Assignments

Exams

Grading

Preparation Time

Please read this information carefully before you begin the course. It contains information about the text, what you will be graded on, how you can determine your grade, course objectives, and prerequisite mathematics that are required for the course.

This course studies the basic elements and applications of finite mathematics. The first half of the class covers the language of set theory, principles of counting and combinatorics, probability theory for equally likely outcomes, elementary stochastic processes, conditional probabilities, and repeated experiments. The concept of a random variable is developed, along with expectation and variance. The second half of the class explores systems of linear equations and matrix algebra, linear programming, and Markov chains. This course considers a broad range of applications in business, the life sciences, and the social sciences. Desired learning outcomes (as determined by the Department of Mathematics at BYU) are listed as follows:

Part 1: Probability Models (14 lectures)

- Sets Theory (2 lectures)
- Describe sets using set-builder notation.
- Solve problems involving set membership, subsets, intersections, unions, and complements of sets.
- Identify the various partitions of a Venn diagram.
- Determine the number of elements in a partition based on set counting rules for unions, complements, and products.

- Combinatorics and Counting (3 lectures)
- Describe the sample space of an experiment and the set of all possible outcomes using trees and the multiplicative principle, as appropriate.
- Explain what a permutation is, and how many permutations there are for a given set.
- Demonstrate how to count more sophisticated permutation problems involving products and restrictions to sets.
- Use the notion of partitions to reduce permutation problems to combinations where the order does not matter.
- Solve various hybrid counting problems with and without replacement, with and without order.
- Apply ideas from combinatorics and counting, and formulate real-world problems.

- Probability (6 lectures)
- Describe the notions of outcomes and events in probability, and the axioms of a probability space.
- Use ideas from combinatorics to determine the probabilities of various events with equally likely outcomes.
- Demonstrate understanding of probabilistic independence.
- Describe a stochastic process and compute probabilities of events on trees.
- Explain Bayes’ theorem and demonstrate proficiency with conditional probability.
- Use Bayes’ formula to compute probabilities of various conditionals.
- Be proficient with Bernoulli trials and solve basic problems.
- Apply ideas from probability, and formulate real-world problems.

- Random Variables, Expected Values, Variance (3 lectures)
- Demonstrate understanding of random variables.
- Describe the probability density function and the distribution of a given random variable.
- Show how to compute the expectation, variance, and standard deviation of a random variable.
- Read a table of a normal distribution and compute the probabilities of given events.
- Apply ideas of uncertainty, and formulate real-world problems.

Part 2: Linear Models (18 lectures)

- Systems of Linear Equations (5 lectures)
- Use elimination and substitution methods to solve linear systems of two or three variables.
- Reduce a linear system into row echelon form, then solve with back substitution.
- Solve a linear system by transforming it into reduced row echelon form.
- Identify whether a system of linear equations has no solution, exactly one solution, or infinitely many solutions.

- Matrix Algebra and Applications (4 lectures)
- Perform the matrix algebra operations of addition and multiplication.
- Compute the inverse of a matrix; identify when a matrix is not invertible.
- Study in detail at least one application involving matrix algebra (e.g., Leontief economic models).

- Linear Programming (6 lectures)
- Formulate linear programming problems from various application areas, such as business, resource management, and so forth.
- Describe the constraints, the feasible set, and the objective function of a given linear optimization problem.
- Solve a linear program using the graphical method, when possible.
- Explain the standard form of a linear program.
- Describe the following concepts from the simplex method: slack variable, pivot column, tableau.
- Solve, by hand, a given linear program using the simplex method.
- Solve, by computer, a given linear program.
- Explain and use the dual formulation of a given linear program.

- Markov Chains (3 lectures)
- Describe a Markov chain.
- Identify when a Markov chain is regular, irregular, and absorbing.
- Describe how to determine the stable probabilities of a regular Markov chain.
- Describe how to compute the fundamental matrix of an absorbing Markov chain.
- Apply ideas from Markov chains, and formulate real-world problems. Determine the transition matrix and states of a given application.

Successful completion of Math 118 requires basic arithmetic and algebra skills. In particular, students are expected to be able to do the following:

- Add, subtract, multiply, divide, and reduce fractions.
- Add, subtract, multiply, and divide decimal numbers.
- Write a decimal or ratio of decimals as a fraction.
- Calculate exponents of integers.
- Solve
*a*x +*b*=*c*x +*d*. - Simplify square roots; rationalize denominators (only for correlation coefficients).
- Graph lines in standard form and
*y*-intercept form. - Find the equation of a line using two points or point-slope formula.
- Graph linear inequalities in two variables.

In order to assess readiness, each student is required to take a pretest that covers the above material. The pretest is available at the end of this lesson. Students must take the pretest before they will be given access to the rest of the course.

There is one lesson per section in the course. As you plan your course of study, be aware that the exams are rigidly structured. Thus, the course outline assumes you will be studying the topics in numerical order. As you will see below, the exams will assume this order.

There is no required material; the textbook is included within this course.

If you would like, you may purchase a similar text: *Finite Mathematics* (9th edition) by Lial, Greenwell, and Ritchey.

ISBN-13: 978-0321760043

ISBN-10: 0321760042

This course includes a helpful tool to allow you to track your mastery of the material. This tool, or Study Plan, can be found directly after each textbook reading, and contains problems and quizzes which will reinforce your understanding of the principles you are learning. **These activities will not count toward your final grade** and are intended only to ensure your thorough comprehension of the material. When you first enter your study plan, use the "Chapter 0" assessment to teach yourself how to use this tool.

All homework for the course is done online. You will find a homework assignment after each set of textbook reading. When you go into the homework assignment, you will first see an introductory page which will show you the different sections of the assignment with an explanation of the material to be covered. Click on the first section; it will take you to a page from which you can access each individual question. We suggest that you write down your solutions to each problem and keep your work in a notebook that you can review when necessary.

Each unit ends with a quiz which should allow you to assess your knowledge of the material you just learned. These quizzes** will **count toward your final grade and, when used correctly, should help prepare you for midterm exams and the final.

There will be three midterm exams and a final exam in the course.

Exam | Sections covered |
---|---|

1 | 1.1–1.6, 2.1–2.5 |

2 | 3.1–3.3, 4.1–4.3, 5.1–5.6 |

3 | 6.1–6.3, 7.1–7.3 |

The final will be comprehensive and will cover all sections covered in the course outline.

Grades in this course are determined as follows:

Category | Percent |
---|---|

Pretest | 1% |

Exam 1 | 20% |

Exam 2 | 20% |

Exam 3 | 20% |

Homework | 8% |

Online Quizzes | 6% |

Final | 25% |

Please note that according to Independent Study policy, you must pass the final exam in order to pass the course.

Your grade will be determined by the following scale:

Score | Grade |
---|---|

93+% | A |

90–92% | A− |

87–89% | B+ |

84–86% | B |

80–83% | B− |

77–79% | C+ |

74–76% | C |

70–73% | C− |

67–69% | D+ |

64–66% | D |

60–63% | D− |

0–59% | E |

Adequately prepared students should expect to spend a minimum of three hours of work in the course per week for each credit hour. This adds up to a minimum of 12 hours per week. A minimal time commitment is likely to lead to an average grade, B−/C+, or lower. Much more time may be required to achieve excellence. Online students typically need to spend more time on the class because they do not attend any lectures.

The first injunction of the BYU Honor Code is the call to “be honest.” Students come to the university not only to improve their minds, gain knowledge, and develop skills that will assist them in their life’s work, but also to build character. “President David O. McKay taught that character is the highest aim of education” (“Aims of a BYU Education,” p. 6). It is the purpose of the BYU Academic Honesty Policy to assist in fulfilling that aim.

BYU students should seek to be totally honest in their dealings with others. They should complete their own work and be evaluated based upon that work. They should avoid academic dishonesty and misconduct in all its forms, including but not limited to plagiarism, fabrication or falsification, cheating, and other academic misconduct. (Taken from the Academic Honesty Policy, BYU Handbook.)

If a student is found to be cheating in any form, the student will receive a failing grade for that assignment or exam. In addition, the incident will be forwarded to the Honor Code office. If the student is found to have participated in another dishonest activity, the student will receive an E for the course.

These policies are specific to this course. For additional information about general policies, please refer to Independent Study Course Policies page.

8 computer-graded quizzes and 31 computer-graded homework assignments (6.2 does not have a homework assignment).

This course includes a helpful tool to allow you to track your mastery of the material. This tool, or Study Plan, can be found directly after each textbook reading, and contains problems and quizzes which will reinforce your understanding of the principles you are learning. **These activities will not count toward your final grade** and are intended only to ensure your thorough comprehension of the material. When you first enter your study plan, use the "Chapter 0" assessment to teach yourself how to use this tool.

All homework for the course is done online. You will find a homework assignment after each set of textbook reading. When you go into the homework assignment, you will first see an introductory page which will show you the different sections of the assignment with an explanation of the material to be covered. Click on the first section; it will take you to a page from which you can access each individual question. At the top of the page is a link where you can download a copy of the questions for that section. We suggest that you print out the homework and keep the questions and your work in a notebook that you can review when necessary.

You may resubmit each homework assignment as many times as you want. The last submission will be graded.

Each unit ends with a quiz which should allow you to assess your knowledge of the material you just learned. These quizzes will count toward your final grade and, when used correctly, should help prepare you for midterm exams and the final.

Each quiz can be resubmitted once for a fee.

There will be three proctored, computer-graded midterm exams and a proctored, computer-graded final exam in the course.

Exam | Sections covered |
---|---|

1 | 1.1–1.6, 2.1–2.5 |

2 | 3.1–3.3, 4.1–4.3, 5.1-5.6 |

3 | 6.1–6.3, 7.1–7.3 |

The final will be comprehensive and will cover all sections covered in the course outline. You must pass the final exam to pass the course.

Exams can be retaken one time for a fee.

Since this is an Independent Study course, you do not have a regular professor with office hours to help you. You can email virtualmathlab@byu.edu for help, but it will be difficult over email. Please do not email the professor. The above email will go to the TA who is assigned to this course. If you are close to a university or college, they may have an open math lab that you can go to for help. Otherwise, you will need to check the textbook for similar examples, or look for examples on the web.

Please use the help menu in this course to contact Independent Study or your instructor. You can find a list of free tutors available to BYU Independent Study students on the Free Tutoring Services website.

**Note:** The Harold B. Lee Library website provides a number of online resources and librarians are available via phone, chat, and email to answer questions about library-related issues.

All course materials (e.g., outlines, handouts, syllabi, exams, quizzes, media, lecture content, audio and video recordings, etc.) are proprietary. Students are prohibited from posting or selling any such course materials without the express written permission of BYU Independent Study. To do so is a violation of the Brigham Young University Honor Code.

Copyright © 2016 Brigham Young University. All rights reserved.

Published by the

Department of Independent Study

Division of Continuing Education

Brigham Young University

120 MORC

Provo, Utah 84602-1514

USA

COPYRIGHT NOTICE*The materials used in connection with this online course are only for the use of students enrolled in this course for purposes associated with this course and may not be retained or further disseminated. Any copying or further dissemination of these materials may be subject to applicable U.S. Copyright Laws. For questions or more information, please visit the BYU Copyright Licensing Office website. “Members of the BYU community who willfully disregard this Copyright Policy or the BYU Copyright Guidelines place themselves individually at risk of legal action and may incur personal liability for their conduct. The unauthorized use or distribution of copyrighted material, including unauthorized peer-to-peer file sharing, may subject individuals to civil and criminal liabilities, including actual and statutory damages, costs and fees of litigation, fines, and imprisonment… Violations of the Copyright Policy may result in university disciplinary action including termination of university enrollment or employment.” (Emphasis added. Excerpt taken from the BYU Copyright Policy).*

Copyright notice for specific, individual copies

All copies are intended for non-commercial, educational purposes in connection with this registered course and only for students enrolled in this course. Any copying or further dissemination of these materials may be subject to applicable U.S. Copyright Laws.