have another exam or class scheduled at that hour, in which case we will make arrangements). Any exceptions must be approved well in advance, and in no case will exceptions be made for two exams.

Attitude:

Some students think math is merely a list of procedures--a succession of algorithms for "how to do" things. Proof is a major part of mathematics that is not at all like that conception of mathematics. So, you may need to change your attitude about what math really is. It is hard for anyone to change their attitude about anything, so this part may be difficult for you.

Mathematics is a written language (much more so than a spoken one). One goal is to have you learn to read with comprehension. Then you will be able to grasp what mathematical sentences really say (They probably say more than you think!) and learn without relying on the teacher. How can we help you reach this goal?  By making you read and work with material even before there is a lecture on it. You learn to read by reading. So, expect to learn by reading. Lectures will clarify things, but not always introduce things. 

Success:

Higher mathematics requires a significantly different way of thinking. There is a much greater focus on the truth, or falsehood, of statements and connections between facts. There is much less focus on algorithms (methods for doing problems).  
Advice about how to learn math 

Read each section. Do not skip the harder parts. In fact, when the going gets rough you need to slow down and read it several times until it makes sense. If it remains unclear, ask me!  

  • This is hard!  But, you will be learning an extremely valuable skill.
  • Don't skim.
  • Don't expect that only high points are important (Don't read only the bold parts).
  • Don't skip the rest of the paragraph because you want to move along to the next high point. 
  • Really do read the next paragraph in the text. Mathematics is a written language and you learn it best by reading and writing, not by listening in class.

Etiquette:

Proper etiquette is required. During class, students will not engage in any potentially distracting behavior such as reading a newspaper, text-messaging, or whispering about non-math subjects. Cell phones must be turned off and unavailable. Pagers or watches that make a sound, however quietly, must have the sound off. No type of earphones is allowed. 

Cheating: 

I give you permission to work on homework jointly with others in the class. In fact, I encourage you to work with others because math is a language and learning to communicate in the language helps meet the goals of this course. In this course, learning by working with others is not cheating. However, you must hand in your own work and copying someone else's work to get the homework done is unacceptable. The purpose of homework is not "to get it done," rather, "to learn how to do it."  If your homework results in learning, that is all I can ask of it.

  • In contrast, exams must be entirely your own work.

 

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