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# Mathematics 115 - College Algebra

At $3.69 per gallon, 10 gallons of gas will cost $36.90.
But how much will it cost to fill that 23 gallon tank on

your SUV? If you are getting 18 miles per gallon, 10 gallons of gas will take
you 180 miles. Thus, $36.90 will be

the cost of driving 180 miles. But how much gas (and, hence, what will be the
cost of) a 450‐mile trip? When

things are turned around a bit and simple arithmetic is not enough to get the
desired result, we get into the

**realm of algebra.**

In a laboratory experiment, you might measure the temperature at various time
intervals. Plotting those data

points on a coordinate system gives **a picture of the data**, and you can
then go on to model the behavior with a

straight line or some other curve. Being able to decide upon best‐fitting linear
or nonlinear models, as well as

writing down a formula for these that may be used for further purposes, are
additional places for the methods

of algebra.

In algebra, the primary techniques you learn, through** investigation,
practice, and application**, are (1) graphing,

(2) using variables to represent quantities yet to be determined, (3)
determining linear and nonlinear models,

and (4) manipulating the algebraic expressions resulting from such models.
Because of the vast range of uses

for these techniques, to be successful in virtually any field of study, some
ability with algebra is essential.

We will spend time doing practice problems, allowing you to acquire skill with
the techniques. It is equally

important that you also have** opportunities to experiment** and get a better
sense of why things work the way

they do. The simple question of why we add fractions the way we do is an example
of where this is helpful.

Since this class is coordinated with your Chem 108 class, we will have a great
opportunity to develop the algebra

in parallel with applications of interest from your other class. As the term
progresses, it is possible you will

additionally see topics from both Math 115 and Chem 108 being integrated with
your writing for Eng 111.

In class, we spend time working on example problems, as well as attempting
investigations and applied

problems **designed to increase your understanding of the mathematics**.
Outside of class, you will be expected

to complete the material on “hippocampus.org” and further develop ability with
pre‐requisites for this class by

working with “ALEKS” in the Mathematics Achievement Center. You will have
assigned work in your textbook

and other problems as introduced in class. In order to better quantify your
gains, we will use a National Science

Foundation program‐developed diagnostic as a pre‐ and post‐test. Finally, I will
employ surveys and other

“affective” measurements to collect your input on the design of the class, my
performance in helping you be

successful, and so on.

**Material to be covered:**

• Course text – Chapters 1‐4, 9

• ALEKS preparatory program

• Hippocampus program; login to “jeffpde” or use the link on Math 115 web page.

**Final Grade: **You will be graded according to performance on homework,
projects, quizzes, and exams. Relative

weights for each and assignment of final course grades will be as follows.

• Homework, Projects, and Quizzes | 25% |

• ALEKS preparatory final assessment (must be completed in first 3‐5 weeks) | 10% |

• Class exams | 25% |

• Post‐test Diagnostic | 15% |

• Final exam | 25% |

A 90‐100%, B 80‐89%, C 70‐79%, D 60‐69%, F 0‐59%

**Course Policies**

**1. Homework and Projects:** Daily homework will be assigned, but not all of
it will be collected for grading. Projects will

sometimes take the form of extended problem sets from the book and, at other
times, consist of an application which

requires you to utilize ideas and techniques learned while completing homework
problems.

**2. Quizzes and Exams:** Unless otherwise announced, all quizzes/exams will
be closed book and generally consist not only

of problems similar to the homework, but also problems which test your
comprehension of the material. The final

exam will be comprehensive. Calculators may be used, but use of any graphics,
symbolic manipulation, and/or

advanced programming capabilities is not allowed unless announced otherwise
beforehand.

**3. Extension of due dates for homework/projects and make‐up exams may be
granted only in the following instances:**

• Extreme illness (your own). Let me know about your condition as soon as
possible. We will arrange necessary

make‐up work as your good health returns.

• Emergencies (i.e., car accident, death in the family). Again, get in touch
with me as soon as possible, and we’ll

make suitable arrangements.

• Excused absences (i.e., athletic events which are excused by university
officials). Make‐up work must be arranged

and completed in advance.

**4. Office Hours in the Mathematics Achievement Center – Phelps Hall Gym: **
These are times when you have the

opportunity to meet with me outside of class to discuss problems, progress, etc.
It is also a good idea to use these

times to work on ALEKS, and all scheduled ALEKS assessments may take place only
during these times or by other

special arrangement. You are also welcome to contact me via email. The most
important this is to get your questions

answered.

**5. A Note about Study Habits: **A good rule of thumb is to spend 2‐3 hours
of study time outside of class for each hour of

class time. This time should be spent in diligent study, but should not be done
in blocks of time exceeding an hour or

so per study session. 15‐30 minute blocks of otherwise down time, interspersed
throughout the day, can become very

productive if used to work on a small group of problems. Keep a record of
questions that come up in your studies and

get them answered either by yourself, a fellow student, a tutor, or by me.

Studying with a friend or in a group can be a very positive thing, provided that
all participants are contributing.

Since not all assigned homework will be collected for grading, it is very
important that you make a special effort to

complete daily assignments in a timely fashion.

6. In all graded materials, **sufficient work must always be shown** which
supports your results. Answers alone, with no

supporting work, will almost never receive full credit. Your submitted work must
be neat, clearly presented, stapled,

and have your name written legibly on it. Learning to take pride in the
presentation of your work is almost as

important as learning the actual material of a course itself.

7. **You are always responsible **for all information given during the class
period. Additionally, any work done in class for

grade may not be made up due to absence from class (unless excusable as listed
above).

Mathematics 115 – College Algebra is a **Basic Skills in Mathematics** Course

Catalog Course Description: This course will give students a rigorous
preparation in algebra. Topics include

review of basic algebraic concepts, functions and graphs, polynomial, radical,
rational, exponential and

logarithmic functions; equations, inequalities, systems of equations and
inequalities; applications. This is a

University Studies course which satisfies the Basic Skills in Mathematics.

Basic Skills in Mathematics: The purpose of the Mathematics requirement in
University Studies is to help

students develop an appreciation of the uses and usefulness of mathematical
models of our world, as applied in

a variety of specific contexts. Mathematics 115 contains requirements and
learning activities that promote

students' abilities to...

I. use logical reasoning by studying mathematical patterns and relationships;

This is an integral part of nearly every topic in the course. One of the main
focuses of the course is the

function concept, where we examine the relationship between y and x through the
function f(x). Students

will be asked to graph basic function types such as linear, quadratic,
polynomial, and rational functions.

Another main focus of the course is the solution of equations. These will either
be those presented to the

student to solve or equations that are set‐up by the student as part of the
solution of a application

(word/story) problem.

II. use mathematical models to describe real‐world phenomena and to solve
real‐world problems ‐ as well as

understand the limitations of models in making predictions and drawing
conclusions;

Nearly all course topics have an application component to them, where students
will need to use them to

solve real‐world problems. Many of these are word problems which force students
to critically analyze

given information and extract the important elements in order to construct
algebraic expressions and

equations that can then be solved.

III. organize data, communicate the essential features of the data, and
interpret the data in a meaningful way;

Solving word problems forces students to extract from given information (or
data), the important elements

that can then be used to set up equations that allow them to solve the problem.
When graphing polynomial

functions, students will need to identify and communicate important features of
the function, e.g. maxima,

minima, regions where the function is increasing, where it is decreasing, and
concavity changes.

IV. extract correct information from tables and common graphical displays, such
as line graphs, scatter plots,

histograms, and frequency tables;

Graphing is very important component of algebra. In this courses students will
be graphing linear equations;

solving linear inequalities graphically; graphing quadratics & higher order
polynomials, radical functions,

rational functions, exponential, and logarithmic functions. Also students will
be working with relationships

between two variables from a data table.

V. express the relationships illustrated in graphical displays and tables
clearly and correctly in words; and/or

Identification of important features of graphs and where those features come
from mathematically is

stressed. When these graphs represent real‐world phenomenon being to able
express in words what they

show is stressed.

VI. use appropriate technology to describe and solve quantitative problems.

Use of appropriate technology such a graphing calculators and computer‐based
learning resources will be

prevalent throughout the course.