MATHÂ 0015. Discrete Mathematics
Units: 4
Prerequisite: Completion of MATH 30 with grade of "C" or better
Hours: 72 lecture
Study of set theory, relations and functions, logic, combinatorics and probability, algorithms, computability, matrix algebra, graph theory, recurrence relations, number theory including modular arithmetic. Various forms of mathematical proof are developed: proof by induction, proof by contradiction. (CSU, UC)
MATH 0015 - Discrete Mathematics
http://catalog.sierracollege.edu/course-outlines/math-0015/
Catalog Description DESCRIPTION IS HERE: Prerequisite: Completion of MATH 30 with grade of "C" or better Hours: 72 lecture Description: Study of set theory, relations and functions, logic, combinatorics and probability, algorithms, computability, matrix algebra, graph theory, recurrence relations, number theory including modular arithmetic. Various forms of mathematical proof are developed: proof by induction, proof by contradiction. (CSU, UC) Units 4 Lecture-Discussion 72 Laboratory By Arrangement Contact Hours 72 Outside of Class Hours Course Student Learning Outcomes Logically present clear, complete, accurate, and sufficiently detailed solutions to communicate reasoning and demonstrate the method of solving problems. Construct valid proofs of theorems using the following techniques: mathematical induction, direct and indirect proofs, by contradiction, with truth tables, and by logical equivalences. Solve counting problems using combinatorics, recurrence relations, and generating functions. Solve applied problems using discrete probability theory, graph theory, tree diagrams, and Boolean Algebra. Course Content Outline I. Predicate Calculus A. Propositional Equivalences B. Universal and Existential Quantifiers II. Proofs A. Counterexample B. Direct C. Indirect D. Contradiction E. Mathematical Induction F. Truth Tables G. Logical Equivalences III. Algorithms A. Complexity B. Growth C. The Division Algorithm D. The Euclidean Algorithm E. Number Bases IV. Counting Principles A. Combinatorics B. Generating Functions C. Difference Equations V. Probability A. Conditional Probability B. Independence C. Expected Value VI. Relations A. Equivalence Relation VII. Graphs and Trees A. Euler and Hamiltonian Paths B. Shortest Distance Applications VIII. Boolean Algebra A. Logic Gates and Switching Circuits IX. Matrices A. Operations B. Applications C. Systems of Equations Course Objectives Course Objectives 1. Create mathematical proofs directly, indirectly, and by contradiction; 2. Use mathematical induction to create a mathematical proof; 3. Create a mathematical proof with truth tables and logical equivalences; 4. Translate mathematical statements using universal and existential quantifiers; 5. Use sets to organize and quantify data; 6. Create an algorithm using pseudocode; 7. Evaluate a series; 8. Model using permutations and combinations and numerically evaluate appropriate applied problems; 9. Model using probabilities, including conditional probabilities; 10. Solve counting problems using a generating function; 11. Assess that a relation is an equivalence relation; 12. Create a graph and a tree to describe the structure of a system; 13. Use Boolean algebra to mathematically model electronic circuits; 14. Verify functions are one-to-one and onto; 15. Use matrices to solve applied problems. Methods of Evaluation Classroom Discussions Objective Examinations Reading Assignments 1. Throughout the course, read assigned topics from text. For example, how to verify the validity of a mathematical formula by mathematical induction. Students should be prepared to discuss in class. 2. Search the library or the internet for applications of the golden ratio and the Fibonacci sequence and be prepared to discuss in class. Writing, Problem Solving or Performance 1. Write mathematical proofs. For example, given a function f, prove that the image of the intersection of two sets is a subset of the intersection of the images of those two sets. 2. Prove that the limit of the ratio of a Fibonacci number to its predecessor is the golden ratio. Other (Term projects, research papers, portfolios, etc.) Methods of Instruction Lecture/Discussion Distance Learning Other materials and-or supplies required of students that contribute to the cost of the course.
SOC 0015 - Introduction to Statistics in Sociology
http://catalog.sierracollege.edu/course-outlines/soc-0015/
Catalog Description DESCRIPTION IS HERE: Prerequisite: Completion of intermediate algebra or appropriate placement Advisory: Concurrent enrollment in a support course (SOC 15S or SOC 815S) is strongly recommended for those who have not recently completed intermediate algebra Hours: 54 lecture Description: Introduction to the use of descriptive and inferential statistics in the analysis of sociological data, including: levels and types of measurement, measures of central tendency and variability, distributions, probability, estimation, hypothesis testing, correlation, and regression. Social science statistical software will be explored as an aid in processing and analyzing sociological data. (C-ID SOCI 125) (CSU, UC-with unit limitation) Units 3 Lecture-Discussion 54 Laboratory By Arrangement Contact Hours 54 Outside of Class Hours Course Student Learning Outcomes Conduct statistical analysis of sociological data. Interpret and critically analyze the results of statistical analysis. Organize, classify, and display sociological data in various forms. Demonstrate familiarity with utilizing statistical software to analyze sociological data. Course Content Outline I. Research design and the role of statistics II. Organizing data and measures of central tendency III. Descriptive statistics for uni-variate distributions IV. Descriptive statistics for joint distributions V. Statistical inference VI. Statistical tests: one-way and factorial analysis of variance VII. Analysis of variance VIII. Correlation and nonparametric statistical analysis Course Objectives Course Objectives 1. Practice mathematical techniques and apply them to social science data; 2. Conduct numerical computations; interpret and critically analyze the results in written form; 3. Organize, classify, and represent quantitative data in various forms: tables, graphs, rates, percentages, measures of central tendency and variability; 4. Make statistical inference using estimation, hypothesis testing, correlation, and regression; 5. Demonstrate familiarity with applications in statistical software. Methods of Evaluation Essay Examinations Objective Examinations Problem Solving Examinations Skill Demonstrations Reading Assignments 1. Prior to reading chapter, please read the handout entitled "Overcoming Math Anxiety" by Sheila Tobias. This reading will help with any anxiety you may have about taking a statistics course. 2. Read chapter and the case study by Margaret L. Anderson and Patricia Hill Collins entitled "Race, Class, and Gender" which demonstrates the sampling distributions discussed in chapter. Writing, Problem Solving or Performance Sample Writing and Problem Solving Questions for Assignments or Exams: 1. You listen to a debate between two politicians discussing the economic health of the United States. One politician says that the average household income in the United States is $126,500; the other says that the average household income is only $70,784, so Americans are not as well off as the first politician claims. Is it possible for both of these politicians to be correct? If so, explain how. 2. Using the data about the upcoming election, calculate the 95% Confidence Interval for the proportion of registered voters voting for Candidate A. Is it possible they will lose the election based on this Confidence Interval? Explain your response. 3. Regular written check-in assignments with students about course content as well as needs outside of class. Other (Term projects, research papers, portfolios, etc.) At the beginning of the semester, students will choose a sociological topic they are interested in and then complete analysis for each statistic they learn throughout the semester. At the end of the semester, students will compile all of their calculations and critical analysis into one cohesive assignment demonstrating their knowledge of sociological statistics and their application to sociological topics. Methods of Instruction Lecture/Discussion Distance Learning Other materials and-or supplies required of students that contribute to the cost of the course. SPSS software
Course Identification Numbering System (C-ID)
...0142 MATH 120 MATH 0019 MATH 140 MATH...0270 BUS 140 IT 0015 CDEV 100 HDEV...
Information Technology
http://catalog.sierracollege.edu/departments/infotech/
...Business Applications 3 IT 0015 Business Information Systems...for Many Uses 3 MATH 0013 Elementary Statistics...
Administration of Justice
http://catalog.sierracollege.edu/departments/administration-justice/
...Introduction to Sociology SOC 0015 Introduction to Statistics in Sociology or MATH 0013 Elementary Statistics...
