Download Jefferson State Community College - Finite Mathematics Course Outline (MTH 110) and more Study notes Mathematics in PDF only on Docsity!
Date Adopted 1998 Dates reviewed 2007 Dates revised 2004, 2008
Alabama
Department of
Postsecondary Education
Representing Alabama’s Public Two-Year College System
Jefferson State Community College
MTH 110
Finite Mathematics
I. MTH 110 Finite Mathematics - 3 Semester Hours
Core Area III, Code A
II. Course Description
This course is intended to give an overview of topics in finite mathematics together with their applications, and is taken primarily by students who are not majoring in science, engineering, commerce, or mathematics (i.e. students who are not required to take Calculus). This course will draw on and significantly enhance the student’s arithmetic and algebraic skills. The course includes sets, counting, permutations, combinations, basic probability (including Baye’s Theorem) and introduction to statistics (including work with Binomial Distributions and Normal Distributions), matrices and their applications to Markov chains and decision theory. Additional topics may include symbolic logic, linear models, linear programming, the simplex method and applications.
III. Prerequisite
All core mathematics courses in Alabama must have as a minimum prerequisite high school Algebra I, Geometry, and Algebra II with an appropriate mathematics placement score. An alternative to this is that the student should successfully pass with a C or higher in Intermediate College Algebra.
IV. Textbook
Finite Mathematics, For the Managerial, Life, and Social Sciences, Tan 8th^ Ed. Thomson Brooks/Cole, 2006.
V. Course Objectives
The objective of this course is to provide the non-calculus mathematics needed for students in many disciplines. This course shows through applications the relevance of mathematics to both real life and future courses in many disciplines. It also provides a general mathematics background for students who need a terminal core mathematics course. The student will develop an understanding of the concepts, develop competent skills, and demonstrate applications in the following areas.
- Analytic interpretation of linear systems, matrix algebra, and set theory.
- Analytic interpretation of measurements of central tendency, probability, and statistics.
VI. Course Outline of Topics
A. This course shall include the following topics as a minimum.
- Applications of linear functions
- Equations of straight lines
- Two lines: relating the geometry to the equations
- Systems of linear equations
- Linear systems having one or no solutions
- Linear systems having many solutions
- Matrix algebra
- Matrix multiplication and applications
- The inverse of a matrix
- Counting techniques
- Sets
- Application of Venn diagrams
- The multiplication principle
- Permutations
- Combinations
- Basic concepts of probability
- Outcomes with unequal probability; odds
- Discrete random variables and expected value
- Additional topics in probability
- Conditional probability
- Multiplication rules for probability; independent events
- Bayes’ Theorem
- Statistics
- Measures of central tendency
- Measuring the dispersion of data
- Continuous random variables and the normal distribution
- The normal approximation to the binomial distribution
- Markov chains
- Regular Markov chains
- Absorbing Markov chains B. Optimal topics may include the following.
- Linear modeling
- Regression and correlation
- Linear programming
a. the distance between two given points, stating and using the appropriate formula b. the slope of the line passing through two given points, stating and using the appropriate formula.
- express a linear equation in slope-intercept form.
- graph linear functions.
- perform matrix addition, subtraction, and multiplication.
- determine the scalar product and the transpose of a matrix.
- determine the inverse of a given matrix, if it exists.
- use matrices to solve systems of linear equations.
- use Markov chains for problem solving. C. The student will demonstrate knowledge of sets and counting by his/her ability to:
- perform the union and intersection of given sets.
- draw a tree diagram displaying possible outcomes of an event.
- use the generalized multiplication principle.
- classify a given problem as a permutation or a combination.
- determine the number of permutations of an event.
- determine the number of combinations of an event. D. The student will demonstrate knowledge of probability and statistics by his/her ability to
- determine the sample space for a given experiment.
- find the probability distribution associated with a given set of data.
- use the laws of probability to find the probability of a given event in an experiment.
- find the expected value of a random variable X from a given probability distribution.
- calculate the following measures of central tendency from a given set of data: a. mean b. median c. mode
- calculate the following measures of dispersion of data from a given probability distribution: a. variance b. standard deviation
- use normal distributions to solve applied problems.
- use binomial distributions to solve applied problems.
XI. Attendance
Students are expected to attend all classes for which they are registered. Students who are unable to attend class regularly, regardless of the reason or circumstance, should withdraw from that class before poor attendance interferes with the student’s ability to achieve the objectives required in the course. Withdrawal from class can affect eligibility for federal financial aid.
XII. Statement on Discrimination/Harassment
The College and the Alabama State Board of Education are committed to providing both employment and educational environments free of harassment or discrimination related to an individual’s race, color, gender, religion, national origin, age, or disability. Such harassment is a violation of State Board of Education policy. Any practice or behavior that constitutes harassment or discrimination will not be tolerated.
XIII. Americans with Disabilities
The Rehabilitation Act of 1973 (Section 504) and the Americans with Disabilities Act of 1990 state that qualified students with disabilities who meet the essential functions and academic requirements are entitled to reasonable accommodations. It is the student’s
responsibility to provide appropriate disability documentation to the College. The ADA
Accommodations office is located in FSC 300 (205-856-7731).
