Core 098 - Quantitative Skills
This course develops the skills needed for other mathematics courses at Kings College, and emphasizes the organizational and analytical skills required for success in a problem solving society. Mathematically, this course focuses on the structure of arithmetic and directly relates this understanding to the more theoretical topics of algebra. Students will review and relearn the fundamentals of real numbers and use this knowledge as a bridge to the abstract concepts of algebra. The arithmetic and algebraic concepts covered in the course are used to introduce the basics of problem solving and mathematical reasoning. Topics include; whole numbers and integers, fractions, decimals, and mixed numbers, exponents, roots, simplifying algebraic expressions, solving first and second degree equations, factoring algebraic expressions, and simplifying rational expressions.
In any career or life path that you choose, it is likely that you will encounter problems where the solutions are based on mathematical and logical principles. Therefore, the basic concepts of mathematics are a necessary component of a liberal arts education. This course is designed to bridge the gap between high school and college mathematics courses. The emphasis of the course is on relearning known topics and learning new topics for the purpose of understanding and then using this knowledge as a foundation for learning other concepts that are essential for success in future mathematics courses at Kings College and everyday life.
- Students will understand the rules of algebra and how they extend from the basic principles of arithmetic.
- Students will become prepared for further mathematics courses at Kings. Students will gain a firm understanding of the fundamentals needed to perform more complex calculations in advanced classes.
- Students will become more comfortable and confident with mathematics and relieve any anxiety by concentrating on linking the known basics of arithmetic to the more abstract concepts of algebra. Students will begin to appreciate their progression of knowledge in mathematics as an extension of what they already know and not a new and unrelated topic.
- Students will learn important steps in organization and problem solving. While some topics covered in this course may not be encountered by people outside a mathematics classroom, the analytical and procedural skills needed to solve these problems are used daily in any career or life path.
As a result of taking this course, students will:
- Understand and be able to communicate and apply the techniques of mathematics using precise terminology (i.e., be able to think like a mathematician.)
- Perform basic arithmetic operations with real numbers such as addition, subtraction, multiplication, division, factoring, and simplifying expressions.
- Formulate exponent rules based on past arithmetic examples and simplify expressions using these rules.
- Apply arithmetic examples of addition, multiplication, and the distributive property to perform operations with polynomials.
- Employ different methods to factoring polynomials and be able to choose when it is best to use the different methods.
- Analyze percent application problem solving to find the missing variables.
- Solve quadratic equations by either factoring or using the quadratic formula.
- Recognize the difference between linear, quadratic and rational equations and be able to solve each for the missing variable.
- Perform operations on rational expressions corresponding to existing rules for numerical fractions.
- Sketch linear equations and be able to find the linear equation given the point and slope. Sketch quadratic equations by finding the roots and the vertex.
Introductory Algebra, 11th edition, Marvin L. Bittinger, Addison Wesley Higher Education, 2011. ISBN: 0-321-59921-7
There will be three in-class tests that will be announced at least one week in advance. The format for these tests will vary depending on the content covered in class. Since this course is meant to hone your mathematical skills, completing homework assignments, reviews, and practice problems will be the best way to prepare for each exam. You learn math by doing math!
B) Final Exam
The primary purpose of this course is for students to walk away with a much improved mastery of the mathematical skills examined in the course. As a result, the final exam will cover all material from the course. This exam will be given during finals week at a date and time to be determined by the registrar.
C) Homework/ Homework Quizzes:
- Homework is essential for learning mathematics and your success in the course depends on the commitment you make to the daily assignments. Homework should be brought to class every day, and individual students will take an active roll in checking and correcting their assignment.
- Only a limited time will be spent discussing homework from the previous night. It is the responsibility of the student to see the professor during office hours for additional help on questions that are not answered in class.
- There will frequently be homework quizzes. These quizzes will consist of questions on homework related topics that have been covered and discussed.
- If the instructor has the impression that the class is not attempting the homework, then homework may be collected and graded the class after it is assigned.
- One homework/homework quiz grade during the semester will be dropped.
- You will be required to visit at least two tutoring sessions during the semester; this will count towards your homework grade.
D) Classroom Participation and Attendance:
- You will be graded based on your attendance, involvement, and overall classroom demeanor. Your grade will benefit from trips to the blackboard, questions asked and answered in class, positive interactions with others, completed homework assignments, homework discussion, and office hour and tutoring visits if beneficial to the learning process.
- Negative participation as well as any disruption of classroom activities will detract from your participation grade.
- Students are expected to attend every class on time and be prepared to discuss the previous nights homework and be actively involved in classroom discussion. Remember, attendance plays a roll in your participation grade.
- If circumstances develop that cause you to miss class (serious personal illness, family emergency, documented school function, etc&) it is required that you contact me as soon as possible in advance of the absence (or A.S.A.P.) to make arrangements to complete any class work. The absence will otherwise be considered unexcused. You will be responsible to make-up any work missed prior to the next class meeting.
- Any student failing to follow this procedure on a test date will not be given a makeup test. Evidence of the reason for absence may be required.
- For missed exams due to an excused absence, a MORE CHALLENGING make-up exam will be given. For missed homework quizzes due to an excused absence, you are responsible for handing in the homework assignment for a grade.
All students who have a learning disability or a physical handicap should schedule an appointment with the instructor during the first week of class to discuss accommodations for the classroom and/or assignments and examinations.
- Students are expected to complete their own assignments. Refer to the Kings College Students Handbook for the policy on Academic Integrity.
- Cell phones or other items that may cause distractions in class are not permitted.
The course covers selected topics in the textbook along with supplemented topics.
|Problem Solving, Arithmetic, and Pre-Algebra||Textbook Section|
|Factoring polynomials and Quadratic Equations|
|Rational Expressions and Equations|
Prerequisite: CORE 098 Mathematical Skills
All students enrolled in this course should have taken CORE 098 Mathematical Skills and attained a minimum grade of C in that course, or they should have been exempted from the requirement of taking Core 098 by the mathematics department.
Textbook: P. Tannenbaum, Excursions in Modern Mathematics, 7th edition, Pearson Prentice Hall, 2010. ISBN: 0-321-56803-6
In order to fully participate in society today, a person must have knowledge of the contributions of mathematics. Mathematics has become an indispensable tool for analysis, quantitative description, decision-making, and the efficient management of both private and public institutions. Consequently, a familiarity with essential concepts of mathematics is necessary for one to function intelligently as both a private individual and a responsible citizen. As such, this course is divided into four units, each covering an aspect of mathematics that is conceptually significant and highly relevant. The first unit deals with issues of fairness and strategy in voting and elections. In the second, students learn about collecting, organizing, interpreting, and presenting statistical data. The third unit involves the use of mathematics to solve problems related to organizing and managing complex activities, and a final unit on symmetry and fractal geometry establishes connections between mathematics and art and highlights some applications. On some occasions, units on other suitable topics may replace those denoted here.
In this course, all students will gain experience with and increase proficiency in working with mathematics on a conceptual level, and develop an appreciation for the utility of mathematics. Specifically, students will
- Construct and analyze good examples and counterexamples.
- Communicate using precise, technical terminology.
- Look at the same problem in multiple ways.
- Prove statements.
- Construct and apply algorithms.
- Create structures and systems that model problems and information.
- Develop and apply abstractions of concrete ideas.
- Appreciate the relevance and significance of math in the world around them, especially in unexpected areas.
Classes are mainly composed of lecture/discussion and group work. Homework is discussed in class regularly. In addition, we frequently use computer demonstrations in class to illustrate mathematical ideas and techniques.
This course consists of four units. At the end of each unit, there will be a one-period in-class test. The last such test will be given during the final exam period. There will be no comprehensive final exam. Each test will cover the material examined during the preceding unit. Questions will not only be computational in nature, but rather they will also require students to offer written explanations of and logical arguments based on the various concepts from the unit. Each exam will be worth 20% of the final grade.
B) Class Participation and Attendance
Persistence and commitment are necessary if one intends to achieve her or his full potential, and they are necessary attributes for success in mathematics. Students are expected to prepare for, attend, and participate in every class. If a student must miss a class, she or he should inform the instructor why she or he will not attend by calling or emailing the instructor prior to the class. Unexcused absences will negatively affect the final grade. Class participation and attendance is worth 10% of the final grade.
C) The remaining 10% of the final grade is determined by work chosen by the professor (e.g. quizzes, homework, projects, etc.)
Make-up exams will only be given as a result of extreme circumstances, such as sudden accidents, illnesses, and court appearances. If you are unable to attend an exam, then you should inform the instructor prior to the exam time. The instructor determines whether or not you should be given a make-up exam.
If the instructor decides to give a student a make-up exam, then the exam is scheduled at the instructors discretion. Make-up exams will not be the same as the original exam, and in general they will be more challenging than the original exam. This is not a punishment, but rather a matter of fairness. No two exams have the same difficulty level, and as a matter of fairness, the more challenging exam should go to the person who is being granted an exception from following the ordinary course schedule.
You will be allowed to use a calculator on exams. Only a basic scientific calculator is necessary for this course. While you may use a graphing calculator, there is certainly no advantage to having one.
Outline of Material Covered (tentative):
I. The Mathematics of Social Change
This deals with mathematical applications in social science. How do groups make decisions? How are elections decided? How can power be measured? When there are competing interests among members of a group, how are conflicts resolved in a fair and equitable way?
1. The Mathematics of Voting: The Paradoxes of Democracy
1.1 Preference Ballots and Preference Schedules
1.2 The Plurality Method
1.3 The Borda Count Method
1.4 The Plurality-with-Elimination Method
1.5 The Method of Pairwise Comparisions
2. The Mathematics of Power: Weighted Voting Systems
2.1 An Introduction to Weighted Voting Systems
2.2 The Banzhaf Power Index
In one way or another, statistics affects all of our lives. Government policy, insurance rates, our health, and our diet are all governed by statistical laws. This section deals with some of the basic elements of statistics. How are statistical data collected? How are they summarized so that they say something intelligible? How are they interpreted? What are the patterns of statistical data?
13. Collecting Statistical Data: Censuses, Surveys, and Clinical Studies
13.1 The Population
13.3 Random Sampling
13.4 Sampling: Terminology and Key Concepts
13.5 The Capture-Recapture Method
13.6 Clinical Studies
14. Descriptive Statistics: Graphing and Summarizing Data
14.1 Graphical Descriptions of Data
14.3 Numerical Summaries of Data
14.4 Measures of Spread
III. Management Science
This deals with methods for solving problems involving the organization and management of complex activities that is, activities involving either a large number of steps and/or a large number of variables (building a skyscraper, putting a person on the moon, organizing a banquet, scheduling classrooms at a big university, etc.). Efficiency is the name of the game in all these problems. Some limited or precious resource (time, money, raw materials) must be managed in such a way that waste is minimized. We deal with problems of this type (consciously or unconsciously) every day of our lives.
5. The Mathematics of Getting Around: Euler Paths and Circuits
5.1 Euler Circuit Problems
5.2 What is a Graph?
5.3 Graph Concepts and Terminology
5.4 Graph Models
5.5 Eulers Theorems
5.6 Fleurys Algorithm
1.7 Eulerizing Graphs
6. The Mathematics of Touring: The Traveling Salesman Problem
6.1 Hamilton Paths and Hamilton Circuits
6.2 Complete Graphs
6.3 The Traveling Salesman Problems
6.4 Simple Strategies for Solving TSPs
6.5 The Brute-Force and Nearest-Neighbor Algorithms
6.6 Approximate Algorithms
6.7 The Repetitive Nearest-Neighbor Algorithm
6.8 The Cheapest Link Algorithm
IV. Growth and Symmetry
This deals with nontraditional geometric ideas. What do sunflowers and seashells have in common? How do populations grow? What are the symmetries of a pattern? What is the geometry of natural (as opposed to artificial) shapes? What kind of geometry lies hidden in a cloud?
11. The Mathematics of Symmetry: Beyond Reflection
11.1 Rigid Motions
11.5 Glide Reflections
11.6 Symmetry as a Rigid Motion
12. The Geometry of Fractal Shapes: Naturally Irregular
12.1 The Koch Snowflake
12.2 The Sierpinski Gasket
12.3 The Chaos Game
12.4 The Twisted Sierpinski Gasket
12.5 The Mandelbrot Set