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College of DuPage FY Fall/17 ACTIVE COURSE FILE Curricular Area: Mathematics Course Number: 1218 Title: General Education Mathematics Semester Credit Hours: 3 Lecture Hours: 3 Lab Hours: 0 Clinical Hours: 0 This course is an IAI approved general education course: M1 904. Changes from the present course must be accompanied by a yellow Course Revision or Deletion Form. Course description to appear in catalog: Designed to fulfill general education requirements and not designed as a prerequisite for any other college mathematics course. Focuses on mathematical reasoning and the solving of real-life problems, rather than routine skills. Logic and set theory will be studied. Two other topics from the following list are to be studied in depth: counting techniques and probability, game theory, geometry, graph theory, statistics, and mathematics of finance. The regular use of calculators and/or computers will be emphasized. Prerequisite: Math 0465 or Math 0482 (or college equivalent) with a grade of C or better or a qualifying score on the mathematics placement test. A. General Course Objectives: Upon successful completion of this course, students should be able to do the following: 1. 2. 3. 4. 5. Define the elements of a set Count the elements of a set Perform operations with sets Construct Venn diagrams Use mathematics to solve a variety of problems from the following list: a. Counting techniques and probability b. Statistics c. Game theory d. Geometry e. Graph theory f. Mathematics of finance 5. Use problem-solving skills 6. Use technology in problem solving B. Topical Outline: Three topics from the following are to be studied in depth, with Topic 1 required. The two additional topics may not include both Topic 2 and Topic 3: 1. Logic and set theory a. Sets b. Set operations c. Venn diagrams d. Number of elements in a set e. Sets as a problem-solving tool f. Statements g. Truth tables h. Compound statements i. Euler diagrams j. Valid arguments 2. Counting techniques and probability a. The Fundamental Counting Principle b. Permutations c. Combinations d. Miscellaneous counting methods e. Sample spaces and probability f. Computation of odds g. Counting techniques and probability h. Computation of probabilities i. Conditional probability j. Independent and dependent events k. Mathematical expectation 3. Statistics a. Descriptive statistics 1) Collecting and describing data 2) Correlation and regression b. Normal distribution c. Statistical inference 1) Hypothesis testing 2) Confidence interval estimation 4. Game theory a. Two-person games – constant sum 1) Pure strategies 2) Mixed strategies b. Two-person games – variable sum c. Larger games d. Application of game theory e. Theory of moves f. Cyclic games 5. Geometry a. Non-Euclidean geometry 1) Lobachevskian geometry 2) Riemannian geometry 3) Other non-Euclidean geometries b. Fractal Geometry 1) Koch snowflake 2) Sierpinski gasket 3) Mandelbrot Set c. Computer applications 1) Geometer’s sketchpad 2) Fractal generators 6. Graph theory a. Euler circuits b. Directed graphs c. Hamiltonian circuits d. Spanning trees e. Critical paths 7. Mathematics of Finance a. Interest b. Annuities c. Loans d. Amortization C. Methods of Evaluating Students Students will be evaluated by unit tests at appropriate intervals. Other methods may include quizzes, homework, projects, and a comprehensive final examination. _______________________________ Initiator Date _______________________________ Sponsor Date _______________________________ Division Dean Date Textbook for Math 1218 Title: Thinking Mathematically, 6th Edition Author: Robert Blitzer Publisher: Prentice Hall Copyright: 2015 Topic Chapter Sections Logic and Set Theory 2,3 All sections Mathematics of Finance 8 Sections 8.2 – 8.6, 8.7, 8.8 (Section 8.1 is optional) Geometry 10 Section 10.7 (Other sections optional) The Active Coursed File states “NonEuclidean Geometry”. Please see Active Course File for topics to cover. Graph Theory 14 All sections Counting Techniques and Probability 11 All sections Statistics 12 All sections In some instances, depending on the topic selected, the instructor may have to provide supplemental material. Use of Technology in Math 1218 Instead of relying on algorithms to solve problems encountered in this course, computers and calculators should be used. The use of such technology is an integral part of this course. In all Mathematics courses, students with a documented learning disability that specifically requires a calculator as determined by Health Services, will be allowed to use a basic calculator for all test/quiz questions where arithmetic calculations are not the main objective. The specific disability must be verified with Health Services before the accommodation can be made.