# Mathematics

MATH 110: College Algebra

Fall 2006, 4 Credits, MWF 1:10 pm., R 1:00 pm MRC 436
Instructor: Dr Michael Wodzak, Associate Professor of Mathematics
Office: MC 530, 796-3659;
Email: mawodzak@viterbo.edu
Hours: MWF 9 – 10, WF 11 – 12,R 9—11,  and by appointment
Final Exam: Friday DEC 15th 12:50--2:50

Course Description: Review of basic algebra, second-degree equations and inequalities, roots of polynomials, exponential and logarithmic functions, and systems of equations. Not applicable toward mathematics major or minor sequence. Prerequisite: acceptable score on placement exam, grade of B-minus or better in one year of high school algebra, or grade of C or higher in MATH 001.

TextCollege Algebra, by Beecher, Penna, Bittinger, Second Edition, 2005.

CORE SKILL OBJECTIVES:

Thinking Skills: The students will engage in the process of inquiry and problem solving that involves both critical and creative thinking.  They shall usereasoned standards in solving problems and presenting arguments.

Life Value Skills: The students will analyze, evaluate and respond to ethical issues from informed personal, professional, and social value systems. 1)

Communication Skills: The students will communicate orally and in writing in an appropriate manner both personally and professionally.  They are expected to read comprehension and the ability to analyze and evaluate.  They shall listen with an open mind and respond with respect.

Cultural Skills: The students will understand their own and other cultural traditions and respect the diversity of the human experience.

COURSE OBJECTIVES

Thinking Skills:  Students will:
Briefly study the basic ideas of a first algebra course.
Solve quadratic equations by factoring, completing the square, and by use of the quadratic formula.
Improve the ability to read and solve application problems by means of constructing appropriate algebraic models and then applying algebraic techniques to find a solution.
Explore exponential and logarithmic functions, including application problems, and the efficient and appropriate use of logarithms and their properties.
Learn the techniques of solving systems of equations and appropriately apply these processes to word problems.

Communication Skills: Students will:
Communicate both in writing and orally throughout the course; particular attention will be paid to the accurate and appropriate use of the language of algebra.
Use calculators to solve problems, communicate solutions and explore options.

Life Value Skills: Students will
Appreciate the intellectual honesty of deductive reasoning; a mathematician’s work must stand up to the scrutiny of logic, and it is unethical to try to pass off invalid work.
Do their own work, honestly challenging themselves to master the material.

Cultural Skills: Students will
Read, write and manipulate mathematical notation.
Experience mathematics as a culture of its own, with its own language and modes of thinking.

Aesthetic Skills:
Appreciate the austere intellectual beauty of deductive reasoning.
Appreciate mathematical elegance.

It is also worth mentioning the NCTM (National Council of Teachers of Mathematics) "standards" for mathematics education, because they are also a list of some overall goals we strive for in this course:
The students shall develop an appreciation of mathematics, its history and its applications.
The students shall become confident in their own ability to do mathematics.
The students shall become mathematical problem solvers.
The students shall learn to communicate mathematical content.
The students shall learn to reason mathematically.

FURTHER COURSE NOTES: This course is designed to give students the algebraic tools required in subsequent courses, specifically MATH 180 (Elementary Functions), MATH 230 (Elements of Statistics), or MATH 270 (Managerial Mathematics). “Tools” here means both symbol manipulation and the logical and problem-solving skills - in short, how to “do” algebra and “what to do with it”.

There are those who view College Algebra as a remedial or review course, since it covers the same material as does high school’s Algebra II. It is nevertheless a college course, and I will reguard it as such.  I am far more interested in your real understanding of the material than I am in your “loading and dumping” huge lists of definitions and formulas. We will cover the material at about three times the pace of the typical high school version, and much more will be expected of you outside the classroom. The rule of thumb, “2 hours outside of class for each hour in class”, is probably appropriate here. You need to see yourself as an active learner, to take responsibility for your own learning, to avail yourself of the aids in place (tutors, the teacher, study groups, computer software, web sites) but to make sure that you honestly learn how to do what is required of you – you can only rely on others up to a point!

Mathematics can be very deceptive, you may understand exactly what is presented in class and, if you are shown how to do a problem, see where each step came from.  THIS DOES NOT MEAN YOU CAN DO IT. Think about listening in on a conversation in some other language; you may understand what the people in the conversation are saying, but this does not mean you can join in the conversation very easily.  Think of listening to some music that you particularly enjoy.  Can you sit down and play it? This takes practice, and the same is true of Math.  If you need help with a question, and you have been shown how to do it, try to do one just like it later that day when you are alone.  Try a day later.  Try again a week later.  If you can still do it a week later, you are on your way to owning that particular skill.

You should be capable of success, as long as you apply yourself sufficiently. You are here because your ACT score, your placement exam, or your grades in previous courses, or some combination of these, indicate that this is the appropriate level for you – you are ready for this material, but not yet ready to move on to the course beyond this one. This does not mean this course will be “easy” for you, but that you should be able to handle it.

You must believe that “Mathematics is not a spectator sport”. You are the LEARNER and you must engage in the learning process. The purpose of the course is not for me to convince you that I know algebra, but for you to learn it. Again, it comes down to your accepting responsibility for your learning.

Technology You will find the course much easier if you have some sort of graphing calculator.  If you have anything other than a TI machine and need some help using it, it will take me a little while to research how your machine works.  At the very least, you should have a scientific calculator for some of the work later in the semester.

Assessment Procedures:

Semester grades in this course will be awarded according to a standard scale:
945—1050pts      (90% and above)    = A
892—944pts          (85% and above)  =AB
840—891pts          (80% and above) = B
787—839pts          (75% and above)  = BC
735—786pts          (70% and above)  = C
682—734pts          (65% and above)  =CD
630—681pts          (60% and above)  = D
Less than 630pts (Below 60%)           = F

Semester grades are calculated purely on a points basis, that is, the letter grades you earn on individual exams are purely guidelines for you to gauge your progress.  For example, if you miss a particular grade on an exam by a certain number of points, it is still possible to make up those points (and get into that grade bracket) in other parts of the course, perhaps on the next exam.  On the other hand, just because you got a good grade on one test, you should realize that you can lose enough points to get into a lower grade bracket by doing poorly in another area of the course.  Once again: it is points that count.

Homework questions                            100 pts.

(Full credit is given for each completed assignment)
Homework will be due one class week after it has been assigned.  Any questions regarding how to do particular homework problems will be welcomed in the intervening class meetings or in my office but not in class on the day that the homework is due.  Late homework will be penalized by a deduction of 20% of the assigned grade for each schoolday -- including schooldays on which class does not meet – that the work is late, so that, if the work is one week late, it will not receive any points.

Please note that the assigned homeworks are odd numbered questions and that the answers to these are at the back of the book.  This is so that you can check your work as you go.  It does, however, bring up a couple of points 1) SIMPLY COPYING DOWN THE ANSWERS FROM THE BACK OF THE BOOK DOES NOT CONSTITUTE DOING HOMEWORK and 2) your correct answer may not match the correct answer at the back of the book – this should be viewed as a learning experience (how do the two answers match up?)

Examinations                                           700 pts

There will be seven in class exams worth 100 pts apiece, and lasting 50 minutes each.

Participation                                              50 pts

Participation points are easy to acquire and you probably already know how to get them; don’t chat to your neighbors when I’m lecturing (asking a neighbor to help if you didn’t understand what I said is, however, always acceptable).  General politeness counts.  Cheerfulness, engagement, willingness to push buttons on your calculator, asking me to clarify if you are stuck, taking advantage of my office hours, these are all, to quote the Sound of Music, a few of my favorite things.

Cumulative Final Examination          200 pts

Total                                                1050  pts

Attendance Policy:

You can afford to miss no more than the equivalent of one week of class.  Any more absences are a dangerous loss of classtime percentage. Once you have had 4 unexcused absences, every unexcused absence from that point onward will incur a penalty of 10 pts from your participation and attendance score.
Make up exams situations will be considered on a case-by-case basis, but invariably they require as much forewarning as possible -- and documentation.  You know when the exams are; please do not book flights home, or your wedding, etc, etc on those dates.  If your, or your best friend's, or your uncle's hairdresser's poodle's (if you're from the Coast) wedding is already booked for any of those dates, please let me know ASAP. I will not give make up tests without good reason, and if you should miss a test that is not made up, your score for that test will be zero.
The sad fact is that it is a rare semester when some student doesn't have to rush home to tend a family crisis, or bury a loved one.  Often this interferes with exams.  Should such sadness happen to you, I will need to ask you for some sort of verification (obituary, hospital record, etc) and then we will try to get your semester moving again.

RESOURCES: Tutoring is available in the Learning Center  - third floor, Murphy Center. I also want you to consider coming to see me if you have a problem with some material. Sometimes we can resolve in a few minutes a difficulty that can cause problems for weeks. I don’t resent your coming – it’s part of my job! I want your success as much as you do.

FINAL COMMENTS: You, as the student, are the learner, and "to learn" is an active verb; you must be actively engaged in the learning process, and this is best accomplished by your DOING mathematics. I am not here to show you how much I know - I am here to be "a guide on the side, not a sage on the stage". Please feel free to ask questions in class, either of me or of your group-mates. Please feel free to come to my office to discuss problems you might be having. Please feel free to go visit the learning center for tutoring help if necessary. The bottom line is that you must take responsibility for your own learning. Please believe that "Mathematics is not a spectator sport!"

AMERICANS WITH DISABILITY ACT: If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see me or Wayne Wojciechowski (MC 320, 796-3085) within ten days to discuss your accommodation needs.

Course Schedule:

28 Aug <R.1> Real Number System,                                                                     p6, #1-77 odd
30 Aug <R.2> Integer Exponents, Scientific Notation and Order of Operations       p13, #1-85 odd
31 Aug <R.3> Addition, Subtraction and Multiplication of Polynomials,                  p 19, #1-41 odd
01 Sept <R.4> Factoring,                                                                                      p28, #1-85 odd

04 Sept LABOR DAY
06 Sept <R.5> Rational Expressions,                                                                     p35, #1-61 odd
07 Sept <R.6> Radical Notation and Rational Exponents,                                      p44, #1-123 odd
08 Sept Review

11 Sept Exam #1, Chapter R
13 Sept <2.1> Equations,                                                                                     p66, #1-49 odd
14 Sept <2.2> Applications,                                                                                 p77, #1-35 odd
15 Sept <2.3> Quadratic Equations,                                                                     p91, #1-49 odd

18 Sept <2.4> Complex Numbers,                                                                      p102, all odds
20 Sept <2.5> Other Types of Equations,                                                            p109, #1-71 skipped odds
21 Sept <2.6> and <2.7> Inequalities,                                                                 p119, #41-69 odd, p127, #1-39 odd
22 Sept  Review

25 Sept Exam #2, Chapter 2
27 Sept <3.1> and <3.2> Cartesian Graphs,                                                       p156, #1-21 odd, 35-55 skipped odds,65,73,75
28 Sept <3.3> Lines,                                                                                          p172, #1-55 odd
29 Sept <3.4> Functions,                                                                                   p190, #1,3,17,19,21-53 odd

02 Oct <3.5> Graphs of Functions,                                                                    p209, #1-65 odd
04 Oct <3.6> Quadratic Functions,                                                                    p223, #13-27 odd, 35-49 odd
05 Oct <3.7> Operations on Functions,                                                             p236, #1-41 odd
06 Oct Review

09 Oct Exam #3, Chapter 3
11 Oct <4.1> Polynomial Functions of Higher Degree,                                        p255, #1-37 odd
12 Oct <4.2> Polynomial Division; The Remainder and the Factor Theorem,       p265, #1-45 odd
13 Oct <4.3> Theorems About Zeros of Polynomial Functions,                           p277, #1-43 odd

16 Oct <4.4> Complex and Rational Zeros,                                                        p287, #1-23 odd
18 Oct <4.5> Rational Functions,                                                                       p304, #7-43 odd
19 Oct <4.6> Variation and Application,                                                            p312, all odds
20 Oct MID SEMESTER BREAK

23 Oct   Review
25 Oct Exam #4, Chapter 4
26 Oct <5.1> Inverse Functions,                                                                        p329, #1-51 odd
27 Oct <5.2> and <5.3> Exponential Functions and Graphs,                              p339, #1-11 odd, 33-47 odd, p352 #3,15

30 Oct <5.4> Logarithmic Functions and Graphs,                                               p365, #1-51 odd
01 Nov <5.5> Properties of Logarithmic Functions,                                            p376, #1-45 odd
02 Nov <5.6>  Solving Exponential and Logarithmic Equations,                          p388, #1-77 skipped odds
03 Nov  Review

06 Nov Exam #5, Chapter 5
08 Nov <6.1> and <6.2>Systems of Equations in Two Variables,                      p406, #1-47 odd,  p416, #1-19 odd
09 Nov <6.5> Systems of Equations in More Variables,                                     p449, #1-27 odd
10 Nov <6.6> The Algebra of Matrices,                                                            p460, #1-29 odd

13 Nov <6.7> Matrix Inverses,                                                                         p467, #1-27 odd
15 Nov <6.8> and <6.9> Determinants and Cramer’s Rule,                              p474, #9-19 odd,  p483, #33-41 odd
16 Nov <6.3> and <6.4> Systems of Inequalities and Linear Programming,       p424, #1-25 odd, p433, #1-13 odd
17 Nov Review

20 Nov Exam #6, Chapter 6
22 Nov THANKSGIVING BREAK
23 Nov THANKSGIVING BREAK
24 Nov THANKSGIVING BREAK

27 Nov <8.1> The Parabola,                                                                           p587, #1-43 odd
29 Nov <8.2> The Circle and the Ellipse,                                                         p600, #1-47 odd
30 Nov <8.3> The Hyperbola,                                                                         p612, #1-39 odd
01 Dec Further Work with Conic Sections,                                                       p616, #1-31 odd

04 Dec Review
06 Dec Exam #7, Chapter 8
07 Dec Final Review
08 Dec Final Review

FRI 15th  Dec Final Exam, 12:50 to 2:50 PM