MATHÂ 0017. Concepts of Mathematics
Units: 3
Prerequisite: Three years of high school mathematics which includes two years of algebra and one year of geometry; or MATH D and B with grades of "C" or better; or placement by matriculation assessment process
Hours: 54 lecture
Exploration of mathematical patterns and relations, formulation of conjectures based on the explorations, proving (or disproving) the conjectures. Includes different problem solving techniques, number theory, probability, statistics, sequences and series, and geometry. Intended for students interested in elementary education. (CSU, UC-with unit limitation)
MATH 0017 - Concepts of Mathematics
http://catalog.sierracollege.edu/course-outlines/math-0017/
Catalog Description DESCRIPTION IS HERE: Prerequisite: Three years of high school mathematics which includes two years of algebra and one year of geometry; or MATH D and B with grades of "C" or better; or placement by matriculation assessment process Hours: 54 lecture Description: Exploration of mathematical patterns and relations, formulation of conjectures based on the explorations, proving (or disproving) the conjectures. Includes different problem solving techniques, number theory, probability, statistics, sequences and series, and geometry. Intended for students interested in elementary education. (CSU, UC-with unit limitation) Units 3 Lecture-Discussion 54 Laboratory By Arrangement Contact Hours 54 Outside of Class Hours Course Student Learning Outcomes Develop and implement strategies for approaching unfamiliar mathematical problems. Evaluate, improve, and correct orally presented or written solutions. Logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving problems. Course Content Outline Concepts of Mathematics is a course designed to encourage critical thinking skills in students as they explore various investigation topics and open-ended questions. Students will observe patterns, analyze data, make conjectures about these observations and prove (or disprove) their conjectures. Their process and results will be formally communicated in writing and in oral presentations. This course is also designed to show students the beauty of Mathematics, along with providing them with an opportunity to discover the joy and power of mathematical thinking. I. Problem Solving Techniques A. Common approaches to problem solving - look for a pattern, guess and check, convert to algebra B. Organization of information - making tables, draw a diagram, use a graph II. Number Theory A. Divisibility, greatest common divisor, division algorithm B. The Euclidean Algorithm, primes III. Set Theory A. Sets, subsets, and complements B. Venn Diagrams IV. Probability and Statistics A. Calculate probabilities with Venn Diagrams, counting techniques, appropriate formulae using experimental techniques B. Calculate statistics with appropriate formulae and using experimental techniques V. Geometry and Networks A. Eulerian paths B. Hamiltonian paths C. Networks D. Sperner's Lemma E. Geometry - tessellation, polygons, polyhedra VI. Sequences and Series A. Use of sequences to represent given problem data B. Use of series to find sums of given problem data Course Objectives Course Objectives For each topic, the students will: 1. Develop a strategy for approaching problems with which they are unfamiliar; 2. Construct clear and logical solutions or proofs for each problem; 3. Evaluate orally presented or written solutions for flaws and/or mistakes and correct these flaws or mistakes. I. PROBLEM SOLVING TECHNIQUES A. Examine and organize information in unfamiliar problems as an initial approach to solving; B. construct tables, graphs, and diagrams and utilize as a problem solving technique; C. utilize algebraic solutions to presented problems, which include systems of equations in solution; II. NUMBER THEORY A. Propose, test, debate, and construct a clear, logical, and sound solution to these problems in groups; B. Solve other problems using the Euclidean Algorithm; III. SET THEORY A. Categorize information in a problem into clear sets, subsets, and complementary sets; B. Calculate the number of elements in intersections and unions of sets using Venn Diagrams; IV. PROBABILITY AND STATISTICS A. Propose, test, debate, and construct a solution to the Buffon Needle (Noodle) Problem based on experimental data; B. Solve problems using counting techniques, which include the use of combinatorics; C. Select the best solution to a problem using probability and expected values; V. GEOMETRY AND NETWORKS A. Propose, test, debate, and construct a solution to the Highway Inspector Problem (an adaptation of Eulerian Networks); B. Design Eulerian and Hamiltonian networks with given numbers of vertices and test them for transportivity; C. Propose, test, debate, and construct solutions to open-ended problems involving geometry including Sperner's Lemma; VI. SEQUENCES AND SERIES A. Propose, test, debate, and construct a solution to the Handshake Problem and its variations, which includes summation of finite series; B. Create solutions and verify their validity to infinite sum problems in the form of geometric sequences and series; C. Predict the entries in a sequence by following the pattern in a sequence; D. Construct a series that correctly represents information in a problem and find its sum, may be finite or infinite. Methods of Evaluation Objective Examinations Problem Solving Examinations Reading Assignments 1. Find an internet source on Venn Diagrams and come to class prepared to discuss the logic of the Venn Diagram. 2. Read the homework handouts to determine the questions being asked and the work that will need to be done to accomplish the solution. 3. Read a solution to a problem prepared by another group and analyze that solution for correct logic or implied flaws. 4. Read article "Teaching Mathematics Requires Special Skills" by Debbie Ball (or similar article on same topic). Write journal entry and discuss in class. Writing, Problem Solving or Performance 1. Working in groups, develop a possible solution for the "Highway Inspector" network problem. Test the conjecture for accuracy and write up a clear, logical proof for the solution. 2. Within a group that has discovered a flaw with another group's solution to a problem, write a paper indicating how the solution was in error and a proposal on how to fix that error. Other (Term projects, research papers, portfolios, etc.) 1. Geometry Group Project - Polyhedra building/investigation dualism, stellating, truncating, and compounds. 2. Collection and organization of experimental data for Buffon Needle (Noodle) problem. 3. Research historical math approaches to various problems given in class, with use of a library or internet. 4. Research mathematicians past or present and give presentation in class, with use of library or internet. Methods of Instruction Lecture/Discussion Distance Learning Other materials and-or supplies required of students that contribute to the cost of the course.
POLS 0017 - Introduction to Political Science Research Methods
http://catalog.sierracollege.edu/course-outlines/pols-0017/
Catalog Description DESCRIPTION IS HERE: Advisory: Completion of MATH 13 with grade of "C" or better; completion with grade of "C" or better or concurrent enrollment in any POLS course Hours: 54 lecture Description: Surveys research methods employed in political science. Introduces research design, experimental procedures, descriptive methods, instrumentation, collection, interpretation, and reporting of research data, and the ethics of research. (C-ID POLS 160) (CSU, UC) Units 3 Lecture-Discussion 54 Laboratory By Arrangement Contact Hours 54 Outside of Class Hours Course Student Learning Outcomes Devise hypotheses concerning political behavior and plan appropriate and ethical research designs to evaluate. Interpret data using inferential statistics. Demonstrate and explain results of data collection and analysis. Evaluate and synthesize published peer-reviewed research. Course Content Outline 1. History and development of the empirical study of politics 2. The scientific method 3. Theories, hypotheses, variables, and units 4. Conceptualization, operationalization and measurement of political concepts 5. Elements of research design including the logic of sampling 6. Qualitative research methods and means of analysis 7. Quantitative research methods and means of analysis 8. Research ethics Course Objectives Course Objectives 1. Explain the basic principles of the scientific method. 2. Explain the relationship between theory and research. 3. Describe general research designs, experimental and non-experimental methods, and standard research practices. 4. Select and defend research designs and data collection procedures appropriate to test hypotheses. 5. Critically evaluate reports of research findings, assess the generalizability of research results, and synthesize a body of research findings. 6. Explain the ethical treatment of participants in research and the institutional requirements for conducting research. Methods of Evaluation Classroom Discussions Essay Examinations Objective Examinations Problem Solving Examinations Projects Reading Assignments 1. Read the assigned textbook chapter on the development of the empirical study of politics and prepare to offer examples in class. 2. Read the APSA journal article on typical problems with research designs and consider solutions. Writing, Problem Solving or Performance 1. Thirty-question objective exam on qualitative research. 2. Term paper comparing two different research designs employed by published authors. Other (Term projects, research papers, portfolios, etc.) 1. Discussion of ethical questions that particular research designs raise on the Discussion Board. 2. Quantitative data handling exercise employing appropriate software. Methods of Instruction Lecture/Discussion Distance Learning Other materials and-or supplies required of students that contribute to the cost of the course.
Course Identification Numbering System (C-ID)
...0142 MATH 120 MATH 0019 MATH 140 MATH...0003 POLS 160 POLS 0017 PSY 110 PSYC...
