## Colorado State University — Pueblo, Spring 2015 Math 124, Pre-calculus Math, Section 1

Here is a shortcut to the course schedule/homework page.

Here is a shortcut to the summary table below of components of the grades for this course.

Lectures: MTWΘF 8-8:50am in PM 106      Office Hours: M1-1:50pm and T$\Theta$ 12-1:50pm, or by appointment

Instructor: Jonathan Poritz     Office: PM 248     E-mail: jonathan.poritz@gmail.com
Phone: 549-2044 (office — any time); 357-MATH (personal; please use sparingly)

Text: Precalculus: Mathematics for Calculus, 6th ed., by Stewart, Redlin, and Watson.

Prerequisites: Satisfactory placement exam score or Math 121 or equivalent. (A grade of C or better is required for prerequisite courses.)

Postrequisites: This course is one of the six classes which satisfy the Quantitative Reasoning Skill of the General Education Requirement. It is also required for the CET major, is a prerequisite for CET 312, CET 412, and MATH 126, and is one required option for CM 231 and MATH 207. Many students take 124 as a step towards the calculus sequence that is needed in many (most) STEM (="Science, Technology, Engineering, and Mathematics") majors.

Course Content/Objective: The Catalog describes it as:

Polynomial, rational, exponential and logarithmic functions; solution of systems of equations; trigonometric, circular and certain special functions.
(In practice, we tend not to spend very much time on systems of equations.) A more precise list of what you will know about by the end of this class is:
1. Functions
• basic idea and notation
• graphing
• transformations and combinations
• one-to-one functions and inverses
2. Polynomial and Rational Functions
• polynomials
• factoring and roots
• graphing
• complex roots
• The Fundamental Theorem of Algebra
• rational functions
• examples
• graphing, typical forms
• horizontal, vertical, and slant asymptotes
3. Exponential and Logarithmic Functions
• exponential functions
• algebra, manipulation
• graphing, basic properties
• the natural exponential function
• logarithmic functions
• as inverses
• graphing, basic properties
• the natural log
• The Log Laws
• exponential and logarithmic equations, solutions
• applications
4. Trigonometry
• unit circle approach
• definition
• graphs
• applications
• right triangle approach
• definitions
• "solving" triangles
• The Law of Sines
• The Law of Cosines
• analytic trigonometry
• trigonometric identities
• double- and half-angle formulæ
• trigonometric equations, solutions
• conic sections
• systems of equations
• matrices, vectors
• polar coordinates

Calculator: A calculator is necessary throughout this course, often in class and when doing homework, always on quizzes and during tests. The calculator you use must be capable of performing basic scientific computations (including logarithms, exponentials and trigonometric functions) and of doing basic plots. Essentially any Texas Instruments calculator from the TI-83 up will suffice; the instructor will use a TI-84 Plus.

The Mathematics Department does have a TI-84 Plus calculator rental program, with rental of a limited number of calculators available on a first come, first served basis for a non-refundable fee of $20 per semester payable at the Bursar's window in the Administration Building. For more information, contact Prof. Tammy Watkins in the Math Learning Center (PM 132). Attendance and workload: Regular attendance in class is a key to success — don't skip class, don't be late. But more than merely attending, you are also expected to be engaged with the material in the class. In order for this to be possible, it is necessary to be current with required outside activities such as reading textbook sections and doing homework problems: you are expected to spend 2-3 hours per hour of class on this outside work. This is not an exaggeration (or a joke!), but if you put in the time and generally approach the class with some seriousness you will get quite a bit out of it (certainly including the grade you need). If you absolutely have to miss a class, please inform me in advance and I will video the class and post the video on the 'net. You should e-mail me no earlier than a few hours after class (to allow for upload time) asking for the link to that video, and you can then watch the class you missed in the comfort of you home and (hopefully) not fall behind. Classes I have videoed will have the icon next to that day's entry on the schedule/homework page to remind you of the available video. Even if you are not the one who originally requested the video, you may want to watch it (as part of reviewing for a test, maybe) — but you have to e-mail me for the links as the videos cannot simply be found by a search on YouTube. Homework: Mathematics at this level is a kind of practical (although purely mental) skill, not unlike a musical or sports skill — and, like for those other skills, one must practice to build the skill. In short, doing problems is the only way truly to master this material (in fact, it is the only way to pass this course). Note that what I mean by "doing a problem" usually includes steps like: • reading and rereading a problem statement; • reading and rereading the associated book section and class notes; • struggling with the problem on your own, with classmates and/or friends, going to my office and/or the Math Learning Center for suggestions, e-mailing me for a hint ... but, in the end, understanding the problem yourself; • writing down your notes, ideas, fragments of solution, and a rough draft; • checking your answer wherever possible; • [hopefully] eventually writing down a final, complete solution, with indications of what you are doing at each step, what all your notation (variables) means, why each step is legal -- such as which result (theorem) from the book or class you are using; • looking over corrected homework, quiz and test problems when they are handed back and making absolutely sure that you could do that problem — or any similar one — accurately yourself in the future. The above strategy, and the attitude behind it, are particularly important: in the roughly twenty-five years I have been teaching college-level mathematics, I have had only a handful of students who put in the time and energy on their math course (time and energy being, of course, the most basic required student inputs) who were not successful ... and it was always because of skipping some of the above steps. The easiest to skip are usually the understand it yourself and learn from your mistakes steps: e.g., if you have a really helpful tutor who dictates complete solutions to you, and you also do not look over returned HW, quizzes, and tests, then you will get nothing out of (and therefore most likely fail) this class. To give you plenty of this problem-solving practice, there will be daily, fairly extensive homework set. We will also spend much of our time in class discussing problems. In fact, I am happy to work with you during class time on the homework set due on the following day (or even due that very day). Here are some specifics about the homework: • Homework is due each day either in class or at my office, no later than 2pm. • Homework will be assigned in sets, but each problem will be graded separately, worth 3 points, meaning: 1. problem entirely missing (sometimes this happens because a student simply does the wrong problem — this actually happens depressingly often; so make sure you check the problem assignment carefully on the homework web page before you do it!) or a single algebraic or numeric answer is stated with absolutely no work/explanation shown ... even if it is the correct number or foruma, without an explanation it is worth 0 points! 2. some work present, but also several errors and/or important missing parts; 3. most of the correct content is present, but there is at least one key idea or step which is missing, and/or there is a significant flaw in exposition (a variable used without definition, that kind of thing); 4. all content is present, all notation is defined, all steps are explained and justified. • Homework problems will appear on the homework web page in pairs, looking like "17[19]", for example. You should only do the first problem of each pair, when that homework set is due. For each problem on which you make a mistake and therefore are not given the credit points, you may turn in, the very next class, a solution to the second problem of the pair. So, if the assignment reads "17[19]", your solution of 17 is flawed, and thus you do not earn full credit for 17, you may earn back the missing points by handing in a correct solution to problem 19 on the very next class day. We will call these the second chance problems. • Late homework will count, but at a reduced value — generally, the score will be reduced by around 20% for each day late, unless you use a Homework Late Pass [see below]. • Exception: Late homework will count as zero, even even if you try to use a Homework Late Pass, if handed in after the next major test (the next hour exam during the semester, and the final for the end of the course). • Exception to the exception: revisions of graded homework [see below] can always be handed in at the next class meeting after the graded work was returned, even if that is after the midterm ending a unit of the class. • After you complete HW0, you will receive a sheet of 10 Homework Late Passes which may be used to hand in homework late but without penalty, subject to the restrictions mentioned above. It is your responsibility to keep track of these passes — don't loose them, they are valuable! Any unused passes may be turned in at the end of the term for general course extra credit. • Homework will always be returned the next day, if humanly possible. Please look over your returned homework and make sure that you know the cause of every point you lost, and that you know how to do those problems correctly the next time — you can test/prove this corrected knowledge by doing the second problems in the pairs on the homework assignment, as described above. • Please try to be neat (how can I give you credit for your work if I cannot read it?), or at least clear. In particular, don't skimp on paper! And please cut off ragged paper edges when possible and use staples to attach multiple pages (and not that terrible thing where you sort of chew on the corner of the pages -- better simply to write your name on each page and hand in the stack of separate pages). But I absolutely care much more about the content than the form of your work, so don't worry if you just have bad handwriting or something (I certainly do!). • Make sure to label each assignment you hand in with your name and date, the course number, and number of the homework assignment (from the HW page); if you are handing in something which is not stapled, please write your name on each page. • The point of homework is for you to practice using the techniques we are discussing, not to get "the right answer". You don't care about the answers of these problems, and neither do I. I do care about you learning the techniques, and showing that to me clearly. Therefore, you must explain everything you do in your homework (and also quizzes and tests). In short, I am not saying "you must show your work on HW", but rather that the HW is the showing of your work, far more than it is the "answer" at the end of your work. That's why a correct "answer" without complete an clear explanation is worth zero points, while a good explanation which accompanies an incorrect "answer" (due, for example, to an arithmetic mistake), will usually be worth full credit. • Since so much paper is involved in these daily homeworks, we should be mindful of the carbon footprint of this class. So I ask that you reuse paper whenever possible, by taking any pages you can find that are blank on one side (handouts from other classes, drafts of your work for this or other classes, etc.), putting a big "X" over the previously used side, and doing your HW for this class on the blank side. To encourage this, I will keep track of how many such reused pages you hand in and they will be worth (a small amount of) extra credit at the end of the term; these are called Green Points. • Your lowest ten HW scores (on problems, not sets) will be dropped. Big Ideas [BIs]: Along with every homework set, you must turn in a written explanation of the Big Idea of the last class. This should be at least a clear and complete sentence, although sometimes several (or a paragraph, or an equation with explanatory sentences) will be more appropriate. The goal here is to get some practice with good exposition of mathematical facts and with mathematics as a body of general results and ideas, not merely a collection of worked examples. Some specifics: • The BIs will be graded out of 2 points, according to the following scheme: 1. missing; 2. present but very skimpy or wrong in some important respect; or 3. present, completely, and (essentially) entirely correct. • Please hand in your BI each day attached to the regular HW, but a clear indication of which is which. • Late BIs will be handled the same way as late HWs; if you use a homework pass to hand in a late HW without penalty, it will also apply to a BI if you choose to attach one. • You should think of the BIs as a complete outline of and study guide for the course which you will be assembling bit by bit through the whole term. So each BI should be written in such a way that it will be clear and complete to you even weeks (months? years?) later. • The most common issues students have with BIs are: • Submitting a BI which is more the name of some content than the content itself. For example, • Today we studied the Pythagorean Theorem. merely names something without giving the content, which might be • If a triangle has sides of lengths$a$,$b$, and$c$, and a right angle between the sides with lengths$a$and$b$, then$a^2+b^2=c^2$. This second version would make a fine BI (in the right class). • BIs must be general results, not merely examples. So • Today we did$x^2-9=(x-3)(x+3)$. is just an example; and even the version • Today we did things like$x^2-9=(x-3)(x+3)$. just talks about examples. On the other hand, • Quadratics of the form$x^2-a^2$, where$a$is any real (or complex) constant, can always be factored as$x^2-a^2=(x-a)(x+a)$. is a nice, useful general result, and would make a fine BI. • All parts of a BI must be explained in a complete and precise way, including all variables. For example, • In a right triangle,$a^2+b^2=c^2\$.
is pretty much meaningless, because the variables are not defined; this would be a very weak BI. A better version of this is the one given just above (beginning with "If a triangle has sides of lengths...").
Since we cover a lot of content in this course, there is a rich source of material for potential BIs. You are also doing them without time pressure and at home where you can consult your notes. You should therefore expect to get perfect scores on essentially all of your BIs, at least once you have figured out, in the first few days of class, what kind of thing I am looking for.

That discovery process (of finding out what is good content and style for a BI) at first may be a little frustrating, but students have told me years later that they remember "that whole Big Idea business" and it has served them more than anything else they did in my class.

Quizzes: Most Fridays, during weeks in which there is no hour exam, there will be a short (10-15 minute) quiz at the end of class. These will (usually) be closed book, but calculators will (usually) be allowed. Quizzes will be graded out of 5; your lowest quiz score will be dropped.

Exams: We will have four in-class hour exams: Test I on Chapter 2 of the text, tentatively scheduled for Friday, January 30th; Test II on Chapters 3 and 4, around Friday, February 27th; Test III on Chapters 5 and 6, around Friday, March 13th; and Test IV on Chapters 7 and 11, around Monday, April 20th (these dates are reasonably approximations, but might change — always with a week or more advance notice). Our comprehensive final exam is in two pieces, on Thursday, April 30th and Friday, May 1st, both 8-10:20am in our usual classroom.

Revision of work on BIs, quizzes, and tests: A great learning opportunity is often missed by students who get back a piece of work graded by their instructor and simply shrug their shoulders and move on — often depositing their graded work in a trash can without even looking at it! In fact, painful though it may be, looking over the mistakes on those returned papers is often the best way to figure out exactly where you tend to make mistakes. If you correct that work, taking the time to make sure you really understand completely what was missing or incorrect, you will often truly master the technique in question, and never again make any similar mistake. This is what is behind the "second chance HW problems" described above.

In order to encourage students to go through this learning experience also in the other parts of the course, I will allow students to hand in revised solutions to all BIs, quizzes, and midterms. There will be an expectation of slightly higher quality of exposition (more clear and complete explanations, all details shown, all theorems or results that you use carefully cited, etc.), but you will be able to earn a percentage of the points you originally lost, so long as you hand in the revised work at the very next class meeting. The percentage you can earn back is given in the "revision %" column of the table below.

Grades: On quiz or exam days, attendance is required — if you miss a quiz or exam, you will get a zero as score; you will be able to replace that zero only if you are regularly attending class and have informed me, in advance, of your valid reason for missing that day.

In each grading category, the lowest n scores of that type will be dropped, where n is the value in the "# dropped" column. The total remaining points will be multiplied by a normalizing factor so as to make the maximum possible be 100. Then the different categories will be combined, each weighted by the "course %" from the following table, to compute your total course points out of 100. Your letter grade will then be computed in a manner not more strict than the traditional "90-100% is an A, 80-90% a B, etc." method. [Note that the math department does not give "+"s or "-"s.]

pts each # of such # dropped revision % course % 5 ≈10 1 33.3% 12% 3/prob ≈55 sets≈150 probs 10 probs 100% (on it's 2nd chance prob) 16% 2 ≈55 (≈1 per HW set) 3 50% 4% >100 4 0 33.3% 44%(=4×11) >200 1 0 0% 24%

Contact outside class: Over the years I have been teaching, I have noticed that the students who come to see me outside class are very often the ones who do well in my classes. Now correlation is not causation, but why not put yourself in the right statistical group and drop in sometime? I am always in my office, PM 248, during official office hours. If you want to talk to me privately and/or cannot make those times, please mention it to me in class or by e-mail, and we can find another time. Please feel free to contact me for help also by e-mail at jonathan.poritz@gmail.com, to which I will try to respond quite quickly (usually within the day, often much more quickly); be aware, however, that it is hard to do complex mathematics by e-mail, so if the issue you raise in an e-mail is too hard for me to answer in that form, it may well be better if we meet before the next class, or even talk on the telephone (in which case, include in your e-mail a number where I can reach you).

Math Learning Center, located in PM132, is a great place to work with other students or get help from fantastic tutors. It is always a good place to go if you want some interactive help and I'm not in my office. The MLC is open 8:30am-5:00pm Monday to Thursday and 8:30am-3:00pm on Friday.

A request about e-mail: E-mail is a great way to keep in touch with me, but since I tell all my students that, I get a lot of e-mail. So to help me stay organized, please put your full name and the course name or number in the subject line of all messages to me. Also, if you are writing me for help on a particular problem, please do not assume I have my book, it is often not available to me when I am answering e-mail; therefore, you should give me enough information about the problem so that I can actually help you solve it (i.e., "How do you do problem number n on page p" is often not a question I will be able to answer).

Academic integrity: Mathematics is more effectively and easily learned — and more fun — when you work in groups. However, all work you turn in must be your own, and any form of cheating is grounds for an immediate F in the course for all involved parties. Please do not use a cell phone during class. You may not use a cell phone or share a calculator with another student during a test.

Nota bene: Most rules on due dates, admissibility of make-up work, etc., will be interpreted with great flexibility for students who are otherwise in good standing (i.e., regular classroom attendance, homework (nearly) all turned in on time, no missing quizzes and tests, etc.) when they experience temporary emergency situations. Please speak to me — the earlier the better — in person should this be necessary for you.

Students with disabilities: The University abides by the Americans with Disabilities Act and Section 504 of the Rehabilitation Act of 1973, which stipulate that no student shall be denied the benefits of education "solely by reason of a handicap." If you have a documented disability that may impact your work in this class for which you may require accommodations, please see the Disability Resource Coordinator as soon as possible to arrange accommodations. In order to receive accommodations, you must be registered with and provide documentation of your disability to: the Disability Resource Office, which is located in the Library and Academic Resources Center, Suite 169.

 from xkcd.com