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Mathematics Department Discrete Mathematics Course Syllabus 2012-2013 Instructor: Lisa Novalis e-mail: [email protected] Phone: 973-228-1200 X789 A. Grading Policy – course work will be graded as follows: a. Summative Assessments (test, quizzes, projects) – 90% of grade b. Formative Assessments (homework) – 10% of grade c. All grades should be verified in Genesis on a regular basis B. Classroom a. Rules of Conduct i. Follow all rules as stated in student handbook ii. Come prepared to class with all required materials iii. No food or drinks in classroom iv. No cell phone in class b. Required Material i. Textbook ii. Pencils iii. Graphing calculator iv. Three ring binder/ Spiral Notebook with Folders c. Homework i. All homework will be posted on the teacher’s school website ii. Homework will not be accepted late unless the student has been absent and/or has a medical excuse iii. Missed homework should be made-up for understanding of concepts d. After School Help i. Available Tuesdays, Wednesdays, Thursdays ii. Will notify students if I cannot stay on a particular day e. Attendance i. Follow all rules as stated in student handbook ii. One day to make up work for every day absent iii. Work assigned prior to absence(s) will be due on the first day back f. Academic Integrity i. Students are to hand-in their own work 1. Receiving assistance is different from copying ii. Cheating will result in a zero on the assessment and a call home to the parent C. Course Description Discrete mathematics explores the arrangement of distinct objects and is used for decision making. Our focus will be on enhancing your problem solving skills and ability to analyze and utilize numbers to make reasonable decisions. The goal of the course is to provide an extension of previously learned skills up to and including Algebra II. The course also includes a strong development of trigonometry, probability, statistics and provides a good preparation for college entrance exams in mathematics. D. Course Objectives a. The student will be provided a review and extension of certain algebraic and geometric concepts. i. How can formulas be manipulated to solve for specific variables? ii. How can you use lines to represent and analyze data? iii. How can you apply geometric concepts to real life situations and modeling? iv. How can you reason quantitatively and use units to solve problems? v. What is a function? vi. What is the domain and range of a function? vii. How do you graph quadratic functions? viii. How do you use an appropriate factoring technique to factor expressions completely? ix. How can you find approximate solutions for the intersections of linear functions? x. How can you use matrices to solve systems of equations? b. The student will be introduced to trigonometry. i. How can you develop and apply the definitions of trigonometric ratios for the acute angles of a right triangle, the relationship between the sine and cosine of complementary angles, and the Pythagorean Theorem on right triangles in applied problems? ii. How can you use radian measure of an angle? iii. How can you explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers? iv. How can you construct trigonometric functions that model periodic phenomena with specified amplitude, frequency and midline? c. The student will be able to draw inferences and conclusions from data. i. How are Venn diagrams used to analyze data? ii. How does set theory help solve survey design and interpretation problems? iii. How do you summarize, represent, and interpret data on a single count or measurement variable, and two categorical and quantitative variables? iv. How do you make inferences and justify conclusions from sample surveys, experiments and observational studies? v. How can you use independence and conditional probability and use them to interpret data? vi. How can you use the rules of probability to compute probabilities of compound events in a uniform probability model? vii. How can you calculate expected values and use them to solve problems? viii. How can you use probability to evaluate outcomes of decisions? ix. What are the applications of geometric probability? x. What is a binomial probability distribution? xi. How is the binomial probability distribution use to solve problems? d. The student will be introduced to exponential and logarithmic functions and their graphs. i. How are the properties of exponents used to simplify equations? ii. What are logarithms? iii. How do you graph exponential and logarithmic functions, showing intercepts and end behavior? iv. How are exponential and logarithmic functions used in real life? e. The student will be prepared for further study in mathematics and focus on developing problem-solving skills. i. How can you make sense of problems and persevere in solving them? ii. How do you reason abstractly and quantitatively? iii. How can you construct viable arguments and critique the reasoning of others? iv. How do you model with mathematics? v. How do you use appropriate tools strategically? vi. How do you attend to precision? vii. How can you look for and make use of structure? viii. How can you look for and express regularity in repeated reasoning? E. Text(s)/resources/Software: Miller, C.D., et al, Mathematical Ideas – 11th Edition, Pearson AddisonWesley, © 2008 TI-83/84 Plus calculator SmartBoard and its Tools (Math, Notebook and Responders) TI SmartView interactive software for TI-84